On the use of dispersion analysis for model assessment in structural identification

Abstract

One of the most important issues faced in parametric time-domain identification and subsequent experimental/ operational modal analysis is the correct estimation of model order, which in turn determines the number of structural vibration modes. The aim of this study is to provide a quantitative and physically meaningful framework for model order assessment that is characterized by global applicability, in the sense of implementation in both state-space and transfer function model representations. To this end and under the assumption of stationary wideband excitation, a novel dispersion analysis scheme is proposed for the quantification of every mode's relative importance to the total stochastic response, which is based on a modal decomposition of the covariance matrix. Subsequently, after defining the modal dispersion matrix, a corresponding metric is introduced and used either as a stand alone tool for model order assessment, or as an extension of existing tools, such as stabilization diagrams. The method is validated through both simulated (NASA Mini-Mast truss) and experimental (suspended steel subframe flexible structure) identification problems, for which a subspace and a prediction-error estimation method are utilized and compared under the proposed quantitative indices. Moreover, performance comparisons with other energy-based metrics are also reported. The results indicate that the proposed method can be effectively used in parametric time-domain structural identification, for both order assessment and comparison of diverse model-based estimation methods.

GP-ARX-Based Structural Damage Detection and Localization under Varying Environmental Conditions

“…In establishing Ψ, attention should be paid to the proper distinction of structural from "erroneous" modes, as well as to the matching of eigenvectors associated to the same mode. This is accomplished by applying dispersion analysis [70][71][72] and formulating the modal assurance criterion (MAC).…”

“…To elaborate further on the model order selection, Figure 8c shows the frequency stabilization diagrams (FSDs), corrected using the dispersion analysis method described in Dertimanis and Chatzi [71]. The correction is based on the energy associated to each estimated structural vibration mode and on a low threshold (herein set as greater than 1% of the mode with the highest energy content) that distinguishes structural from erroneous, or "artificial" modes [70]. The dispersion-corrected FSD indicates that mode and dispersion stabilization occurs at p = 38, which is the finally selected order for all three ARX models.…”

A Covariance Feedback Approach to Covariance Control of Nonlinear Stochastic Systems

“…e variance of a random variable is very important in most of the control researches such as predictive systems analysis and state estimation problems. Many researchers have done huge researches to reach and control the constrained variance objectives in related control goals to have a convergence in identification and estimation systems [1,2] and data filtering fault detection and diagnosis [3] or have a better convergence rate of some intelligent algorithms such as genetic algorithm [4] and neural network [5]. Choosing an incorrect variance can cause instability in the whole system and can reduce the performance of the system.…”