The Risk Source–Risk Exposure–Mitigation Force Theory of Urban Safety and Its Enabling Space–Air–Ground Integrated Monitoring Technologies

Abstract

The safe and continuous operation of modern cities is fundamental to national security and development, and urban safety requires maintaining essential functions under interacting risks. Existing frameworks mainly explain how hazards affect exposed systems, while elements enabling mitigation are generally subsumed within broader concepts rather than represented as an independent fundamental element. Such frameworks also provide limited representation of context-dependent functional role transformations and do not fully link monitoring to quantitative safety assessment. This study develops and formalizes the Risk Source–Risk Exposure–Mitigation Force Theory of Urban Safety (SEM Theory). It positions Mitigation Force—the integrated ensemble of risk cognition, mitigation organization, technology and resources—as a third fundamental element alongside Risk Source and Risk Exposure, and represents their interactions and scenario-dependent functional transformations. A two-layer mathematical formulation converts heterogeneous observations into functional equivalents and assesses urban safety by comparing effective risk load with comprehensive bearing capacity. The theory further guides Space–Air–Ground integrated monitoring, linking SEM Theory-derived parameters with collaborative sensing, cross-tier data fusion, information interpretation, and group-level assessment. An illustrative application to over 350 buildings demonstrates the monitoring workflow’s operational feasibility, while the integrated framework provides a unified pathway from system-level urban-safety theory to cross-scale assessment, early warning and targeted intervention.

Graphical abstract

Keywords

Urban safety / Risk Source–Risk Exposure–Mitigation Force Theory / Space–Air–Ground integrated monitoring / Quantitative safety assessment

Highlight

	● SEM Theory formalizes three co-equal fundamental elements of urban safety.
	● Mitigation Force integrates cognition, organization, technology, and resources.
	● SEM elements interact and undergo functional transformations across risk scenarios.
	● Functional equivalents link heterogeneous observations to safety assessment.
	● SEM Theory guides Space–Air–Ground monitoring and cross-tier data fusion.

1 Introduction

Cities can be conceptualized as open complex giant systems in which populations, wealth, and critical functions are highly concentrated, making their safe and continuous operation integral to national security and development [1,2]. Over recent decades, cities have expanded worldwide, although the pace and spatial patterns of urbanization have varied markedly across regions [3]. China, in particular, has undergone an urbanization transition exceptional in both scale and speed [4]. Although dense agglomeration improves efficiency, the spatial concentration disproportionately exposes populations and assets to hazard-prone zones, increasing susceptibility to severe weather and cascading failures. Localized disruptions can propagate and amplify across interdependent urban systems and infrastructure networks [5−7]. Urban safety, therefore, cannot be reduced to an aggregation of sector-specific safety concerns; it is a system-level condition in which essential urban functions remain above defined safety thresholds under disturbances.

As urban morphology and risk structures have evolved, the conceptualization of urban safety has expanded to encompass three distinct yet coexisting paradigms. The first emphasizes post-disaster relief and experience-based prevention, as evidenced by the fortifications, drainage systems, fire patrols, and grain reserves of early cities. A second paradigm prioritizes increasingly specialized and institutionalized ex-ante prevention. Historical precursors to this proactive approach include spatial planning linked to urban commerce following the 1666 Great Fire of London [8], and John Snow’s 1854 epidemiological mapping of cholera, which combined mortality records and spatial data to prove a waterborne etiology [9]. A third orientation focuses on cognition, communication, coordination, and control during crisis management, facilitating the translation of disaster experiences into systemic urban adaptation [10,11]. Despite the concurrent application of these approaches, current scholarship and practice remain siloed across specific hazards, disciplines, and administrative mandates. Consequently, the common framework of urban safety integrating the boundaries, fundamental elements, states, and capacities remains lacking [12−14].

These conceptual limitations point to a deeper theoretical problem. P. W. Anderson argued that fundamental laws alone cannot reconstruct complex wholes [15]. Research in complex systems and urban science likewise views cities as coupled, evolving systems whose system-level behavior must be understood using data and models spanning spatial and temporal scales [16]. Conventional frameworks in disaster and risk research, however, primarily explain how hazards affect people, engineered assets, environmental resources, and urban systems, thereby causing losses. For example, United Nations Office for Disaster Risk Reduction (UNDRR) represents disaster risk through hazard, exposure, vulnerability, and capacity [17−19]. The capacity element is often treated as the inverse of vulnerability, an attribute of the exposed object, or an external condition. Moreover, assigning fixed roles to individual elements cannot capture dynamic transformations, such as damaged infrastructure becoming a secondary risk source or a failed mitigation facility itself beginning to generate risk. These gaps call for a systems theory that can represent risk-generating factors, exposed objects and systems, and active mitigation within a unified framework and explain their interactions and transformations.

A parallel technical gap concerns city-scale sensing of urban safety states. Cities contain vast numbers of buildings, infrastructure assets, and environmental objects that vary widely in type and spatial distribution. Conventional manual inspections provide snapshots of local conditions but cannot deliver continuous citywide coverage. Spaceborne remote sensing enables wide-area, periodic observation and multiscale information extraction [20,21]. Airborne platforms offer flexible deployment and diverse viewing angles, supporting detailed local inspection, including in concealed or hard-to-access spaces [22]. Ground-based sensors, in turn, provide continuous, high-precision measurements of critical assets. Yet each monitoring tier faces different constraints related to spatial resolution, timeliness, endurance, signal obstruction, deployment cost, and model interoperability. Digital twins, artificial intelligence, and multisource data fusion create new opportunities for cross-tier state updating, simulation, and decision support; however, data quality, real-time performance, computational cost, and governance coordination remain major barriers to operational deployment [23−26]. A unified spatiotemporal framework is therefore needed to integrate the complementary strengths of spaceborne, airborne, and ground-based monitoring and enable cross-scale collaborative sensing, information interpretation, and safety-state assessment.

This study addresses these conceptual and technical gaps through three main lines of research. First, it defines urban safety and its fundamental characteristics from the perspective of cities as open complex giant systems. Second, it proposes the Risk Source–Risk Exposure–Mitigation Force Theory of Urban Safety (SEM Theory). The theory assigns Mitigation Force the same analytical status as Risk Source and Risk Exposure, explains their interactions and dynamic role transformations, and formalizes these relationships mathematically. Third, it develops an SEM Theory-driven Space–Air–Ground integrated monitoring system. The system links a collaborative sensing indicator framework with methods for cross-tier data fusion, information interpretation, and safety-state assessment. Together, these three lines of research establish a coherent chain from conceptual definition and theoretical modeling to operational monitoring.

2 Connotation and Characteristics of Urban Safety

A clear conceptualization of urban safety is essential for developing both its theoretical foundations and governance framework. With rapid urbanization and increasing functional interdependence, modern cities are no longer simply spatial agglomerations of people and physical assets. They have evolved into complex giant systems comprising interconnected subsystems of production, living, ecology, and governance. These subsystems continuously exchange material, energy, information, and services with one another and with the external environment. As an open and dynamic system, a city is characterized by multilevel structures, complex interactions, continuous evolution, and emergent system-level functions [1,2,27,28].

Against this background, urban safety cannot be adequately understood by examining individual hazards, infrastructures, or sectors in isolation. This study defines urban safety as the state in which an urban complex giant system maintains its basic functions of production, living, ecology, and governance under multiple risk threats, together with the capacity to sustain and safeguard that state (as shown in Fig. 1). These threats may arise from natural hazards, accidents, public health emergencies, public security incidents, ecological risks, macro-level risks, or their interactions. Urban safety therefore concerns not the complete elimination of risk, but the ability of a city to maintain its essential functions within an acceptable safety boundary despite disturbances. It constitutes a fundamental prerequisite for the stable operation and sustainable development of cities.

From this system-oriented perspective, urban safety exhibits five key characteristics (as shown in Fig. 1).

(1) Strategic importance

Urban safety has strategic significance because cities increasingly concentrate the population, economic activities, critical functions, and innovation capacity on which national development depends. The share of the global population living in cities increased from approximately 20% in 1950 to 45% in 2025 [29]. In China, prefecture-level and above cities generated RMB 77.0 trillion in GDP in 2023, accounting for 61.1% of the national total [30]. As urbanization proceeds, megacities, metropolitan regions, and urban agglomerations are becoming increasingly important nodes of national economic activity, technological innovation, industrial development, and public services.

This concentration is particularly evident in major metropolitan regions. Japan’s National Capital Region, comprising Tokyo and seven surrounding prefectures, accommodates approximately 30% of Japan’s total population [31], while Tokyo alone accounted for approximately 21% of Japan’s GDP in fiscal year 2023 [32]. The Seoul Metropolitan Area is even more concentrated, accounting for approximately half of the Republic of Korea’s population and 53% of its GDP in 2020 [33]. Together, these cases show that modern cities—particularly megacities and major urban agglomerations—are not merely regional growth poles but critical spatial carriers of national strength and development capacity.

Importantly, the concentration that generates agglomeration benefits also concentrates risk exposure and potential losses. Major disasters can simultaneously cause casualties, economic losses, infrastructure disruption, and interruption of essential urban functions. Their consequences may further propagate through infrastructure networks, industrial and supply chains, and interregional economic linkages [7,34]. Urban safety is therefore no longer merely a local issue of protecting individual cities. It has become an important foundation of national economic security, social stability, and sustainable development. In highly urbanized societies, national security increasingly depends on the safe and stable functioning of cities.

(2) High consequence sensitivity

Urban safety events exhibit high consequence sensitivity. Even events with limited direct physical damage may generate disproportionate social, economic, and governance impacts when critical urban functions or highly visible assets are involved. Their consequences are therefore determined not only by casualties and economic losses, but also by functional importance, spatial location, public risk perception, social amplification, and confidence in urban governance.

The 2021 shaking incident of SEG Plaza in Shenzhen illustrates this characteristic. Subsequent investigations confirmed that the building remained structurally safe for continued use, and no casualties were reported. Nevertheless, the incident attracted widespread public concern and prompted an extensive technical investigation, partly because it involved a landmark high-rise in a major commercial district [35]. The societal response was therefore substantial relative to the direct physical consequences.

This example demonstrates that the significance of an urban safety event cannot be assessed solely in terms of physical damage. The same level of physical disturbance may produce markedly different societal consequences depending on where it occurs, which functions are affected, and how the event is perceived by the public [36]. This sensitivity makes urban safety closely intertwined with public confidence, social stability, and the perceived effectiveness of urban governance.

