Structural System Identification Research Articles

Inverse WKB recursive solution method for dynamic load identification of linear time-varying structural systems

Inverse WKB recursive solution method for dynamic load identification of linear time-varying structural systems

An adaptive generalized extended Kalman filter for real-time identification of structural systems, state and input based on sparse measurement

An adaptive generalized extended Kalman filter for real-time identification of structural systems, state and input based on sparse measurement

Structural system modelling from base excitation measurements using swarm intelligence

Structural system identification is a fundamental task in mechanical engineering since it enables the characterization of the dynamic behaviour of structures from experimental data. The identification of the mass, stiffness, and damping matrices of a structure is essential for the design, analysis, and control of mechanical systems. This paper proposes a novel method for identifying the spatial properties of a structure using base excitation measurements and swarm intelligence. Maintaining relevant physical properties is ensured by placing algebraic constraints on factors of the mass and stiffness matrices. This formulation circumvents the complexities of additional constraints in metaheuristic techniques. Consistency of the eigenvalues with respect to the test data is assured through an integrated refinement process during the stiffness matrix estimation. A healing process enables the rescaling of the mass matrix, guaranteeing an accurate representation of the structure’s total mass. The search space definition only requires prior knowledge of the total mass of the structure and an estimate of anticipated maximum natural frequencies within the targeted frequency range. The efficacy of this method is tested on a numerical example.

An unscented Kalman filter under unknown input without direct feedthrough for joint input and system identification of structural systems

Given the difficulty of accurately measuring external inputs acting on structures, the research on joint input-system identification has gained significant attention in recent years. Among them, several unscented Kalman filters under unknown input (UKF-UI) based methods have been proposed for joint input and system identification. However, the existing UKF-UI methods require unknown inputs to be presented in the observation equations, which is not always available in practical engineering. To solve this problem, an unscented Kalman filter under unknown input without direct feedthrough (UKF-UI-WDF) is proposed in this paper for real-time joint input and system identification of structural systems without direct feedthrough using limited response measurements. The proposed UKF-UI-WDF is derived for recursive identification of the structural states, parameters, and unknown inputs by integrating unknown input estimation into the conventional UKF framework. In each identification step, the unknown inputs are first identified by minimizing posterior residuals of measurements, and then the structural states and parameters are identified by a traditional unscented Kalman filtering using the identified unknown inputs. According to whether the uncertainty of the identified unknown inputs can be quantitatively described or not, two implementation algorithms are provided in this paper. In algorithm 1, only the mean values of unknown inputs can be identified. In algorithm 2, the unknown inputs are identified as a set of sigma points, so not only the mean values but also the variance of the unknown inputs can be estimated. The effectiveness of the proposed method is examined by the joint input and system identification of various case studies of linear and nonlinear hysteretic shear structures subjected to unknown external or base excitations, respectively. The results show that the proposed UKF-UI-WDF method can effectively perform real-time joint input-system identification of structural systems without direct feedthrough using limited response measurements.

Physics-guided generative adversarial network for probabilistic structural system identification

Structural system identification (ID) is an important tool for many structural and infrastructure applications, such as structural health monitoring and structural model updating. A novel physics-guided generative adversarial network (PG-GAN) is proposed in this study for probabilistic structural parameter ID. The PG-GAN leverages the powerful distribution learning ability of GANs while also enabling physical awareness by incorporating additional generators for physical parameters and developing a physics-based loss function that links the data generator with the parameter generators through existing physics knowledge to guide the training of generative models. Two experiments are performed to validate the effectiveness of the PG-GAN for structural parameter ID and demonstrate its application in structural damage detection. The PG-GAN is shown to successfully capture the uncertainty inherent in structural parameter estimation and accurately locate and quantify structural damages in terms of probabilistic distributions of the damage extent. The main contributions of this study are threefold: (1) compared with traditional methods for structural parameter ID, the proposed PG-GAN provides an intelligent framework for probabilistic identification of structural parameters without the need for any assumption on the data distribution and does not require an initial guess of parameters; (2) unlike traditional data-driven GANs, the proposed PG-GAN provides a linkage between GAN and physics knowledge to enables physical awareness in generative model training; and (3) the proposed PG-GAN can serve as an intelligent diagnostic system to better inform the decision-making on structural health management as it can quantify the uncertainty in the structural damage extent.

