Eigenfrequency analysis of bridges using a smartphone and a novel low-cost accelerometer prototype

Abstract

Researchers are paying increasing attention to the development of low-cost and microcontroller-based accelerometers, in order to make structural health monitoring feasible for conventional bridges with limited monitoring budget. Parallel with the low-cost sensor development, the use of the embedded accelerometers of smartphones for eigenfrequency analysis of bridges is becoming popular in the civil engineering literature. This paper, for the first time in the literature, studies these two promising technologies by comparing the noise density and eigenfrequency analysis of a self-developed, validated and calibrated low-cost Internet of things based accelerometer LARA (low cost adaptable reliable accelerometer) with those of a state of the art smartphone (iPhone XR). The eigenfrequency analysis of a footbridge in San Sebastian, Spain, showed that the embedded accelerometer of the iPhone XR can measure the natural frequencies of the under study bridge.

Graphical abstract

Keywords

smartphone / modal analysis / eigenfrequency analysis / low-cost / accelerometers / Arduino / Raspberry / Internet of things

1 Introduction

It should be mentioned that bridges are typically designed to last between 50 to 120 years. Several parameters and conditions, including environmental factors, construction faults, and fatigue, can degrade a structure’s safety, performance, and serviceability over time [1,2].

The American Society of Civil Engineers (ASCE), issues a report card for America’s infrastructure every four years, showing the state and performance capabilities of all types of infrastructures in the United States of America (USA). According to their report in 2021 [3], over 42% of the 617000 analyzed bridges were at least 50 years old. It is important to note that the majority of these bridges were designed for a service life of 50 years. As a result, it is expected that a rising number of these bridges will require maintenance and additional monitoring over time. Furthermore, more than 7.5% of the analyzed bridges are reported to be structurally inadequate or were in bad conditions. According to the same report, in the USA alone, more than $125 billion should be needed for bridge maintenance work [4].

The growing need for infrastructure monitoring and rehabilitation [5] is not limited to the USA. The Polcevera Viaduct collapse in Genoa led to an assessment of Italian bridges, which served as a cautionary tale that a bridge’s lifetime cannot be guaranteed by its well-built construction alone [6,7]. In fact, in the absence of continual maintenance and repair efforts, rate of pathologies [8] in infrastructures increases [9]. Clearly, these structural pathologies can jeopardize structural stability and safety, and therefore, the ability to correctly analyze structural performance [10] is required to reduce the hazards associated with these pathologies [11]. The serviceability of structures [12] is normally assessed by visual examination [13] or non-destructive testing [14]. These inspections can be complemented with structural system identification techniques [15] to enhance the knowledge of the actual parameters of the structure and to detect structural damages [16].

The purpose of structural system identification [17] is to analyze the integrity and condition of a structure to determine its actual mechanical characteristics [18]. To detect and quantify structural damages, structural system identification methodologies require the measurement of structural responses [19]. This information is often gathered through the use of sensor-based structural health monitoring (SHM) programs [20,21].

Historical civil structure failures have received the attention of scholars in SHM applications [22] as a fundamental mechanism for avoiding future catastrophes and human mortality [23]. SHM is generally divided into the following four stages: 1) data acquisition: measuring and acquiring the response of a structure using sensors [24]; 2) structural system identification: identifying the mechanical characteristics of the structure [25]; 3) structural condition evaluation: analyzing the safety and the state of the structure [26]; and 4) decision-making and maintenance: making decisions such as in the creation of a maintenance plan, the demolition of the structure, or rehabilitating it [27]. These four stages are presented in Fig.1.

This work focuses on the data acquisition stage. Specifically, this work should focus on the use of accelerometers to collect SHM data [28]. It should be noted thataccelerometers are widely used in SHM applications [29]. Accelerometers are inertia-based sensors attached to a seismic mass [28]. First, the mass is subject to inertia in the presence of acceleration. Secondly, the displacement can be used to generate an electrical signal, which may be calibrated to represent acceleration and stored using data acquisition equipment [30]. During vibration, displacement, velocity and acceleration all vary periodically, so by sensing fluctuations in structural reaction, accelerometers can be used to determine the structure’s dynamic features (such as eigenfrequency, damping ratio and mode shapes) [31].

