*2.2. Cyber-Physical System*

As a new emerging technology, CPSs attract significant attention from numerous research and industry fields in the last decade. The link and coordination between physical objects and computational resources set the fundamental system goal, which in return, brings different disciplines such as computer, control, electronic, and mechanical systems together [51]. Combining multilayered computer architectures [52] with embedded systems, sensors and control [53], or expanding WSNs to take action in the physical world [54], CPSs present a diverse interpretation of the up-to-date existing technologies.

The overall motivation of the CPS platform presented in this study is to connect the physical, cyber, and sensor system objects through a multilayered information processing SHM framework. The physical object formulated in this scheme is the bridge structure which represents the outer layer of the developed CPS system, as shown in Figure 3. The physical parameter of interest is the bridge vibrations, which can be gathered by smartphone accelerometers with the help of pedestrian volunteers. Moreover, the sensing process is enhanced by the hybrid foundation of pedestrians and sensors, composing the citizen sensor layer. Eventually, the bridge vibrations sensed by smartphone accelerometers are submitted to the server where the signal processing and data analytics take place. With the help of the cloud-based acceleration record manager system, which is the innermost layer, the vibration data can be stored, viewed, reprocessed, and their results can directly be extracted by the system administrators. Interconnecting these components successively forms the two core elements (sensor networks and application platforms) with transactions (sensing and knowledge) of a typical CPS and produce the actuation information with intelligent decision systems to complete the cyber-physical loop [39]. To summarize, citizen sensors provide the binding components of the smartphone-based SHM network by integrating the civil infrastructure with the cloud services, and the numerical representations of the bridge (FEMs) can be fed with the actual bridge response through the cyber-physical SHM system phases.

Formerly, the bridge is registered to the CS4SHM online server system and database to store, process, and monitor its structural vibrations. An iOS application is developed as a data acquisition interface to enable smartphone users gather vibration data from the bridge and submit it to the server. Pedestrians with bridge access are assigned as the test group and submitted 135 vibration measurements in total. The data is processed through the online server system, and modal identification results are recorded. These identification results can be used to calibrate the mathematical model of the bridge by following the FEM updating procedure. Figure 4 shows an exemplary citizen sample in the time and the frequency domains. Based on the whole set of submission records, first, second, and third modal frequencies are identified in [32] as 8.5, 19, and 30 Hz, respectively.

**Figure 3.** Conceptual CPS scheme for smartphone-based SHM.

**Figure 4.** Exemplary crowdsourced submission time histories and Fourier spectra.

#### *2.3. Finite Element Model Updating*

In order to predict the structural response accurately, the available information should be effectively used such that FEM parameters can be determined to the best extent. In this modeling example, the design drawings and material properties are unavailable, therefore, the initial FEM is based on site observations and estimations. The observations include the length and the outer diameter of structural members by scaling the pixel values with respect to the known dimensions (i.e., window size). Although the outer diameter can be determined using bridge photographs, the cross-sectional thickness or the inner diameter is unknown. Likewise, support restraints are set as uncertain parameters with possible realizations such as fixed, pinned, or roller. Other than these, contribution of the nonstructural components is difficult to estimate, therefore, mass sources are assigned based on crude assumptions. The analysis primarily considers displacement demand in the vertical direction which is influential on glass façade safety, and the paper presents time history analysis results in z-direction. The model consists of 48 nodes and 98 beam-column elements. Figure 5 shows the node and element tags for the baseline model.

Figure 6 shows the modeling uncertainties taking place without the necessary documentation. To summarize, tubular structural member section dimensions, distributed mass due to non-structural components, and support restraints all contribute to the modeling uncertainties and will be determined throughout the FEM updating process.

The proposed FEM updating method consists of generating a large number of models changing in uncertain parameters, comparing the modal analysis results of each FEM with the experimental data, and selecting the model which minimizes the error between the simulation (model) and the reality (identification). In order to establish an autonomous parameter study and FEM updating procedure, an OpenSees-Matlab integration loop is pursued. Specifically, OpenSees scripts are simultaneously generated, run, and evaluated by a controller Matlab code. As mentioned previously, three different parameters are selected to create different FEM batches. These are the boundary conditions, element stiffness values, and nodal masses, respectively. For each boundary condition combination changing in fixity definitions, a set of models with varying stiffness and mass values are generated. Each of the model batches are evaluated according to the difference between the first, second, and the third FEM and identification results. This is conducted by developing an objective function quantifying the error between a model and the reference modal parameter values.

