Systemic reliability of bridge networks with mobile sensing‐based model updating for postevent transportation decisions

This paper proposes the upscaling of conventional individual bridge health monitoring problems into urban regions and transportation networks via mobile and smart sensing techniques together with an innovative reconnaissance procedure. The paper associates structural failure probabilities with systemic features and proposes decision criteria to optimize postdisaster actions. Twenty bridges constituting transportation network infrastructure compose the testbed region and utilize smartphone accelerometers for dynamics characterization in a vibration‐based framework. In this framework, reconnaissance output serves for model development, and mobile sensor data enable finite element model updating. Structural reliability analyses merged in a chain setting generate the systemic behavior of cascaded bridge performance. Combining systemic reliability with transportation and health services demand, one can optimize the response strategies of the bridge population and strategize disaster‐related decisions in a postevent assessment setting. Based on a testbed region with remote access to nearby vicinities, 18 earthquake scenarios are conducted to visualize the optimal evacuation strategies on the network, taking systemic bridge performance into consideration. Cost‐free mobile sensing support adds one more fundamental information source for reducing the uncertainty of the models and, therefore, improves associated mitigation actions.


INTRODUCTION
Structural health monitoring (SHM) systems have been used for civil infrastructure safety and integrity assessment in the last four decades (Brownjohn, 2007). Among the abundant branches of SHM applications, damage prognosis (Farrar & Lieven, 2007), residual life assessment restricted to prioritized structures with research incentives rather than practical needs. However, following disastrous events, that is, earthquakes, the authorities need a global picture of the infrastructure asset conditions to prioritize mitigation plans, for example, identify the conjunct risk of transportation system under bridges subject to seismic hazards (Kiremidjian et al., 2007;Lee et al., 2011;Padgett & DesRoches, 2007;Shiraki et al., 2007) and merge the two distinct domains such as intelligent transportation networks and SHM (Khan et al., 2016).
The new century has been dedicated to solving some of these SHM needs through the new generation sensors incorporating smart and mobile frontiers (Malekloo et al., 2021;Sony et al., 2019). Due to the progress in low cost, wireless, sparse sensor configuration potential, the smartphone industry has emerged as an additional SHM data source enabling large-scale, yet rapid system identification opportunities (Alavi & Buttlar, 2019;Ozer, 2016). Crowdsourcing-based (Mei & Gül, 2019), multisensory (Ozer et al., 2017), and model-engaged (Ozer & Feng, 2019) methods empowered by smartphone technologies are proposed as upscaling pillars in the next-generation SHM discipline.
The characterization of earthquake signals is essential to reflect the understanding of civil infrastructure damage following a seismic event (Zhou & Adeli, 2003). Ground motion prediction equations (GMPEs) express the attenuation pattern and connect earthquake magnitude/distance to the intensity measure. GMPE models can have numerous bases, some of which take the form of Monte Carlo simulation (Yuen & Mu, 2010) and Bayesian learning (Mu & Yuen, 2016). GMPE incorporates uncertainty, and with spatially distributed systems, it is essential to account for the spatial correlation of ground motions (Jayaram & Baker, 2009). There have been recent efforts on modeling spatially distributed civil infrastructures' seismic performance. In terms of rapid loss assessment for postemergency service allocation, Bayesian network was utilized to update prior loss estimation using the GMPEs and the fragility curves of spatially distributed systems (Gehl et al., , 2022. Such a framework was also applied for multihazard assessment (e.g., earthquakes and ground failures; Gehl & D'Ayala, 2016) and resiliency indicators through the restoration process (Gehl & D'Ayala, 2018) for bridge-network systems. A probabilistic framework was introduced to assess the community resiliency as a metric to determine the effect of uncertainty in seismic hazards, physical vulnerabilities, and other lifeline infrastructures . More generally, the framework of interaction between the road network and built environment in a probabilistic manner reveals that the target system's performance is a key indicator of systemlevel resiliency and should be treated as a system-on system model (Argyroudis et al., 2015). Similar risk assessment frameworks are not limited to bridges but alternative critical infrastructure types, for example, gas distribution networks (Esposito et al., 2015).
Applications of machine learning and deep learning have become the forefront of the SHM field in the last decade. There have been numerous utilizations of learning models in SHM systems as reviewed in Amezquita-Sanchez et al. (2016) that take advantage of wireless smart sensors  for a plethora of applications in SHM. Supervised learning models (Mariniello et al., 2021;Oh et al., 2017), unsupervised learning methods (Eltouny & Liang, 2021a;Sarmadi & Yuen, 2021), and deep learning approaches (Gao et al., 2021;Sajedi & Liang, 2021b) are some of the notable recent examples for damage detection and localization. Moreover, machine vision-based target tracking systems with advanced signal processing methods for signal reconstruction, such as compressive sensing, have also been widely adapted for modal analysis (Kong & Li, 2018;Ngeljaratan et al., 2021). Significant developments have also been made in time-frequency signal processing techniques, namely, wavelet transform and Hilbert-Huang transform. Although the standardized form of these algorithms suffers from noise for large structures, different variations of them, however, have proven to be more effective and reliable for analyzing nonlinear and nonstationary signals (Amezquita-Sanchez & Adeli, 2015;Amezquita-Sanchez et al., 2017;Z. Li et al., 2017;Perez-Ramirez et al., 2016). Model updating is a model-driven path toward SHM applications, where machine learning techniques are applicable. The multiphysics model (Ceravolo et al., 2020) and Bayesian neural network (Yin & Zhu, 2020) are some examples that have shown robust model updating implementations.
