Structural System Identification Research Articles

Estimation of Soil–Structure Model Parameters for the Millikan Library Building Using a Sequential Bayesian Finite Element Model Updating Technique

We present a finite element model updating technique for soil–structure system identification of the Millikan Library building using the seismic data recorded during the 2002 Yorba Linda earthquake. A detailed finite element (FE) model of the Millikan Library building is developed in OpenSees and updated using a sequential Bayesian estimation approach for joint parameter and input identification. A two-step system identification approach is devised. First, the fixed-base structural model is updated to estimate the structural model parameters (including effective elastic modulus of structural components, distributed floor mass, and Rayleigh damping parameters) and some uncertain components of the foundation-level motion. Then, the identified structural model is used for soil–structure model updating wherein the Rayleigh damping parameters, the stiffness and viscosity of the soil subsystem (modeled using a substructure approach), and the foundation input motions (FIMs) are estimated. The identified model parameters are compared with state-of-practice recommendations. While a specific application is made for the Millikan Library, the present work offers a framework for integrating large-scale FE models with measurement data for model inversion. By utilizing this framework for different civil structures and earthquake records, key structural model parameters can be estimated from the real-world recorded data, which can subsequently be used for assessing and improving, as necessary, state-of-the-art seismic analysis and structural modeling techniques. This paper presents an effort towards using real-world measurements for large-scale FE model updating in the soil and structure, uniform soil time domain for joint parameter and input estimation, and thus paves the way for future applications in system identification, health monitoring, and diagnosis of civil structures.

Strategy for performance improvement in piezoelectric semi-active structural system identification by excluding switching failures using pseudo-state feedback

System identification in vibrating structures is useful for structural health monitoring. Onsite structural system identification must be achieved with low energy consumption. Accordingly, semi-active inputs should be considered to apply onsite system identification because they can be generated with low energy consumption. However, conventional identifications that use semi-active inputs could not continuously generate inputs suitable for system identification because of switching failure. Switching failure is caused by the mechanism of the semi-active input generation circuit. Due to switching failure, properties of semi-active inputs deviate from the property suitable for identification. Their results deviate from the results obtained using suitable inputs. Moreover, semi-active identification could not be used for structural health monitoring because they cannot determine the cause of significant variations in the identification results (either because of system identification faults from switching failure or because of structural damage). To solve these drawbacks of semi-active identification, we propose a new strategy to generate semi-active inputs that can realize ideal identification. The proposed strategy has two novelties compared to conventional semi-active identification methods: (1) The strategy prevents switching failures and continuously provides semi-active inputs suitable for identification. (2) The strategy is modeled as an optimization problem and provides appropriate circuit control to generate semi-active inputs suitable for identification by solving binary search. Numerical simulations and experiments confirm that the proposed strategy exhibits better identification performance than the conventional strategies. In addition, small variances are observed in the identification results in all time domains. The semi-active inputs generated by the proposed strategy can contribute to precise structural health monitoring using onsite structural identification because it provides accurate identification results with less variation and energy consumption.

Low-energy-consumption structural identification with switching piezoelectric semi-active input

Herein, we propose a structural system identification method that uses semi-active inputs generated from piezoelectric transducers. Previous onsite structure identification methods consumed significant amounts of energy to generate input signals and thus could not be actively implemented. The proposed method consumes less energy to generate input signals during identification. Two problems limit the use of semi-active inputs for identification purposes: (1) a control strategy to generate semi-active inputs suitable for identification does not exist, and (2) the polarity of the semi-active input cannot be freely controlled. To solve the first issue, we constructed a semi-active input generation strategy that matches the polarities of semi-active inputs with target signals appropriate for identification. To address the second problem, the mechanism by which polarity control is possible and impossible is clarified based on an analytical solution of a semi-active input generation circuit. A data calibration method focusing on sign similarity was proposed to improve the identification accuracy when polarity control cannot be implemented. The proposed semi-active identification method successfully identified the frequency response of a structure using 98% lesser energy than that used by conventional active methods. The proposed method was validated through simulations and experiments. The proposed method achieved accurate identification and can be used for onsite structural health monitoring.