Observing Material Properties in Composite Structures from Actual Rotations

The shear deflection effects are traditionally neglected in most structural system identification methods. Unfortunately, this assumption might lead to significant errors in some structures, like deep beams. Although some inverse analysis methods based on the stiffness matrix method, including shear deformation effects, have been presented in the literature, none of these methods are able to deal with actual rotations in their formulations. Recently, the observability techniques, one of the first methods for the inverse analysis of structures, included the shear effects into the system of equations. In this approach, the effects of the shear rotation are neglected. When actual rotations on-site are used to estimate the mechanical properties in the inverse analysis, it can result in serious errors in the observed properties. This characteristic might be especially problematic in structures such as deep beams where only rotations can be measured. To solve this problem and increase the observability techniques’ applicability, this paper proposes a new approach to include the shear rotations into the inverse analysis by observability techniques. This modification is based on the introduction of a new iterative process. To illustrate the applicability and potential of the proposed method, the inverse analysis of several examples of growing complexity is presented.

Physics-Informed Neural Networks for System Identification of Structural Systems with a Multiphysics Damping Model

Physics-Informed Neural Networks for System Identification of Structural Systems with a Multiphysics Damping Model

A Markov chain Monte Carlo-based Bayesian framework for system identification and uncertainty estimation of full-scale structures

Identifying modal parameters and updating finite element models (FEMs) of real structures through ambient tests is essential in Structural Health Monitoring (SHM). However, efficiently solving the high-dimensional identification problem for full-scale structures and rigorously quantifying the uncertainties remain challenging. To address these two difficulties, a novel Bayesian framework based on Markov chain Monte Carlo (MCMC) is developed. The basic idea is to identify the high-dimensional posterior probability density functions (PDFs) in both modal analysis and model updating through constructing Markov chains by sampling in the important region of the parameter spaces. The sampling is done by Bayes-Mode-ID and the adaptive sequential Monte Carlo (ASMC) for modal analysis and model updating, respectively. A new formulation is developed to link the results from modal analysis, model updating and model class selection using the Markov chain samples. Thus, the propagation of the posterior uncertainties from the identified modal parameters to the updated model parameters can be quantified. Furthermore, the original ASMC method, which was developed by the authors, is extended for model class selection based on the set of generated Markov chain samples. To demonstrate the effectiveness of the proposed framework, multi-setup ambient vibration tests on a busy footbridge were conducted for measuring the accelerations at some pre-selected measurement points. The most probable modal and model parameters of the footbridge were identified together with the associated uncertainties by the proposed framework.

Publisher Correction: A hybrid Modified Artificial Bee Colony and extended Kalman filter algorithm for structural system identification

Publisher Correction: A hybrid Modified Artificial Bee Colony and extended Kalman filter algorithm for structural system identification

A hybrid Modified Artificial Bee Colony and extended Kalman filter algorithm for structural system identification

A hybrid Modified Artificial Bee Colony and extended Kalman filter algorithm for structural system identification

Functionally Graded Beams as Surrogate Structural Models: Shear Beam with Exponentially Graded Rigidity

An exact analytical solution, in terms of Bessel functions, was derived for the dynamic response of a shear beam with uniform cross section and mass density, and shear modulus that varies exponentially in the axial direction. The solution was generalized to a chain of such beam elements. The model may be appropriate for frame structures, which deform predominantly in shear, with gradually increasing rigidity toward the base. The results of a parametric study are presented for the frequencies of vibration and their ratios, mode shapes, transfer functions, and impulse response functions. The gradation affected the ratios between the frequencies of the higher modes of vibration and that of the fundamental mode, which were smaller than the corresponding ratios for a homogeneous shear beam and were progressively smaller for larger gradation constants. The mode shapes and the ratios of the amplitudes of the pulses in impulse response functions had amplitude amplification toward the top, which was larger for larger gradation constants, and suggests trapping of energy in the upper part of the structure. This effect may be responsible for observed damages and failure of structures in parts far from the base. The gradation also affected the symmetry and shape of the pulses in impulse response functions. The results of the parametric study may be useful for interpretation of the seismic response of full-scale structures. The model is intended for use as a simple surrogate model in structural system identification and health monitoring of frame structures.