The desirable characteristics of the accelerometers used (such as sampling frequency ratio and acceleration amplitude range) depend, to a great extent, on the characteristics of the structures to be measured [32].

For example, the natural frequencies of most civil structures vary between 0.1 to 100 Hz [33], between 3 and 30 Hz in short span bridges [34] and between 0.1 and 8 Hz in medium and long span bridges [35]. In terms of maximum acceleration amplitude, ambient vibrations in civil constructions have modest magnitudes [36]. In fact, the acceleration amplitudes of most structures do not exceed the range of 0.04g and 0.5g (where g is acceleration due to Earth’s gravity) [37].

The most common types of vibration sensing technologies are based on one of the three following concepts: piezoelectricity [38], piezoresistivity [39], or differential capacitive measurement [40]. Based on these principles, the four most popular accelerometers are outlined below.

1) Piezoelectric accelerometers are based on the piezoelectric action of specific materials, and, typically, operate at a broad range of frequencies (up to 12 kHz) and capture dynamic changes in mechanical variables [41].

2) Piezoresistive accelerometers, also known as strain gauge accelerometers, may detect the change in electrical resistance of a piezoresistive element due to changes in shape which may be due to the inertia of a mass [42].

3) Differential capacitive accelerometers estimate the seismic mass movements by measuring changes in capacitance [43].

4) Micro electro mechanical systems (MEMS) can be made using any of the acceleration measuring methodologies outlined above (piezoelectricity, piezoresistivity, or differential capacitive measurement) [44]. Typically, signal processing circuitry is included in the majority of MEMS sensors. MEMS accelerometers can be applied in a variety of industrial scenarios because of considerable continual technical improvements [45]. However, MEMS accelerometers, especially the low-cost ones, are commonly affected by intrinsic noises [46]. This type of noise is normally generated by circuit components (such as resistors and semiconductors) [47]. Fig.2 relates the most common accelerometer types with their basic principles.

A key factor in the dynamic monitoring of structures with accelerometers refers to cost. Moreover, the price of instrumentation is not limited to the cost of the accelerometers. In fact other equipment such as data collecting equipment, as well as the installation and maintenance expenses add to the costs. This high cost of instrumentation (such as the accelerometers, data acquisition equipment, installation costs) may exclude SHM applications from being used in conventional structures with a relatively low monitoring budget [48].

To deal with the high price of data acquisition procedures necessary for SHM applications, some researchers have focused on the development of low-cost accelerometer prototypes for economical SHM of bridges [49]. Among the accelerometer prototypes presented in the literature some highlights are shown below.

A low-cost accelerometer developed from ADXL335 chipset was validated by Grimmelsman and Zolghadri [50]. In their study, the performance and capabilities of this low-cost prototype were compared with those of conventional instrument-grade accelerometers (PCB 393A03 and 3741E122G). Girolami et al. [51] proposed a system for providing a structural modal analysis using several synchronized low-cost accelerometers developed from LIS344ALH chipsets. To verify the synchronization of the developed sensors, the accelerometer prototypes were distributed along a simple supported beam. The developed sensors’ identified mode shapes were then compared to theoretical ones. Ozdagli et al. [52] used the chipset MPU6050 for making a vibration acquisition system entitled LEWIS. The acquired data with LEWIS were compared to those of a commercial accelerometer (PCB 3711B1110G) and a linear variable differential transformer (LDVT) sensor. Meng and Zhu [53] proposed a low-cost accelerometer made up of a LSM9DS1 chipset and controlled by a Raspberry Pi 4. The readings were compared to those of an LDVT sensor of a commercial accelerometer (PCB 356B18). Komarizadehasl et al. [40] represented a cost hyper efficient arduino product (CHEAP). To validate CHEAP’s performance, several laboratory experiments were carried out, and the findings of CHEAP were compared with those of two commercial seismic accelerometers (PCB 393A03 and PCB 356B18). In another work, Komarizadehasl et al. [43] developed an upgraded version of CHEAP. This upgraded accelerometer prototype is an entitled low-cost adaptable reliable accelerometer (LARA). LARA is a wireless Internet of things (IoT)-based accelerometer with an attached data acquisition device with post-synchronization capability. A footbridge was fitted with four LARA accelerometers and the eigenfrequency and mode shape analyses of the system were compared with those of a commercial sensor (HI-INC) and an analytical software model [33].