Structural system identification and damage detection using adaptive hybrid Jaya and differential evolution algorithm with mutation pool strategy

Engineering applications of swarm intelligence optimization algorithms have been widely employed to identify structural systems and damages owing to their merits of simplicity, flexibility, robustness etc., while they often suffer from the defects of slow efficiency, premature convergence or even trapping into local optima in solving the inverse problem of nonlinear optimization-based parameter identification with partial noise-contaminated measurements. To deal with this issue, an adaptive hybrid Jaya and differential evolution (AHJDE) algorithm is proposed based on Jaya algorithm and differential evolution (DE) by effectively combining the advantages of both algorithms. In the proposed AHJDE, four improvements including adaptive mutation strategy, dynamic mutation and crossover operators, sampling-based resizing search space and linear resizing population size are integrated. The effectiveness of the proposed method is verified using a numerical example of 20-DOF linear system by comparing its performance with particle swarm optimization, modified artificial bee colony algorithm, clustering tree seeds algorithm, improved butterfly optimization algorithm etc. considering known mass case and unknown mass case. In addition, numerical studies on a nonlinear single degree-of-freedom system with classical Bouc-Wen hysteretic model and improved Bouc-Wen model are implemented to investigate the applicability in the field of nonlinear system identification. Finally, a series of experimental tests on a five-story steel frame structure are conducted in the laboratory to further validate the performance of the proposed approach in damage identification. Identification results demonstrate the proposed AHJDE can accurately and effectively identify the unknown system parameters and damages with limited sensors and noise-polluted responses.

Self-sensing method for semi-active structural identification by removing piecewise bias from piezoelectric voltage

Structural system identification (SSI) that uses many actuators and sensors will be more accessible as a sensing technology if the number of these devices decreases. Recently, a semi-active SSI using a piezoelectric transducer and a unique semi-active input generation circuit was proposed. The semi-active SSI outperforms conventional SSIs with low energy consumption. If the semi-active input and its vibration response are estimated from the voltage generated by a piezoelectric transducer, some sensors will become redundant. Conventional self-sensing methods estimate structural vibrations without using vibration sensors. The semi-active SSI in combination with the self-sensing method will be more accessible than current technologies from the perspectives of a lower energy consumption and fewer number of devices. However, the following two problems exist: (1) A semi-active input generation circuit cannot introduce conventional hardware-based self-sensing methods with additional electric circuits because the electrical components in the additional circuits degrade the performance of the piezoelectric transducer. (2) Software-based self-sensing methods, such as the Kalman filter, cannot be used in system identification scenarios because the electromechanical parameters and models are unknown. To overcome these drawbacks, a novel software-based self-sensing method that does not require electromechanical models is proposed in this paper, and the effectiveness of the proposed method is thoroughly investigated using both simulations and experiments. The identification performance of the proposed method using the estimated input and output is the same as that using directly measured data. The proposed method can especially contribute to the predictive maintenance of structures in isolated environments. • A self-sensing method for piezoelectric semi-active control is proposed. • The elongation and inflow charge of the transducer is estimated from the piezoelectric voltage. • The proposed self-sensing method does not use additional circuits. • The structural system identification is implemented using estimated data.

A generalized extended Kalman particle filter with unknown input for nonlinear system‐input identification under non‐Gaussian measurement noises

It is necessary to investigate the identification of structural systems and unknown inputs under non-Gaussian measurement noises. In recent years, a few scholars have proposed methods of particle filter (PF) with unknown input for such task. However, these PF with unknown input require that unknown inputs appear in structural measurement equations. Such requirement may not always met, which restrict their practical application. To overcome this limitation, a generalized extended Kalman particle filter with unknown input (GEKPF-UI) is proposed for the simultaneous identification of structural systems and unknown inputs under non-Gaussian measurement noises. The proposed method is more general than the existing methods of PF with unknown input as it is applicable whether measurement equations contain or do not contain unknown inputs. It is proposed to establish the importance density function of PF by the generalized extended Kalman filter with unknown input (GEKF-UI) recently developed by the authors, in which GEKF-UI is utilized to generate particles and allow particles to carry the latest observational information. The effectiveness of the proposed method is verified through two numerical identification examples of a nonlinear hysteretic structure under two types of unknown inputs, including unknown external excitation and unknown seismic inputs, respectively.