Structural reliability assessment aims to determine the probability of failure in different engineering systems given a certain demand and capacity (Dai & Cao, 2017;Dai et al., 2012). It is also extended to other coupled systems, such as bridge-network performance assessment (Allen et al., 2021;Nabian & Meidani, 2018). There is also a significant investment made in utilizing machine learning models for structural damage detection and reliability analysis. Particularly, probabilistic machine learning methods such as Bayesian learning are becoming more popular for early damage detection of critical infrastructures (Eltouny & Liang, 2021b;Kuok & Yuen, 2021;Perez-Ramirez et al., 2019;Sajedi & Liang, 2021a). Bayesian methods have been incorporated for damage detection, localization, and novelty detection in the case of unsupervised learning models.
Summarizing from the above, smartphone-based SHM has remained of limited scale in the last few years despite all the scalability potential. Smartphone-based SHM research has been limited to the perspective that compares sensor accuracy at the signal level and, if not, at the identification level. To the best of the authors' knowledge, this paper is the first attempt to bring smartphonebased SHM above the standard computations by comparing the sensor and identification performance and systematizing smartphone sensing and data computation beyond sole damage assessment or prediction for high-end products, for example, network effects and infrastructure actions. The main novelty comes from the unified computational scheme and linking the low-abstraction smartphone data to high-abstraction decision-making processes, which has yet to exist in the computational civil infrastructure engineering literature.
Other than the unified scheme, the secondary novelties are also threefold. This research is a primary initiative to bring SHM to the population-scale analytics and is unique in the way it brings SHM-calibrated bridge-specific fragilities into the seismic performance of transportation networks. While exemplary research is rare in the former dimension, existing alternatives in the latter dimension predominantly rely on typology-specific fragilities, which omit detailed modeling information and are not open to vibration-based model updating. Finally, all these aspects are covered in an integrated computational scheme compatible with client-side and server-side platforms , which can contribute to the next decade of smart city applications accounting for data-fed bridge network safety and resiliency.
Encouraged by the recent advances in sensor technologies and to address prolonged gaps in the SHM field, this paper uses publicly accessible smart technologies as a reconnaissance add-on tool revealing structural vibration features in a portable and cost-free setting. According to the framework, bridge vibration features can be extracted from smartphone accelerometers that can serve as proxies of the mechanical characteristics such as stiffness and indirectly material strength and section features, with certain restraints brought by environmental/operational variability on dynamic behavior. Bridge modal identification through smartphone data has an updating potential for bridge finite element models (FEMs), providing a baseline for future performance estimation attempts. Due to the simplicity of the items used in the methodology, SHM data can be produced with minimal effort during reconnaissance procedures. Since the monitoring methodology is scalable, city-scale or even nationwide deployments are possible, bringing a new dimension to SHM from individual-scale to systemic-level applications. In parallel, transportation network applications fed by structural and earthquake engineering analyses reduce modeling uncertainties through mobile sensing-based dynamic calibration.
In this paper, 20 bridges surrounding a reference site region are monitored with smartphone accelerometers for modal identification. The identification results are used for FEM updating, which is used for bridge reliability estimation. When the multiple bridge SHM results are evaluated together and fed into the performance assessment process, bridge population reliabilities reveal systemic behavior expressing connected effects of failure probabilities. Eighteen postevent disaster mitigation scenarios are pursued to interpret the region-scale SHM findings from a decision maker's perspective. It is worth mentioning that the framework is flexible in terms of adopting alternative postevent decision processes other than emergency actions, for example, retrofit and reconstruction actions effective under interdependency (González et al., 2016;N. Zhang & Alipour, 2020).
The paper is designed as follows: Section 2 explains the methodological background of modal identification, FEM updating, reliability estimation, postevent actions, and transportation-scale prognostics. Section 3 presents the implementation of the method on a bridge population surrounding an area in need of emergency response. Section 4 introduces the results and discussions drawn from the implementation case study, and Section 5 presents the conclusions and future pathways of this research.

METHODOLOGY
This section explains the details of the massive-scale bridge monitoring and reliability assessment framework, including the theoretical background, information flow, implementation details, and testbed features. In summary, the assessment process starts with a traditional reconnaissance procedure accompanied by rapid vibration monitoring applications. The information collected from site visits is used for FEM development, and vibration data leading to modal identification serve for FEM updating. Updated models aim at characterization of material and sectional features that are complementary to the existing knowledge. Afterward, reliability estimation under seismic exposure is performed for bridges starting at an individual scale. Based on their functional role in the transportation network, systemic reliability is determined based on the connectivity features of individual bridges considering postdisaster seismic scenarios and mitigation actions. With the combination of the structural performance at a systemic level with transportation and hospital configurations, optimal decision-making can be performed concerning a catastrophic event, improving the local evacuation strategies or access to the emergency services for the testbed region. Figure 1 outlines the flowchart depicting