Currently, many civil engineers are spending a lot of time on development of low-cost accelerometer prototypes. The development of these prototypes requires a practical knowledge of electronics, circuit design, heavy programming of microcontrollers and microprocessors and soldering. Several researchers have investigated an alternative low-cost solution without the need for the heavy programming, circuit design, or use of traditional commercial accelerometers. One of the most essential found alternatives is repurposing old smartphones as low-cost accelerometers [54]. The embedded accelerometer of smartphones that were actually developed by the producer company for everyday use (such as step detecting and GPS data stabilizing) of a user, can also be used for measuring and acquiring the vibration of structures.

It should be noted that smartphones are normally equipped with MEMS accelerometers. A thorough literature review of the use of smartphones in SHM is presented in Ref. [55]. Another work in the literature dealing with the use of smartphones as accelerometers highlights their use in the monitoring of long-span bridges with high acceleration amplitudes [56]. Smartphones have also been used in eigenfrequency and modal analysis of structures [57]. Ozer et al. [58] used 21 iPhone smartphones for the modal analysis of the Golden Gate Bridge in the USA. In this research, six different models of iPhones (3gs, 5, 6plus, 6s, 7, and X) were used. In addition, this work also presented a novel identification method to deal with the synchronization and sampling frequency of the different devices. Shrestha et al. [56] presented the feasibility of using iPhones for long-term SHM applications for bridges. This system was deployed on the Takamatsu Bridge in Miyazaki (Japan). Quqa et al. [59] introduced an application to perform an indirect SHM of a bridge using an iPhone SE of a bicycle rider. This novel application used the GPS and accelerometer sensors of the riders’ smartphones to extract the eigenfrequency and the modal amplitude of a footbridge in Italy from the information obtained by crossing it while riding a bicycle. The analysis of the literaturefinds that many researchers have used various models of iPhone smartphones as vibration signal acquisition devices [60]. All these works evidence the promising features of the MEMS accelerometers inside smartphones for SHM applications.

It is essential to declare that both accelerometer prototypes and smartphones use MEMS chipsets together with other components in their design. It is also important to bear in mind that after development of a novel accelerometer prototype, additional investigations for laboratory validations and calibrations are needed. However, smartphone companies normally have to calibrate and validate their product before selling it. Furthermore, to keep up with the latest trend of technology, they have to develop better sensors (such as accelerometers) with a higher accuracy than that achieved by other smartphone companies.

In addition, the used or outdated products of these companies can be purchased for a fraction of their initial cost. For example, in 2018 an iPhone XR (base model) in Spain cost 859 € but in 2022, a second-hand modelcould be purchased for 316 € [61]. The following gaps are identified in the literature: 1) comparisonof the low-cost sensors and smartphones for SHM applications, 2) accurate measurement of the noise density and resolution of accelerometer prototypes as well as embedded accelerometers of smartphones, and 3) comparing the results of these sensors in a field test carried out on a real bridge.

To fill this gap, this paper for the first time in the literature performs an eigenfrequency analysis on a medium-span footbridge using a smartphone and a validated low-cost accelerometer prototype. LARA is chosen to be the accelerometer prototype. This is due to the fact that the accuracy of this sensor has been previously validated in both laboratory and field experiments and its use is proven to be feasible for SHM of bridges [43]. In addition, this validated LARA can verify the performance of a smartphone in laboratory and field tests. Further in this work, the acquired data of LARA and a smartphone are compared with each other. Moreover, the noise density and resolution of both systems are measured and compared with each other. Finally, this paper discusses whether the low-cost MEMS accelerometers embedded in smartphones are accurate enough for low-budget eigenfrequency analysis of bridges.