Influence of Hankel matrix dimension on system identification of structures using stochastic subspace algorithms

In stochastic subspace methods, the modal analysis results are highly dependent on the dimensions of the Hankel matrix. Increasing the dimensions of the Hankel matrix (especially the number of rows) improves the estimation of the modal features by decreasing the impact of noise effects. Due to processing time and memory use, it is impossible to adjust the size of the Hankel matrix to the maximum compatible value. Therefore, this study uses a sensitivity analysis of the dimensions of the Hankel matrix to pick models with the slightest estimate error in the data-driven (DD-SSI) method. First, using the condition number criteria, the desirable models in which the effects of system errors are not predominating are determined. Second, the modal properties of desired models are validated by clustering the damping ratios and modal frequencies using the Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm and assessing the complexity of shape modes with the Modal Complexity Factor (MCF). Finally, the optimum models are identified by analyzing the estimated error of modal properties (particularly damping ratio) and the coefficient of variation (CV) of damping of validated clusters. The proposed method was investigated for a two-dimensional simulated concrete building frame, a three-dimensional experimental model, and the Namin city Overpass Bridge ambient vibration tests. Sensitivity analysis was performed for canonical correlation analysis (SSI-CCA) and canonical variate analysis (SSI-CVA) methods. Analyses of computational and laboratory models revealed that the likelihood of non-physical modes arising outside the system's maximum order is relatively high. Also, the MCF is valuable for identifying computational and noise modes. These criteria accurately detected the flexural mode of the foundation set, which was clustered as the stable mode of the slab deck in the practical bridge. Furthermore, the CV analysis revealed that the desired dimension obtained from the condition number could be a reasonable estimate of the optimal system dimension.

Accelerating computations in two-stage Bayesian system identification with Fisher information matrix and eigenvalue sensitivity

Structural system identification aims at identifying the parameters of a theoretical (e.g., finite element) model using measured data of a constructed structure. As a means of extracting relevant information from noisy vibration data, one common strategy is to adopt a ‘two-stage’ approach, where natural frequencies and mode shapes are first estimated from Stage I (modal identification), and then used for further estimating the structural model parameters (e.g., stiffness, mass) in Stage II. In a Bayesian statistical context with sufficient data so that model parameters can be identified uniquely, the identification result is characterized by the ‘most probable value’ (MPV) that gives the best estimate, and a covariance matrix that quantifies the remaining uncertainty. Computationally, determining the MPV involves solving an optimization problem with a measure-of-fit function; the covariance matrix involves taking the Hessian of the function. Exploiting the mathematical structure of the measure-of-fit function in the two-stage problem, this work proposes a Fisher scoring method for determining the MPV, where the Hessian matrix in a Newton’s iteration is replaced by the Fisher information matrix to eliminate repeated computations of second order derivatives and to improve convergence robustness. Advanced techniques of eigenvalue sensitivity are applied so that the gradient and Hessian involved in MPV and covariance matrix computations can be obtained accurately and efficiently by solving full-rank matrix equations for the subject modes only. The proposed methodology is investigated with synthetic and laboratory experimental data. Performance in terms of convergence robustness and efficiency is compared with existing methods, including simplex search and Newton’s method.

