Key uncertainty events impacting on the completion time of highway construction projects

Abstract

This paper examines the uncertainty events encountered in the process of constructing highways, and evaluates their impact on construction time, on highway projects in South Africa. The rationale for this examination stems from the view held by scholars that the construction of highways is a complex process, taking place in changing environments and often beset by uncertainties; and that there is a lack of appropriate evaluation of these uncertainty events occurring during the construction process. The research made use of a review of extant literature in the area of uncertainty management, and modeling in infrastructure projects, to guide the direction of the study. The inquiry process consisted of brainstorming by highway experts and interviewing them to identify the uncertainty factors that impact construction time.

An uncertainty matrix for South African highway projects was developed, using a quantitative model and descriptive statistics. It emerged from the study that the uncertainty events affecting the construction time of highway projects are distributed across economic, environmental, financial, legal, political, social and technical factors. Also, it was found that each factor might account for several uncertainty events which impact on construction time differently, through a combination of the uncertainty events of the individual construction activities.

Based on the obtained data, an Adaptive Neuro Fuzzy Inference System (ANFIS) has been developed, as a simple, reliable and accurate advanced machine learning technique to assess the impact of uncertainty events on the completion time of highway construction projects. To validate the ANFIS model, the Stepwise Regression (SR) models have been designed and their results are compared with the results of the ANFIS. Based on the predicted impact size of uncertainty events on the time of highway projects, it can be concluded that construction time on South African highway projects is significantly related to the social and technical uncertainties factors.

Keywords

ANFIS, construction time / impact assessment, highway project / South Africa / uncertainty

Introduction

Highway construction projects are subject to uncertainties and risks (^{Moret and Einstein, 2016}). There are various uncertainties existing in highway construction projects that affect construction performance differently. Uncertainties have different probabilities of occurrence that impact project performance (^{Moghayedi and Windapo, 2018}) causing schedule delay or cost overrun (^{Wang and Chou, 2003}; ^{Zayed and Halpin, 2004}; ^{Chapman, 2006}). The number and importance of such events depend on the size and complexity of the construction project (^{Zavadskas et al., 2010}). Highway projects are some of the most dynamic, challenging and complex construction projects because they are exposed to different uncertainties and risks (^{Mills, 2001}). According to ^{Flyvbjerg (2007)}, the uncertainty events in the highway projects number more than in other construction projects, because of the unique features of highway construction. These features include complexity in the relationship between major construction activities, the long duration of construction, the dynamic process of construction, the repetition within a linear project and the risks associated with any mobile construction site (^{Moghayedi and Windapo, 2017}).

Uncertainty events vary in their magnitude and impact, the probability of occurrence, and severity (^{Gadd et al., 2003}; ^{Institute, 2013}). Quantification of these factors with classical methods such as probability analysis and influence diagrams is very difficult (^{Zeng et al., 2005}). The efficient applications and quantification techniques are difficult and complex; furthermore, exact data are required (^{Winch, 2010}). Unfortunately, such data either does not exist at all or is hard to obtain. However, most of the existing assessment models for analysis and evaluation of the magnitude of different parameters are based on quantification methods and need numerical data. A limited number of studies have examined the use of subjective data in systematically identifying and modeling these uncertainty events and their sources, in order to assess and manage their impact in each highway construction activity and over the whole duration of the project.

The uncertainty model involves identifying, evaluating and modeling various events in the construction process of highway projects, with the aim of quantifying the impact of different sources of uncertainty in the construction activities. The systematic assessment models are classified in two major forms: classic models, or probability analysis, and conceptual models, or fuzzy sets analysis (^{Kangari, 1988}). The limitation of the classic models is the need to vary negligible quantity data, which in reality is difficult to access; and the applicability of these models in the uncertainty analysis of real construction projects are limited.

These limitations have been adduced to the fact that a significant number of issues and concerns in the construction projects are uncertain and ambiguous and they are mostly based on conceptual and mental structures, which classic models are unable to use (^{Kangari, 1988}).

Construction projects are subject to uncertainties and their analysis depends on the thought process of the individual doing the evaluation. This issue prevents the application of many assessment methods. Most of the conventional mathematical assessment methods, such as differential equations, are quantitative in nature and they are not well suited to uncertainty problems (^{Youssef, 2004}). Also, these methods are based on statistical or computing techniques and they cannot cover qualitative data which are used in the evaluation of uncertainties. The Fuzzy Inference System (FIS) on the other hand, is used in modeling the qualitative aspects without employing precise quantitative analyzes. It provides standard practical methods for transformation into the rule base, as well as effective methods for enhancing the performance index of Membership Functions (MF), and it is very useful in undertaking complex problems (^{Jang, 1993}).

