Observability Method for 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.

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.

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.

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

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.

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.

During the past 15 years I and my colleagues have studied the dynamics of free (gravity-driven) subduction using a twofold approach: numerical simulations using the boundary-element method (BEM), and interpretation of the solutions using the theory of thin viscous shells. The basic model comprises a shell with thickness h and viscosity η1 subducting in a mantle with viscosity η2. The mantle has a finite depth H (in 3-D Cartesian geometry) or an outer radius R0 (in spherical geometry). The key length scale governing subduction is the 'bending length' lb, the sum of the slab length and the lateral extent of the  seaward flexural bulge. A dimensionless 'flexural stiffness' St = (η1/η2)(h/lb)3 determines whether the subduction rate is controlled by η1 or η2. 3-D BEM simulations closely reproduce laboratory experiments, and reveal the physical mechanisms underlying the different modes of subduction observed.   In spherical geometry, subduction is controlled by St and a 'dynamical sphericity number' Σ = (lb/R0) cotθt, where θt is the angular radius of the trench. Spherical BEM solutions demonstrate the 'sphericity paradox' that the effect of sphericity on flexure is greater for small (more nearly flat) plates than for large ones  (e.g. hemispherical). Another surprising result is that state of stress in a doubly-curved slab is dominated by the longitudinal normal ('hoop') stress. BEM predictions of hoop stresses in slabs with positive and negative Gaussian curvature agree well with earthquake focal mechanisms in the Mariana slab. Linear stability analysis shows that a slab under compressive hoop stress is unstable to longitudinal buckling, which may explain the peculiar geomery of the Mariana slab. Finally, I will describe a new hybrid boundary-integral/thin-shell approach to coupling mantle flow with the deformation of a thin shell having non-Newtonian rheology. 

Flexural behavior of FRP and steel reinforced glulam beams: Experimental and theoretical evaluation

Among the several safety checks that must be performed during the design of small to medium single span railway viaducts, the one concerning vertical accelerations is often crucial for high speed railways, since under these conditions resonance is much likely to occur.Recent results [1]–[3] of several field measurements carried out on simply supported medium span concrete railway viaducts showed that the non-linear behaviour of the superstructure composed by ballast and rails can play an important role in the dynamic behaviour of the structure and consequent evaluation of its maximum vertical accelerations. The conclusions drawn from those measurement results pointed out that the superstructure must be taken into account in the numeric analysis of small to medium span bridges, mainly what global ballast-structure damping is concerned. This revealed to be particularly important when decisions are to be taken, related to the strengthening of existing structures in order to increase traffic speeds and when comfort of passengers is an important issue.In order to evaluate the vertical vibrations of the bridges when the dynamic behaviour of the track is taken into account, same authors have already proposed different models including vertical springs, dampers and masses, which are interpose between loads and structure in order to simulate the railway track behaviour. These models include the rail with flexural stiffness in vertical and lateral direction and axial stiffness in longitudinal directions, the rail pads as vertical springs and dampers, the sleepers as rigid bodies with masses, and finally the ballast as springs and dampers.The main purpose of this paper is to compare the dynamic behaviour of ballasted simple supported viaducts with and without the referred track models, taking into account the structural dynamic response obtained from the field measurements, in order to evaluate the influence of the track in the safety check. Furthermore, the response acceleration of the ballasted simple supported viaducts is also compared with the results obtained from the simplified methods proposed by the ERRI D214 Committee used to estimated the maximum acceleration at mid-span of simply supported bridges decks, namely the DER Method (Decomposition of Excitation at Resonance Method) and the Virtual Influence Line Method.

Kalman filter method for the real-time optimal identification of linear structural systems based on generalized discrete state equations

A method of physical-parameter system identification is proposed here for three-dimensional (3D) building structures with in-plane rigid floors in which the stiffness and damping coefficients of each structural frame in the 3D building structure are identified from the measured floor horizontal accelerations. A batch processing least-squares estimation method for many discrete time-domain measured data is proposed for the direct identification of the stiffness and damping coefficients of each structural frame. While previous researches on the system identification of 3D building structures are limited to a class of structures with regular eccentricity, the present paper removes this limitation. Advantageous features of the proposed identification method are that it is unnecessary to specify the stiffness eccentricities (location of center of stiffness) before identification and the identification of all stiffness and damping parameters can be performed simultaneously. The reliability and accuracy of the proposed method are demonstrated by numerical simulations.

Identification of nonlinear structural system is an important but challenging task for structural health monitoring. Due to the complexities of structural nonlinearities, it is hard to establish proper mathematical models for some structural nonlinear behaviors. Moreover, only partial structural responses can be measured in practice; it is essential to conduct identification of nonlinear structural systems using only partial measurements of structural responses. To cope with these issues, an algorithm is proposed in this article for the identification of some model-free structural nonlinear restoring forces using only partial measurements of structural responses. First, an equivalent linear structural system is introduced for the identification of the locations of structural nonlinearities. Then, a model-free structural nonlinear restoring force is approximated by a power series polynomial. The unknown coefficients of the power series polynomials together with other structural parameters are identified by the extended Kalman filter so that the characteristics of the behaviors of the model-free of nonlinear restoring forces can be identified. Some numerical examples including the identification of two nonlinear multi-story shear frames and a planar nonlinear truss with different structural nonlinear restoring forces are used to validate the proposed algorithm.

Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and reflect on the application of polynomial homotopy continuation methods to solve polynomial systems in the cloud. Via the graph isomorphism problem we organize and classify the polynomial systems we solved. The classification with the canonical form of a graph identifies newly submitted systems with systems that have already been solved.

This report contains a review of the technical literature concerning the detection, location, and characterization of structural damage via techniques that examine changes in measured structural vibration response. The report first categorizes the methods according to required measured data and analysis technique. The analysis categories include changes in modal frequencies, changes in measured mode shapes (and their derivatives), and changes in measured flexibility coefficients. Methods that use property (stiffness, mass, damping) matrix updating, detection of nonlinear response, and damage detection via neural networks are also summarized. The applications of the various methods to different types of engineering problems are categorized by type of structure and are summarized. The types of structures include beams, trusses, plates, shells, bridges, offshore platforms, other large civil structures, aerospace structures, and composite structures. The report describes the development of the damage-identification methods and applications and summarizes the current state-of-the-art of the technology. The critical issues for future research in the area of damage identification are also discussed.

Rheology, stability and filtration characteristics of Colloidal Gas Aphron fluids: Role of surfactant and polymer type