Comparative Analysis between Genetic Algorithm and Simulated Annealing-Based Frameworks for Optimal Sensor Placement and Structural Health Monitoring Purposes

The arbitrary placement of sensors in concrete structures measures a considerable amount of unnecessary data. Optimal sensor placement methods are used to provide informative data with the least cost and maximum efficiency. In this study, a robust optimal sensor placement framework that combines an optimization-based algorithm, the simulated annealing (SA) algorithm, and the ensemble Kalman filter (EnKF) are presented for structural health monitoring and system identification. The SA algorithm randomly generates an initial population of sensor locations, while the framework undergoes a minimization process. The objective function used is the difference between the actual measured data and their corresponding EnKF predicted values. A comparative analysis between the genetic algorithm–ensemble Kalman filter (GA-EnKF) and the simulated annealing–ensemble Kalman filter (SA-EnKF) approaches is presented. The performance and computational burden of both algorithms, which converge to the best sensor locations for damage detection purposes, are tested on a 10-story building subjected to a seismic excitation. The results are compared to the optimal sensor locations of the brute-force search methodology. The GA-EnKF outperforms the SA-EnKF in terms of accuracy in converging to the optimal results, yet the computational cost of the SA-EnKF is considerably lower.

Symbolic Deep Learning for Structural System Identification

Closed-form model expression is commonly required for parametric data assimilation (e.g., model updating, damage quantification, and so on). However, epistemic bias due to fixing the model class is a challenging issue for structural identification. Furthermore, it is sometimes hard to derive explicit expressions for structural mechanisms such as damping and nonlinear restoring forces. Although existing model class selection methods are beneficial to reduce the model uncertainty, the primary issue lies in their limitation to a small number of predefined model choices. We propose a symbolic deep learning framework that alleviates the constraint of fixed model classes and lets the data more flexibly determine the model type and discover the symbolic invariance of the structural system. A design principle for symbolic neural networks has been developed to leverage domain knowledge and translate data to flexibly symbolic equations of motion with a good predictive capacity for new data. A two-stage model selection strategy is proposed to conduct adaptive pruning on network and equation levels by balancing the model sparsity and the goodness of fit. The proposed method’s expressive strengths and weaknesses have been analyzed in several numerical case studies, including systems with nonlinear damping, restoring force, and chaotic behavior. Results from an experimental case study revealed the potential of the proposed method for flexibly interpreting hidden mechanisms for real-world applications. Finally, we discuss necessary improvements to transfer this computational method for practical applications.

Sensitivity-based constitutive parameter identification of nonlinear structures with unknown input earthquake excitation

System identification methods are widely developed in structural health monitoring, in which the force or structural damage is identified from a linearised structure. However, the real-world civil infrastructures are generically nonlinear and subject to extreme loading conditions, such as earthquake. This study proposes a system identification method for material constitutive nonlinear structures subject to earthquake, where sensitivity analysis is developed to accelerate the complicated nonlinear system identification. First, the nonlinear structural model based on the material constitutional law is constructed by fiber beam-column elements. The earthquake input is parameterized by Chebyshev orthogonal polynomials in a recognizable form. Afterwards, the dynamic response sensitivities with respect to the constitutive parameters and the orthogonal factors of earthquake excitation are derived to accelerate the system identification from a complex material constitutive model. Finally, the constitutive parameters and the earthquake input are simultaneously identified by an optimization process. Numerical structures subjected to earthquake excitation are employed to verify the accuracy of the proposed method, by which the influence of parameter's order, input intensity and measurement noise is discussed. The proposed method develops Chebyshev parameterization to recognize the earthquake input and sensitivity analysis to accelerate the optimization, which leads to an accurate nonlinear system identification of civil structures.