Bridge population and network
The cascaded features of the transportation network define the systemic performance of the bridge infrastructure. Depending on the strategic importance of the bridge to keep the network functional, structural failure can have a negligible or significant impact following a seismic event. Therefore, the quantification of bridge failure effects is characterized by the structural features as well as the transportation demand, hospitals, and bridge population topology. Figure 2 denotes a simplistic transportation network connecting adjacent vicinities denoted by and a subscript expressing the vicinity identity. Connectivity of each vicinity is enabled by the transportation lines denoted as and subscripts of the vicinities being connected. The functionality of each transportation line depends on the structural condition of the bridges associated with it denoted as , represented by the same line subscripts and a superscript identification number. Connectivity effects (series, parallel, and complex combinations) on the bridge population performance are further explained in Section 2.7. For low complexity transportation problems, from hereon, the methodology incorporates a decision-tree-based approach that suits the testbed region and postdisaster mitigation scenario. However, as the network behavior becomes intricate, an optimization scheme needs to be followed.

Field surveys and data acquisition
The structural reconnaissance procedure can support three parallel purposes. The common purpose is to gather information essential for FEM dimensioning and relevant details, for example, bridge length, deck thickness, secondary beams, cross-sectional features, pier sizes, and connection types, if available. In addition, site visits serve to collect transportation-related metrics, for example, demand and capacity features of the road network, which can also be alternated by existing digital sources, for example, Google Maps application programming interface (API). Finally, vibration samples are acquired from bridges through smartphone accelerometers, which are used for modal identification. This final step provides the necessary field observation, which enables calibrating the bridge model developed based on reconnaissance drawings. In addition to the baseline modeling potential, preevent and postevent data acquisition can also reveal structural dynamics changes occurring due to a damaging event and reflect these on FEM. Modeling and updating details are explained in the forthcoming subsections (Sections 2.3 and 2.4).

Seismic response analysis
The structural reliability assessment procedure reflecting the seismic performance of a bridge relies on the FEM and analysis under a series of input ground motions and a collection of nonlinear responses. Fiber section models using OpenSees are introduced to perform nonlinear time history analysis, which sets the baseline for bridge-specific fragility curves. Material-section characteristics are updated, accounting for stiffness degradation and mobile vibration data for calibration. The scheme addresses a standard bridge profile observed on the testbed, which is bearing-free frame-type integral bridges, where bridge piers and decks constitute possible damage mechanisms. Under a range of ground motions representative of regional seismicity (detailed in Section 2.6), the probabilistic distribution of the structural response, and therefore, failure probability, can be associated with fragility curves F I G U R E 3 Nonlinear modeling and fragility curve development concepts over ground motion intensity. Different response thresholds can accommodate a range of different performance limits ranging from no structural damage to complete failure. Figure 3 demonstrates the snapshots of the seismic performance assessment items of a typical bridge structure. FEM updating and reliability estimation methodologies are further explained in the following subsections (Sections 2.4 and 2.7).

Mobile technology integration for calibration (model updating)
In a typical seismic performance evaluation process of an existing structure, the conventional methodology addressing material behavior looks into destructive test results of core samples. Access to such test results may be unavailable under ordinary circumstances, primarily if the assessment procedure is performed in a massive-scale framework. For this reason, an innovative characterization procedure using mobile accelerometer data is adopted in this paper. Especially for bridges with simple geometry, bridge stiffness features can be linked to the material character (e.g., concrete class) and sectional features. These features can be indirectly extracted from the dynamic response measurements following modal identification and model updating procedures, subject to assumptions limiting the complexity of the bridge.
In other words, an optimization scheme such as gradient descent matching field tests with FEM modal analyses can best-fit the model and the measurements based on objective function minimization. For the parameter where the objective function is minimal, FEM updating is accomplished. For further specification, the objective function characterized by the stiffness parameter EI can search the optimal value for a range of FEMs and their modal frequencies. For an idealized beam with given boundary conditions, the fundamental frequency is sufficient to define the dynamic signature of the structure. If a range of EI values is searched through a series of FEMs, the optimal EI minimizes the error between the FEM and the modal identification result. The subscript i corresponds to the number of individual FEM that parameterize the stiffness term over the domain. In summary, the objective function can be idealized with a generalized expression as follows: (1) and where and are the identified modal frequencies from the measurements and the natural frequency of the th FEM, respectively. MAC corresponds to the modal assurance criteria between the identification-based and the finite element-based mode shapes. The two modal parameter contributions (frequency and mode shape) to the objective function can be harmonized by weighing coefficients and representing the influence of frequency-induced and mode shape-induced errors of the n th mode on model updating.
According to the generalized expression, represents a particular mode, and represents the total number of modes considered within the updating framework. It should be noted that the damping ratio can also be incorporated into the framework; however, it is excluded from the scheme due to its relatively less identifiable nature. and can be quantified, accounting for confidence in the identified parameters as well as the role of the constraints set by them. Certain beamlike model updating examples can solely rely on modal frequencies, corresponding to zero weight for mode shapes (e.g., Oh et al., 2015).
In this study, the identification problem is simplified to 1 set equal to unity while other coefficients equal to null. This minimizes the equipment node number and duration of the field tests; however, it is limited to identifying global characteristics of beam-like structures with well-known boundary conditions and nonlocal damage. With a compromise on these concerns, one can better capture the dynamic behavior of the structure and adjust an updating scheme more sensitive to local features as well as boundary conditions.
The stiffness term becomes optimal ( optimal ) where the error function is minimized. In addition to the material characteristics, boundary conditions play an important role in bridge dynamics; however, smartphone data under the proposed reconnaissance setting have limits due to the single-output-only updating nature. To incorporate the variation in boundary conditions, the analyses comprise three condition couples, which are fixed-fixed, simply supported, and fixed-pinned, which depict a broad range of restraint uncertainties. Depending on the availability of device number and test duration meeting safety requirements, these uncertainties can be further removed with a dense smartphone sensor configuration.
In the simplest case, dense computation of the objective function through a parameterized FEM can reveal the objective function features. For a more efficient approach, an optimization algorithm can be deployed to avoid excessive computations for model updating. The authors use the gradient descent search technique to estimate the next step increment/decrement of the stiffness term based on the reduction/increase of the objective function in the subsequent computations. The following describes the searching technique: where is the step size. The proposed optimization scheme is expected to be efficient in the case of extensions into multiparameter identification to achieve minimal computational expenses.