(3) Complex system coupling

Urban safety is fundamentally shaped by strong interdependencies among urban subsystems, through which local disturbances can propagate and develop into cascading and systemic risks [7,34]. Transportation, energy, communications, water supply, healthcare, industry, ecosystems, and governance do not operate independently. Instead, they are connected through material, energy, information, service, and functional dependencies. A disruption in one subsystem may therefore impair others, creating nonlinear amplification and cascading consequences across sectors and spatial scales.

The catastrophic rainstorm that struck Zhengzhou on July 20, 2021, provides a representative example. Extreme precipitation caused severe flooding and simultaneously disrupted transportation, electricity supply, communications, and other essential services, significantly impairing normal urban functioning [37]. Similarly, the 2005 explosion at a chemical plant operated by Jilin Petrochemical Company provides another example. Approximately 100 tons of pollutants containing benzene and nitrobenzene entered the Songhua River after the accident [38], forming an approximately 80-km toxic slick. Water withdrawal in Harbin was suspended for several days, millions of residents along the river were affected, and the downstream movement of the contamination subsequently raised transboundary concerns.

These events demonstrate how an initially localized disturbance can propagate through interdependent systems and spatial networks, transforming a sector-specific event into a broader systemic risk. Urban safety analysis must therefore move beyond isolated hazards and individual infrastructures toward understanding interactions, dependencies, and cascading processes within the urban complex giant system.

(4) Significant dynamic evolution

Urban safety is inherently dynamic because hazards, urban systems, and the capacity to manage risks all evolve over time.

The risk environment itself is constantly changing due to climate change, technological development, demographic shifts, and socioeconomic transformation. These changes reshape the types, intensity, frequency, and spatial distribution of threats faced by cities [39,40].

At the same time, cities themselves continuously evolve. Population distribution, urban form, industrial structure, infrastructure conditions, mobility patterns, and the spatial concentration of critical functions change throughout urban development. These changes reshape both exposure and vulnerability [41,42].

Meanwhile, advances in risk awareness, governance mechanisms, monitoring technologies, emergency response, and disaster mitigation modify the capacity of urban systems to anticipate, withstand, and respond to disturbances [10,11,26].

Urban safety should therefore not be regarded as a fixed condition measured at a single point in time. Rather, it represents a continuously evolving state emerging from the interaction between a changing risk environment, a changing urban system, and changing governance and mitigation capacities. This dynamic nature also means that safety assessments and governance strategies must be continuously updated rather than based solely on historical risk patterns.

(5) Increasing governance challenges

The governance of urban safety is becoming increasingly difficult as urban systems grow more interconnected while risks become more diverse, compound, and cascading [7,34]. Modern cities must simultaneously address natural, technological, public health, ecological, and socioeconomic risks, many of which may interact and evolve across sectoral and administrative boundaries. Consequently, identifying risks, anticipating cascading effects, and evaluating system-wide consequences are substantially more difficult than managing isolated hazards.

Governance complexity further arises from the institutional structure of cities. Urban safety involves multiple levels of government, administrative departments, infrastructure operators, enterprises, communities, and citizens [10]. These actors possess different responsibilities, information, resources, and decision-making authority, making cross-sector coordination and information sharing essential but difficult. Moreover, because urban safety is an emergent property of an open complex giant system, it cannot be adequately represented by a single indicator, model, or intervention.

Contemporary urban safety governance therefore faces several closely related challenges, including understanding systemic risks, coordinating multiple actors, and implementing precise and adaptive interventions. The global relevance of these challenges is reflected in Sustainable Development Goal 11 (Sustainable Cities and Communities), which calls for cities and human settlements to become “inclusive, safe, resilient and sustainable”. Similarly, the Sendai Framework for Disaster Risk Reduction 2015–2030 emphasizes integrated disaster risk reduction and resilience at both national and local levels [43,44]. Urban safety has thus become a long-term global governance challenge rather than a problem that can be addressed through conventional sector-specific risk management alone.

3 The Risk Source–Risk Exposure–Mitigation Force Theory of Urban Safety (SEM Theory)

Urbanization concentrates population, wealth, and critical functions in cities while creating dense interdependencies among their engineering, social, information, and ecological systems. From a systems perspective, a city can be viewed as a living, adaptive organism rather than a static collection of people, infrastructure, and functions. It is sustained by exchanges of matter, energy, and information within the city and with its external environment, and performs functions analogous to perception, cognition, response, and recovery. Meanwhile, traditional risks are evolving, and cities face novel, compound, cascading, and extreme risks. A central task in developing urban safety theory is therefore to identify a set of fundamental elements with general applicability, explanatory power, and operational value. These elements should clarify how urban risks arise, propagate, and intensify, how interventions alter these processes, and how urban systems recover.

The regional disaster system theory developed in China explains disaster formation through interactions among the hazard-formative environment, hazard-formative factors, and hazard-affected bodies, which refer, respectively, to the conditions under which hazards develop, the processes or agents that generate them, and the people, assets, and systems subject to their effects [45−48]. For urban safety analysis, however, the active risk-reduction roles of governments, communities, and the public are generally incorporated into descriptions of environmental conditions or treated as aspects of vulnerability, resilience, or capacity. In such formulations, the integrated set of cognitive, organizational, technological, and material elements that collectively enables prevention, preparedness, response, and recovery is not represented as an independent fundamental element of urban safety. This categorical structure also makes scenario-dependent shifts in functional role difficult to represent—for example, when damaged infrastructure becomes a secondary risk source or when a failed protective facility shifts from a mitigation asset to a risk source.

The need to represent these mitigation-related elements independently is evident when cities facing comparable risk sources and similarly exposed populations, assets, and systems experience markedly different outcomes depending on their risk cognition, organizational arrangements, technological capabilities, resource availability, and emergency response capacity. This indicates that the elements enabling mitigation are not merely external conditions but collectively constitute an endogenous element capable of altering the severity of impacts, propagation pathways, system-wide damage, and final outcomes. To address this theoretical gap and represent this element explicitly, Yue et al. systematically introduced the concept of “Mitigation Force”, which can be defined as an integrated set of cognitive, organizational, technological, and material elements that support urban risk prevention, response, and recovery before, during, and after an urban safety incident [17]. Through coordinated operation, these elements may reduce the impacts of risk sources, strengthen the resistance and recovery capacity of exposed objects and systems, or alter the pathways through which risk propagates. The level of Mitigation Force is not determined solely by the availability or nominal capacity of its constituent elements, but by the extent to which they are effectively mobilized and coordinated in a specific risk scenario. Hereafter, “Risk Source” denotes any element, process, or combination of elements that may threaten urban safety, whereas “Risk Exposure” denotes the people, assets, and systems subject to the resulting effects. By embedding urban governance within the process of risk evolution, Mitigation Force links Risk Source and Risk Exposure and constitutes a third fundamental element of urban safety at the same analytical level as the other two.

Building on these three concepts, we developed the SEM Theory (Fig. 2), which provides a triadic structure for analyzing risk formation, system response, and proactive governance [17,49]. This theory treats the emergence and evolution of urban safety incidents, together with urban response and recovery, as parts of a dynamic process. The elements represented within Risk Source, Risk Exposure, and Mitigation Force interact with and constrain one another through flows of matter, energy, and information. As risk scenarios and interdependencies change, the same element may assume a different functional role and shift from one category to another. The SEM Theory provides a common conceptual basis for representing, assessing, and simulating urban safety states and identifies the objects and relationships to be captured through its technological implementation. Viewed through the analogy of the city as a living organism, the envisioned full implementation of the SEM Theory follows the Sharp Eye–Smart Brain–Skilled Hand architecture: Sharp Eye integrates spaceborne, airborne, and ground-based observations for coordinated sensing; Smart Brain interprets multisource observations to support risk identification, safety-state assessment, and early-warning support; and Skilled Hand translates warnings and decisions into resource deployment and response actions. At the current stage, Sharp Eye is the component that has been developed into a concrete technical system, and the following section therefore presents in detail the Space–Air–Ground integrated monitoring technologies that constitute Sharp Eye. Together, the three components are intended to form a perception–cognition–action loop through which the constituent elements of Mitigation Force are mobilized and coordinated in practice, thereby supporting more systematic, anticipatory, and precise urban safety governance.

3.1 Risk Source

Within the SEM Theory, Risk Source denotes any hazard-producing entity, event, or process that may, individually or jointly, threaten urban safety. During urban operation and development, cities may face multiple types of risks, including those associated with rainstorms, earthquakes, fires, infectious disease outbreaks, and technological failures. When overall urban safety risk is taken as the macro-level object of analysis, these specific risks can themselves be regarded as risk sources. Within complex and highly interconnected urban systems, Risk Source exhibits several fundamental characteristics and contemporary evolutionary trends.

Risk Source exhibits three fundamental characteristics (Fig. 3):

First, coupling and cascading. Different types of risk sources may interact through flows of matter, energy, and information, as well as through functional dependencies among urban systems. The impacts generated by these risk sources and their interactions may propagate along causal, functional, and spatial chains across physical, social, and informational spaces, thereby spreading across systems, regions, and scales [50]. Ultimately, the continued propagation of risk across systems, regions, and scales forms extensive and interwoven risk-propagation networks within cities, increasing the complexity of urban safety risks and substantially altering the nature and severity of the resulting consequences.

Second, urban specificity. Cities differ substantially in their geographic settings, climatic conditions, resource endowments, population size and distribution, industrial structures, spatial forms, infrastructure configurations, and governance capacities. Consequently, the same type of risk source may differ across cities in its intensity, spatial distribution, occurrence pattern, and evolution.

Third, macro-environmental sensitivity. Changes in the global climate, geopolitical and geo-economic conditions, industrial and supply chains, and rapidly evolving technologies may alter the conditions under which risk sources emerge, as well as their magnitude, spatial reach, and mechanisms of impact.

In addition to these fundamental characteristics, risk sources are also exhibiting new evolutionary trends (Fig. 3):

First, traditional risk sources are undergoing new changes, including but not limited to their patterns of occurrence and impact. Traditional risk sources, including floods, earthquakes, fires, environmental pollution, and infectious disease outbreaks, have long affected cities, and their general mechanisms and conventional management approaches have been extensively studied. Nevertheless, high-density urban agglomeration, highly interconnected infrastructure, and climate change are altering their frequency, duration, intensity, spatial extent, mechanisms and social impact.

