Identification of Structural Systems Using an Evolutionary Strategy

In the system identification using finite element method (FEM), system responses of overall degree of freedoms (DOFs) are necessary. Because of the limitation of sensor and other experiment equipment, the responses of unspecified DOFs have to be contained in the design variables. This increase of the design variable makes difficult to solve the inverse problem. It is one of the solutions about the problem of limited responses that the responses of unspecified DOFs are represented by the responses of specified DOFs, using the condensation method. In the previous study, we applied iterative inverse perturbation method (IIPM) to enhance the efficiency and the solution convergence of the structural system identification problems using the condensation method. So we efficiently identify structural system through solving the optimization problem with design variables which have the same number of elements. However, if the size of problem developed to analyze practical model is increased, the number of design variables which had to be considered in solving process is extremely increased. To identify large structural system, optimization strategy to efficiently change design variables during the iteration of optimization is required. In this study, we suggest two optimization strategies which are adaptive sub-domain method and genetic concept method. Numerical examples are presented to verify the efficiency of the proposed methods and to compare with those methods.

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.

Recently, blind source separation (BSS) methods have gained significant attention in the area of signal processing. Independent component analysis (ICA) and second-order blind identification (SOBI) are two popular BSS methods that have been applied to modal identification of mechanical and structural systems. Published results by several researchers have shown that ICA performs satisfactorily for systems with very low levels of structural damping, for example, for damping ratios of the order of 1% critical. For practical structural applications with higher levels of damping, methods based on SOBI have shown significant improvement over ICA methods. However, traditional SOBI methods suffer when nonstationary sources are present, such as those that occur during earthquakes and other transient excitations. In this paper, a new technique based on SOBI, called the modified cross-correlation method, is proposed to address these shortcomings. The conditions in which the problem of structural system identification can be posed as a BSS problem is also discussed. The results of simulation described in terms of identified natural frequencies, mode shapes, and damping ratios are presented for the cases of synthetic wind and recorded earthquake excitations. The results of identification show that the proposed method achieves better performance over traditional ICA and SOBI methods. Both experimental and large-scale structural simulation results are included to demonstrate the applicability of the newly proposed method to structural identification problems.

A direct and effective approach is presented for the inverse problem of dynamic structural systems, which is related to structural optimization, system identification, and damage detection. The structural modifications are sought for the characteristic changes assigned from the design goals or modal measurements. A finite element method is used for the system analysis and inverse problem. Mathematical programming techniques are applied for the minimization of the deviation of the finite element model from the desired inverse system, along with an objective function of least structural change. The modal method is based on the perturbation equations of a set of selected degrees of freedom and the energy equation associated with the frequency change. The mode shape change is expressed as the sum of the baseline mode shape and complementary vector, which plays a very important role in the search for the inverse solution. The linear perturbation equation is employed to get an initial approximation, which can be improved through iterations with the nonlinear perturbation equation. The proposed method does not involve the system reduction. Therefore, it is believed to be superior to conventional methods, which suffer from the residual error due to transformation of the eigenproblem.

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.

The common assumption in the so-called linear inverse vibration problem, which provides the mass/stiffness/damping matrices of second order dynamic models, is the availability of a full set of sensors and actuators. In “reduced-order” problems (with limited number of instrumentation), only the components of the eigenvector matrix regarding the measured degrees of freedom can be successfully identified while nothing can be said about the components connected to the unmeasured degrees of freedom. This paper presents a recently developed “reduced-order” model and expands such a model to a “full-order” one that is quite useful in damage detection. The five representative categories of “reduced-order” problems, defined by considering different types of geometrical conditions, are analyzed and a discussion on their solution space has been performed. The effectiveness and robustness of this approach is shown by means of a numerical example.

We first review the concept of computational tomography (CT) and laser technique using the photon diffusion equation. The forward and inverse problems are two key problems concerned with the diffusion equation, while the solution to the latter one is the goal of research in optical CT. The inverse problem can be stated as follows: given the photon density measured from the detectors outside the tissue, we need to find the anomalies (benign or malignant) inside the tissue. We model the forward and inverse problems using state-space equations and pose the inverse problem as a system identification problem. The nonlinear filtering techniques, namely the extended Kalman filter and the second order filter, are proposed to solve the inverse problem. Comparisons are made through an example of a medical imaging problem.

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.

Structural system identification is a critical task in resilience assessments, especially following a natural hazard. In this paper, we propose PIDynNet, a novel physicsinformed approach that produces an ordinary differential equation-constrained neural network model for structural system identification. PIDynNet improves the estimation of structural parameters of nonlinear structural systems by embedding an auxiliary physicsbased loss term into the overall loss function as well as a supervised data-driven loss term. The proposed framework has the generalization capability to predict nonlinear structural response given unseen ground excitations. Two nonlinear numerical experiments are conducted to demonstrate the advantage of PIDynNet over other identification methods in problems with or without latent variables.

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

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 using Least Mean Square (LMS) adaptive technique

<p> The structural response of any structure is traditionally predicted by simplistic physics-based models. In these models the mechanical and geometrical properties are assumed as known. Nevertheless, this is not the case in most actual structures where the values of the actual properties (such as axial or flexural stiffness) are unknown due to uncertainties in the materials, in the construction methods or in the stress state. In some cases, a calibration of the computer models is required to improve de accuracy of the predicted structural response. To carry out this task Structural System Identification (SSI) methods can be used.</p><p> In this paper, a new parametric method for SSI from static excitation response is proposed. This method is based on the observability of the structure, understanding as such the problem of identifying which is the subset of characteristics of the structure, such as Young’s modulus, area, inertia, and/or products of them (axial or flexural stiffnesses) that may be uniquely determined when a subset of deflections and forces at nodes is provided. This method has lead to the development of a powerful mathematical tool to deal efficiently with polynomial systems of equations with a number of applications in many fields of science and engineering.</p><p> To illustrate the applicability of the proposed method, the analysis of the SSI of two structures of growing complexity is presented.</p>

On the optimal location of sensors for parametric identification of linear structural systems

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.