The Adaptive Neuro-Fuzzy Inference System (ANFIS) combines the strengths of Artificial Neural Network (ANN) with FIS to create an efficient method for analyzing the impact of risks on performance (^{Ebrat and Ghodsi, 2014}). ANFIS, trained to develop fuzzy rules and determine MF for input and output variables of the system (^{Huang et al., 2002}) is an intelligent system which is able to estimate the variables and fuzzy rules intelligently and does not require a systematic method for the design of fuzzy systems. ANFIS has the capability to handle uncertainty, nonlinearity, and complex problems which are involved in most construction management decision-making processes (^{Jin, 2010}). Also, neural network fuzzy systems interpret human knowledge and deduce it into a mathematical model (^{Negnevitsky, 2005}).

ANFIS has been used in various fields of engineering; however, there is limited research about the use of ANFIS in the field of construction management. For instance, ^{Ugur (2017)} developed ANFIS to estimate the costs of the residential building. While ^{Fragiadakis et al. (2014)} assessed the occupational risk in the shipbuilding industry, ^{Ebrat and Ghodsi (2014)} applied ANFIS to assess the risk in construction projects in the Middle East. ^{Li et al. (2011)} forecast building energy consumption using a hybrid of ANFIS, and ^{Güneri et al. (2011)} used ANFIS to overcome supplier selection problems in Turkish construction projects. ^{Shahhosseini and Sebt (2011)} used ANFIS to establish a fuzzy adaptive decision-making model for the selection and assignment of human resources to construction projects in Iran based on competency. ^{Wang and Elhag (2008)} developed an ANFIS based risk assessment model for bridge maintenance projects in China, and ^{Elhag and Wang (2007)} designed an ANFIS model to assess the risk of bridge maintenance projects in the UK.

This study examines the uncertainty events in the construction of South African highway projects and whether there are key risks which have a significant impact on the completion time of highway construction projects, toward developing a systematic ANFIS model for use in assessing the impact of risks on the completion time of highway construction projects in South Africa.

Identification of uncertainty events in highway construction projects

The effect of uncertainty events on the infrastructure objectives in projects have been identified in several works of literature (^{Anderson et al., 2007}; ^{Barker and Haimes 2009}; ^{Renuka et al., 2014}; ^{Antunes and Gonzalez, 2015}; ^{Moret and Einstein, 2016}). Uncertainty events in highway construction projects are more frequent than in other construction projects, due to the unique features of highway projects; these include the complexity of interaction between major construction activities, the lengthy duration of construction, dynamic processes, repetitive linear projects and mobile construction sites (^{Flyvbjerg, 2007}). Due to the peculiar nature of uncertainty, there is a need to identify and classify the uncertainty events and their factors, using an impact assessment and risk management process to assess their effect on construction time (^{Moghayedi, 2016}). The current study employed an extant literature review in the area of uncertainty and risk, to identify all the potential uncertainty factors and events in highway construction projects in South Africa.

One of the most comprehensive studies in the field of uncertainty factor identifications was done by ^{Aziz and Abdel-Hakam (2016)}. They explored 293 disruptive events as causes of delay in road construction projects in Egypt, in 15 major delay groups. Other notable research was done by ^{Odediran and Windapo (2018)}. They identified 81 risks in African construction markets, across five major factors, namely political, social, economic/financial, procurement, design and construction. Similarly, ^{Assaf and Al-Hejji (2006)} evaluated 73 uncertainty events as causes of delay in different types of large construction projects in Saudi Arabia, according to the following factors: project, owner, contractor, design, materials, equipment, labor and external factors.

A review of extant literature in the area of uncertainty and risk was undertaken to identify all the potential uncertainty events and their main factors in the delivery of a construction project. The literature review suggests that the uncertainty events in highway construction projects can be grouped into seven main factors: economic, environmental, financial, legal, political, social and technical.

