Structural System Identification Research Articles

Sparse component analysis with optimized clustering for underdetermined blind modal identification

Modal identification performs one of the most important roles in structural dynamics analysis and structural health monitoring, especially when the input excitations are not measurable. Most of the traditional blind source separation approaches can only handle determined or overdetermined blind modal identification, where the number of observed sensors is equal to or greater than the number of active modes. When the number of observed sensors is less than the number of active modes, new methods to perform underdetermined blind modal identification should be considered. To tackle this issue, a novel operational modal identification method based on an enhanced sparse component analysis with optimized clustering is proposed. Firstly, a robust K-means clustering with differential evolution algorithm is put forward to estimate the mode shape matrix utilizing the sparse property of observed mixtures. Secondly, the modal responses are recovered by the least squares method from the incomplete knowledge of the mode shape matrix and the system outputs. Subsequently, the modal responses are transformed into a time domain through time-frequency transformation, where the modal parameters are extracted. Finally, numerical simulation and experimental verification demonstrate that in both the determined and underdetermined case, the proposed method can perform accurate and robust parameter identification of structural systems.

An efficient algorithm for architecture design of Bayesian neural network in structural model updating

AbstractThere has been growing interest in applying the artificial neural network (ANN) approach in structural system identification and health monitoring. The learning process of neural network can be more robust when presented in the Bayesian framework, and rational architecture of the Bayesian neural network is critical to its performance. Apart from number of hidden neurons, the specific forms of the transfer functions in both hidden and output layers are also crucially important. To the best of our knowledge, however, the simultaneous design of proper number of hidden neurons, and specific forms of hidden‐ and output‐layer transfer functions has not yet been reported in terms of the Bayesian neural network. It is even more challenging when the transfer functions of both layers are parameterized instead of using fixed shape forms. This paper proposes a tailor‐made algorithm for efficiently designing the appropriate architecture of Bayesian neural network with simultaneously optimized hidden neuron number and custom transfer functions in both hidden and output layers. To cooperate with the proposed algorithm, both the Jacobian of the network function and Hessian of the negative logarithm of weight posterior are derived analytically by matrix calculus. This is much more accurate and efficient than the finite difference approximation, and also vital for properly designing the Bayesian neural network architecture as well as further quantifying the confidence interval of network prediction. The validity and efficiency of the proposed methodology is verified through probabilistic finite element (FE) model updating of a pedestrian bridge by using the field measurement data.

Structural system identification by measurement error‐minimizing observability method

This is the accepted version of the following article: [Lei, J, Lozano‐Galant, JA, Xu, D, Turmo, J. Structural system identification by measurement error‐minimizing observability method. Struct Control Health Monit. 2019; 26:e2425. https://doi.org/10.1002/stc.2425], which has been published in final form at https://doi.org/10.1002/stc.2425

Experimental identification of distributed nonlinearities in the modal domain

This paper deals with the nonlinear system identification of structures exhibiting distributed nonlinearities, which has become of great interest recently, due to the continuous interest to improve the performance of structures. This brings the need for designing lighter and more flexible structural elements, which are usually characterized by moderate and large deformation, resulting in a distributed nonlinear behavior. In this framework, system identification remains a particularly challenging problem, especially when experimental measurements are considered. This work proposes a method to perform such a task, based on a convenient model order reduction of the considered structure, followed by a nonlinear system identification algorithm. The methodology is validated on a very thin beam undergoing large-amplitude oscillations, firstly using numerical data and then considering an experimental test bench. On the experimental side, the nonlinearity is first characterized using just the measured data, in order to acquire information that would help the identification process. Eventually, nonlinear system identification is performed in the reduced-order domain. An ad-hoc version of the nonlinear subspace identification (NSI) algorithm is used, but the presented methodology can also be applied with other nonlinear identification tools. Results confirm the goodness of the identification strategy in obtaining a reliable model which takes into account the distributed nonlinear behavior.