Second, novel risk sources are emerging. Advances in information technologies, new energy systems, and advanced materials are introducing new failure modes, unintended effects, and pathways of disruption [51−53]. The resulting risk sources are often difficult to observe, highly uncertain, and recognized only after a substantial delay. By the time some emerging risk sources become observable, the associated technologies and dependencies may already be deeply embedded in socioeconomic systems, allowing disruptions to cascade through critical urban functional networks.

Third, coupled and cascading risks are becoming prevalent and complex. A risk originating at a single point may spread rapidly through urban lifeline systems, essential societal functioning systems and information networks. During this process, it may also interact and couple with risks associated with natural disasters, accidents, and public health emergencies, thereby amplifying the resulting consequences and potentially causing systemic failure.

Fourth, extreme risk scenarios happen more frequently. Climate change and human activities are altering the frequency, magnitude, and duration of certain hazards [54]. When combined with concentrated urban exposure and densely interconnected systems, these changes may generate scenarios that exceed cities’ existing resistance and response capacities. Such events may cause prolonged losses of essential urban functions and alter long-term urban development trajectories. Under such circumstances, greater demands are placed on urban resilience and recovering capacity.

Given these fundamental characteristics and evolutionary trends, risk sources can be characterized along multiple dimensions, including origin, formation mechanism, state of recognition, hazard domain, spatial distribution, magnitude, spatial reach, and temporal duration. Consistent identification, classification, and characterization of risk sources provide a structured basis for urban risk assessment, scenario development, monitoring and early warning, and tiered and category-specific governance.

3.2 Risk Exposure

Risk Exposure refers to the people, communities, economic activities, engineered assets, resources, and environmental systems that are subject to the effects of risk sources (Fig. 4). The resulting consequences may include casualties, property losses, functional degradation, environmental damage, or disruption of social order.

Within the SEM Theory, Risk Exposure is both the bearer of risk consequences and an important factor shaping the spatial extent of risk propagation, the severity of the resulting losses, and the pathways through which a risk event evolves [17]. Urbanization and modernization have given rise to four defining “high” patterns of Risk Exposure in cities, collectively termed the “4H” patterns. The first pattern is high population density. Permanent residents, temporary residents, and highly mobile populations are concentrated within limited built-up areas [55,56]. The second pattern is high asset concentration. Buildings, industries, public service facilities, and infrastructure networks are both densely concentrated and high in value. The third pattern is a high concentration of elements critical to national security. Central cities and megacities serve as major hubs for core political, economic, scientific and technological, cultural, social-governance, and cyber-information functions. The fourth pattern is high systemic coupling. Energy, transportation, communication, and water supply and drainage systems depend closely on one another [34]. A localized functional failure may trigger cascading effects across systems.

Risk Exposure in cities should therefore not be understood as a collection of isolated and static objects. Instead, exposed people, assets, resources, and systems collectively constitute an open complex giant system composed of heterogeneous elements, hierarchical structures, and multifunctional subsystems [1]. The safety state of this system not only depends on the degree of exposure and the vulnerability of individual objects, but also depends on the structural relationships, functional dependencies, and coupling mechanisms that connect different systems. From a functional perspective, the urban complex giant system comprises four basic systems, as shown in Fig. 4. The production system generates wealth, provides employment, and sustains economic circulation. The living system encompasses education, healthcare, culture, community, and public services, thereby supporting daily life and social interaction. The ecological system provides resources, environmental capacity, and natural regulation. The governance system maintains order, allocates resources, coordinates relationships, and safeguards public safety. These four systems both support and constrain one another. Together, the four systems define the basic functional architecture of urban operation.

From the perspective of safety assurance, the urban complex giant system can also be analyzed in terms of six key subsystems: energy, transportation, communication, water supply and drainage, ecology, and governance (Fig. 4). These two partitions are complementary: one describes overall urban functions, while the other identifies key systems for urban safety and risk propagation. Of these six key subsystems, the first four—energy, transportation, communication, and water supply and drainage—constitute the urban lifeline systems and respectively ensure power supply, the movement of people and materials, information transmission, and basic water security. The ecology subsystem provides resources, environmental capacity, and natural regulation. The governance subsystem provides organizational coordination, order maintenance, and emergency response. A city can continue to operate under a risk shock when the six subsystems retain their basic functions and possess sufficient redundancy, substitutability, and recoverability [57]. Essential urban functions can thereby remain above their safety thresholds.

The key subsystems are tightly coupled, highly open, and susceptible to cascading failures. Within a single subsystem, the failure of one node or link may propagate through the network and degrade service capacity. Sustained propagation may interrupt function altogether. Across subsystems, energy, information, transportation, resource, and organizational linkages create multiple interdependencies, through which a localized failure may evolve into a cross-system chain reaction [7,58]. Meanwhile, external shocks, including extreme weather, public health emergencies, cyberattacks, and disruptions to industrial and supply chains, may affect exposed people, assets, resources, and systems in cities through infrastructure systems, population mobility, material supply, and information-dissemination networks, causing localized risks to evolve into compound and systemic risks [59]. Research on Risk Exposure should therefore not only identify the exposure and vulnerability of individual objects but also focus on revealing the structural dependencies, functional coupling, and cascading-failure mechanisms among key subsystems.

3.3 Mitigation Force

Within the SEM Theory, Mitigation Force refers to an integrated set of cognitive, organizational, technological, and material elements that collectively enable a city to prevent or reduce safety risks, withstand and respond to their impacts, recover from resulting disruptions, and adapt to changing risk conditions. Mitigation Force constitutes the third fundamental element of urban safety, existing alongside and interacting with Risk Source and Risk Exposure [17]. Unlike Risk Source and Risk Exposure, Mitigation Force is characterized by proactive intervention. Protective capacity is attributed to Mitigation Force only when it results from an identifiable mitigation intervention, whereas the intrinsic robustness, redundancy, and recoverability of exposed entities and systems remain attributes of Risk Exposure and are not counted as Mitigation Force. Its intervention may be directed toward Risk Exposure, by strengthening the capacity of exposed people, assets, and systems to withstand and recover from risk impacts; toward Risk Source, by controlling specific risk sources and reducing their harmful effects; or toward the risk-evolution process, by altering the pathways of risk evolution and propagation. However, mitigation facilities, equipment, and other physical assets may themselves become new risk sources if poorly configured or if they fail in operation; the inappropriate allocation of related resources or implementation of mitigation measures may also increase the vulnerability of exposed people, assets, and systems.

Mitigation Force is supported by four interrelated dimensions—risk cognition, mitigation organization, mitigation technology, and mitigation resources—which together encompass both engineering and non-engineering foundations (Fig. 5). Risk cognition provides conceptual guidance for mitigation activities. It encompasses a city’s safety philosophy, risk awareness, safety culture, and public participation, and provides a basis for the rational allocation and effective use of mitigation resources [10]. Mitigation organization provides the institutional foundation for coordinated mitigation action. It encompasses urban safety laws and regulations, emergency management system, plans and standards, and mechanisms for grassroots mobilization. These arrangements support overall coordination, unified command, and collaboration across government and society. Mitigation technology provides the technical means for risk prevention and response. It encompasses monitoring, risk assessment, intelligent situation analysis, and decision support [18]. It thereby supports a shift in urban safety practice from reactive response to proactive prevention and from experience-based judgment to data-informed decision-making. Mitigation resources provide the material foundation for Mitigation Force. It includes emergency equipment and supplies, risk-reduction engineering projects, financial support, and investments that strengthen the resistance and recovery capacity of exposed people, assets, and systems [60]. These resources provide essential material support for maintaining basic protection and response functions under extreme scenarios. The four dimensions reinforce one another and operate in coordination, jointly determining the overall level of Mitigation Force in a city.

Mitigation Force exhibits three basic features. First, multi-element coordination. Mitigation Force is not the arithmetic sum of individual measures, resources, and capabilities. Rather, it emerges through the coordination of the above elements across departments, systems, and levels of governance. A deficiency in any supporting dimension may therefore become a bottleneck that constrains the overall effectiveness of urban safety governance. Second, full-cycle adaptability. Mitigation Force is realized throughout the full cycle of a risk event, including the periods before, during, and after the event [12]. Before an extreme event, mitigation activities focus primarily on risk prevention and strengthening the resistance of exposed people, assets, and systems. During the onset and evolution of an event, the emphasis shifts to monitoring, early warning, and emergency response. After an event, continued rescue, recovery, and reconstruction become central. Mitigation Force must therefore combine the precision and efficiency required in routine governance with the reliable protection of essential functions required under extreme events. Third, Mitigation Force is amenable to deliberate development and optimization. Risk Source and Risk Exposure are strongly shaped by natural conditions and existing urban endowments. By contrast, governments, social organizations, and the public can deliberately strengthen and optimize Mitigation Force by developing relevant capabilities, improving coordination, and allocating resources [11,40]. Mitigation Force therefore provides a direct and actionable leverage point for urban safety governance.

Within the SEM Theory, strengthening Mitigation Force can be understood as the coordinated regulation of the urban complex giant system across systems and scales [19]. Fig. 5 summarizes the four modes of regulation through which this coordination can be achieved. Targeted regulation is applied under routine conditions and relies on monitoring, early warning, and fine-grained governance. Extreme-scenario regulation is activated when risks exceed routine response thresholds and relies on emergency mobilization, extraordinary resource allocation, and the protection of essential functions. Evolutionary regulation operates over longer time horizons, adapting mitigation arrangements to urban development and changing risk conditions. Regional regulation operates at the urban-agglomeration scale through cross-jurisdictional coordination in risk prevention and response. Across these four modes, Mitigation Force is realized through three principal action pathways: controlling risk sources, strengthening the resistance and recovery capacity of exposed people, assets, and systems, and safeguarding essential urban functions [61]. Mitigation Force thus represents the integrated protective effectiveness realized in a city’s efforts to withstand risk shocks. Mitigation Force also provides the link through which risk identification and assessment are translated into governance intervention. Strengthening Mitigation Force requires the coordinated development of engineering measures, organizational arrangements, cognitive foundations, technological tools, and material resources. Such coordinated development can help cities maintain a dynamic balance between safety and continued urban development.