Transportation and hospital network demand
The functionality of bridges in extreme events has been studied in many works (Bocchini & Frangopol, 2012;Dong et al., 2013;Padgett & DesRoches, 2007;W. Zhang et al., 2017). The travel time delay due to a reduction in the bridge capacities in different damage states can result in traffic congestion and hence affect the postearthquake emergency operation. In this study, based on our initial assumption and to simplify the calculation, the total travel time is calculated based on the free-flow travel time on each link, that is, the time taken by a user to travel a path when the traffic density (flow) is zero (i.e., the normal duration). For example, it can be assumed that traffic on the network is mostly occupied by emergency vehicles, and therefore, traffic congestion would unlikely occur. In fact, previous studies, as reviewed by Hall (2001), agreed empirically on the fact that speed-flow model curves remain constant even at high flow rates. In cases where the network is capacity-constrained, either due to an increased flow rate near or at capacity or change in the network capacity, travel time is generally calculated based on the empirical function developed by the US Bureau of Public Roads: where 0 is the free-flow travel time on link ; is the flow on link ; is the true capacity of link ; and and are two parameters that depend on the level of service of link (typically assumed to be 0.15 and 4, respectively).
depends on the availability of origin and destination (OD) data and is solved based on static or dynamic user equilibrium (UE). The general procedure for UE traffic assignment in the analysis of urban transportation network flow subject to earthquake damage can be found in (Chang et al., 2011;Shiraki et al., 2007). It is assumed that the bridge condition after an event is either in service ( = 1) or out of service ( = 0). Therefore, in the rerouting capabilities of the network, there is no change in free-flow speed and capacity. To put simply, the users are diverted to the next shortest path on the network in case a bridge is out of service.
In addition to the transportation infrastructure features, for the disaster mitigation problem, one needs to identify the health service capacities per specific node assigned to the network as well as the demand following a seismic event. One can associate casualties in a region as a function of seismic intensity exposed to the infrastructure stock. An empirical approach (Jaiswal et al., 2009) suggests that the fatality estimate depends on empirical parameters defining the standard normal cumulative distribution as a function of the intensity measure .
whose and values are based on the region and Pp denotes the population residing in the destination vicinity exposed to shaking intensity . For the testbed expressed in the next section, these values refer to 11.057 ( ) and 0.105 ( ) (Jaiswal et al., 2009). This can be roughly extended to the injuries through the ratio of mortality to morbidity, , approximately one-third, for a typical Richter magnitude range between 6.5 and 7.4 (Alexander, 1985). The aforementioned expression can reveal the probabilistic demand on the hospitals in a vicinity, whereas the capacity can be inferred from the bed number, , in the facilities. Accordingly, the probability of not failing to receive medical services in the vicinity w following an earthquake can be defined as which is a function of the shaking intensity . More detailed research on hospitals in the event of a seismic disaster can be found in the seismic resilience literature (Achour & Miyajima, 2020;Ceferino et al., 2018Ceferino et al., , 2020Cimellaro et al., 2009;Dong & Frangopol, 2017;Seligson et al., 2004;So & Spence, 2013).

Ground motions for fragility curve development
Synthetic ground motions can be simulated following earthquake characteristics extracted from real records at a site. For the sake of this study, different ground motions with a range of intensities but similar frequency content and duration to the target earthquake can be generated based on the nonstationary Kanai-Tajimi model (Fan & Ahmadi, 1990;Lin & Yong, 1987). The model is an improved version of the original mode (Kanai, 1957;Tajimi, 1960) given the power spectral density (PSD) function. The details of the source ground motion features are explained in Section 3.2.