Economic factors

Economic risk factors involve issues or concerns associated with the macroeconomic impact in the community and region where the construction project is to be located. Various studies in the literature identify the fluctuation of prices of materials and equipment, the monopoly of material and equipment suppliers, a saturated market and the fluctuation in the foreign exchange rate as the key economic risks affecting project performance (^{Tah and Carr, 2000}; ^{Dey, 2001}; ^{Iyer and Jha, 2005}; ^{Saqib et al., 2008}; ^{Zavadskas et al., 2010}; Wang and Yuan, 2011; ^{Banaitiene and Banaitis, 2012}; ^{Kuo and Lu, 2013}; ^{Aziz and Abdel-Hakam, 2016}; ^{Odediran and Windapo, 2018}).

Environmental factors

Environmental risk factors involve issues associated with environmental problems, concerns, and activities confronting the project. Weather, natural disasters, remote location cost, and terrain/topological condition of the site was identified in the literature as important environmental risk factors that impact on construction project performance (^{Tah and Carr, 2000}; ^{Iyer and Jha, 2005}; ^{Saqib et al., 2008}; ^{Ehsan et al., 2010}; Wang and Yuan, 2011; ^{Banaitiene and Banaitis, 2012}).

Financial factors

Financial risk factors involve issues associated with project financing. Several researchers identify tax and legal fees, cash flow difficulties, poor financial control, lack of capital, high tender price, high cost of materials, equipment and labor as the important factors affecting construction project performance (^{Tah and Carr, 2000}; ^{Dey, 2001}; ^{Shen et al., 2001}; ^{Bunni, 2003}; ^{Saqib et al., 2008}; ^{Zayed et al., 2008}; ^{Ehsan et al., 2010}; ^{Banaitiene and Banaitis, 2012}; ^{Fang et al., 2012}; ^{Taghipour et al., 2015}).

Legal factors

Legal risk factors involve concerns associated with the significant legal consequences that flow from actions attributable to the project. Right of way acquisition, deficient documentation, difficulties in importing equipment and materials, changes in government regulations and laws, unclear arbitration process for legal disputes between construction parties, changing of bankers’ policies for loans, ineffective delay penalties, types of contracts, problems in dispute settlement due to law, and contract failure are identified in the literature as the legal risk factors that affect construction project performance (^{Shen et al., 2001}; ^{Bunni, 2003}; ^{Zou et al., 2007}).

Political factors

Political risk factors involve issues associated with the local, regional, and national political and regulatory situation confronting the project. Political risk factors identified in literature as affecting the performance of infrastructure projects comprise of the political situation, encroachment problems and human-made disasters (^{Tah and Carr, 2000}; ^{Dey, 2001}; ^{Baloi and Price, 2003}; ^{Iyer and Jha, 2005}; ^{Saqib et al., 2008}; ^{Zayed et al., 2008}; ^{Ehsan et al., 2010}; ^{Zavadskas et al., 2010}; ^{Banaitiene and Banaitis, 2012}; ^{Taghipour et al., 2015}).

Social factors

Social risk factors are associated with the social and cultural impacts of the community and region in which the construction projects are to be located. Literature cites cultural heritage issues, personal conflicts among labor, social and cultural impacts, rehabilitation of affected people, diseases, security and corruption as the important social risks impacting on the construction project performance ((^{Saqib et al., 2008}; ^{Zavadskas et al., 2010}; Wang and Yuan, 2011; ^{Kuo and Lu, 2013}).

Technical factors

Technical risk factors are associated with the technology used in the construction project by the different stakeholders during construction. These technical risk factors are further distributed across the variables of general issues, labor, material, equipment, technology, specialist consultants and contractors. Various researchers concur that technical risks are major factors affecting the performance of infrastructure projects (^{Tah and Carr, 2000}; ^{Dey, 2001}; ^{Shen et al., 2001}; ^{Bunni, 2003}; ^{Assaf and Al-Hejji, 2006}; ^{Dikmen et al., 2007}; ^{Saqib et al., 2008}; ^{Zayed et al., 2008}; ^{Ehsan et al., 2010}; ^{Zavadskas et al., 2010}; ^{Nieto-Morote and Ruz-Vila, 2011}; Wang and Yuan, 2011; ^{Banaitiene and Banaitis, 2012}; ^{Fang et al., 2012}; ^{Mahendra et al., 2013}; ^{Marzouk and El-Rasas, 2014}; ^{Aziz and Abdel-Hakam, 2016}; ^{Odediran and Windapo, 2018}).

