System Identification of Large-Scale Bridges Using Target-Tracking Digital Image Correlation

Measurement and identification of the nonlinear dynamics of a jointed structure using full-field data, Part I: Measurement of nonlinear dynamics

Infrastructure systems and key components such as bridges are usually considered for structural health monitoring especially with the increasing deterioration and rising need for repair or replacements. Moreover, in cases of extreme loading, e.g. earthquake, the dynamic response of bridges and their condition after the event need to be rapidly evaluated. This is to make decisions with respect to opening the bridge for traffic, for instance, if no immediate repair is needed. Using modern technologies and non-contact methods such as wireless sensing or vision- based tracking, e.g. target-tracking Digital Image Correlation (DIC), can provide to the means to monitor our infrastructure for cases of extreme events and advance the current state-of-practice in SHM. Vision-based monitoring systems still face several challenges such as the high cost of high-speed or monochrome cameras used for monitoring. Therefore, it is beneficial to assess the possibility of using commercial or lower-end cameras for SHM purpose. In this study, an application of DIC for monitoring the behavior and seismic response of a large-scale bridge model behavior was applied using commercial DSLR cameras and high-speed monochrome cameras. The bridge model was a two-span concrete bridge that was tested on multiple shake tables under white noise and incremental seismic excitations at the University of Nevada, Reno. The objectives of the tests were to: (1) compare the monitoring performance between commercial and highend monochrome cameras; (2) determine the modal properties of the bridge using system identification from DIC measurements and then compare it to the results from conventional contact sensors, e.g. accelerometers. The results show that feasible hardware such as commercial DSLR cameras can provide reasonable means to monitor and capture modal properties of bridges.

The structural responses and vibration properties such as frequencies and mode shapes are directly related to the structural mass and stiffness. Changing structural conditions will affect the structural responses and vibration properties. Structural conditions can thus be identified through measurements of structural vibration. However, certain uncertainties associated with structure models, changing ambient environmental conditions, changing loading conditions, equipment noises and various signal processing techniques used in extracting structural vibration properties, etc. is inevitable. The influences of these uncertainties on structural vibration properties might be more significant than that of the structural damage, therefore, cause false identification or result in the true structural damage not identifiable. This paper studies the applicability and reliability of a few popularly used modal identification methods including time-domain, frequency-domain and time-frequency domain methods for civil structural system identification. The results indicate that on average a 2% to 3% error tends to be yielded by using different signal processing techniques for vibration frequencies identification when the signal is not heavily noise contaminated, which should be taken into account when estimating the damage detection results. The applicability of the time-frequency domain methods to the identification of time-varying system either with sudden change or continuous variance is also discussed.

Damage detection and structural health monitoring have always been of great importance to civil engineers and researchers. Vibration-based damage detection has several advantages compared to traditional methods of non-destructive evaluation, such as ground penetrating radar (GPR) or ultrasonic testing, since they give a global response and are feasible for large structures. Damage detection requires a comparison between two systems states, the baseline or “healthy state”, i.e., the initial modal parameters, and the damaged state. In this study, system identification (SI) was carried out on a pedestrian bridge by measuring the dynamic response using six low-cost triaxial accelerometers. These low-cost accelerometers use a micro-electro-mechanical system (MEMS), which is cheaper compared to a piezoelectric sensor. The frequency domain decomposition algorithm, which is an output-only method of modal analysis, was used to obtain the modal properties, i.e., natural frequencies and mode shapes. Three mode shapes and frequencies were found out using system identification and were compared with the finite element model (FEM) of the bridge, developed using the commercial finite element software, Abaqus. A good comparison was found between the FEM and SI results. The frequency difference was nearly 10%, and the modal assurance criterion (MAC) of experimental and analytical mode shapes was greater than 0.80, which proved to be a good comparison despite the small number of accelerometers available and the simplifications and idealizations in FEM.

Summary Identifiability of parameters in structural system identification (SSI) is of primary importance in any SSI method. It depends on the number and the location of the measurements, which is linked with sensor configuration. In this paper, under the framework of SSI by observability method (OM), the number of necessary measurements to identify all parameters of structural system was clarified first. Then, an example was solved step by step to show the lacking constraints among unknowns in SSI by OM. In a frame example, it was found that no measurement set having as many measurements as the number of unknowns was able to identify all parameters. To further understand this phenomenon, the observability of a simply supported beam was analyzed in an exhaustive way using 252 possible measurement sets. Three quarters of these sets were not able to identify all the parameters. In order to solve this issue, for the very first time, SSI by constrained observability method (COM), which appends the nonlinear constraints to SSI by OM, was proposed. With SSI by COM applied, the observability of the structural parameters with respect to the 252 sets was greatly improved. Finally, the efficacy of SSI by COM was verified by a 13-story frame building.