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

This paper characterizes the extensive research activities conducted in the Earthquake Engineering Laboratory of University of Nevada, Reno, in the field of dynamic monitoring and system identification of three 1/3-scale two-span bridges. The first part of the study briefly presents the verification of target-tracking Digital Image Correlation (DIC) results as compared to conventional sensors, e.g. string potentiometers and triaxial accelerometers from one of the three bridge tests. Structural system identification is presented in the second part for the other two bridges with focus on determining structural model parameters based on the DIC measured response data. All bridges were tested under bidirectional earthquake loading using the multiple shake table array. However, the system identification used data collected from the white noise runs before and after the seismic tests. A quasi-linear response of the system was assumed because of the low intensity white noise base excitation, and the modal parameters were estimated accordingly. Using the structural vibration data recorded by target-tracking DIC at various locations on the bridges, five system identification methods were applied to analyze the modal parameters of the tested bridges. The results were used to estimate the frequency, damping ratio, and mode shapes, of the bridges in two states. The initial state is before seismic testing and the end state is the damaged state after the completion of the seismic tests. The results show that the applied methods provide a reasonable estimate of the natural frequency and damping ratio of the bridge systems in the original and damaged states.

Response sensitivity for geometrically nonlinear displacement-based beam-column elements

Accurate and efficient response gradients are required in structural reliability, optimization, and system identification applications where the structural system is expected to yield under significant deformations. The direct differentiation method (DDM) is applied to the response sensitivity of displacement-based beam-column finite elements with geometric nonlinearity due to moderate rotations in the basic system. The derived sensitivity equations are implemented in the OpenSees software framework. Stand-alone sensitivity analyses using the DDM and finite difference method (FDM) validate the sensitivity equations for example structures with nonlinear static and dynamic response. Finite element reliability analysis of a steel frame shows that, relative to a geometrically linear formulation, using geometrically nonlinear displacement-based elements increases the probability of failure and affects the importance ranking of the random variables. In addition, for a performance function based on residual capacity at a target lateral displacement, the frame strength at the design point is higher than that obtained when using geometrically linear elements. The developed sensitivity equations increase the number of nonlinear finite element formulations available for gradient-based applications in structural engineering.

Frequency Domain State Space–Based Mode Decomposition Framework

AbstractFor system identification of structures using responses comprised of contributions from multiple modes, one usually decomposes responses into individual modes prior to identifying parameter...

Model selection for dynamic reduction-based structural health monitoring following the Bayesian evidence approach

Abstract There usually exist multitudinous finite element (FE) models with varying level of complexity which can be developed from the engineering judgment for the purpose of structural system identification and health monitoring. By following the theory of Bayesian evidence statistic, this paper proposes a methodology to investigate the issues of FE model-class selection for choosing suitable parameterized structural models utilized in dynamic reduction-based structural health monitoring (SHM). By employing the concept of information divergence, the amount of information needed to be extracted from the measured data is explicitly quantified during the procedure of FE model updating-based structural health monitoring. Then, for achieving a trade-off between the complexity of a parameterized FE model class and that of its corresponding information-theoretic interpretation, such information is utilized for penalizing the complexity of model class to ensure that a relatively simple parameterization scheme can be achieved. The proposed methodology consists of calibration and subsequent monitoring stages, and the information obtained in the former stage is utilized as pseudo-data which is learned by the latter stage to improve the model parameter estimation by implementing the delayed rejection adaptive Metropolis algorithm. Through numerical case studies conducted for a four-storey two-bay steel frame structure considering semi-rigid connections as well as laboratory experiment performed for a two-storey bolt-connected steel frame model, the feasibility and validity of proposed methodology is demonstrated.