Through a review of the literature, a long list of uncertainty events was identified. These events were analyzed and ranked according to their occurrence in each study. The top 20 uncertainty events mentioned in the literature review and which were adapted for use in this study, are listed in Table 1.

Research methodology

The study made use of a sequential mixed-method research approach in identifying the uncertainty events and their causative sources in the South African highway construction projects and assessing their impact on the completion time of construction highway projects. An ANFIS was developed and used in the assessment of the impact of uncertainty events on project completion time. It was developed in the MATLAB environment, which helps to assess and prioritize the uncertainty events based on their impact on the construction time of highway projects. The use of ANFIS provides a more systematic and efficient way to assess, compared to the existing assessment approaches which require a large number of subjective judgments from construction experts. The researcher developed and used the ANFIS method in the assessment of the impact of uncertainty events on project completion time.

Data collection

Data was collected using a brainstorming meeting with six highway experts with more than 25 years’ experience in South African highway construction projects. The highway expert panel reviewed the uncertainty events identified in the literature review and justified events using a technique of content analysis. By using this technique, overlapping events were either combined or eliminated, and the researcher was able to isolate 76 uncertainty events affecting South African highway construction projects. The expert panel grouped these uncertainty events into seven major factors, as shown in Table 2. The uncertainties tabulated in Table 2 were used as a framework during data collection by participants, to guide their precise evaluations of each event.

To assess the impact size of uncertainty events on completion time, the survey questionnaire was designed in the form of a five-point linguistic Likert scale (see Appendix). The required data (probability of occurrence and severity of event) was obtained from the questionnaires completed by 32 highway project managers with a minimum of 20 years of experience in South African highway construction projects.

To obtain the impact size of uncertainty events from two input variables (probability of occurrence and severity event) in linguistic value, the ISO 31000 (International Standard Organization) impact matrix was used (^{ISO, 2009}). Figure 1 shows the input variables and impact sizes as output in the Linguistic value. The impact size is a function of the probability of occurrence and its severity (^{Gadd et al., 2003}; ^{Institute, 2013}).

In the next step, the linguistic values of probability of occurrence, the severity of event, and the impact size of event are converted to fuzzy values. A Fuzzy value is logic for dealing with imprecise data. Fuzzy logic is a multi-value logic that allows intermediate values to be defined between conventional evaluations (^{Zadeh, 1996}). To convert a linguistic value to a fuzzy value, fuzzy triangular numbers have been used, since the probability of occurrence and time variables underlie the triangular distribution (^{Tang and Ang, 2007}). The fuzzy values and a fuzzy graphical diagram of each of these linguistic variables in terms of probability of occurrence, severity, and risk have been shown in Table 3.

After converting the linguistic values of variables into the fuzzy value, the Center Of Area (COA) method was used to defuzzify the fuzzy values into numerical values, using Best Non-fuzzy Performance (BNP) (^{Chen and Lu, 2001}).

The deterministic values of probability of occurrence, severity, and impact size of all 76 uncertainty events calculated by BNP using Eq. (1) are outlined in Table 4.

(1)M_A{\displaystyle \frac{a_l+\mathrm{2}{a}_m+a_u}{\mathrm{4}}},

where: A=(a_l,a_m,a_u)\mathrm{.}

Table 4 shows the numerical values of probability of occurrence, the severity of event, and impact size, based on Table 2 fuzzy values.

Developing ANFIS structure

The main objective of this study is to quantitatively analyze and assess the impact of uncertainty events on the completion time of highway construction projects, through numerical analysis of uncertainty causation factors. As mentioned earlier, the impact size of the uncertainty event is a function of the probability of occurrence and severity of the outcome of the event.

The Sugeno ANFIS model was proposed for a systematic approach to generating fuzzy rules from a given input-output data set (^{Negnevitsky, 2005}). ANFIS employs neural networks and fuzzy inference systems together because they function in complementary ways. While the mission of fuzzy “if-then” rules is to model expert knowledge, that of the neural network is to optimize the membership functions and to minimize the error rate in the output. In ANFIS, ^{Takagi and Sugeno (1983)} type fuzzy rules are employed, which include the antecedent part, using linguistic input variables to describe the condition, and the consequent part using the mathematical function. If the mathematical function is constant, the model is called a “zero-order Sugeno Fuzzy Model” and if it is a first-order polynomial, the model is called a “first-order Sugeno Fuzzy Model.”