Probabilistic Identification of Multi-DOF Structures Subjected to Ground Motion Using Manifold-Constrained Gaussian Processes

Bayesian uncertainty quantification has a pivotal role in structural identification, yet the posterior distribution estimation of unknown parameters and system responses is still a challenging task. This study explores a novel method, named manifold-constrained Gaussian processes (GPs), for the probabilistic identification of multi-DOF structural dynamical systems, taking shear-type frames subjected to ground motion as a demonstrative paradigm. The key idea of the method is to restrict the GPs (priorly defined over system responses) on a manifold that satisfies the equation of motion of the structural system. In contrast to widely used Bayesian probabilistic model updating methods, the manifold-constrained GPs avoid the numerical integration when formulating the joint probability density function of unknown parameters and system responses, hence achieving an accurate and computationally efficient inference for the posterior distributions. An eight-storey shear-type frame is analyzed as a case study to demonstrate the effectiveness of the manifold-constrained GPs. The results indicate the posterior distributions of system responses, and unknown parameters can be successfully identified, and reliable probabilistic model updating can be achieved.

Structural system identification via synchronization technique and fuzzy logic

In this paper, a new approach is proposed for parameter identification in seismically excited structures based on synchronization method and fuzzy logic. The main contribution of this paper is providing a general solution for the estimation of the identifier coefficients using fuzzy logic. These identifier coefficients adjust the convergence rate and accuracy of the identification. The fuzzy controller uses triangular membership functions as input and output. The input parameters to the fuzzy controller are functions of displacement and velocity of the top story subjected to earthquake excitation. By using appropriate fuzzy rules the results are obtained for identifier coefficients. Additionally, a novel and simple formulation to identify structural unknown parameters based on synchronization is presented. The performance of the proposed approach is investigated using different shear frames under various excitations. The sensitivity of the proposed method to different noise levels and modeling uncertainties is analyzed. Numerical examples indicate that the presented method can identify the unknown parameters of the structure with high accuracy and reasonable computational time.

Research for Pedestrian Steel Bridge Design of Neural Network in Structural Model Updating

The application of the neural network method in health monitoring and structural system identification has received extensive attention. A reasonable neural network structure is very important for its performance. This paper takes the pedestrian bridge of the Xingfu intersection in Urumqi, China, as the research object and uses MIDAS/Civil to establish a finite element analysis model. Taking the natural vibration frequency obtained from the dynamic test of the actual bridge as the target, two kinds of neural networks are used to predict the structural material parameters. An appropriate bridge model correction method is selected by comparing the prediction results of the BP neural network and the GRNN. The test results show that the pedestrian bridge model based on MIDAS/Civil has a high accuracy, but it still does not meet the actual needs. The modified model based on the BP neural network is close to the actual measured results, and a more accurate finite element analysis model can be established by this method, which makes the modified model closer to the real stress state of the structure.

Low-Cost Sensors Accuracy Study and Enhancement Strategy

Today, low-cost sensors in various civil engineering sectors are gaining the attention of researchers due to their reduced production cost and their applicability to multiple nodes. Low-cost sensors also have the advantage of easily connecting to low-cost microcontrollers such as Arduino. A low-cost, reliable acquisition system based on Arduino technology can further reduce the price of data acquisition and monitoring, which can make long-term monitoring possible. This paper introduces a wireless Internet-based low-cost data acquisition system consisting of Raspberry Pi and several Arduinos as signal conditioners. This study investigates the beneficial impact of similar sensor combinations, aiming to improve the overall accuracy of several sensors with an unknown accuracy range. The paper then describes an experiment that gives valuable information about the standard deviation, distribution functions, and error level of various individual low-cost sensors under different environmental circumstances. Unfortunately, these data are usually missing and sometimes assumed in numerical studies targeting the development of structural system identification methods. A measuring device consisting of a total of 75 contactless ranging sensors connected to two microcontrollers (Arduinos) was designed to study the similar sensor combination theory and present the standard deviation and distribution functions. The 75 sensors include: 25 units of HC-SR04 (analog), 25 units of VL53L0X, and 25 units of VL53L1X (digital).