This paper is organized as follows. In Section 2, the hardware and software characteristics of LARA are presented. In Section 3, a smartphone with a low-cost accelerometer is chosen from those available in the market. Next, the information about its embedded accelerometer and the needed software for using this smartphone as an accelerometer are presented. In Section 4, the noise density and resolution of these sensors are measured and compared with each other. Section 5 illustrates the case study of a bridge located in Andoain using both the accelerometer prototype and the used smartphone. Further in this section, a detailed comparison of the presented solutions together with their pros and cons are shown. Finally, in Section 4 the main conclusions are drawn.

2 Low-cost adaptable reliable accelerometer

In this section, the hardware and software information of the LARA are presented.

2.1 Low-cost adaptable reliable accelerometer desgin and hardware

In this subsection, the main characteristics of LARA together with two ways of producing it are detailed.

LARA is a low-cost wireless triaxial accelerometer that can be programmed, controlled, and monitored remotely. This system has a sampling frequency of 333 Hz and a verified acceleration range of ±1.0g. LARA is composed of the following. 1) Sensing part (accelerometer): The sensing part of LARA is composed of five aligned synchronized MPU9250 chipsets and a multiplexor (TCA9548A). MPU9250 is a chipset that incorporates an accelerometer, gyroscope and magnetometer [62] (Fig.3(a)). 2) Data acquisition part (Fig.3(b)). The data acquisition part of LARA has two components. Firstly, Arduino Due is connected to the sensing part using the Inter-Integrated Circuit (I²C) communication port and is in charge of keeping the sampling frequency of LARA steady and functions as a data conditioner. Secondly, Raspberry Pi acquires, with the accurate time of the Internet (for post synchronization of various nodes), the streamed data of the Arduino Due a Pi. The components required for manufacturing LARA are shown and named in Fig.3.

It should be noted that even though the Raspberry Pi itself has an I²C communication port, the Arduino Due cannot be eliminated from this system. This is because during system development the Raspberry Pi cannot hold a constant sampling frequency. However, Arduino Due shows an excellent performance regarding a steady sampling frequency with no fluctuations.

LARA is based on the validated methodology in Ref. [40] that the vibration outputs of several aligned synchronized accelerometers improve the accuracy and resolution of the system. This way, the main captured signal to be studied is not affected by averaging the outputs of many dynamic sensors. The intrinsic dynamic noises (also known as intrinsic noise) of the sensors, on the other hand, are averaged over the number of coupled sensors. Smaller dynamic changes, such as acceleration or angular speed, can be noticed when the magnitude of these dynamic disturbances decreases.

The performance and accuracy of LARA were previously verified through several laboratory experiments presented in previous works [40,63]. Through these experiments, the eigenfrequency analysis and acceleration amplitude measurement of LARA were validated. However, one of the biggest drawbacks of the production method presented in the aforementioned works is the sensor alignment and soldering process. This process required about 16 h (two working days) for preparing a single sensing part. Both the plan and the section of a LARA produced by hand are shown in Fig.4(a). This figure also includes the dimensions before boxing. The dimension of the used box for protecting the sensing part of LARA, was 70 mm × 60 mm × 40 mm. Another major difficulty of the production of this device, was assembling the system in a box with dimensions close to those of the sensing part. On some occasions, this issue showed itself in human errors such as miss-soldering, miss-mounting of sensors or miss-wiring. To overcome these limitations, LARA was redesigned and produced using a machine assembly process. This automation of the process made the production rate faster, easier and cheaper. Fig.4(b) presents the produced LARA using the machine assembly.

It is also important to mention that the sensing part produced by using machine assembly was calibrated by Applus company as a further verification confirmation of the sensor accountability [64]. This calibration was done in the vibration frequency range of 5 to 160 Hz and an acceleration amplitude of 0.5g.

2.2 Remote access of low cost adaptable reliable accelerometer and automation

In this subsection, the automatic steps that how LARA to initiate a data acquisition procedure and how to remotely access LARA are presented.

LARA is an IoT based sensor and is produced to be user-friendly. After mounting the sensor on a bridge or a shaking table, the system only needs to be connected to a battery with an output of 5 V and 2.5 A or to a power source using the Raspberry Pi adaptor. Right after being powered up, LARA starts acquiring data and sends the acquired data to a Google Drive account once every 30 min.