In this study, a first-order Sugeno fuzzy inference system proposed by ^{Takagi and Sugeno (1983)} is employed to assess the impact size of uncertainty events in the construction time of highway projects. In this inference system, the output of each rule is a linear combination of two input variables added by a linear term of “AND” logic. The final output is the weighted average of each rule’s output (^{Buragohain and Mahanta, 2008}). Figure 2 illustrates the Takagi and Sugeno ANFIS structure in 5 layers which developed for this study. To model this ANFIS, the following 25 fuzzy rules “If-Then” are considered.

(2)\mathit{If}(\mathit{P}\mathrm{i}\mathrm{s}{P}_i)\mathit{AND}(\mathit{S}\mathrm{i}\mathrm{s}{S}_i)\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{n}{f}_i=a_i\mathit{p}+b_{i}s+r_i,i=1,2,3,4,5,

Where Pand Sare numerical inputs while p_i and s_i are numerical variables. These variables are identified by membership functions. Also, a_i, b_i and r_i are parameters that determine the relationship between input and output.

The first layer is the input layer: it designates the numerical input values, the probability of occurrence (P) and severity of event (S) to a different fuzzy set.

{\mu }_{Pi}(P),\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}i=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},

(3){\mu }_{Si}(S),\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}i=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},

where {\mu }_{Pi} and {\mu }_{Si} are the membership functions for fuzzy sets of probability and severity. There are eight membership functions which are shown in Table 4.

The second layer is the inference layer: the “AND” operator is used for achieving the output (firing strength), which shows the degree of satisfaction of each of 25 fuzzy rules for the different value of two input variables.

(4){\omega }_i={\mu }_{Pi}(P)\cdot {\mu }_{Si}(S),\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}i=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},

The third layer is the implication layer: the firing strengths are normalized in this layer.

(5){\overline{\omega }}_i={\displaystyle \frac{{\omega }_i}{\sum {\omega }_i},}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}i=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5.}

The fourth layer is the aggregation layer: the normalized firing strengths are multiplied with the function of the Sugeno fuzzy rules, which generates a consequent set of parameters that are adjusted with the hybrid learning algorithm.

(6){\overline{\omega }}_i{f}_i={\overline{\omega }}_i(a_{i}p+b_{i}s+r_i),\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}i=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},

where a_i, b_i and r_i are the set of consequent parameters which is adjusted with the learning algorithm.

The fifth layer is the defuzzification layer: the weighted average method is used to perform the process of defuzzification, which transforms the fuzzy result into a single numerical (crisp) output.

(7)F=\sum {\overline{\omega }}_i,f_i,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}i=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5.}

ANFIS performance evaluation

An ANFIS is designed in the MATLAB environment to model and assess the impact size of uncertainty events on the time (duration) of highway construction projects. Eighty percent of the data (probability of occurrence and severity of events from expert participants and relevant predicted impact size from impact size matrix) was used for training of the system. These aspects of probability and severity included the probability of occurrence, the severity of events as reported by expert participants, and the relevant predicted impact size, from the impact size matrix. The balance of 20% was used for checking the neural network, which set the system parameters. The model structure of the ANFIS that was designed for this study is illustrated in Fig. 3. The ANFIS model structure is implemented using the fuzzy logic toolbox of MATLAB.

Figure 3 illustrates the five membership functions of each input (inputmf) variable, 25 rules (AND rules), 25 membership functions for output (outputmf) variables and the single output of the uncertainty event impact assessment model in ANFIS.

From the surface 3D surface diagram (Fig. 4), it can be inferred that with the increase in probability of occurrence and severity of event, the size of the impact of the uncertainty event on the completion time of the highway construction projects is increased, which is aligned with the risk impact matrix shown in Fig. 1. As discussed, the capability of neural networks to learn from training and to adapt the network’s parameters with the training data are the main advantage of using a neural network in the design of fuzzy systems (^{Huang et al., 2002}). To train FIS and determine the relationship between input and output variables of current research, the hybrid learning algorithm is used.

To identify the best membership function, the ANFIS model had been designed with the eight available membership functions. The performance of each model is evaluated by four types of error tests and correlation coefficient value between the real data and predicted data as shown in Table 5. The model with the minimum errors and R-value closest to 1 is chosen as the best model.