Bayesian model selection considering model complexity using stochastic filtering

AbstractThis paper proposes a Bayesian model selection framework to determine optimal, parsimonious models for given building structures under ground motion excitation using stochastic filtering. Structural system identification at a regional scale after an earthquake is nominally a monumental task due to its inherently high computational cost. This challenge is currently addressed in the literature by using simplified structural models that bear analytical solutions, such as Timoshenko or shear beams, and shear building models. However, a low computational effort usually leads to an increased prediction error and consequently, a higher model uncertainty. This poses the dilemma of prediction accuracy versus model complexity when selecting a model class to represent a building structure. The proposed framework selects the model class that strikes the best balance between the two. To this end, the notion of cumulative evidence is introduced here as the integral of local evidence over the ground motion duration, which is then formulated as the difference between the cumulative likelihood of the observed measurements and the cumulative penalty. The likelihood measure promotes models whose predictions better match the observations. This is counteracted by the penalty, which is devised as an “Ockham factor,” and penalizes models with higher information gains due to their higher complexities, for example, a larger number of parameters. The proposed approach also yields the best tuning parameters of the stochastic filter for each model class and the best initial values of the identification parameters. The proposed framework is verified using a synthetic example, and validated using recorded data from the Millikan Library building in California and the ANX building in Japan.

A Smoothing EKF-UI-WDF Method for Simultaneous Identification of Structural Systems and Unknown Seismic Inputs without Direct Feedthrough

It is of great significance to identify structural state-parameters and the unknown seismic inputs using partial measurements of structural acceleration responses for the rapid evaluation of structures after unknown seismic excitations. However, unknown seismic inputs do not directly appear in the observation equations of measured absolute floor accelerations of building structures, i.e., there is no direct feedthrough of unknown seismic inputs in the observation equations. Current methods for the identification of joint structural systems and unknown inputs are either inapplicable or greatly influenced by measurement noises. In this paper, a method so-called smoothing extended Kalman filter with unknown input without direct feedthrough (smoothing EKF-UI-WDF) is proposed. The identification algorithm is derived in the framework of minimum-variance unbiased estimation (MVUE), and the smoothing technique is adopted to introduce subsequent observation steps in the current identification step. Then, structural states, parameters, and unknown seismic excitations without direct feedthrough are simultaneously identified recursively with only a few steps delay, and the identification results are tolerant to measurement noises. The proposed method is verified by a numerical simulation model and a practical engineering case study. Both identification results validate the effectiveness of the proposed method for the simultaneous identification of structural systems and seismic inputs without direct feedthrough.

A Baseline Free Method for Multiple Damage Identification and Localization using the Roving Mode Shape Response

The identification of structural systems with unknown vibration signature response is still a challenging issue which has been addressed by many reviewers. The current sensor technology states that the sensor position should be very close to the damaged element in order to identify and localize the damage. The primary goal of this research is to present a baseline-free method using the roving mode shape response based, multiple damage localization in a cantilever beam. Consequently, the damage location indicator is based on the roving mode shape approach (DLRA). The theoretical development is carried out on a cantilever beam, a finite element model. The different cases for multiple damages i.e. 2 elements damage, 3 elements damage and 5 elements to be damage, at a time, have been modelled on the structural member. The system response, for the healthy and damaged structural systems, has been determined using the roving mode shape approach. Further, the algorithm has been developed for multiple damage identification and localization using MATLAB software. The combined mass and stiffness damage, as well as only the mass change damage, both cases were considered. From the results, it was found that the proposed method can reliably identify the damage and its position. The method will also be helpful while keeping the sensor’s position very close to the damage. The novelty of this method is that it uses the response which is basically a field output and no prior assumptions have been made at the damaged element's location.

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.