The steps that LARA performs automatically right after being booted up are detailed as follows. 1) Connectivity: the Raspberry Pi is configured to connect to the Internet through Wi-Fi, LAN, or SIM Card when LARA is powered up. This step can only happen automatically as long as the Wi-Fi credentials are changed to those that LARA is already programmed to match. 2) Cloud access: after having access to the Internet connection, LARA will have access to a preprogrammed Google drive. 3) Data acquisition setting: for starting a data acquistion, LARA will download a Python code from the established Google Drive. This code is open source and it can be modified. For example special settings such as a scheduled vibration acquistion and a data acquistion with a specific duration, can be included in the Python code. This way, LARA does not need to be reprogrammed for different data acquistion procedures. 4) Data storage: after termination of data acquisition, the files are moved to a specific folder on the mounted Google Drive. As long as an Internet connection (through Wi-Fi or LAN) is available, the hard disk of LARA never becomes overloaded or completely full. It is important to note that if there is no Internet connection, or the Internet connection is cut, the data collected will remain on the LARA’s hard drive until the Internet connection is restored. It should be mentioned that external hard drives may be used to enhance the storage [33].

Attention should be paid to the possible problems or malfunctions with the Raspberry Pi and its programmed duties. Rebooting LARA can resolve unanticipated software issues such as lack of response of the accelerometer, connectivity troubles with Arduino, and restricted access to Google Drive.

LARA is programmed to be self-sufficient. In an emergency, however, a manual reboot or reprogramming can be performed remotely using the virtual network computing (VNC) viewer program. A detailed step-by-step tutorial for remotely accessing LARA using the VNC program is presented in Ref. [42].

3 Smartphone as a low-cost accelerometer

This section, first, presents software that enables the use of the embedded accelerometer of smartphones as a vibration acquisition device. Then, some useful information about the phones of two famous manufacturers is illustrated. Finally, a smartphone useful for the purposes of this paper is chosen.

The RWTH Aachen University’s Second Institute of Physics created an application entitled Phyphox [65]. This software can be downloaded for free and gives access to the embedded sensors of smartphones and tablets (such as accelerometer, gyroscope, magnetometer, and pressure sensors). This software allows a user to use all the embedded sensors of a smartphone including its accelerometers. Moreover, Phyphox has the ability to acquire the information and save it. Phyphox is available for both Apple and android devices and has been successfully used in a number of smartphone-based applications. Barrajón and Juan [66] used this software for studying the feasibility of using smartphones for measuring lift (elevator) velocity. The acquired information of the experiments is compared to those of a commercial solution (Speed4Lifts). Christoforou et al. [67] used the software for validating an image analysis algorithm that can be used for studying the characteristics of movement of people. However, this software has not been described yet in civil engineering literature.

As a way of contributing to this application, some useful information of embedded sensors of smartphones (such as the standard deviation and average measured value) can be shared with the Phyphox database platform. It should be noted that the technical information about the used device for this test and its sensors will be gathered as part of this experiment, which then can be contributed to the database website of Phyphox website [68]. This database is open for public access for helping with the understanding of the availability and capabilities of sensors across various devices. To submit this request, the user must put the device in resting mode (the resting mode is when the phone is laying on its back). After briefly gathering data, the user can submit the information to the database of Phyphox software. Fig.5 shows the X and Y axes of a smartphone. In the resting mode the Z axis should be parallel with the gravitational force of the earth. This figure also shows the technical information of an iPhone XR that can contribute to the database of the Phyphox software.

Tab.1 details some information about the accelerometers of Apple and Samsung products from the database of the Phyphox software [68] and is organized by the sample size of the acquired data. This table is limited to devices with a sample size higher than 100 units available in the database of Phyphox database center. This table includes the following information sorted into columns. 1) Manufacturer. 2) Model. 3) Price: the indicated cost of the smartphones is based on a recent quote from the Backmarket [61] website, which sells refurbished used devices. The indicated prices might be different in different countries and may be updated later. 4) Sample size: This column includes the total number of devices that contributed to the database of Phyphox software. It should be noted that only one set of data are accepted from each user. As a result, the sample size reflects the actual number of physical devices that were evaluated for this entry. 5) Z axis samplingfrequency: representing the sampling frequency of the accelerometer that measures the gravitational field strength. 6) RMS-Z: Including the root mean square (RMS) values measured by the vertical accelerometer (Z direction), 7) X and Y axes Frequency: This column presents the sampling frequencies of the accelerometers that detect the vibrations in X and Y directions in the resting mode, and 8) RMS-X,Y: This column presents the RMS values measured by the accelerometers that detect the vibrations in X and Y directions in the resting mode.