3.4 Interactions and functional transformations among Risk Source, Risk Exposure, and Mitigation Force

Within the SEM Theory, the functional role of an element is context dependent rather than intrinsic or fixed. Damage, functional overload, or changes in the risk context may cause the same element to assume a different role within the urban system.

For instance, the 2011 Great East Japan Earthquake triggered the failure of the Fujinuma earth-fill dam, releasing impounded water that inundated the downstream area. The failed dam therefore underwent a functional-role shift from an exposed asset forming part of Risk Exposure to a secondary risk source [62]. Similarly, a liquefied natural gas (LNG) storage tank may assume different functional roles under different risk scenarios. In an operational-failure scenario, an accidental loss of containment may cause the tank to function as a risk source by initiating a fire or explosion. During an earthquake, however, the same tank forms part of Risk Exposure because ground shaking and soil deformation may threaten its structural integrity [63,64].

More specifically, the functional role of the same physical element may also vary with the hazard considered and the object to be protected. Accordingly, the same element may form part of Risk Exposure in one scenario and serve as a mitigation asset within Mitigation Force in another. An automatic fire sprinkler system provides a clear example. During an earthquake, the sprinkler system is itself susceptible to structural or functional damage and therefore forms part of Risk Exposure. During a fire, by contrast, it serves as a mitigation asset by activating automatically to suppress the fire.

Protective facilities that normally serve as mitigation assets may themselves become risk sources when they are inadequately designed, poorly maintained, or improperly operated. Under such conditions, these facilities may cease to perform their intended protective functions and may instead facilitate the propagation and amplification of risk. During Hurricane Katrina in 2005, the failure of several levees and floodwalls in New Orleans allowed storm-surge water to enter low-lying areas that the structures had been designed to protect. Once breached, the affected levees and floodwalls ceased to function as mitigation assets. Instead, the breaches provided major pathways for floodwater to enter the city, thereby intensifying urban inundation. This case illustrates how a protective facility can shift from a mitigation asset to a secondary risk source following functional failure [65].

Sections 3.1–3.3 define Risk Source, Risk Exposure, and Mitigation Force as three conceptual categories rather than numerical state variables. The quantitative formulation therefore does not assign numerical values directly to the entities belonging to these categories. Instead, it quantifies the functional effects or state attributes associated with them within a specified urban subsystem, risk scenario, spatial boundary, and time interval. The independence of the three elements refers to their semantic and accounting separation rather than statistical independence: their interactions are explicitly represented in the model, while the same baseline functional contribution is not directly assigned to more than one initial variable. Cross-variable influences are represented separately through explicit coupling terms. Scenario-dependent changes in functional role are operationalized when the initial variables are constructed: if an element changes role, its corresponding functional contribution is reassigned to the appropriate variable for that scenario or time step. The equations below therefore describe interactions among the resulting functional variables rather than directly converting one conceptual category into another.

To balance mechanistic interpretability with computational tractability, the formulation is organized into a coupled-transformation layer that maps the initial functional variables to their effective states and a safety-evaluation layer. Fig. 6 illustrates how the functional variables associated with the three conceptual elements interact and jointly affect urban safety as external disturbance intensifies. In the coupled-transformation layer, R^{\ast }, B^{\ast } and M^{\ast } denote the effective risk load generated by specific risk sources, the comprehensive bearing capacity of the exposed entities identified as Risk Exposure, and the realized mitigation contribution attributable to identifiable interventions, respectively, after interactions and functional transformations have been taken into account. The coupled effects among these variables are represented mathematically as follows:

(1)M^{\ast }={\left[M_0+{\tau }_{\text{RM}}{R}_0+{\tau }_{\text{BM}}{B}_0\right]}_{+}

(2)B^{\ast }={\left[B_0-{\tau }_{\text{RB}}{R}_0+{\tau }_{\text{MB}}{M}^{\ast }\right]}_{+}

(3)R^{\ast }=R_{\text{p}}+{\tau }_{\text{BR}}{[R_{\text{p}}-B^{\ast }]}_{+}

Where R_0 denotes the initial functional demand or loss load generated by the identified risk sources; B_0 denotes the baseline bearing capacity inherent in the exposed entities identified as Risk Exposure before additional mitigation intervention; and M_0 denotes the mobilizable mitigation input attributable to identifiable interventions. Within a specified subsystem and scenario, all three quantities are expressed in the same functional service unit U_j over the same time interval.

M^{\ast } denotes the realized mitigation contribution after cognitive, organizational, technological, and material elements have been mobilized and coordinated for the specified scenario.

B^{\ast } denotes the comprehensive bearing capacity after risk-induced degradation and intervention-attributable enhancement have been considered.

R_{\text{p}} represents the residual functional risk load after risk-reduction actions have been applied under the net risk-entropy state \mathrm{\Delta }H, as expressed below:

(4)R_{\text{p}}=[R_0-{\tau }_{\text{MR}}(\mathrm{\Delta }H)M^{\ast }{]}_{+}

R^{\ast } denotes the final effective risk load after the load-reduction effects of mitigation have been considered, and the positive-part operator ensures that neither residual load nor overload becomes negative. The coupling-response {\tau }_{ij} is dimensionless and quantifies the strength with which pathway i induces, enables, or modifies the response of pathway j, with values from 0 to 1. These coefficients represent cross-pathway response effects rather than physical transfers or conservation-based reallocations of functional quantities. These coefficients are scenario- and subsystem-specific and must be estimated from observed or simulated functional responses rather than assumed to be universal constants.

Intrinsic robustness, redundancy, and recoverability are represented directly through B_0, whereas only additional support or load reduction attributable to an identifiable mitigation intervention is represented directly through M_0. The effects of M_0 on R^{\ast } and B^{\ast } are introduced only through the explicitly defined coupling terms and therefore do not constitute duplicate assignment of the baseline capacity.

Net risk entropy characterizes the balance between the disordering tendency induced by risks and the ordering effects generated through Mitigation Force. Net risk entropy operates throughout the risk-evolution process rather than emerging only after the safety index falls below 0.5. Before the critical point, the urban system can generally absorb these effects through its reserve bearing capacity and the coordinated operation of Mitigation Force, preventing them from altering its overall evolutionary trajectory. Once the effective risk load and comprehensive bearing capacity reach critical equilibrium, however, the system becomes markedly more sensitive to disorder-inducing disturbances. Beyond this point, entropy-increasing, entropy-balanced, and negative-entropy-dominated conditions produce divergent risk-evolution trajectories, causing the effective risk-load curve and safety-index curve to branch.

As external disturbance intensity increases, the risk load generally rises and bearing capacity may decline because of risk-induced damage, while the realized mitigation contribution reflects the extent to which its constituent elements can be mobilized and coordinated under the functional constraints of the exposed systems. Rather than entering the safety index as an independent additive term, the realized mitigation contribution affects safety through two pathways: it increases B^{\ast } through capacity compensation and decreases R^{\ast } through risk suppression. We therefore express the safety index as the proportion of comprehensive bearing capacity in the combined total of comprehensive bearing capacity and final effective risk load:

(5)S(\xi ,\mathrm{\Delta }H)=\frac{B^{\ast }(\xi ,M^{\ast },R^{\ast })}{B^{\ast }(\xi ,M^{\ast },R^{\ast })+R^{\ast }(\xi ,M^{\ast },B^{\ast },\mathrm{\Delta }H)}

The intersection of R^{\ast } and B^{\ast } indicates that the final effective risk load exactly equals the comprehensive bearing capacity; at this point, the safety index equals 0.5. The value of 0.5 is therefore defined within the SEM Theory as a theoretical critical threshold separating a capacity-sufficient functional state from functional overload. Before the intersection (B^{\ast }>R^{\ast },S>0.5), the city can generally maintain its functions; after the intersection (), functional overload occurs. Other intersections in Fig. 6, such as B^{\ast }=M^{\ast } and R^{\ast }=M^{\ast }, indicate only equality between the corresponding functional-equivalent values and do not define the urban safety threshold.

To quantify both the functional condition and safety state of a city, the formulation builds on the SEM Theory and explicitly represents how the functional support provided through Mitigation Force is allocated between risk reduction and bearing-capacity enhancement, as well as how the overload of exposed systems feeds back to generate secondary risk. We then characterize urban safety by the balance between comprehensive bearing capacity and final effective risk load. The resulting method is designed around a parsimonious set of parameters that can be estimated from monitoring data, engineering models, or scenario-specific calibration and yields an easily interpretable safety index, thereby providing a practical basis for applying and extending the SEM Theory. On this basis, the following subsystem-level formulation specifies how the initial functional variables are constructed, transformed, and aggregated for quantitative urban-safety assessment.

3.4.1 Identification of critical urban subsystems

Critical urban subsystems, including energy, communications, transportation, water supply and drainage, ecology, and governance, serve as the basic units of calculation, with j indexing the subsystem. Within each subsystem, Risk Source identifies the hazard-producing entity, event, or process; Risk Exposure identifies the people, assets, and functions subject to impact; and Mitigation Force identifies deliberate cognitive, organizational, technological, and material interventions. Their quantitative effects and state attributes are introduced immediately before the corresponding functional-mapping equations. Within a given scenario, each functional contribution is directly assigned to one variable and one action pathway only, preventing semantic overlap and double counting. This subsystem-based representation also reflects the strong interdependencies among critical urban infrastructures [17,18,59].

3.4.2 Conversion of raw data into functional equivalents

Raw observations retain their original physical or statistical units at data ingestion, but heterogeneous quantities are not added or compared directly. For each subsystem j, a common functional service unit U_j is specified according to its service function, such as megawatts, passengers per hour, cubic metres per hour, or patients per day. In the mapping equations below, R_j, B_j, and M_j denote the functional risk load, baseline functional capacity, and mobilized mitigation support, respectively. The coefficients a_j, b_j, and c_j convert the corresponding raw observations into U_j; consequently, R_j B_j, and M_j share the same subsystem-specific unit and can be consistently compared and combined. Comparability is required only within the same subsystem and scenario; functional loads or capacities are not summed across different subsystems. Cross-subsystem integration is performed later using the dimensionless safety indices S_j. The first-order functional mapping is written as follows:

(6)\begin{array}{c}{R}_j=a_j{h}_j\\ B_j=b_j{e}_j\\ M_j=c_j{m}_j\end{array}

In Eq. (6), h_j, e_j, and m_j are raw observations associated with the load generated by Risk Source, the capacity attributes of Risk Exposure, and the resources mobilized through Mitigation Force, respectively. The coefficients a_j, b_j, and c_j carry dimensions of U_j per unit of the corresponding raw variable; therefore, Eq. (6) is a dimensional conversion rather than a normalization. The linear expressions are admissible only as validated first-order measurement models. The coefficients must be derived from engineering standards, rated service capacities, performance or fragility curves, controlled simulations, or paired observations of the raw indicator and delivered service. If proportionality is unsupported, the corresponding linear term is replaced by a validated nonlinear or piecewise mapping without changing the subsequent safety equations. Thus, population, hospital beds, fire stations, and transport capacity are never converted by arbitrary or transferable coefficients; each is used only in a subsystem-specific mapping with a documented physical interpretation and validation record.

