Constrained observability method in static structural system identification

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.

<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>

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.

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

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

<div class="htmlview paragraph">Structural system identification was applied to small sample problems and to large automotive structures. The technique combines mass and stiffness matrices from a finite element model with experimental mode shapes and natural frequencies to produce improved mass and stiffness matrices. In numerical experiments on small problems the procedure enabled us to identify regions of original finite element models where changes of model parameters were required to bring finite element predictions into better agreement with exact results. Also, node point displacements were calculated for small structures subjected to time-dependent sinusoidal loads, and it was found that predictions of displacements from “improved” models were more accurate than original finite element model predictions when forcing frequencies were within the range of experimental frequencies used with structural system identification calculations. When applied to two large automotive structures. regions within the finite element models identified as candidates for parameter changes to, in one case, bring about a shift in predicted frequencies, and, in the other case, improve correlation with test results, were found to be consistent with our engineering judgement.</div>

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.

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.

Structural system identification using Least Mean Square (LMS) adaptive technique

To avoid potential life and economic loss, structural health monitoring has become increasingly important for bridge systems. As a key component of structural health monitoring, structural system identification (SSI) tries to identify the structural parameters through the measured response. However, due to the ill-posedness of inverse analysis, the estimation of parameters is greatly affected by measurement errors. To alleviate the adverse effect of errors, the relations among the displacements in beam structures (for instance bridges), compatibility conditions, are derived analytically via a symbolical approach. Then a set of compatible displacements is obtained by an optimization procedure that finds the closest compatible deformation shape to the measured one. The final estimations of the parameters are obtained by providing the compatible displacements to SSI. The proposed method is validated by the numerical simulations on a simply supported bridge and on a continuous bridge.

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.

Despite its importance in some structures, shear deformation is systematically neglected by most static structural system identification methods. To fill this gap, this paper analyzes, for the first time in the literature, the effect of the shear deformation in the inverse analysis of structures. This study is focused on a parametric structural system identification method: the observability technique. As the majority of the methods, this technique is based on the Euler-Bernoulli beam theory. The method presented in the literature is unable to identify correctly the characteristics of a structure (such as flexural stiffness) when shear deformation is not negligible. In fact, in this method, the effects of shear deformation are close to those produced by measurement errors. To solve this problem, the observability procedure is updated according to the Timoshenko’s beam theory. This formulation uses an algebraic approach combining both a symbolical and a numerical application. Thus, the updated observability formulation is able to obtain not only flexural stiffness but also shear stiffness. Besides this, for the first time in the literature, a parametric equation of the estimates is obtained. Some examples are presented to illustrate the validity of the new formulation.

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.

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

<p>The condition assessment of pedestrian bridges might be overlooked due to the small scale of these structures. A short list of accidents is provided to justify the necessity of condition assessment on pedestrian bridges. In this paper, the structural system identification by observability method is applied in two traditional arrangements of pedestrian bridges. In the simply supported beam example, the symbolical expressions of the estimation for bending stiffnesses are derived first. The validity of the method is justified by the accurate estimations using error-free measurements. However, as the real-life measurements are inevitably polluted by errors, the effect of measurement errors is thoroughly studied according to measurement errors in a particular measurement, loading cases and errors in all measurements. The simulation errors of the method is also demonstrated by a two-span continuous beam. The results show that the loading case is important regarding the accuracy of the estimations.</p>