Systemic reliability and risk estimation
Based on the nonlinear time history analysis batches performed under the given range of ground motions, a bridge-specific fragility curve can be generated based on a lognormal cumulative distribution function fitting the failure and survival data (Ozer, Feng, & Soyoz, 2015;Shinozuka et al., 2000). Accordingly, the fragility curve for a single bridge is characterized as follows: where , , and correspond to the ground motion intensity, mean, and standard deviation, respectively. The curve fitting operation can be conducted through maximum likelihood estimation.
where corresponds to the ground motion index and corresponds to the failure or survival outcome per analysis (binary as 1 or 0 depending on the exceedance of the damage threshold or otherwise). The mean and dispersion values, which characterize the fragility curve, best fit the analysis outcomes, where the likelihood estimation's derivative reached zero. Accordingly, one can reinterpret the seismic fragility of an individual bridge's reliability as Systematic reliability herein depends on the spatial distribution of the bridge population and the connectivity among them. For series reliability, the systemic response takes the form of where refers to the ground motion intensity imposed on bridge , is the associated reliability of that bridge, and m is the total number of bridges providing the series connection. For parallel reliability, the definition of the systemic response becomes and through the combinations of the aforementioned conditions, the complex systemic behavior can be expressed following the bridge nodes in a transportation network. Accordingly, the reliability of a transportation path connecting vicinities q and w can be linked to the collective behavior of series and parallel alignment of bridge nodes such as and the reliability of reaching from the qth vicinity to any other vicinity with the available mitigation services can be described as where denotes the number of vicinities available for evacuation. However, reliability data alone do not reflect the capacity of the network in terms of transportation and health services. From here on, one can extend the reliability formulation into risk through consideration of the travel time measure as a function of transportation demand characteristics as well as the availability of mitigation services. Risk minimization, alternatively, utility maximization objectives include minimizing the travel time as well as maximizing the probability of receiving health services, that is, ℎ in vicinity w.
One can express the utility of a transportation route in a postevent emergency management manner as a function of systemic reliability, service probability, and travel time as which will lead to the maximum utility and the optimal route o is the route that enables To summarize, the postevent evacuation scheme is supported by three parameters regarding (i) travel to the mitigation facility, (ii) probability of receiving essential services, and (iii) reliability of the transportation network connecting the vicinity to the target area. It should be noted that multiple criteria are merged into a single decision utility in this framework; however, they can take alternative multiattribute forms if stakeholder preferences are present, for example, those in modern earthquake early warning systems (Cremen & Galasso, 2021) and transportation asset management (Bai et al., 2021). approximately 5000 residents, which may need to find an optimal evacuation route in the event of a seismic disaster. The transportation network connecting Kalkanli to the nearby vicinities consists of 20 bridges with structural properties and material types collected through a series of reconnaissance visits. A field survey was conducted for each bridge to identify their characteristics for modeling, including a 3D model of each bridge, and vibration measurements were collected via smartphones for calibrating the models. These calibrated models will serve for fragility analysis, which composes the systemic decision-making framework's bridge failure probabilities under a range of scenarios. Figure 4 shows the scene from an exemplary reconnaissance visit, and a summary of the bridge population is provided in Table 1 and the bridge photographs of the entire network are given in the Appendix, Figure A1. The real network connecting Kalkanli to the remaining nearby cities is illustrated in Figure 5. To reduce the topology to a decision-tree compatible level, the network is abstracted into Figure 6 with the layouts of bridges, hospitals, and neighbor vicinities. In the abstract representation of the network, only the useable main roads for emergency traffic are identified and demonstrated. The network also denotes the connection between the regions and the parallel or series route components, including the bridges. Following the assumption of free-flow travel time collected from Google Maps API, Figure 6 also shows the node-tonode travel time, in addition to the hospitals' capacities in each region. The free-flow speed is determined from the posted speed limit on each link.