When the same subsystem contains multiple mitigation elements, we further express its available level of Mitigation Force as:

(7)M_j=\sum _{p=1}^{q_j}{c}_{jp}{m}_{jp}

Here, m_{jp} is the observed quantity of mitigation resource p, and c_{jp} is its verified service contribution in units of U_j per resource unit. Equation (7) permits aggregation only after every resource has been mapped to the same subsystem-specific service unit. Interaction, saturation, or threshold effects must be represented by a non-additive mapping when diagnostic tests show that simple summation is inadequate.

3.4.3 Functional allocation of Mitigation Force to risk reduction

A portion of the available functional support provided through Mitigation Force is allocated to monitoring and early warning, hazard screening, evacuation, and risk control, thereby reducing the risk load before it affects the exposed subsystem. Let {\theta }_j denote the proportion of this functional support assigned to anticipatory prevention. The resulting reduction in risk load is:

(8)M_{R,j}={\theta }_j{M}_j

where:

(9)0⩽{\theta }_j⩽1

Following mitigation intervention, the residual risk load that acts on the exposed subsystem is:

(10)R_{0j}=[R_j-{\theta }_j{M}_j{]}_{+}

When , only part of the risk load is reduced; when {\theta }_j{M}_j⩾R_j, it effectively controls the risk load.

3.4.4 Functional allocation of Mitigation Force to bearing-capacity enhancement

Beyond anticipatory prevention, the remaining functional support provided through Mitigation Force is allocated to emergency rescue, resource deployment, and functional recovery, thereby augmenting the baseline bearing capacity of the exposed subsystem. The portion allocated to this pathway is:

(11)M_{B,j}=(1-{\theta }_j)M_j

Because emergency resources do not necessarily convert completely into actual support capacity, this study introduces the matching-efficiency coefficient {\mu }_j. The resulting effective capacity compensation is therefore expressed as:

(12)\text{Δ}{B}_j={\mu }_j(1-{\theta }_j)M_j

Accordingly, the comprehensive bearing capacity of the exposed subsystem is expressed as:

(13)B_j^{\ast }=B_j+{\mu }_j(1-{\theta }_j)M_j

where:

(14)0⩽{\mu }_j⩽1

The coefficient {\mu }_j represents the match between mitigation resources and actual risk demands. It approaches 1 when emergency resources arrive promptly and match disaster needs, and it decreases when road disruptions, dispatch delays, facility failures, or resource mismatches occur. Allocating the available functional support between the two pathways prevents the same resource from being counted in full for both risk reduction and capacity compensation and therefore avoids double counting.

3.4.5 Calculation of the Risk Source entropy-increase state

Building on the functional-equivalence model of the SEM Theory, this study introduces generalized risk entropy to characterize the tendency of critical urban subsystems to evolve from orderly operation toward disordered failure. Risk sources introduce disorder into the urban system through the superposition and coupling of multiple risk factors, thereby constituting the entropy-increase term. In contrast, Mitigation Force introduces information and order through monitoring and detection, early warning and response, resource allocation, and effective intervention, thereby constituting the negative-entropy term. The intensity, diversity, and coupling complexity of the risk sources are first synthesized as follows:

(15)W_{H,j}=1+\sum _{i=1}^{n_j}{w}_{ij}{T}_{ij}

Before Eq. (15) is evaluated, each raw risk-factor observation is transformed into a non-negative, dimensionless state score T_{ij} using a prespecified reference value, engineering threshold, or empirical distribution. A value of zero denotes the reference state and larger values denote a stronger disordering contribution. The weights w_{ij} are non-negative and sum to 1 within subsystem j. Consequently, W_{H,j} is dimensionless and strictly positive, and the constant 1 is added to a dimensionless weighted sum solely to define a positive neutral baseline for the logarithm. This entropy-layer standardization is distinct from the functional-unit conversion in Eq. (6): the raw data used to estimate R_j, B_j, and M_j may remain dimensional, whereas inputs to the logarithmic entropy ratio must be dimensionless. For example, an energy subsystem may use dimensionless scores for extreme heat, transmission-facility failure, fuel-supply interruption, and demand surge; a transportation subsystem may use scores for pluvial flooding, road damage, traffic pressure, and critical-node disruption. R_j represents the magnitude of functional load, whereas W_{H,j} represents the diversity, coupling, and disordering tendency of its contributing factors; the two measures are therefore not interchangeable.

3.4.6 Calculation of the negative-entropy input from mitigation force

Suppose that subsystem j contains q_j constituent indicators of Mitigation Force that can generate negative-entropy input. Each indicator is first converted to a non-negative, dimensionless score on a documented reference scale. The equivalent negative-entropy input is then calculated as follows:

(16)W_{M,j}=1+{\alpha }_j\sum _{p=1}^{q_j}{v}_{jp}{Z}_{jp}

subject to

(17)v_{jp}⩾0,\sum _{p=1}^{q_j}{v}_{jp}=1

Here, Z_{jp} is the dimensionless state score of Mitigation Force indicator p in subsystem j, obtained from a prespecified reference value, performance target, or empirical distribution. The indicator weights v_{jp} are non-negative and sum to 1, and {\alpha }_j is a positive dimensionless scale coefficient used to make the negative-entropy composite comparable with W_{H,j} under a documented reference condition. Thus, W_{M,j} is dimensionless and strictly positive, and the constant 1 has the same neutral-baseline interpretation as in Eq. (15).

3.4.7 Calculation of net risk entropy

The entropy-increasing effect of risk sources and the entropy-reducing effect of Mitigation Force jointly determine the net risk entropy of the system:

(18)\text{Δ}{H}_j=k_c\ln \frac{W_{H,j}}{W_{M,j}}

The sign of net risk entropy is interpreted according to the following criteria :

(19)

Net risk entropy is not directly added to the risk load or bearing capacity as an independent variable. Instead, it dynamically modifies the feedback coefficient governing the conversion of exposure overload into secondary risk. When the entropy-increasing effect of risk sources dominates, exposure overload is more likely to induce functional failure and cross-system cascading risks. Conversely, when the negative-entropy input generated through Mitigation Force dominates, overload feedback and the propagation of secondary risks are suppressed. In this way, risk entropy links risk-source complexity, the organizational effectiveness of Mitigation Force, and exposure-overload feedback, enabling the original SEM Theory-based equations to further capture the disorder-driven evolutionary dynamics of complex urban systems.

3.4.8 Risk-entropy-based adjustment of overload feedback

Let {\gamma }_j^H denote the amplification coefficient governing the conversion of exposure overload into secondary risk. This coefficient is dynamically adjusted by net risk entropy as follows:

(20){\gamma }_j^H={\gamma }_{0j}\text{exp(}{\lambda }_j\frac{\text{Δ}{H}_j}{k_c})

Substituting the net risk entropy equation yields:

(21){\gamma }_j^H={\gamma }_{0j}{(\frac{W_{H,j}}{W_{M,j}})}^{{\lambda }_j}

Here, {\gamma }_{0j} denotes the dimensionless baseline ratio of secondary risk load to overload in subsystem j under entropy-neutral conditions. {\gamma }_j^H is the realized feedback coefficient after net risk entropy has been considered, and {\lambda }_j is a non-negative, dimensionless entropy-sensitivity parameter. Assigning {\lambda }_j=1 is permitted only as an initial reference case; practical applications must calibrate it from historical incidents or scenario simulations and report sensitivity or uncertainty when observations are insufficient.

When the residual risk load does not exceed the comprehensive bearing capacity, the critical urban subsystem can generally maintain normal operation:

(22)R_{0j}⩽B_j^{\ast }

When the residual risk load exceeds the comprehensive bearing capacity, the excess load may cause infrastructure damage, service disruption, or systemic failure:

(23)L_j={[R_{0j}-B_j^{\ast }]}_{+}

where L_j denotes the overload magnitude of the j-th subsystem. Overload of an exposed subsystem not only impairs its own functioning but may also cause affected components to function as new risk sources. For example, failure of the power-supply system may further disrupt communications, water supply, and transportation systems. To represent this feedback process, the risk-entropy-adjusted feedback coefficient {\gamma }_j^H is applied, and the resulting secondary risk load is expressed as:

(24)R_{\text{sec,}j}={\gamma }_j^H{L}_j

Accordingly, the final effective risk load is given by:

(25)R_j^{\ast }=R_{0j}+{\gamma }_j^H{[R_{0j}-B_j^{\ast }]}_{+}

Substituting the risk-entropy-adjusted feedback coefficient into Eq. (21) yields:

(26)R_j^{\ast }=R_{0j}+{\gamma }_{0j}{(\frac{W_{H,j}}{W_{M,j}})}^{{\lambda }_j}[R_{0j}-B_j^{\ast }{]}_{+}

When no overload occurs, [R_{0j}-B_j^{\ast }{]}_{+}=0, and risk entropy does not artificially generate secondary losses. When the subsystem is overloaded and net risk entropy is positive, the feedback coefficient increases, thereby intensifying secondary risks and cross-system cascading effects. Conversely, when overload occurs but the negative-entropy input generated through Mitigation Force is sufficiently strong, the feedback coefficient decreases and the propagation of risk is suppressed.

