PHYSICS-INFORMED NEURAL NETWORK FOR NONLINEAR STRUCTURAL SYSTEM IDENTIFICATION

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.

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

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.

<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>

<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>

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.

Direct differentiation method for response sensitivity analysis of a bounding surface plasticity soil model

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.

<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>

A nonuniform Timoshenko beam model of a building, with piecewise constant properties along the height, is presented, along with an algorithm for structural system identification from earthquake records. The model accounts for shear and flexural deformation, rotatory inertia, and variation of building properties with height. The model stiffness parameters are identified by matching (in the least-squares sense) propagating pulses in impulse response functions. To minimize the effects of soil–structure interaction, the fit is performed on a band excluding the fundamental mode of vibration. This algorithm is a new development in a wave method for structural health monitoring of buildings, intended for use in seismic alert systems to facilitate decision making on evacuation immediately after the earthquake, and for general condition monitoring. The model can also be used with an earthquake early warning system for quick linear response prediction to decide on safe shutdown of sensitive equipment in advance of strong shaking. Identification and response prediction are demonstrated on the north–south response of the Los Angeles 54-story Office Building, a tall, steel-frame building in downtown Los Angeles.

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

Accurate finite element (FE) models are required in many applications of civil engineering. Non-structural elements (NSEs) often interfere with the main structure, altering its stiffness and modal signature. Neglecting such interaction in modelling, although a common design practice, may lead to unreliable predictions of future events and biased interpretations of in-field dynamic tests. In the current literature, the role of NSEs in vibration-based structural system identification (SSI) is well documented for NSEs working in parallel (P-NSEs) with the main structure (e.g. masonry infills in buildings, pavements or railings in bridges and footbridges) but is totally unexplored for NSEs working in series (S-NSEs) with the main structure (e.g. non-structural appendages such as chimneys, parapets, tanks, but also partitions and claddings in their out-of-plane modes). Presenting various numerical and experimental case studies, the present paper shows how in-series NSEs, through augmenting the modal model and by chance resonating with some structural mode, might significantly alter the dynamic behaviour of the main structure, and severely invalidate SSI if not properly accounted for while performing modelling and dynamic identification.

A theory for structural system identification which utilizes strains and translational displacements as measured outputs is presented. The state variables of the fundamental first-order form consist of the strains and the elemental or substructural rigid-body motion amplitudes. The theory is applicable to, and to some respects, motivated by the advances and expanded use of embedded piezoelectric sensors and fiber optics. A distinct feature of the present theory is its ability to provide rotational flexibility without having to measure rotational quantities. The theory is illustrated by simple ideal examples.

Errors of the third kind in engineering