A novel unscented Kalman filter for recursive state-input-system identification of nonlinear systems

Abstract The unscented Kalman filter (UKF) has proven to be an effective approach for the identification of nonlinear systems from limited output measurements. However, the conventional UKF requires that measurements of the input excitations are available to successfully perform nonlinear system identification, which limits its application in cases where it is difficult or impractical to measure the inputs. In this paper a novel unscented Kalman filter with unknown input (UKF-UI) is proposed for the simultaneous identification of nonlinear structural systems and external excitations. Based on the estimation-based procedures of the conventional UKF, the analytical recursive solutions of the proposed UKF-UI are derived in an analogous fashion resulting in a recursive nonlinear least-squares problem for the unknown input. Moreover, data fusion of partially measured acceleration and displacement responses is used to alleviate the drifts typically observed in the estimated inputs and displacements. Numerical and experimental validation examples are used to demonstrate the effectiveness of the proposed UKF-UI algorithm for the simultaneous identification of nonlinear parameters and unknown external excitations using data fusion of partially measured system responses.

Nonlinear System Identification of Structures Subject to Stochastic Loadings

This paper intends to explore the application of the Reverse Multiple Input Multiple Output (R-MISO) technique in the system identification of nonlinear structural behaviour. This paper introduces two concepts in improving the identification estimates of multiple inputs and nonlinear systems, which is the conditioned spectral estimation technique and the inversion of the frequency response function formulas. In this paper, a linear equation of motion with a nonlinear Duffing oscillator is modelled and tested using this technique in order to model the typical nonlinear stiffness characteristics of materials and their design limit. The results indicate a good fit between the predicted physical parameters and the model properties. The nonlinearities were successfully isolated in a non-iterative procedure and the parameters were correctly identified. Multiple coherency was used as a tool to describe the various contributions of the inputs to the system outputs.

Structural-System Identification via a Reduced System and the Sensor-Location Selection Method

The structural-vibration behavior of a plate model is expressed as a combination of the initial state behavior of the structure and its associated perturbations. The dynamic behavior obtained from a limited number of accessible nodes and their associated degrees of freedom is employed to detect structural changes that are consistent with the perturbations. The equilibrium model is described in terms of the measured and unmeasured modal data. Unmeasured information is estimated using an iterated improved reduction scheme. Because the identification problem depends on the measured information, the quality of the measured data determines the accuracy of the identified model and the convergence of the identification problem. The accuracy of the identification depends on the measurement/sensor location. In this study, a more accurate identification method using the optimal sensor-location selection method is proposed. Experimental examples are employed to examine the convergence and accuracy of the proposed method applied to an inverse problem of system identification.

A literature review of next-generation smart sensing technology in structural health monitoring

Advent of computationally efficient smartphones, inexpensive high-resolution cameras, drones, and robotic sensors has brought a new era of next-generation intelligent monitoring systems for civil infrastructure. Vibration-based condition assessment has garnered as a prominent method of evaluating the health of large-scale infrastructure. The use of contact-based sensors for acquiring vibration data becomes uneconomical and tedious due to their instrumentation cost, centralized nature, and densification required to collect sufficient data for system identification of modern complex structures. A need to advance and develop alternative methods for efficient sensing system results in next-generation measurement technology of structural health monitoring. The abundance of handheld smartphones with easily programmable framework has helped in modifying relevant software to acquire vibration data using embedded sensors in the smartphone. The inexpensive cameras have been used to capture images and videos that are utilized to understand the structural behavior with the aid of advanced signal processing techniques. The inaccessible components of structures require noncontact sensors such as unmanned aerial vehicles (UAVs) or so-called drones and mobile sensors to acquire structural data. To the authors' knowledge, this paper first time presents a comprehensive review of a suite of next-generation smart sensing technology that has been developed in recent years within the context of structural health monitoring. The state-of-the-art methods have been presented by conducting a detailed literature review of the recent applications of smartphones, UAVs, cameras, and robotic sensors used in acquiring and analyzing the vibration data for structural condition monitoring and maintenance.