3.4.9 Calculation of the safety state of critical subsystems

The safety index of a critical subsystem is defined as the ratio of its comprehensive bearing capacity to the sum of its comprehensive bearing capacity and final risk load:

(27)S_j=\frac{B_j^{\ast }}{B_j^{\ast }+R_j^{\ast }}

Substituting the relationships derived above for risk reduction, capacity compensation, and overload feedback gives:

(28)S_j=\frac{B_j+{\mu }_j(1-{\theta }_j)M_j}{B_j+{\mu }_j(1-{\theta }_j)M_j+[R_j-{\theta }_j{M}_j{]}_{+}+{\gamma }_{0j}{({\displaystyle \frac{W_{H,j}}{W_{M,j}}})}^{{\lambda }_j}{[[R_j-{\theta }_j{M}_j{]}_{+}-B_j-{\mu }_j(1-{\theta }_j)M_j]}_{+}}

The index is bounded as follows:

(29)0⩽S_j⩽1

The theoretical critical threshold is 0.5. When S_j>0.5, or B_j^{\ast }>R_j^{\ast }, comprehensive bearing capacity is sufficient and the subsystem remains dynamically stable. When S_j=0.5, or B_j^{\ast }=R_j^{\ast }, the subsystem reaches critical equilibrium. When , or , the subsystem becomes overloaded or functionally impaired.

3.4.10 Calculation of the overall urban safety level

After obtaining the safety index of each critical subsystem, we calculate the overall urban safety index as a weighted sum:

(30)F_{\text{city}}=\sum _{j=1}^n{w}_j{S}_j

subject to:

(31)w_j⩾0,\sum _{j=1}^n{w}_j=1

Here, w_j is the dimensionless weight of critical subsystem j and is distinct from the risk-factor weight w_{ij} in Eq. (15). Subsystem weights are non-negative and sum to 1. They may be estimated from service criticality, interdependency analysis, policy priorities, or outcome-based calibration. Equal weights should be reported as a benchmark, and the stability of the overall ranking should be tested under alternative defensible weighting schemes. Because the aggregation operates on dimensionless S_j values, it does not require direct conversion between the physical service units of different subsystems. For example:

(32)\begin{array}{rl}{F}_{\text{city}}=& w_1{S}_{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}+w_2{S}_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}+w_3{S}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}+\\ & w_4{S}_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{y}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{d}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{g}\mathrm{e}}+w_5{S}_{\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{y}}+w_{6}S{}_{\mathrm{g}\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\end{array}

A larger F_{\text{city}} indicates stronger overall bearing capacity relative to the risk loads across critical urban subsystems and, consequently, a higher level of urban safety. The theoretical threshold of 0.5 can be used to classify the city’s overall state:

(33)

The framework follows a direct functional logic: Risk Source is represented by the functional pressure it generates, Risk Exposure by the baseline bearing capacity of exposed systems, and Mitigation Force by its effects on risk reduction and bearing-capacity enhancement, while overload of exposed systems feeds back to amplify risk. The index therefore represents the relative balance between the functional support available to the urban system and the risk load imposed on it. Because the overall urban index is a weighted average, however, it may mask severe impairment in an individual critical subsystem. We therefore report F_{\text{city}} together with the following critical-subsystem shortfall indicator:

(34)S_{\text{min}}\text{= min(}{S}_1,S_2,\dots ,S_n{)}_{}

When F_{\text{city}}>0.5 but , the overall index indicates that the city remains operational, but at least one critical subsystem is overloaded and should be prioritized for warning and intervention.

Grounded in the SEM Theory, this formulation focuses on how the functional support provided through Mitigation Force is allocated between risk reduction and bearing-capacity compensation, and on how overload of exposed systems feeds back to generate secondary risk. It thereby translates interactions among the three element classes into quantifiable functional-equivalent relationships suitable for computation and highlights the central regulatory role of Mitigation Force in urban safety. The formulation can be further extended by incorporating additional interaction pathways and transformation mechanisms to accommodate different risk types and research objectives, thereby retaining flexibility and broad applicability.

3.4.11 Parameter determination, calibration, and uncertainty

The parameters in the formulation are not universal constants. They are determined only after the subsystem boundary, risk scenario, analysis interval, and functional service unit have been fixed. Table 1 summarizes their dimensions, admissible domains, and practical determination routes. Where event records are available, calibration minimizes the discrepancy between observed and modelled residual load, overload, secondary functional loss, or recovery capacity, followed by cross-event or split-sample validation. Where observations are sparse, engineering standards, process-based simulations, and structured expert elicitation define transparent prior ranges. Unidentifiable parameters are retained as scenario ranges rather than reported as precise point estimates, and uncertainty is propagated to S_j and F_{\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}} through Monte Carlo or global-sensitivity analysis.

4 Space–Air–Ground Integrated Monitoring Technologies

Urban safety monitoring deals with a complex giant system with strongly coupled subsystems. Traditional inspection and appraisal methods capture only a snapshot of an individual object and therefore cannot provide the spatiotemporal continuity that city-scale monitoring demands. Structural health monitoring can track an individual asset in real time and diagnose fine-grained changes in its condition, but it generally gives limited attention to external risk sources, cross-system propagation mechanisms, or citywide safety states and thresholds. Urban safety monitoring must therefore acquire information on risk sources together with data on the states of exposed people, assets, and systems, thereby supporting multiscale and multidimensional monitoring and early warning across the city.

Space–Air–Ground integrated monitoring provides a key technical pathway for urban safety monitoring and early warning. The three tiers differ in spatial coverage, measurement accuracy, and timeliness; integrating them requires solving three progressively scientific problems:

(1) Multiscale, high-precision, and high-density spatiotemporal sensing: increasing data density and measurement accuracy across city-scale areas, while unifying spatial and temporal references over temporal resolutions ranging from the full-service life of an asset to hertz-level sampling;

(2) Deep information interpretation through multidimensional knowledge embedding: extracting multidimensional features from multisource data, mapping them onto real-world physical space, and incorporating physical priors to reveal the mechanisms underlying observable phenomena;

(3) Cross-scale information fusion for safety performance assessment: integrating multilevel, multisource monitoring information with prior knowledge of geometry, materials, and boundary conditions to support safety assessment for urban systems.

Fig. 7 summarizes the relationships among these three progressive scientific problems, the corresponding tier-specific monitoring capabilities and cross-tier integration tasks, and the future research directions discussed later in this section.

4.1 Space-based monitoring

Space-based monitoring acquires data from satellites and is the primary means of achieving citywide coverage. It identifies Risk Source—typhoons, rainstorms, storm surges, and waterlogging [66,67], and monitors the safety of Risk Exposure, including buildings, bridges, and roads [68–70]. Buildings and infrastructure, as a category of Risk Exposure, undergo varying degrees of deformation before collapse, making deformation one of their most prominent observable features. Change detection, GNSS, and InSAR can each identify deformation and the precursor changes that may develop into deformation. Change detection using visible-light, multispectral, and SAR imagery, for instance, reveals illegal roof loading, snow loading, and unauthorized additions; instantaneous collapse occurs once the loading exceeds the limit. GNSS and InSAR monitoring, in contrast, directly measure structural deformation, which is typically small relative to the deformation associated with instantaneous collapse and develops gradually over long-term service. Building on these capabilities, the framework for space-based urban safety monitoring links SEM Theory-derived monitoring targets with spaceborne observation, accurate and efficient sensing, mechanism-informed interpretation, and urban-safety outputs (Fig. 8).

4.1.1 Sensing: synergistic improvement of accuracy and efficiency

Satellite monitoring of buildings and infrastructure depends on two key factors: accuracy and efficiency.

First, accuracy should be enhanced for buildings and infrastructure monitoring. In optical and SAR change detection, intelligent algorithms improve the performance of extracting ground objects and their changes in complex three-dimensional urban environments. In GNSS deformation monitoring, extending applications from ideal settings such as large bridges and dams to buildings in complex urban environments requires new adaptive algorithms and hardware. , which may cope with large height differences, signal occlusion, and severe diffraction effects. For InSAR deformation monitoring, refined inversion requires a high density of detectable points, together with high positioning and deformation accuracy. Within the current framework, simultaneously improving all three relies mainly on mining the statistical and spatiotemporal characteristics of radar signals and on tracing and quantitatively modeling the errors at each interpretation step. For engineering applications, this framework should incorporate domain knowledge and be linked to real three-dimensional urban space. For detectable-point density, the key metric will shift from the number of points per unit image area to the effective coverage of buildings, infrastructure, and their critical components by reliable points. This requires a density definition that incorporates structural priors. For the joint improvement of positioning and deformation accuracy, urban models and building pixels provide geometric priors, whereas building physical parameters and detrimental-deformation indicators serve as physical priors. Together, these two types of priors enable object-level InSAR inversion for buildings and infrastructure. For components critical to structural safety-performance assessment—the foundations, interstory levels, and roofs of high-rise buildings—novel devices should be developed to replace traditional metal corner reflectors. This changes the approach from the passive identification of available scatterers to the active generation of artificial radar scattering points, while metastructures tune the phase of radar echoes and metamaterials amplify radar reflections.

Second, efficiency of monitoring and interpretation should be improved. As optical and SAR satellite constellations expand, revisit periods may shorten from monthly or daily to hourly or even minute-level intervals. This fundamentally changes both the data volume and the underlying technical mechanisms, making research on efficiency essential to keep pace with satellite upgrades and translate high-frequency monitoring into practice. For satellite–ground links and data transmission, rapid revisit produces explosive growth in data volume that overwhelms conventional ground-based processing. Onboard computing, preprocessing and compression, real-time on-orbit imaging, and feature extraction can then increase data throughput at the source. In data processing, taking InSAR processing as an example, spatial baselines and orbital errors dominate under extremely short temporal baselines. Existing analyses designed for static or slowly varying conditions cannot capture the rapid dynamics of data updated at hourly intervals. This calls for quantitative error control together with nonstationary, nonlinear, high-frequency time-series modeling. In terms of safety assessment, manual interpretation cannot cope with TM-level, hourly-updating data. And AI-driven, fully automated end-to-end processing pipeline should be employed. It is necessary to investigate technologies such as urban safety foundation models and few-shot generalization, to enable efficient and rapid identification of precursor information on safety risks. Research on efficiency bridges the gap between data output from hourly-revisit satellite constellations and engineering applications, thereby realizing the full benefit of high-frequency revisit.

Third, a high-precision urban spatiotemporal reference is required to support the joint improvement of accuracy and efficiency. In complex urban environments, remote-sensing calibration sites at the building and infrastructure level, in key engineering sites, or within local areas constitute the primary form of this reference. Unlike traditional calibration sites suited only to ideal, uniform surfaces, urban calibration sites address accuracy calibration and error tracing for InSAR and other remote-sensing technologies under actual urban conditions.