The low value of test error indicates the reliability of the model for impact assessment, and the closeness of the R-value to 1 verifies the fitness of the model for impact evaluation. As shown in Table 5, the correlation coefficient values of all membership functions are very close to 1. However, triangular membership function (trimf) has the minimum error values among all four tests; and since the time variable underlies the triangular distribution, trimf was selected as the best membership function to model and assess the impact size of uncertainty events on the completion time of highway construction projects.

Data presentation and analysis

To evaluate the ANFIS performance, the Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and the correlation coefficient value of predicted impact size of each of the 76 uncertainty events are calculated and presented in Table 6.

To identify the impact size of an event, the optimum values of two input variables (probability of occurrence and severity of event) are inserted by a trained ANFIS rule viewer, and the relevant impact size of the event is predicted by a focused ANFIS model. For instance, the optimum probability of occurrence (0.66875) and severity (4.5625) value of event EC1 (fluctuation of prices of materials and equipment) were inserted to the input box of the trained ANFIS rule viewer, and the model predicted the impact size of event (3.7) to the time of highway construction projects (Fig. 5).

Figure 5 illustrates the total size of each numerical input of event EC1 to triangular fuzzy memberships function and the predicted impact size of this event. The predicted impact size of 76 uncertainty events is predicted and prioritized in Table 7.

Table 7 showed the optimum value of probability of occurrence, the severity of event and predicted impact size of each uncertainty on the completion time of highway construction projects. Based on the results shown in Table 7, the events with the highest values of probability of occurrence (almost certain) are: latent ground conditions (0.84375), inadequate planning and scheduling (0.8125) and human-made disaster (0.8125) respectively. However, the events with the highest values of severity (catastrophic) are: latent ground conditions (8.3125) and inaccurate time and cost estimation (8.3125). All the 76 uncertainty events existing in the South African highway construction business are prioritized based on the predicted value output from the ANFIS model. For instance, the latent ground conditions event has the highest impact on time of construction, with an impact size of 4.95.

Furthermore, based on the predicted impact size, the uncertainties were clustered into five groups. The underlying events extracted were named as (1) minimal, (2) low, (3) moderate, (4) high and (5) extreme, as presented in Table 8.

As shown in Table 8, the latent ground conditions (TG11), inaccurate time and cost estimation (TCS6), inadequate planning and scheduling (TG5), human-made disaster (PL3), rehabilitation of affected people (SO4), specification change (TG9), difficulty of schedule (TG4), and disease (SO5) are events having an extreme effect on the completion time of South African highway construction projects. However, slow mobilization of equipment (TG1), tax and/or legal fees (FI1) and size of contract (TE2) have a low impact on the time of highway construction, and there is no event with a minimal effect on the completion time of highway construction projects.

Validation of the ANFIS model

To validate and verify the result and performance of developed ANFIS model, the results and performance of the ANFIS model are compared with that of regression analysis as one of the common classical statistical methods in construction management to forecast different variables. Regression analysis methods are relatively easy to implement, and the main advantage of these methods is that the relationship between the input variables and output variables is easy to comprehend.

As mentioned earlier, the impact size of uncertainty events as the dependent variable is a function of the probability of occurrence and severity of relative uncertainty (^{ISO, 2009}). Generally, multiple regression methods of impact size can be presented as Eq. (8).

(8)Uncertainty\hspace{0.17em}impac{t}_i=a_{i}p+b_{i}s+r_i,

where r_i is a constant value, a_i and b_i represent regression coefficients of independent variables.

The linear regression analysis was used to generate correlation coefficients of the two independent variables, namely impact size of uncertainty events, due to the low correlation between the independent' variables and the dependent variable, as presented in Table 9. The Stepwise Regression (SR) method has been applied.

The SR model is an extension of Multiple Regression Analysis. The SR model is a mathematical model with a strong mathematical background; therefore, this method has been chosen for validation of the ANFIS model. SR models have been used extensively in different areas of construction management. These areas include, for instance, assessing the critical factors affecting the cost performance of public construction projects (^{Sinesilassie et al., 2017}); modeling the construction risk ratings and estimating contingencies in highway projects (^{Diab et al., 2017}); identifying the success factors for public and private partnership projects (^{Yun et al., 2015}); evaluating project risks (^{Ebrat and Ghodsi, 2014}); evaluating the risk factors leading to cost overrun in highway construction projects (^{Creedy et al., 2010}); analyzing the risk perception of build–operate–transfer road project participants (^{Thomas et al., 2003}); developing models to forecast the actual construction cost and time (^{Skitmore and Ng, 2003}); and designing a multivariate analysis to build project success factors (^{Chan et al., 2001}).