Piezoelectric elements (PEMs) are used in a variety of applications. In this paper, we developed a full analytical model and a simple system identification (SI) method of a piezoelectric actuator, which includes piezostack elements and a three-stage amplification mechanism. The model was derived separately for each unit of the system. Next, the units were combined, while taking into account their coupling. The hysteresis phenomenon, which is significant in piezoelectric materials, is described extensively. The theoretical model was verified in a laboratory setup. This setup includes a piezoelectric actuator, measuring devices and an acquisition system. The measured results were compared to the theoretical results. Some of the most well-known forms of system identification are shown briefly, while a new and simple algorithm is described systematically and verified by the model. The main advantage of this work is to provide a solid background and domain knowledge of modelling and system identification methods for further investigations in the field of piezoelectric actuators. Due to their simplicity, both the model and the system identification method can be easily modified in order to be applied to other PEMs or other amplification mechanism methods. The main novelty of this work lies in applying a simple system identification algorithm while using the system-level approach for piezoelectric actuators. Lastly, this review work is concluded and some recommendations for researchers working in this area are presented.

Accurate and timely identification of modal parameters of long-span bridges is important for bridge health monitoring and wind tunnel tests. Wavelet analysis is one of the most advantageous methods for identification because of its good localization characteristics in both time and frequency domain. In recent years, the wavelet method has been applied more frequently in parameter identification of linear and nonlinear systems. In this article, based on wavelet ridges and wavelet skeleton, the improved modal parameter identification method was studied. To find the appropriate time-frequency resolution, an optimal wavelet basis design principle based on minimum Shannon entropy was proposed. Aiming at endpoint effect in wavelet transform, a prediction continuation method based on support vector machine (SVM) was proposed, which can effectively suppress the endpoint effect of the extended samples. In view of the fact that the ridges of metric matrices obtained by the traditional crazy climber algorithm cannot fully reflect the distribution of ridges of modulus value matrices of wavelet coefficients, an improved high-precision crazy climber algorithm was put forward to accurately identify the position of the ridge of wavelet coefficients. Finally, taking a long-span cable-stayed bridge and a long-span suspension bridge as the engineering background, improved continuous wavelet transform (CWT) was applied to modal parameter identification of bridge under ambient excitation. The modal parameters such as modal frequency, damping ratio, and mode shape were obtained. Compared with the calculation value of the numerical simulation of long-span cable-stayed bridge and wind tunnel test of long-span suspension bridge, the reliability of CWT for modal parameter identification of long-span bridges under ambient excitation was verified.

Mobile sensing has emerged as an economically viable alternative to spatially dense stationary sensor networks, leveraging crowdsourced data from today's widespread population of smartphones. Recently, field experiments have demonstrated that using asynchronous crowdsourced mobile sensing data, bridge modal frequencies, and absolute mode shapes (the absolute value of mode shapes, i.e., mode shapes without phase information) can be estimated. However, time‐synchronized data and improved system identification techniques are necessary to estimate frequencies, full mode shapes, and damping ratios within the same context. This paper presents a framework that uses only two time‐synchronous mobile sensors to estimate a spatially dense frequency response matrix. Subsequently, this matrix can be integrated into existing system identification methods and structural health monitoring platforms, including the natural excitation technique eigensystem realization algorithm and frequency domain decomposition. The methodology was tested numerically and using a lab‐scale experiment for long‐span bridges. In the lab‐scale experiment, synchronized smartphones atop carts traverse a model bridge. The resulting cross‐spectrum was analyzed with two system identification methods, and the efficacy of the proposed framework was demonstrated, yielding high accuracy (modal assurance criterion values above 0.94) for the first six modes, including both vertical and torsional. This novel framework combines the monitoring scalability of mobile sensing with user familiarity with traditional system identification techniques.