(a) The nature of the sites and their calibration objectives differ fundamentally. Traditional calibration sites are located primarily on ideal, uniform surfaces—Gobi deserts, sandy land, and farmland. They correct systematic radiometric and geometric errors in satellite sensors, ensuring the accuracy of basic remote-sensing data. Urban calibration sites, by contrast, reproduce actual, complex urban environments and address the specific problems encountered by InSAR in cities—positioning bias, point-cloud confusion, elevation ambiguity, and deformation error. They aim to ensure the correct spatial attribution of points, resolve building-facade deformation at the floor level, and obtain error magnitudes consistent with actual working conditions.

(b) The technical logic of error control is exactly the opposite. Traditional calibration sites suppress complex ground-object interference, such as multipath effects and layover, to maintain a stable calibration reference. Conversely, urban calibration sites actively simulate and quantify various forms of complex scattering error in urban areas and build targeted error-correction models that systematically improve the accuracy of urban InSAR monitoring.

The spatiotemporal reference ultimately takes the form of a high-precision network covering entire cities and urban agglomerations. Intelligent sensing terminals integrating deformation, temperature, vibration, tilt, and other functions constitute its unit nodes. This network can be fused with the InSAR measurement-pixel network. Through unified adjustment, it improves accuracy through space–ground synergy and enables submillimeter-level monitoring of deformation in clusters of buildings and infrastructure.

4.1.2 Interpretation: embedding deep physical knowledge into apparent monitoring information

Once remote sensing, GNSS, and other techniques capture observable features of buildings and infrastructure with high precision and frequency, analyzing the safety condition of the structures themselves requires the deeper incorporation of physical knowledge.

For change detection, features from optical and SAR image should be correlated with the change characteristics of buildings and infrastructures. For example, when extracting features of illegal buildings from optical imagery, the corresponding multidimensional remote-sensing vectors should be embedded according to the physical characteristics of specific scenarios. Soil-covered roofs used for planting are mostly vegetated and thus require vegetation indices such as NDVI. Color-coated steel structures added to roofs call for a steel-tile index. Local roof extensions and additional stories, which alter roof texture and color, rely on texture and color features, including the gray-level co-occurrence matrix, RGB, and HSV.

For deformation monitoring, both GNSS and InSAR monitoring capture the observable deformation features of buildings and infrastructure: the former yields high-frequency features at individual nodes, whereas the latter yields low-frequency features in linear or areal form. Safety analysis and early warning therefore rely on establishing a mapping between observable deformation and structural-deformation mechanisms. For instance, tilting and settlement in multistory frame-structure buildings primarily manifest as overall rigid-body deformation. Midspan and edge bending in long-span spatial-structure roofs manifest as global and local buckling, respectively. Settlement of high-speed bridge piles may cause tilting of girders and slabs. Implementation can proceed through engineering analyses based on accident cases and “positive” samples or through finite-element analysis.

Deep physical embedding ultimately enables satellite-based observations of apparent phenomena to carry a traceable structural-mechanics interpretation. As sensing accuracy and efficiency improve, physical embedding throughout the sensing–interpretation workflow, together with integrated space–ground fusion, will advance the safety of buildings and infrastructure. In this way, building- and infrastructure-safety practices can advance from historical review and early risk identification toward short-term early warning.

4.2 Air-based monitoring

Air-based monitoring uses low-altitude platforms such as unmanned aerial vehicles (UAVs) as mobile platforms. By flexibly adjusting the observation distance and viewing angle, it provides continuous coverage across the scales between macroscopic aerial surveying and close-range detailed inspection. It thereby acquires three-dimensional spatial information on buildings and infrastructure through multi-view stereoscopic observations [71].

When focused on the safety state of buildings and infrastructure, air-based monitoring operates at three scales. The microscale covers component-level surface damage—cracks, leakage, spalling, and corrosion [72–75]; the mesoscale covers individual-building inspection, through which three-dimensional state information is acquired by multi-angle observation [76,77]; and the macroscale covers the identification and detection of changes in groups of urban elements [78,79].

4.2.1 Sensing: synergistic improvement of spatial data density and accuracy in complex environments

Air-based data sensing must increase spatial data density and accuracy through multimodal autonomous navigation and adaptive route planning.

First, multimodal autonomous navigation is required. In densely built-up areas, underground spaces, and tunnel corridors, GNSS signals are often limited or even completely unavailable. Inertial navigation, laser SLAM, UWB positioning, and visual navigation must therefore be fused to maintain stable flight and precise positioning [80,81]. This problem can be divided into three subproblems:

(a) Scenario-adaptive fusion strategies. In densely built-up areas, occlusion by high-rise buildings and signal reflections reduce the number of visible satellites and degrade positioning accuracy; visual–inertial SLAM should play the dominant role, assisted by UWB. In tunnel corridors, the uniform texture of the environment degrades visual-feature extraction, so laser SLAM should play the dominant role, with inertial navigation providing interframe constraints.

(b) Single-modality degradation and robust multimodal switching. Visual–inertial odometry maintains decimeter-level accuracy over distances of hundreds of meters but drifts to the meter level in low-texture areas such as large glass curtain walls, requiring correction through loop-closure detection and global optimization. Positioning errors directly affect subsequent damage identification and localization: a 1° deviation in attitude angle causes a positioning deviation of about 0.87 m for a target 50 m away. This requires investigating the accuracy limits and degradation-compensation strategies of each modality. More importantly, the system must automatically switch to a backup modality when one modality fails.

(c) Unification of multisource positioning references. Inertial navigation provides relative pose in the carrier coordinate system, whereas visual SLAM constructs a local map coordinate system. GNSS and UWB provide absolute positioning in the Earth-centered, Earth-fixed coordinate system and the local base-station coordinate system, respectively. The coordinate frames, accuracy levels, and error characteristics of these modalities are fundamentally different. Multisource fusion positioning therefore presupposes their unification within the same spatiotemporal reference, with no loss of accuracy during transformation.

Second, adaptive route planning is required. The spatial coverage density of air-based monitoring depends on how well the flight route adapts to the distribution of building clusters. The aim is to maximize the effective coverage of target building facades within limited flight endurance [82,83]. Three subproblems are involved:

(a) Planning imaging positions and viewing angles in a complex built environment. Urban near-ground space contains occluders—including trees, cables, and billboards—so fixed routes cannot guarantee complete imaging of key facades. Imaging positions and camera orientations must be adjusted adaptively to the building’s surroundings, with occluded areas supplemented through multi-view integration where necessary.

(b) Joint optimization of viewpoint sequences and sensor parameters. Flight altitude and speed must be matched to camera focal length and frame rate so that image overlap and resolution meet the data-quality requirements of target recognition.

(c) Integrated operation of heterogeneous UAVs. Monitoring complex urban systems often requires multiple UAVs to work together, and the sensors and navigation or positioning systems carried by different UAVs may differ. Integrated coverage planning and cross-platform unification of positioning references must then be addressed within a single task framework. This problem is connected to the unification of multisource positioning references in autonomous navigation and also introduces new constraints on multiplatform task allocation and collision avoidance.

4.2.2 Interpretation: multi-dimensional fusion-based recognition and spatial mapping

Air-based information interpretation involves multiscale, multimodal, and multi-view data and must solve two core problems: fusion-based recognition and spatial localization.

First, multimodal data-fusion recognition is required. The multisource imagery acquired during urban inspection usually requires feature extraction and fusion before it can support damage identification [84]. This involves three subproblems:

(a) Cross-modal feature alignment. Visible-light imagery, thermal infrared imagery, and LiDAR data capture texture and color information, temperature anomalies, and three-dimensional geometric information, respectively. These three modalities complement one another physically but lack a unified mathematical representation in feature space. Mapping heterogeneous modalities into a comparable feature space therefore requires a semantic-alignment framework [85].

(b) Mapping rules between fusion levels and monitoring scenarios. Fusion can be performed at the pixel, feature, or decision level; the level that is appropriate for a given scenario depends on whether the sensors share the same spatial resolution, differ sharply in their sensing mechanisms, or make independent judgments [86]. No systematic theory yet guides the choice of fusion strategy for different inspection scenarios.

(c) Cross-scenario generalization of lightweight models. Large vision models now detect objects with high accuracy, yet their computational and storage requirements far exceed the capacities of airborne edge devices. Models with small parameter counts must therefore remain robust across open urban scenes under strict resource limits, which poses a substantial challenge to fusion-based recognition.

Second, recognition results must be physically localized in space. Damage features exist in two-dimensional images or three-dimensional point clouds, but safety assessment requires them to be assigned to specific locations in the real world [87]. Two subproblems arise:

(a) Mapping from the sensor coordinate system to the engineering coordinate system. Cracks, leakage, and deformation recorded by air-based monitoring are represented in image or point-cloud space [88,89], whereas assessment must evaluate specific structural components in the engineering coordinate system. Errors accumulate progressively, from camera intrinsic calibration through exterior-orientation elements to the spatial-transformation model.

(b) Consistency verification of multi-view localization results. Differences in imaging positions and viewing angles between observations produce systematic deviations in localization [75,90]. Cross-validation and global consistency optimization then ensure that the spatial coordinates assigned to the same feature converge to a consistent position across observations.

4.3 Ground-based monitoring

Ground-based monitoring extends well beyond fixed-point sensor networks. Ground sensing, noncontact measurement, distributed sensing, electromagnetic detection, and mobile platforms all fall within its scope [91], and these approaches overcome the spatial and deployment limits of point sensors without losing accuracy. Extending ground-based monitoring from key points to city-scale coverage nonetheless requires solving the following problems:

First, sensing must extend deeper underground. Ground-penetrating radar (GPR) and the high-density electrical method penetrate the surface to reveal hidden cavities, pipeline leakage, and foundation defects [92–94].

A conflict exists between detection depth and resolution: high-frequency antennas resolve fine details but have limited penetration depth, whereas low-frequency antennas penetrate more deeply but provide lower resolution. Lossy media such as water-bearing clay severely attenuate signals, and combining multiple frequencies with low-frequency matched filtering helps overcome this trade-off [95]. For interpretation, shallow reinforcement meshes and layered media produce strong reflections that mask targets, while variations in target shape and the scarcity of training samples further increase the difficulty. Clutter suppression and three-dimensional inversion driven by deep learning can markedly improve automated interpretation [96].