Regional seismicity and bridge-specific fragilities with SHM calibration
A total of 18 earthquake scenarios in three districts (Girne, Guzelyurt, and Lefke) with magnitudes M = 5.5, 6.5, and 8.0, each with two different depths, 10 and 60 km, are used in this study. The intensity measure at each bridge is The weights are considered according to the shallow earthquake distribution and regional data used in each GMPE (Cagnan & Tanircan, 2010). Figure 7 shows an example of the peak ground acceleration (PGA) distribution under a given scenario. As part of the reconnaissance visits, bridge vibration data are collected via smartphone accelerometers with a variety of settings. According to the alternative configurations, one can consider a deployment scheme depending on the number of devices, such as single versus multiple device availability. Since smartphones are tailored as consumer-grade devices rather than scientific instrumentation, a series of different configurations can help with the credibility of the measurements, especially if a reference sensing device is absent in all tests. This includes (A) checking whether two devices propose similar sensor output, (B) looking at higher-mode effects, which cannot be captured with limited instrumentation and certain locations, and (C) imposing nonambient forces to amplify the signal-to-noise ratio. Figure 8 presents the summary of criteria leading to a systematic performance of the vibration measurements accompanying the reconnaissance procedure. In summary, five tests addressing the F I G U R E 7 PGA distribution of the M = 6.5 event at 60 km depth in Guzelyurt Ath configuration, another one addressing the Bth configuration, and a final one addressing the Cth option are developed and applied during each bridge visit. Two types of phones (Samsung Galaxy S8 and LG G6) are deployed for vibration measurements during field visits. Prior to the tests, both devices were tested in a laboratory environment, with known input and reference output data through small-scale shake table tests, and their accelerometer fidelity was confirmed. Samsung Galaxy S8 has an accelerometer type LSM6DSL manufactured by STM, and LG G6 has a Bosch-made LGE accelerometer. The embedded accelerometer is within the upper sampling range of 500/400 Hz as well as a resolution of 0.002 m/s 2 and a dynamic range of 78 m/s 2 . The phones are attached to the deck surface via double-sided adhesives during the measurements. Figure 9 demonstrates an example of the vibration signal features including time series, PSD, and short-time Fourier transform (STFT) from Bridge B2 under the first option.
In addition to the identification of frequency domain characteristics of each bridge through standard signal F I G U R E 9 Time and frequency features of vibration signals from Bridge B2 (Test Scheme A, Operator 2) processing methods (e.g., PSD), more advanced system identification algorithms can be used; however, they are not expected to outperform due to the spatial limitations and noise exposure of the instrumentation. For example, each bridge test is processed through stochastic subspace identification (Overschee & De Moor, 1996;Van Overschee & De Moor, 1994) under single-output data, and stabilization diagrams are developed; however, this lacks multioutput information limiting the use of stabilization conditions such as mode shapes. Therefore, single-output charts can serve as a supportive finding confirming whether the frequency domain features are likely to be a modal (physical) character rather than a mathematical one (Tran & Ozer, 2020. Figure 11 presents an exemplary stabilization diagram showing test results from testbed Bridge B2. Table 2 presents the test schemes performed for each bridge, and Figure 12 shows their obtained frequencies (indicated as "identified"). It is essential to note that these frequencies are relatively high concerning typical civil infrastructure frequency ranges, and the high range of frequency stems from very short spans of the F I G U R E 8 Instrumentation template and demonstration on Bridge B1 tional cases require alternative modeling approaches (e.g., arch-type bridges and irregular and skewed bridges). In summary, FEM calibration under three extreme boundary conditions is performed, and their parametric effects are documented in Figure 12. It should be noted that boundary condition uncertainties can be removed with conventional high-fidelity instrumentation consisting of multiple nodes, but smartphones' multioutput performance is still in its infancy and needs substantial improvement to capture more advanced modal parameters such as mode shapes, especially for high-frequency structures such as short-span bridges .
Updated bridge FEMs are used for nonlinear time history analyses under a series of ground motions. The ground motion records corresponding to the Cyprus region are collected and reproduced through the nonstationary Kanai-Tajimi spectrum expressed in Section 2.6. The ground motions are constructed based on 50 records of three real earthquakes with magnitudes M = 5.5, 4.0, and 4.5, epicenters located in the Mediterranean Sea (34.81, 32.33), Palaiometocho (35.13,33.20), and Mediterranean  Figure 10 shows the time histories and Fourier spectra of 3 exemplary data from 3 stations in Alefka (Nicosia), Akdeniz (Lefkosa), and Alevkaya (Kyrenia). The artificial ground motions are reproduced in different intensity scales of the reference earthquakes by varying the scaling coefficient in Equation 14, while their dominant frequencies and durations are preserved taking real earthquakes as the baseline. A total of 100 ground motions are imposed on each bridge model paired with the alternative boundary conditions assigned to the bridge. The failure-no failure binary data are fitted via the maximum likelihood estimation procedure expressed in Section 2.7. Eventually, the fragility curve parameters, including the mean and standard deviation values, are identified, converting ductility values into fragilities with different failure criteria and boundary conditions as depicted in Figures 13 and 14, which show fragility curves representing individual bridges up to a 2 g intensity measure. It can be seen that some bridges are never subject to damage exposure under a given ground motion dataset; therefore, their reliability values are set to unity for the next stages of the analyses. Scenario ID S7 S8 S9 S10 S11 S12 Magnitude 5 5 6.5 6.5 8 8 D e p t h( k m ) 1 0 6 0 1 0 6 0 1 0 6 0 Lefke (Lefka) Lat: 35.121 Long: 32.809 Scenario ID S13 S14 S15 S16 S17 S18 Magnitude 5 5 6.5 6.5 8 8 D e p t h( k m ) 1 0 6 0 1 0 6 0 1 0 6 0 Finally, 18 different scenarios are generated to reveal the systemic behavior under a variety of circumstances. Seismic demand on each bridge is estimated per event through the GMPEs and the PGA contours (e.g., Figure 7). Table 3 presents a summary of the seismicity scenarios, and Tables A1 and A2 present the associated mean and standard error values of the intensity measure at each bridge compatible with the formats given in (Worden, 2016). Given that the magnitude and distance are deterministically known following an event, ShakeMap employs an empirical approach that provides the mean and the standard error outputs in terms of the PGA percentile (log in terms of the error term). Based on the reported PGA values, a lognormal probability distribution is generated for each bridge and scenario consisting of 10,000 samples. Figure 15 exemplifies the PGA samples, PGA histograms, lognormal model, and corresponding distribution of the bridge reliabilities as a result of the variation in ground motion. The sampleset is used later on for a Monte Carlo simulation propagating the uncertainty into route selection and producing a discrete probability range for the alternative routes. It can be noted that spatially distributed uncertainty is influential in network-level hazard analysis (Loth & Baker, 2013;Wald et al., 2008), and F I G U R E 1 4 Fragility curve examples from the bridge population under an envelope of boundary conditions F I G U R E 1 5 Exemplary distribution features (Bridge 1) from intensity measure to failure probabilities (PGA sample set, PGA histogram, PGA lognormal distribution model, and failure probability distribution stemming from the ground motion uncertainty) ShakeMap has been a scope of research in terms of spatial correlation (Verros et al., 2017). A detailed report on how the uncertainties are handled in ShakeMap can be found in (Worden et al., 2018). This study also introduces another level of uncertainty analysis in travel time estimation. Google Maps API is used for generating four different travel times for each link, namely, "normal duration," (also shown in Figure 6), "best guess duration," "optimistic duration," and "pessimistic duration." The predicted times are based on historical averages. The best guess duration will give the most useful predictions for the vast majority of use cases as it integrates live traffic information. That said, the other travel metrics are also used, as some of those can provide worst-case analysis of the transportation demand, which has an indirect effect on the serviceability of the hospitals.
Intensity measures provide the bridge failure probabilities under given scenarios and, accordingly, the population behavior. When this information is combined with the travel time and hospital capacities in the network, one can develop a comparative basis on alternative routes and identify those with a high likelihood of successful and timely evacuation to essential medical facilities. Table A3 is a summary of the modified Mercalli intensities (MMI), and Table A4 is the probability of demand on hospitals not exceeding the capacity, conditioned on the seismicity exposed to the region.
Populations per vicinity annotated in Figure 6 are combined with the median fatality rate 11.057 and dispersion of fatality rate 0.105 from the fatality rate formulation (Jaiswal et al., 2009). In summary, from fatality rate to fatality estimates and accordingly morbidities, one can express the probability of morbidity being less than hospital capacity, indicating the probability of receiving service from the hospital in that vicinity.