Modal analysis has developed into a major technology for the study of structural dynamics in the past several decades. Through it, complex structural dynamics phenomena can be represented in terms of structural invariants, i.e., the modal parameters: natural frequencies, damping ratios and mode shapes. Operational Modal Analysis (OMA) deals with the estimation of modal parameters on vibration data measured for operational conditions, when the excitation on the structure is not measured. In this work, OMA is performed on a wind turbine blade undergoing wind tunnel testing. These tests included different wind speeds, pitch angles and also different health conditions of the blade, where masses of different magnitude were fixed to the blade on different locations to emulate damage conditions. In order to monitor the modal parameters across multiple days of varied tests in the wind tunnel, the Polymax modal parameter estimator was implemented, coupled with an Automated Modal Analysis methodology. This methodology included an automatic modal parameter selection technique, using a Machine Learning (ML) clustering algorithm, coupled with a modal tracking procedure which applied statistical thresholds on the modal parameters’ values. The tracking procedure searches for modes similar to the ones calculated for healthy conditions. The results show how the modal parameters of the wind turbine blade vary with the different measured conditions in the wind tunnel. Moreover, a damage detection methodology is implemented to differentiate between the healthy and damaged conditions on the blade, by leveraging an anomaly detection algorithm using the Multivariate Gaussian Distribution (MGD). This algorithm takes as input the modal parameters calculated by the previous Automated Modal Analysis methodology and detects statistical deviations among them which could indicate the presence of damage. All steps of this work contribute to developing an automatic framework able to detect damages on a wind turbine blade, and therefore perform Structural Health Monitoring (SHM) for different operational conditions.

The Alfred Zampa Memorial Bridge (AZMB), a newly built long-span suspension bridge, is located 32km northeast of San Francisco on interstate Highway I-80. A set of dynamic field tests were conducted on the AZMB in November 2003, just before the bridge opening to traffic. These tests provided a unique opportunity to identify the modal properties of the bridge in its as-built condition with no previous traffic loads or seismic excitation. A benchmark study on modal identification of the AZMB is performed using three different state-of-the-art system identification algorithms based on ambient, as well as forced vibration measurements. These system identification methods consist of: (1) the multiple-reference natural excitation technique combined with the eigensystem realization algorithm; (2) the data-driven stochastic subspace identification method; and (3) the enhanced frequency domain decomposition method. Overall, the modal parameters identified using these system identification methods are found to be in very good agreement for each type of tests (ambient and forced vibration tests). For most vibration modes, the natural frequencies and mode shapes identified using the two different types of test data also match very well. However, the modal damping ratios identified from forced vibration test data are, in general, higher than those estimated from ambient vibration data. The identified natural frequencies and mode shapes are finally compared with their analytical counterparts from a three-dimensional finite-element model of the AZMB. The modal properties of the AZMB presented in this paper can be used as baseline in future health monitoring studies of this bridge.

A method of physical-parameter system identification is proposed here for three-dimensional (3D) building structures with in-plane rigid floors in which the stiffness and damping coefficients of each structural frame in the 3D building structure are identified from the measured floor horizontal accelerations. A batch processing least-squares estimation method for many discrete time-domain measured data is proposed for the direct identification of the stiffness and damping coefficients of each structural frame. While previous researches on the system identification of 3D building structures are limited to a class of structures with regular eccentricity, the present paper removes this limitation. Advantageous features of the proposed identification method are that it is unnecessary to specify the stiffness eccentricities (location of center of stiffness) before identification and the identification of all stiffness and damping parameters can be performed simultaneously. The reliability and accuracy of the proposed method are demonstrated by numerical simulations.

Sparse and low-rank methods in structural system identification and monitoring

Estimating the governing equation parameter values is essential for integrating experimental data with scientific theory to understand, validate, and predict the dynamics of complex systems. In this work, we propose a new method for structural system identification (SI), uncertainty quantification, and validation directly from data. Inspired by generative modeling frameworks, a neural network maps random noise to physically meaningful parameters. These parameters are then used in the known equation of motion to obtain fake accelerations, which are compared to real training data via a mean square error loss. To simultaneously validate the learned parameters, we use independent validation datasets. The generated accelerations from these datasets are evaluated by a discriminator network, which determines whether the output is real or fake, and guides the parameter-generator network. The uncertainty in each parameter is quantified by fitting a Gaussian distribution to each parameter, then computing the 95% confidence bounds. Analytical and real experiments show the parameter estimation accuracy and model validation for different nonlinear structural systems.

Structural system identification in time domain using measured acceleration

This paper presents the system identification technique by applying PZT actuators and PVDF sensors. An array of finite-length PVDF films is equally spaced and distributed over a cantilever beans acting as sensors. Two finite-length PZT patches are bonded symmetrically and excited 180°out-of-phase for pure bending excitation. The theoretical base of modal analysis for system identification of piezoceramic beams is presented to derive the frequency response functions (FRFs) in conventional modal format. The physical interpretation of P11 and PVDF mode shape functions are characterized respectively. The FRFs between the PZT actuators and PVDF sensors are experimentally measured. By the operation of a series of FRFs and the application of modal parameter extraction method, the modal parameters. including system natural frequencies, mode shapes and modal damping ratios, can be obtained. Both theoretical and experimental approaches agree very well. The system information can be used for control applications and also be applicable to structural failure diagnosis.