The analysis of Tab.1 shows that Apple products have a more stable sampling frequency for all the axes. For example, the sampling frequency for all three axes of the embedded accelerometers of Apple products is the same. However, the majority of Samsung smartphones or tablets have different sampling frequencies on different axes. In addition, their sampling frequency is not as steady as the Apple products. For example, Samsung model SM-G950F has a sampling frequency of 499.4 Hz for measuring the gravitational gravitational field strength (Z direction) of the earth while it is put in the resting mode and a sampling frequency of 106.3 Hz for both the transversal and Y axes. Further analysis of this table shows that the RMS values for different axes for Apple smartphones are more similar to each other than those of Samsung devices. This is due to the fact that the sampling frequency of the Samsung smartphones’ X and Y axes is different from that of the Z axis. It should be noted that this provided table by the Phyphox website lacks some major characteristics of the introduced accelerometers such as dynamic range, noise level, sensitivity, measurement range.

An iPhone XR is chosen for this paper because of its sample size on the Phyphox website. It is shown in the civil engineering literature review [58] that the iPhone XR incorporates a Bosch Sensotec MEMS accelerometer with a sampling frequency of 100 Hz. In fact, Bosch produces low-cost, highly efficient and accurate accelerometers. More information about the model and characteristics of the embedded accelerometers of Apple products are generally unavailable. In fact, access to this information following the guidelines of the Apple Company is currently not possible [68].

4 Comparison analysis

This section studies the dynamic performance of the accelerometers of LARA and an iPhone XR. To do so, the noise density of these sensors is compared with each other in the laboratory of technology of structures and materials “Lluis Agulló” (LATEM) of the Polytechnic University of Catalonia (UPC) [69].

It is very important to mention that Phyphox software assumes the same sampling frequency for the same smartphone models. However, as presented in Tab.1, embedded accelerometers of smartphones normally do not have a perfect sampling frequency ratio. Phyphox software uses the same sampling frequency (100.00 Hz for all of the Apple products) for the same smartphone models. Because of that, the acceleration spectrum analysis that this software application provides in real-time is not very accurate.

To perform a more accurate eigenfrequency analysis, the raw acceleration data acquired using the Phyphox application is obtained. This data acquisition process provides the acquired vibrations with a microsecond resolution timestamp. In this way, this information can be used to calculate the actual sampling frequency of the embedded accelerometer.

To measure the noise density of both devices, they are mounted on a flat surface using an industrial adhesive [70] in the LATEM laboratory. This is done to make sure that unwanted ambient vibrations do not affect the noise ratio of the accelerometers. Fig.6 shows the mounting of LARA and iPhone XR on a flat surface.

After mounting both devices, a vibration acquisition process is initiated on both systems and the acquired data are proceed using the standard method presented in Eq. (1) [71]. It should be emphasized that the method used in this study to characterize the noise of these systems is the standard one [72]. In fact, usually, noise density value can be found in the datasheet of commercial accelerometers [73].

(1)\mathrm{N}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}=\sqrt{\frac{\sum _1^N{(x_j-\mu )}^2}{N\cdot Fs}},

where x_j is the acquired acceleration amplitudes, μ is the average value of the x_j values, N is the number of used samples, and Fs is the sampling frequency of the used system. Tab.2 shows the noise density of different axes of LARA and the embedded accelerometer of the iPhone XR smartphone.

Analysis of Tab.2 shows that the noise density of the iPhone XR (110 \text{μg}/\sqrt{\text{Hz}}) is more than 30% worse than that of LARA (82 \text{μg}/\sqrt{\text{Hz}}). The time domain representation of the test is evaluated and presented in Fig.7.