The SR Methods have been applied to all 76 events, to predict the impact of uncertainty events using MATLAB. The predicted impact size of uncertainty events on the construction time of highway projects is ranked in Table 4.

To evaluate the performance of SR models on predicting the impact size of uncertainty events, the RMSE, MAPE and the correlation coefficient value of developed models were calculated, and the results are presented in Table 10.

The small error scores of RMSE (e<0.3) and MAPE (e<0.1) proved the reliability of the SRA developed models. However, the fitness of the predicted values varies from 0.441 to 0.954. Table 10 reveals that 20 models have good fitness (r≥0.8), 32 models have acceptable fitness (0.8>r≥0.7), and the other 24 models have a low fitness (r<0.7) to the real data.

Discussion of findings

The current study examined the uncertainties in construction projects and modeled the uncertainty events using ANFIS model, to assess the impact of each event on the completion time of South African highway construction projects. This was the focus of the research because of the high capabilities of an artificial neural network in enabling the prediction, learning, and modeling of human knowledge. The impact assessment of the uncertainty events is necessary to prevent running overtime limits before the signs of these events begin to appear on a project. To validate the results and the performance of the ANFIS model in predicting the impact of uncertainty events on construction time, a stepwise regression model was developed, and its results were compared with those of the ANFIS model.

A comparison of the performance of classical statistics versus the machine learning techniques, in predicting the impact of uncertainty events, has shown that the error values of ANFIS models are much smaller than the error values of SR models when predicting the size of impact. This led to the conclusion that the prediction of impact size using ANFIS models is more reliable than the prediction of SR models. Moreover, the correlation codefined value of ANFIS models is significantly closer to 1 compared to SR models, which strongly suggests that the accuracy of ANFIS models in predicting impact size is extremely high. Therefore, the performance comparison proves that ANFIS is a more accurate tool for predicting the impact of uncertainty events. Convincingly, the predicted impact size from ANFIS models is accurately used to estimate and simulate the time of uncertainty events.

The main contribution of the current study is in integrating the use of impact size matrix method with ANFIS method, to develop a hybrid ANFIS model which involves the advantages of both methods: capturing qualitative input variables instead of exact quantitative variables, performing at a high level to facilitate learning, modeling and predicting of human knowledge, and cutting out ambiguity by using fuzzy values. The developed hybrid ANFIS model is a simple, efficient and innovative machine learning technique that enables construction managers to assess and predict the impact of uncertainty events very precisely, compared to the existing methods of assessing uncertainty.

However, most of the existing uncertainty assessment methods, such as probability analysis and analytic hierarchy processes, are based on statistical data which need to vary negligible quantity data and cannot analyze the qualitative data; this has a marked effect on uncertainty assessment (^{Ahmadi et al., 2017}; ^{Islam et al., 2017}). Some other approaches like the Bayesian network and the fault tree analysis require high computing efforts when several variables, events or experts are involved. This is especially true when evaluating the probabilistic relations and conditional independencies and dependencies between variables (^{Wang et al., 2016a}; ^{Chen and Wang, 2017}).

In addition to the stated advantages of the developed approach for assessment of uncertainty events in construction projects, Table 11 summarizes the advantages of a developed ANFIS hybrid model in the assessment of uncertainty when compared with other existing methods (AHP, ANN, Bayesian network, FAHP, fault tree analysis and probability analysis). These advantages are crisp data, fuzzy values, linearity data, nonlinearity data, learning and modeling of human knowledge and simple computing. In effect, the ANFIS hybrid model combines the advantages of all other methods of assessing uncertainty (^{Ebrat and Ghodsi, 2014}; ^{Asgari et al., 2016}; ^{Wang et al., 2016b}; ^{Ahmadi et al., 2017}; ^{Chen and Wang, 2017}; ^{Islam et al., 2017}).

Clearly, Table 11 verifies that the developed hybrid model is very effective in modeling the uncertainty of construction projects.