Second, existing equipment can assume new sensing functions. With 5G-Advanced and 6G integrated sensing and communication (ISAC), communication base stations and lampposts themselves become sensing platforms. This overcomes the spatial and cost limits of point sensors, allowing wide-area, noncontact monitoring of deformation in key elements of Risk Exposure such as bridges and buildings, as well as the monitoring of low-altitude targets [97–99]. For interpretation, optical fibers, video-surveillance systems, and roadside facilities already provide extensive coverage across cities, and reusing them extends safety monitoring at little additional cost [100]. Optical fibers can also support ambient-vibration and pipeline-leakage monitoring [101,102], and video networks can simultaneously identify structural states and public-safety events [103,104]. Infrastructure thus provides sensing functions in addition to serving its original purposes.

4.4 Integrated sensing, assessment, and early warning

Space-, air-, and ground-based monitoring each have their own capability boundaries, and none alone can meet all the sensing needs of a complex urban system. Integration fuses cross-scale information within a common spatiotemporal reference, aligns multilevel data, and jointly interprets them, thereby enabling a transition from risk sensing to situation assessment. This involves three progressive scientific problems: cross-tier data fusion and spatiotemporal unification; the development of an integrated parameter system oriented to the SEM Theory [17,61]; and the development of safety-performance assessment and early-warning methods for complex urban systems. Building safety is used below to illustrate the construction and application of the integrated parameter system.

Cross-tier data fusion and spatiotemporal unification are required. The three tiers differ by orders of magnitude in spatial resolution, temporal resolution, and measurement accuracy. Integrated monitoring therefore fuses their data at multiple levels within a shared spatial reference and time window, and the fused data provide the basis for the subsequent SEM Theory-driven assessment. At the feature level, space–air fusion classifies InSAR points into building and ground points using building vector outlines [105], and the building points yield differential-settlement indicators that remove regional interference and identify settlement locations. Air–ground fusion jointly processes UAV imagery and ground images to fill in facade details and localize surface damage from all directions [106–109]. Space–ground fusion combines the wide-area InSAR settlement field with GNSS measurements and optical-fiber strain data [110]. InSAR contributes regional settlement trends and gradients, whereas ground observations verify deformation and strain at key points; together, the two confirm the results across scales, from regional trends to point-level accuracy. Cross-tier data transmission and integrated scheduling also physically constrain fusion. Communication links are heterogeneous and time-varying [111,112], and transmitting large-scale monitoring data while processing them in real time creates a resource bottleneck. Under the ISAC framework, UAVs act as both monitoring platforms and relays [113–115] to maintain cross-tier data transmission. The problem, then, is to jointly optimize transmission and computing resources under dynamic, heterogeneous communication links.

An integrated parameter system oriented to the SEM Theory is required. Integrated Space–Air–Ground monitoring does not simply stack platforms; rather, the SEM Theory drives the development of an integrated indicator system and monitoring loop [116,117]. This system is constructed along two dimensions: First, the SEM Theory indicator dimension determines monitoring objects and key parameters based on Risk Source situations and Risk Exposure states [19]; Second, the monitoring-capability dimension considers the capabilities of space-, air-, and ground-based monitoring and determines whether an indicator can be obtained, whether its accuracy is sufficient, and whether its timeliness supports assessment. The two dimensions together form a monitoring loop in which every indicator can be obtained, its accuracy is assured, and its results are fed back into the system.

The screening of existing urban buildings provides an example. A review of 250 building-safety accident cases (2000–2024) and current standards yields a monitorable parameter system. The system spans four kinds of Risk Source—geological conditions, surrounding disturbances, meteorological factors, and sudden events—and five kinds of Risk Exposure—building archives, vector information, settlement deformation, illegal loading, and surface damage. Settlement deformation, illegal loading, and surface damage belong to both Risk Source and Risk Exposure. Based on the theoretical elements of the SEM Theory, this parameter system maps monitorable parameters for building safety screening. The mapping guides the selection and prioritization of parameters in integrated monitoring, and it underpins the later fusion of indicators in group-level safety performance assessment. The resulting category-level mapping distinguishes primary or direct observation from indirect inference or supporting information across the Space-, Air-, And Ground-based monitoring tiers (Fig. 9).

For complex urban systems, Space–Air–Ground integrated monitoring ultimately serves group-level safety performance assessment and early warning through hierarchical fusion. A self-built housing community in an urban village in southern China (180,000 m², with more than 350 buildings) was screened through four progressive steps. First, InSAR identified 26 buildings with abnormal settlement among the more than 350 buildings. Air–ground integrated monitoring then examined roof loading, surface damage, surrounding engineering, and ground collapse. A neural network next identified 15 suspected high-risk buildings, and ground-based cross-validation finally confirmed five as dangerous buildings. In this case, the workflow reduced the manual inspection workload by roughly 96%, confirming that the integrated method can screen a community rapidly and accurately. It also shows that the SEM Theory parameter system, combined with hierarchical fusion, advances from the acquisition of individual parameters to the classification of safety across an entire group.

However, the empirical scope of the above case remains limited to the community-scale application in the building-safety domain, where parameters associated with Risk Source, Risk Exposure, and their scenario-dependent functional roles are mapped to Space–Air–Ground monitoring capabilities. Therefore, this case demonstrates the operational feasibility of the proposed monitoring and screening workflow rather than validating the general applicability of the SEM Theory across all urban systems. At the conceptual level, the theory provides a common structure for organizing Risk Source, Risk Exposure, and Mitigation Force in transportation, energy, water supply and drainage, and other urban subsystems. Its operational extension, however, requires subsystem-specific definitions of the three SEM elements and calibration of the functional units of analysis, monitoring parameters, safety thresholds, and interdependency pathways. Networked systems also differ from individual buildings in their topology, service flows, temporal dynamics, failure mechanisms, and cascading interdependencies; consequently, the present parameter mappings and assessment procedures cannot be transferred directly. Comparative applications across different subsystems, risk scenarios, and cities are therefore required to examine the generalizability of the theory and establish domain-specific calibration and validation procedures.

These limitations are accompanied by unresolved challenges in group-level safety-performance assessment and early warning. The ways in which multisource monitoring parameters interact with structural priors are not yet understood; different infrastructure types lack a shared assessment framework; and assessment data are temporally and spatially incomplete and heterogeneous across sites. The empirical case further reveals a gap between observation and interpretation, and no mechanical link yet connects quantitative monitoring indicators to structural bearing capacity. Three directions require further work: For data sensing, multi-source heterogeneous data require a unified representation and adaptive acquisition; For interpretation, physically embedded explainable AI and cross-modal deep association models are needed; For assessment, the monitoring–assessment loop and system fault tolerance under coupled architectures can be iteratively optimized, so that assessment moves from an experience-driven approach toward an approach jointly driven by mechanisms and data, and Space–Air–Ground monitoring moves from hierarchical progression toward full-process integration.

5 Conclusions and Outlooks

This study addresses the safety needs of modern urban complex giant systems by refining the definition of urban safety, developing the SEM Theory, and establishing SEM Theory-driven Space–Air–Ground integrated monitoring technologies. The principal conclusions and contributions are as follows.

(1) Conceptual contribution: This study defines urban safety in terms of the continuity of essential urban functions. It conceptualizes urban safety as encompassing both the state in which a city maintains its basic functions of production, living, ecology, and governance under multiple risks and the capacity to sustain that state. This function-centered definition establishes a clear safety criterion: essential urban functions must remain above their respective safety thresholds.

(2) Theoretical and methodological contribution: This study proposes the urban safety SEM Theory, which positions Mitigation Force as a third fundamental element alongside Risk Source and Risk Exposure. The theory explains how exchanges of matter, energy, and information give rise to interactions, mutual constraints, and dynamic transformations among the three elements. Its mathematical formulation and representative cases demonstrate its utility in representing urban safety states and supporting their quantitative assessment.

(3) Technical and practical contribution: This study establishes SEM Theory-driven Space–Air–Ground integrated monitoring technologies. It integrates wide-area spaceborne observation, flexible multi-angle airborne sensing, and high-precision ground-based monitoring within a unified spatiotemporal reference. Through cross-tier data fusion and information interpretation, SEM Theory-based collaborative sensing indicators are linked to safety-state assessment and risk warning. This architecture translates the theory into an operational workflow for monitoring and early warning in complex urban systems.

Future research should further develop both the SEM Theory and its associated Space–Air–Ground technical system in light of four major trends.

First, external disturbances are intensifying under climate change. Changes in precipitation and interactions between urban form and extreme rainfall increase infrastructure flood risk [39,41,42], while extreme heat raises population exposure [6]. Research based on the SEM Theory should therefore represent compound and time-varying Risk Sources, shifting Risk Exposure, and adaptive Mitigation Force under alternative climate scenarios. In parallel, the Space–Air–Ground technologies should integrate cross-scale observations with scenario simulation, dynamic warning thresholds, and the real-time allocation of mitigation resources to support climate-resilient urban safety [40].

Second, geopolitical change and armed conflict are expanding the scope of urban safety. Conflict can damage interconnected lifeline systems and interrupt essential services, while interdependencies among infrastructures amplify functional disruption and complicate recovery [7,34,56,118]. Future extensions of SEM Theory should capture cascading failures, cross-system role transformations, and the different configurations of Mitigation Force required during peacetime and wartime. The technical system should support remote damage assessment, continuity monitoring of critical functions, recovery prioritization, and rapid restoration [118,119].

Third, the aging of both urban assets and populations is weakening the foundations of safe operation. The deterioration of facilities reduces the performance of buildings and infrastructure [65], while population aging increases the difficulty of evacuation, medical assistance, and protection during emergencies [120]. The SEM Theory should incorporate the time-dependent deterioration of assets and age-specific patterns of Risk Exposure. Long-term Space–Air–Ground integrated monitoring technologies can then support lifecycle diagnosis and intervention for existing assets while incorporating the needs of older people into warning, evacuation, sheltering, and emergency response.

Fourth, industrial transformation is continually broadening the risk spectrum. Digital technologies, new materials, emerging business models, and new energy systems are becoming integral to urban operation, while risk knowledge, evidence, standards, and regulations continue to lag behind [51–53,57]. The SEM Theory should evolve into an open and updatable framework capable of identifying emerging Risk Sources, newly exposed systems, and gaps in Mitigation Force. The technical system should likewise support adaptive sensing, rapid fusion of multisource data, and iterative updates to assessment and regulatory indicators as new risks emerge.

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