**Figure 5.** Finite element model nodes, elements and axes.

**Figure 6.** Finite element modeling uncertainties.

In the former studies, the authors adopted Least Square Method (LSM) to formulate the objective function [46,47] whereas different approaches are present in the literature [55,56], in this study, the objective function is structured in terms of error between the simulation and the experimental results and multiplication of multiple modal parameter errors. To specify, the objective function, which is a function of the support restraints, stiffness and mass distributions, is formulated as

$$\text{Obj}(\text{BC}, \text{K}, \text{M}) = \prod\_{\text{mode}=1}^{3} \left( |\mathbf{f}\_{\text{mode\\_FEM}} - \mathbf{f}\_{\text{mode\\_Exp}}| / \mathbf{f}\_{\text{mode\\_Exp}} \right)$$

where BC, K, M represent changing FEM parameters such as boundary condition (BC), member stiffness, and mass values, respectively. Each boundary condition, stiffness, and mass combination corresponds to a different set of first, second, and third modal frequencies represented with fmode FEM term, and the model accuracy is determined based on the deviation from experimental values represented with fmode EXP. At the end of the loop analyses, the optimal model which minimizes the error between the

simulated and identified values becomes the updated model. Afterwards, this model can be used as a baseline for seismic response simulations and reliability estimation.

To summarize the updating process, Figure 7 shows the relationship between the OpenSees and Matlab platforms. The finite element model generation and updating process consists of two integrated platforms which are Matlab and OpenSees. Matlab basically works as a commander, it manipulates finite element parameters stored in OpenSees script files and utilizes the time history analysis outputs from OpenSees. OpenSees functions as a script-based modeling program (suitable for automated batch analysis), is used to conduct modal analysis or time history analysis and is controlled by Matlab. The two pieces of software work in harmony to conduct a large number of automated analysis with a common baseline model but differences in updated parameters.

**Figure 7.** Integration scheme of Matlab and OpenSees software.

## *2.4. Structural Reliability Estimation*

In the authors' previous studies, SHM-integrated reliability estimation is performed by generating fragility curves of different performance levels taking peak ground acceleration (PGA) as the random variable [46,47]. This method can result in high computational cost as the number of available seismic ground motions increases. Compatible with the smartphone-based identification procedure presented in this study, it is expected that ground motion demands under a seismic event can be determined by a dense seismic network composed of smartphone seismometers [57]. Besides, as the number of input ground motions increases like in a mobile CPS scenario, accuracy of the fragility curve parameters may run into obstacles due to truncation and round-off errors. Therefore, in this study, the probabilistic structural response is directly obtained from log-normal distribution of the time history analysis results. Damping term in equation of motion is modeled with Rayleigh Damping where the associated matrix is a combination of stiffness and mass proportional damping. Alpha and beta coefficients are determined based on 2% damping ratio at first and third modes.

For each ground motion taken from the 1994 Northridge Earthquake, a time history analysis is conducted, and the simulated response is obtained. Because the bridge considered in this study is a high frequency structure compared to the low frequency character of Northridge Earthquake records, it is assumed that the structure undergoes linear behavior and its response can be simulated with linear time history analysis. In this case, secondary performance indicators such as maximum drift or displacement become important as they are decisive in the basic engineering mechanics assumptions. Therefore, the response from each seismic event is collected in terms of maximum deflection and finally, the distribution demand under the given set of earthquakes is obtained. Looking at the distribution demand as well as the reference code and regulation criteria, it can be predicted whether the structural response will exceed certain performance thresholds. In conclusion, with the proposed reliability estimation framework, the high computational cost of fragility curve development is swapped with a simpler approximation, provided that the ground motion response distribution matches well with log-normal type distribution features.

It should be noted that 1994 Northridge Earthquake records perform as an exemplary dataset thanks to the high number of stations and well-distributed strong motion parameters, however, they do not necessarily mirror testbed site conditions presented in this paper. In other words, they are referred for demonstration purposes. In contrast with California, seismicity in the state of New York possesses a lower risk and lacks a comprehensive dataset available to public. However, in the event of ground motion record lack, synthetic ground motions can be generated for a particular site which has designated earthquake spectra [58]. What is more, in a futuristic scenario where there is seismic activity in urban areas, smartphones have shown feasible performance as low-cost seismometers which can be used to detect input ground motion imposed on civil infrastructure [57].

Considering the similar geometry and accordingly similar dynamic behavior of adjacent buildings, out of phase motions are not taken as a primary source of seismic damage. Therefore, forcing function at the boundaries are assumed to be uniform rather than multi-support excitation. It should be noted that changes in boundary conditions can also be monitored with the help of the proposed model updating procedure. Besides, given that the bridge lays on top of campus area with complete occupant access, glass façade integrity can also add additional life safety concerns in case of a seismic event. To incorporate that, vertical displacement behavior is taken as an exemplary performance parameter for reliability analysis.

## **3. Results and Discussion**

Following the outline presented in the methodology, the testbed bridge data is used for modal identification, FEM updating, and reliability estimation with the updated model. The results obtained throughout the analysis are presented with two subsections discussing objective function minimization (FEM Updating) and simulation of seismic response (Reliability Estimation), respectively.