The results of the ANFIS revealed that from 76 uncertainty events in South African highway construction projects, eight events had an extreme impact, 48 events had a high impact, 17 events had a moderate impact, three events had a low impact, while none of the events had a minimal impact on the completion time. The results of the current study are in accordance with several previous studies. For instance, the identification of latent ground conditions as having the highest predicted impact on time of South African highway projects, is in line with the results of ^{Baloi and Price (2003)}, ^{Assaf and Al-Hejji (2006)}, ^{Zou et al. (2007)}, ^{Zayed et al. (2008)}, ^{Fang et al. (2012)}, ^{Taghipour et al. (2015)}, ^{Aziz and Abdel-Hakam (2016)} and ^{Adam et al. (2017)}. The study shows that the inaccurate time and cost estimation, inadequate planning and scheduling, specification change and difficulty of schedule are the four technical risks that have an extreme effect on the time of construction in South Africa. These technical events are also identified in the studies of ^{Huang et al. (2002)}, ^{Bunni (2003)}, ^{Assaf and Al-Hejji (2006)}, ^{Zou et al. (2007)}, ^{Saqib et al. (2008)}, ^{Ehsan et al. (2010)}, ^{Gosling et al. (2012)}, ^{Mahendra et al. (2013)}, ^{Marzouk and El-Rasas (2014)}, ^{Aziz and Abdel-Hakam (2016)}.

The findings of ^{Marzouk and El-Rasas (2014)}, ^{Aziz and Abdel-Hakam (2016)} and ^{Odediran and Windapo (2018)} are consistent with the findings of this study about the predicted impact of human-made disaster and disease, as political and socially disruptive events that have an extreme impact on construction projects in developing countries in Africa, such as South Africa and Egypt. Furthermore, the findings of the study indicate that technical, social and political factors significantly impact on the completion time of South African highway construction projects. This outcome is aligned with the research results of ^{Marzouk and El-Rasas (2014)} and ^{Aziz and Abdel-Hakam (2016)}. Therefore, the companies that provide highway construction in African developing countries have to consider seriously the social and political risks as well as the technical events, when involved in this market. Finally, the study also found that 56 events (73.7%) had an impact on the completion time of highway construction projects. This indicates that the time taken by highway construction projects in South Africa is very sensitive to uncertainties. The type of uncertainty events experienced in South Africa has to do with protests by labor and by communities, as well as fiscal policy changes (such as VAT increases, changes in interest rates and petrol prices) that affect the prices of goods and services.

Conclusions

The current study adds to existing knowledge, first by means of an extensive literature review to identify the uncertainty events and their causative factors, in highway construction projects. Second, the study established the pattern of disruptive effects caused by uncertainty events, through brainstorming by a panel of highway construction experts. Third, it determined the probability of occurrence and severity of 76 uncertainty events, by gathering data from highway construction experts. Fourth, the study developed an ANFIS model to assess the impact of each uncertainty event on the time spent on construction, in highway construction projects. Fifth, it grouped the uncertainty events into five categories, based on their predicted impact on the time spent on highway construction.

In this study, the ANFIS was applied to assess the impact of uncertainty events on highway construction time, due to its effectiveness in predicting, learning and modeling human knowledge. The strength of the proposed methodology provides a simple and efficient approach over other conventional methods of impact assessment.

Furthermore, the results of this study provide a systematic model to predict accurately (as seen in the very small value of errors and the closeness of the R-value to 1) the uncertainty time of each construction activity, and consequently all the sources of the uncertainty time of a highway construction project. This information helps to create a model of uncertainty in the construction of highway projects.

In other words, based on the ANFIS model results, an accurate time of each activity, including construction time and predicted uncertainty time will be calculated to accurately estimate the whole duration of highway construction projects. To conclude, a similar approach should be applied to predict the impact of uncertainty events on the cost of highway construction projects.

This study is relevant to both practitioners and researchers. It provides practitioners with a simple and straightforward accurate tool to assess and prioritize the impact of uncertainty events on the time of highway construction projects and helps them to manage or diminish the negative impact of these events. It provides researchers with a qualitative and quantitative methodology and a systematic model to evaluate the effect of uncertainty events on the time of construction activity and the whole duration of highway construction projects.

This research provides a detailed analysis and predicts outputs, generating a baseline for future studies. By using this baseline, it is possible to estimate accurately the duration of highway construction projects, by assessing each construction activity in terms of its uncertainty time. It is recommended that a similar methodology and approach should be applied in future studies to prioritize the uncertainty events in different types of construction projects and to design a decision support system to assess these uncertainty events. This proposed systematic approach is also valuable because it is applicable to different construction projects and different geographical regions.

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