Systemic reliability for optimal postevent routes
To conform the systemic performance of the bridge populations in the application region, a decision-tree scheme F I G U R E 1 6 Decision tree identifying the optimal path to hospitals in consideration of bridge population behavior encompassing travel time, path reliability, and probability of receiving hospital service is adopted. Denoted in Figure 16, the tree quantifying utility per path is composed of the root node where the optimal path decision is taken, branches connecting the path decision to the bridge population condition and hospital potential terms, connectors defining alternative paths encountering path-specific reliabilities and service probabilities, and finally the endpoints expressed in terms of utility for each outcome. The probabilistic framework examines each bridge population on specific paths and connects origin (Kalkanli) with the destinations and thus hospital vicinities (Girne, Guzelyurt, Lefke, Lefkosa).
Apart from the bridge reliabilities, hospital capacities, and disaster-induced morbidity demands, travel time is the residual contributor in route optimization. In summary, computed utilities representing expected inverse travel time are visualized in Figure 17 and are observed to be the same regardless of the earthquake scenarios; accordingly, Lefke vicinity is the recommended destination for all scenarios. The ground motion sampleset from the distribution is processed to quantify the probabilistic choice of the alternative routes, and accordingly, Lefke* dominates the discrete distribution with percentages above 81% throughout the scenarios. Figure 18 portrays the uncertainty in terms of the probability of Lefke* destination's utility being larger than their counterparts, which becomes the primary selection per scenario proposed in the scheme.

Hypothetical extensions for optimal postevent routes
As demonstrated in the former subsection, the existing infrastructure conditions point out a unified decision scheme for a range of seismicity scenarios. However, one can impose modifications on the bridge reliability components, hospital capacities, and transportation network to test further hypotheses related to the systemic behavior. In the following, four hypothetical cases are introduced to overwrite the existing optimization scheme and see the deviations from the actual behavior. Accordingly, four cases are introduced into the systemic scheme in Table 4.
As claimed by the cases introduced above, Case 1 refers to the closure of Bridge 1 due to maintenance works, setting a temporary update on the reliability of the bridge equal to 0. In addition, Case 2 corresponds to the capacity reduction in the Lefke region due to an ongoing additional demand F I G U R E 1 9 Utility surface identifying optimal routes per scenario under given suppositional cases (e.g., local viral outbreak or damage introduced into hospital infrastructures) reducing hospital serviceability by 50%. Case 3 follows a minor investment scenario adding bed capacities to the hospital in Guzelyurt and bringing hospital service probability only to 50%, and Case 4 expresses complete capacity maximization of the bridges (Bridges 16,17,18,and 19) connecting Kalkanli and Girne due to retrofitting efforts. Figure 19, A1 presents a snapshot of the utilities observed in each hypothetical case.
For Case 1, an unserviceable Bridge 1 disrupts a significant amount of the network connecting Kalkanli to Guzelyurt, Lefkosa, and Lefke, eventually identifying Lefkosa as the outperforming destination. Looking at Case 2, compared with the current status of the Lefke Hospitals, an abrupt reduction in the available beds shifts the optimal destination to Lefkosa. In addition, Case 3 depicts a slight increase in the bed capacity in Guzelyurt, which is sufficient to bring Guzelyurt into the best possible evacuation terminal. Finally, Case 4 has insignificant changes, compared with the original case since existing bridge reliabilities are already high and near full capacity. In the following subsection, final remarks are presented in line with the results and relevant discussions. Finally, to cover another level of uncertainty as introduced in Section 3.2, three other travel time measurements, in addition to the normal travel time, were used for all four cases. We observed no notable influence on the route decisions that can change the original decision for each case. For example, the pessimistic travel time did not significantly influence the shortest paths for the majority of the links. Therefore, the results of these additional cases are not presented in Table 4.