Free‐Decay Nonlinear System Identification via Mass‐Change Scheme

Methods for nonlinear system identification of structures generally require input‐output measured data to estimate the nonlinear model, as a consequence of the noninvariance of the FRFs in nonlinear systems. However, providing a continuous forcing input to the structure may be difficult or impracticable in some situations, while it may be much easier to only measure the output. This paper deals with the identification of nonlinear mechanical vibrations using output‐only free‐decay data. The presented method is based on the nonlinear subspace identification (NSI) technique combined with a mass‐change scheme, in order to extract both the nonlinear state‐space model and the underlying linear system. The technique is tested first on a numerical nonlinear system and subsequently on experimental measurements of a multi‐degree‐of‐freedom system comprising a localized nonlinearity.

State-of-the-art review on Bayesian inference in structural system identification and damage assessment

Bayesian inference provides a powerful approach to system identification and damage assessment for structures. The application of Bayesian method is motivated by the fact that inverse problems in structural engineering, including structural health monitoring, are typically ill-conditioned and ill-posed when using noisy incomplete data because of various sources of modeling uncertainties. One should not just search for a single “optimal” value for the vector of model parameters but rather attempt to describe the whole family of plausible model parameters based on measured data using a Bayesian probabilistic framework. In this article, the fundamental principles of Bayesian analysis and computation are summarized; then a review is given of recent state-of-the-art practices of Bayesian inference in system identification and damage assessment for civil infrastructure. Discussions of the benefits and deficiencies of these approaches, as well as potentially useful avenues for future studies, are also provided. Our focus is on meeting challenges that arise from system identification and damage assessment for the civil infrastructure but our presented theories also have a considerably broader applicability for inverse problems in science and technology.

Modifying the ERA and fast ERA to improve operational performance for structural system identification

Abstract The eigensystem realization algorithm (ERA) and fast ERA are two popular methods of structural-system identification; however, these two powerful methods have deficiencies when employed in real-life identification projects. The main deficiencies of the ERA and fast ERA methods are that, when the order of the structural system is not known or is infinite, the sample time is not appropriate and/or initial condition is not zero, the identification results using these algorithms are not correct. This paper introduces a theoretical foundation called the modified ERA (mERA) and modified fast ERA (mfERA) to tackle these deficiencies. The simulation and experimental results are presented to demonstrate the validity of these analytical developments.

Applications of higher-order frequency response functions to the detection and damage assessment of general structural systems with breathing cracks

Two types of cracks are often encountered in engineering structural systems and these are the open cracks and the breathing cracks. Existence of open cracks often leads to the loss of physical stiffness, resulting in a mostly linear structure with reduced load bearing capacity and vibration frequencies. The development of breathing cracks not only reduces structural stiffness, but tends to render the otherwise linear structure to become nonlinear, due to their bilinear stiffness characteristics associated with open and closed states. The nonlinear structural vibration responses can then be investigated and potentially employed to detect and identify breathing cracks within a structural system. In the present study, breathing cracks are modeled based on fracture mechanics from which bilinear stiffness values are obtained. These values are then incorporated into finite element models to compute the first- and second-order frequency response functions (FRFs) based on a proposed correlation technique which is both very accurate and resilient against measurement uncertainties. The existence of well-defined second-order FRFs has been firmly established for the bilinear oscillator, as well as a cantilevered beam with breathing cracks. By expressing the bilinear restoring force as a polynomial series, analytical derivation of second-order FRFs of general structural systems such as the GARTEUR AG11 structure with breathing cracks has been established for the first time. Further, a method of identification has been developed to identify the physical parameters of breathing cracks using second-order FRFs. With these new developments that are presented in this paper, a solid foundation has been laid for the potential applications of higher-order FRFs to damage identification and assessment of general real structural systems.