A Practical Bayesian Framework for Structural Model Updating and Prediction

Due to the influence of various uncertain factors, there will inevitably be certain errors between the prediction of finite-element (FE) model and observed data for a target structure. It is thus necessary to calibrate the initial FE model using the measured data to ensure the accuracy of the numerical model for the purpose of structural system identification and health monitoring. Although structural FE model updating methods have been extensively studied in the past few decades, the research based on deterministic methods in the current literature still occupies a large proportion, which cannot account for the uncertain effects during the model updating. The noise robustness of both the updating procedure and the generalization capability of the updated model are expected to be poor. The model updating based on the Bayesian theorem can quantify the uncertainty of model identification results, but it is computationally expensive for the Bayesian inference of regularization hyperparameters since the Hessian matrix is generally required to be evaluated repeatedly especially for a huge amount of uncertain model parameters. Also, effective prediction based on the refined FE model is still lacking in the literature, which is essential for judging and evaluating the quality of the updated model. This paper proposes a practical framework for structural FE model updating and prediction based on the Bayesian regularization with incomplete modal data. The structural model parameters and regularization hyperparameters are identified alternatively in an adaptive manner, and the Gauss-Newton method is used to approximate the true Hessian within the framework of the nonlinear least-squares algorithm. This is expected to improve the efficiency and robustness of model updating and prediction for handling large-scale FE models possessing a large number of uncertain model parameters. The proposed methodology is validated through the model updating and prediction conducted on a real-life pedestrian bridge based on field-testing data.

Damage identification of structural systems by modal strain energy and an optimization-based iterative regularization method

Damage identification of structural systems by modal strain energy and an optimization-based iterative regularization method

Optimal Sensor Placement in Reduced-Order Models Using Modal Constraint Conditions.

Sensor measurements of civil structures provide basic information on their performance. However, it is impossible to install sensors at every location owing to the limited number of sensors available. Therefore, in this study, we propose an optimal sensor placement (OSP) algorithm while reducing the system order by using the constraint condition between the master and slave modes from the target modes. The existing OSP methods are modified in this study, and an OSP approach using a constrained dynamic equation is presented. The validity and comparison of the proposed methods are illustrated by utilizing a numerical example that predicts the OSPs of the truss structure. It is observed that the proposed methods lead to different sensor layouts depending on the algorithm criteria. Thus, it can be concluded that the OSP algorithm meets the measurement requirements for various methods, such as structural damage detection, system identification, and vibration control.

The Behaviour of Wave Propagation for Structural System Identification: A Comparative Study

The way a wave behaves, while propagating across a medium, varies with the wave type and the medium. So, knowledge of the behaviour of a wave in a system with a different form of damage, and behaviour of different types of waves in a particular system is an essential prerequisite for almost all activities in structural system identification and mainly for damage detection and localization of damage. This paper presents a comparative study of various wave propagations, that has been done by researchers in various structural systems. Further, a numerical model of an isotropic plate using finite element is created both with and without damage. The behaviour of waves has been studied. Finally, the comparative result is shown. This paper offers a new perspective for ongoing research by providing the most recent developments, difficulties, and prospects of wave propagation behaviours for damage detection and localization in the commonly used structural systems and structural elements. While propagating through different structural systems and components, the most used waves, which are (a) Shear wave, (b) Rayleigh wave, (c) Ultrasonic wave and (d) Lamb wave, have been thoroughly investigated. Along with several difficult problems for future growth, the summarized observations are provided.

Gradient Methods for Fixed Structure Controller Synthesis and System Identification of Decomposable Systems

In this letter we are considering the problem of fixed structure controller synthesis and system identification for large scale systems. The systems considered are referred to as decomposable systems and can be seen as resulting from the interconnection of a large number of identical subsystems. Combining recent results from nonsmooth controller synthesis with the special structure of decomposable systems, we show that the computational complexity of the controller synthesis and system identification procedure scale linearly with the size of the system. Employing results from robust control, the computational complexity of the controller synthesis can be reduced further, however, at the cost of additional conservatism. Using numerical examples we demonstrate that the proposed method can reduce the conservatism compared to existing LMI methods for full order decomposable controllers.