Output-Only Modal Estimation Using Eigensystem Realization Algorithm with Nonstationary Data Correlation

Chang-Sheng Lin,Ming-Hsien Lin

doi:10.3390/app11073088

Chang-Sheng Lin, Ming-Hsien Lin

Open Access

https://doi.org/10.3390/app11073088

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Abstract

The conventional eigensystem realization algorithm with data correlation (ERA/DC) combines the impulse response or free response data of a structural system with the concept of correlation function to identify the modal parameter of the structural system. Previous studies have shown that the modal parameters of structural systems subjected to stationary white noise excitation can be estimated by ERA/DC from the ambient response without excitation data. This concept is extended in this paper for output-only modal identification for the structural system with complex modes under ambient excitation as a nonstationary process in the form of a product model. Numerical simulations and experimental verification are used to validate the effectiveness of the proposed method for response-only modal estimation, and the stabilization diagram is used with modal assurance criterion (MAC) to distinguish structural modes from fictitious modes.

Highlights

The modal estimation theory uses free response or impulse response data to identify modal parameters, or uses excitation and response data simultaneously for parametric estimation of structures
In 1988, Juang et al [5] proposed the improved method of ERA, that is, the eigensystem realization algorithm using data correlation (ERA/DC), which reduces the effect of noise on modal estimation using the characteristics of a correlation matrix to increase the accuracy of identification
The concept of ERA/DC is extended to nonstationary ambient response in this study

Summary

Introduction

The modal estimation theory uses free response or impulse response data to identify modal parameters, or uses excitation and response data simultaneously for parametric estimation of structures. In 1965, Ho and Kalman [1] proposed the minimum realization algorithm, using the Markov parameter composed of the impulse response function to obtain the minimum-order state-space representation This method could describe the system accurately but disregarded effective estimation of impulse response with noise. In 1988, Juang et al [5] proposed the improved method of ERA, that is, the eigensystem realization algorithm using data correlation (ERA/DC), which reduces the effect of noise on modal estimation using the characteristics of a correlation matrix to increase the accuracy of identification. In 1993, James et al [6] assumed the ambient excitation to be a white noise and calculated the autocorrelation and cross-correlation functions of the response signal They found that the mathematical version of the correlation function was identical to that of free response and impulse response and the modal parameter of the structure was obtained. Kordkheili et al [16] used the method for mode estimation for the flat plate with similar modes and the pulley with repetition frequency mode

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