Sparse structural system identification method for nonlinear dynamic systems with hysteresis/inelastic behavior

Abstract A system identification technique suitable for single degree of freedom (SDOF) and multiple degree of freedom (MDOF) structural systems with either nonlinear elastic or inelastic/hysteretic behavior is proposed in this paper. The method is a parametric modeling technique based on sparse regularization. The proposed framework is capable of discovering the underlying governing equations of the system of interest from input-output data. We build on the work of Brunton et al. (2016) by including functions that allow the discovery of significant nonlinearities, and hystertic or inelastic behavior with permanent deformation. We also present model selection using sparse regularization and cross validation using Akaike criteria. We demonstrate through experimental validation that the technique presented in this paper is applicable to a significantly broader class of problems. The effectiveness of the proposed method is evaluated through numerical examples of a 2-story nonlinear or inelastic building with a adjustable stiffness device. We also present experimental validation using a unique nonlinear structural system that consists of a MDOF structural system and a nonlinear negative stiffness device (NSD) to illustrate the significant ability of the proposed framework. We successfully identify the following structural systems from experimental data: a SDOF yielding frame without NSD; a SDOF yielding frame with NSD; and a 3-DOF frame with NSD. The extracted sparse model also shows potential for generalization.

Modal Expansion Method for Eigensensitivity Calculations of Cyclically Symmetric Bladed Disks

A diverse set of technical fields such as design optimization, structural system identification, and probabilistic modeling require accurate and efficient calculation of modal sensitivities to structural parameters for bladed disks (blisks). However, obtaining sensitivities by traditional finite difference schemes of full blisk finite element models fails to meet the efficiency requirement. An approach is presented here that meets both the accuracy and efficiency requirements for calculating modal sensitivities by formulating a modal expansion method for blisk models. This approach accommodates repeated eigenvalues common to blisks, where traditional approaches result in singular equations when solving for sensitivities. Results illustrate the efficiency and efficacy of the approach for a simple academic model and an industrial model. It is also shown that repeated eigenvalues and eigenvectors also have repeated derivatives.

Performance-based multi-hazard topology optimization of wind and seismically excited structural systems

The integration of topology optimization procedures into modern structural design frameworks is gaining interest as an innovative approach for achieving more efficient designs. To this end, probabilistic performance-based topology optimization frameworks have recently been proposed for the identification of optimal structural systems subject to extreme wind or seismic events considered in isolation. However, there are large geographic regions that are subject to both wind and seismic hazards. Therefore, the development of methods that can ensure that target performance metrics are met within a multi-hazard setting is a crucial step towards improving the reliability of structural systems.This paper is focused on proposing a simulation-centered performance-based topology optimization framework for the identification of optimal structural systems for multi-hazard wind and seismic environments. A probabilistic performance assessment framework is firstly proposed based on synergistically describing the performance of wind or seismically excited systems. Based on this framework, a multi-hazard topology optimization strategy is proposed. In particular, the methodology is centered on the definition of an approximate optimization sub-problem that not only decouples the simulation-based performance assessment from the optimization loop, but also transforms the dynamic and uncertain optimization problem into an explicit static and deterministic problem therefore enabling its efficient resolution using any gradient-based optimizer. Optimal lateral load resisting systems that rigorously meet the probabilistic performance constraints set within the multi-hazard environment are therefore identified. A case study is presented demonstrating the potential of the proposed framework.

Reduced order surrogate modeling technique for linear dynamic systems

The availability of reduced order models can greatly decrease the computational costs needed for modeling, identification and design of real-world structural systems. However, since these systems are usually employed with some uncertain parameters, the approximant must provide a good accuracy for a range of stochastic parameters variations. The derivation of such reduced order models are addressed in this paper. The proposed method consists of a polynomial chaos expansion (PCE)-based state-space model together with a PCE-based modal dominancy analysis to reduce the model order. To solve the issue of spatial aliasing during mode tracking step, a new correlation metric is utilized. The performance of the presented method is validated through four illustrative benchmarks: a simple mass-spring system with four Degrees Of Freedom (DOF), a 2-DOF system exhibiting a mode veering phenomenon, a 6-DOF system with large parameter space and a cantilever Timoshenko beam resembling large-scale systems.