RESULTS AND DISCUSSION
Starting with the mobile bridge identification findings, it is essential to note that the identified modal frequencies (all above 10 Hz) are very high, compared with bridge infrastructure in general. This is expected since the entire structure population is composed of super short-span bridges, for example, maxima of 10-m spans. In line with this note, bridge reliabilities turn out to be very high values (medians above 1 g excitation) and have ignorable effects, compared with other emergency response parameters such as travel time and hospital capacities. Therefore, due to their high bed capacity and relatively close distance to the origin vicinity, Lefke hospitals dominate the destination selection criteria regardless of different seismicity scenarios. The influence of bridge population reliability can be further observed by looking at the hypothetical cases prescribed in the previous subsection. For example, one critical bridge's performance located at the Guzelyurt/Lefkosa-Lefke intersection can radically change the population behavior, such as in Case 1, whereas improvement of the entire bridge series connecting Guzelyurt and Girne cannot reverse the optimal decisions (Case 4). One can rephrase that bridge performance alone has a limited impact on emergency services following damaging events, and complementary information is needed for an improved vision of the systemic performance, such as transportation metrics and hospital vicinities, for an efficient postdisaster strategy.
Finally, concerning a remote location, minor hospital investments can be more urgent actions to increase the mitigation capabilities, and similar reductions in hospi-TA B L E 5 Summary of the evacuation routes per case
tal services can have significant adverse effects, changing the optimal evacuation routes (Case 2 vs. Case 3). In summary, the systemic performance of the transportation network and OD connectivity relies on a proper merge of advanced structural/earthquake engineering knowledge with transportation and health services. Table 5 presents the summary of actual and hypothetical cases studied and shows the variation in optimal decisions based on infrastructure dependence in terms of bridges and hospitals. It should be mentioned that model updating and reliability estimation processes can be computationally expensive processes but are suitable for preprocessing and can also be compressed into surrogate or machine learning models such as neural networks (Adeli, 2001;Azimi & Pekcan, 2020;Lam et al., 2006;Malekloo et al., 2021;Nabian & Meidani, 2018;Xu et al., 2021), which flexibly add even further value concerning the rapid response needs of transportation infrastructure. It is essential to note that the presented systemic dataset and model sets demonstrate the proof-of-concept for a mobile-technology-integrated model updating framework that can periodically monitor networks of bridges with a tradeoff between scanning time and identification quality. While the authors envision that the physical meaning of smartphone-sensed vibrations can reduce modeling uncertainties, especially if bridge documentation (historical information and material characteristics) is unavailable, extension of the proposed framework into long-term monitoring can reveal environmental/operational fluctuations of the bridge frequencies (Soyoz & Feng, 2009), in addition to its cascaded influence on seismic fragility (Torbol et al., 2013), and accordingly reliability-based postdisaster route optimization. For a long-term formulation of this phenomenon, periodical measurements in the forthcoming years should be gathered to understand the variable features of bridge frequencies.
In summary, the novel population-scale SHM implementation presented here is an early contribution to the rise of an emerging era reshaping SHM literature in the 2020s (Bull et al., 2021), is believed to form a well-structured method addressing postdisaster needs of remote vicinities, and combines a plethora of advanced computational techniques in this unique framework. Below, the conclusions obtained from the findings of this study are drawn, and future directions are discussed.

CONCLUSION AND FUTURE WORK
In this study, the authors present a pioneer implementation bringing scalable mobile sensing data into bridge network assessment processes through consumer-grade smartphone sensor technologies and an integrated computational decision-making framework and eventually study a remote vicinity's access to postevent healthcare services. Twenty bridge models are developed based on site-collected information and calibrated to reduce engineering uncertainties with the help of vibration-based updates. Structure-specific fragility curves are developed for each bridge to perform reliability assessment under 18 seismic scenarios. Finally, bridge reliabilities, hospital services, and travel times are merged in a systemic framework based on decision analysis, and optimal routes are identified considering the combined effects of all factors mentioned above.
The results show that bridge conditions have less effect on the systemic performance of the transportation network if the seismic demand-capacity ratio is relatively low. However, loss of a single bridge can have significantly more impact than loss of an array of bridges depending on the remoteness of vicinities in need and surrounding network topography. Moreover, where bridge performances are high in general, alternative metrics such as hospitals and travel times become influential in making optimal postdisaster evacuation decisions. It is interpreted that optimal decisions are nevertheless sensitive to multiple factors, and their combined features are essential to account for the systemic characteristics of a transportation network. It can be noted that dynamic travel demand and seismic safety of hospital infrastructure are also important factors that are excluded in the scope of the work due to lack of data; however, additional issues are recommended for similar region-scale systemic reliability applications with SHM support. It is noted that the current form of the paper is a baseline for future studies, which will have more focus on error propagation from different sources of uncertainties, those related to seismic hazard and environmental frequency variations necessitating a long-term monitoring scope. Future plans include spatially dense high-fidelity identification tests with dedicated instrumentation to further explore mobile technology limitations.
In summary, this study demonstrates that a largescale mitigation framework does not necessarily have to oversimplify local structural features. There is a reconnaissance-friendly mobile technology framework potential that can reduce uncertainties associated with bridge physical features via calibration; however, it is open to further improvement as the limitations are explained. With the new advancements in sensing methods, smartphones form a requisite part of population-scale SHM, which was unavailable prior to ubiquitous data and model calibration through scalable sensor technologies.

A C K N O W L E D G M E N T S
The authors would like to acknowledge Dr Bertuğ Akıntuğ from Middle East Technical University and Arkın Şansalan from Northern Cyprus Highway Department for their kind assistance in supporting the field tests.