Analysis of Fig.7 shows that the vibration acquisition of the Z-axis experiences a decrease in acceleration amplitude between the beginning of the test and a time of 600 s. To make sure that the test is correct, it is repeated four times. In all of the carried out tests, the acquired vibrations on Z-axis becomes stable after 600 s. In other words, the first 600 s of data acquisition process is not reliable. In fact, taking into account the acquired data as of the 600th second of the data acquisition process shows a noise density of 66 \text{μg}/\sqrt{\text{Hz}} for all three axes.

This issue represents an important limitation for data acquisition processes using this phone. This limitation is due to the fact that the sudden decrease of acceleration amplitude acquisition can negatively impact mode shape evaluation techniques. To compare the data acquisition of the iPhone XR with that of LARA, the time domain representation of acquired data of LARA is presented in Fig.8. The acquired data of all three axes are printed on the same chart.

Analysis of Fig.8 shows the stability of the data acquisition procedure of LARA for the X, Y, and Z axes. Comparing this figure with Fig.7 illustrates the better noise resolution of the iPhone XR for the X and Y axes. It can be seen that the resolution of the iPhone XR for the X and Y axes is between −0.02 and 0.02 m/s², while the LARA is between −0.04 and 0.04 m/s².

An accelerometer for SHM of bridges should be reliable without sudden changes of data acquiring such as those observed in Fig.7. From this, it can be deduced that, despite the difficulties of developing an accelerometer prototype such as LARA, the overall performance of LARA is better than that of the iPhone XR.

5 Analysis of a real structure: Case study of the Alondegi Bridge

To compare the eigenfrequency of LARA with that of an iPhone XR, a flexible footbridge, Puente (Bridge) Alondegi (Fig.9(a)) with a total span length of 60 m located in San Sebastian, Basque Country, is instrumented. To do so, two LARAs (LARA1 and LARA2) and an iPhone XR are used to instrument this bridge (Fig.9(b)). LARA1 and the iPhone XR are mounted on the midspan of the bridge, while LARA2 is mounted five meters away from the midspan of the bridge. The LARA accelerometers are mounted on to the web of the main bridge girder using an industrial adhesive. However, unlike LARA, the smartphone, due to its high cost, is not glued to the web of the main bridge beam using an industrial adhesive. Instead, following the same methodology presented in Refs. [74,75], it is mounted on the flange of the main beam using double-sided tape [76].

It should also be noted that because of the higher noise density of the smartphone’s accelerometer in comparison with that of LARA, the excitation of the bridge under the ambient activities does not reveal the first mode shape. In fact, after the termination of the data acquisition by the two LARAs, the smartphone is laid on the bridge next to LARA1. Then, the bridge is excited by the jumping of one person at its midspan for about 100 s. Fig.10 shows the fast Fourier transformation (FFT) analysis output of the vibration acquisition of LARA1, LARA2 and the used smartphone for all three axes. The shown axes in these figures are the general axes of the bridge and not the local axes of the sensors.

Analysis of Fig.10 shows that LARA1 and iPhone XR have identified the same eigenfrequencies in every axis. It should be noted that since LARA2 is located 5 m away from the LARA1 and iPhone XR, it reveals different mode shape frequencies. It is because not all mode shapes can excite every location of a structure [33]. Further analysis of Fig.10 shows that the acquired magnitude of the smartphone for Z and X axes are around 8–10 times higher than those obtained by LARA1 and LARA2. This significant difference can be attributed to the additional vibrations introduced into the footbridge just before the smartphone began recording the vibrations.

It should be noted that, the eigenfrequencies analysis of LARA1 and iPhone XR can be compared with each other due to the fact that they are in the same location. Tab.3 summarizes the comparison of the eigenfrequency analysis of LARA1 and iPhone XR.

Analysis of Tab.3 shows that both systems are able to identify five natural frequencies of the Alondegi footbridge accurately. Further analysis of Tab.3 shows a maximum difference of 0.49% between LARA1 and the iPhone XR accelerometer for the fifth mode shape. Moreover, it can be deducted from this table that the iPhone XR is not able to detect the second and the fourth longitudinal natural frequency of the bridge. There is a possibility that, due to the fact that the longitudinal direction of this bridge was fixed, exciting it by simply jumping is not enough, In addition, mounting the phone using a tape might have reduced vibration transmission. As a result, the iPhone XR could not identify all the eigenfrequencies of this direction.

It can be concluded that a smartphone such as an iPhone XR is able to perform an eigenfrequency accurately as long as the vibrations under study are strong enough. LARA (a self developed accelerometer prototype) is able to detect the natural frequencies of this bridge under the normal ambient vibration such as the human traffic and the wind.

Another major difference between using LARA as a vibration acquisition system and an iPhone XR is the automated remote data acquisition capability of LARA. LARA is an open-access software and hardware system that can get updates and improvements. As presented in this work, LARA is upgraded to automatically perform a data acquisition procedure and acquire available data remotely.

However, access to the hardware and software of a smartphone such as an iPhone for doing the same procedure is limited by the manufacturing company. This limitation can be one of the greatest drawbacks of using a smartphone such as an iPhone as a professional vibration acquisition system. Notwithstanding the fact that an iPhone might be an interesting laboratory in the pocket that can be used for teaching purposes as in Ref. [65], its use in SHM of bridges depends on whether the research can be conducted within the limits set by the smartphone manufacturer.

6 Conclusions

It is crucial to develop and validate low-cost sensors for SHM of structures with limited funding. The long-term monitoring of infrastructures may be inexpensive and practical with low-cost sensors. The use of integrated accelerometers in smartphones as well as low-cost sensor development, for eigenfrequency analyses of bridges, are growing in popularity in the civil engineering literature.

It should be noted that developing an accelerometer prototype requires knowledge of electronics, soldering, and programming, while using a smartphone as an accelerometer is less complicated. This work investigates the feasibility of using the embedded accelerometer of a smartphone for SHM of bridges by comparing its noise density and eigenfrequency analysis with those of a validated low-cost accelerometer prototype.

This paper, in the first place, details the hardware and software of a recently developed LARA. A number of laboratory and field tests have validated the feasibility of using LARA for SHM of bridges. In addition, this accelerometer was calibrated by the Applus company. LARA is an open-source software and hardware accelerometer capable of automatically performing scheduled data acquisition and making the acquired data available on a Google Drive account.

Following that, this work presents Phyphox, a software that can transform a smartphone into a pocket-sized vibration acquisition device. By studying the different smartphones, their price tags, and their characteristics, an iPhone XR is chosen to be used with this software for the laboratory and field tests of this paper.

To compare these two devices a laboratory experiment aiming to measure their noise density and resolution are carried out in the laboratory of technology of structures and material LATEM of the UPC. The noise density and resolution experiment shows the higher reliability of LARA than the used iPhone XR. This conclusion is drawn after testing both systems five times and observing an unexpected decrease in the acceleration amplitude of the Z axis (parallel to the gravitational field of the earth) of the iPhone XR. Moreover, the noise density of all axes of LARA is measured to be more than 30% better than those of the iPhone XR.

Finally, to compare the eigenfrequency analysis of LARA with the iPhone XR, the midspan of a 60-m-long footbridge is instrumented. LARA is able to identify five natural frequencies of the bridge under only the present ambient vibration of the bridge (such as wind and pedestrian traffic). However, despite the fact that the noise density of the iPhone XR is only about 30% higher than that of LARA in the laboratory experiment presented in this work, the iPhone XR is unable to detect the five mode shapes under the habitual ambient vibration. The footbridge is overexcited for the eigenfrequency analysis with the iPhone XR by a single person jumping in the bridge’s midspan. Comparing the first five identified natural frequency analyses of the vertical and transversal axes of the bridge using the acquired data of LARA (without overexcitation) and the iPhone XR (with overexcitation) shows less than a 0.49% difference. However, iPhone XR is not able to identify two of the natural frequencies of the longitudinal axis of the bridge.

Finally, it is concluded that the development of low-cost accelerometers is more challenging than using the ready-to-use embedded accelerometer of smartphones. However, the most important advantages of a self-developed solution are: 1) versatility, 2) open-access hardware, and 3) open-access software.

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