An evaluation of the influence of Eigensystem Realization Algorithm settings on multiple input multiple output system identification

One characteristic of the Eigensystem Realization Algorithm method for system identification concerns about the difficulty of finding more appropriate parameters to run the algorithm. One of this work’s purposes is to tackle the cumbersome task of achieving the ideal algorithm settings, providing additional knowledge about algorithm parameters’ influence, and searching to improve results with quicker settings of the algorithm’s parameters, especially for Multiple Input Multiple Output (MIMO) systems. The application of a Fit Rate indicator to evaluate the identified system arises as a novelty in the Eigensystem Realization Algorithm applications, aiming to assess the system identification performance and drive the algorithm to better adjustments. Another objective of this article regards the application of a Pseudo Random Binary Sequence as excitation signals, which has not been used until now with the Eigensystem Realization Algorithm, despite being successfully applied in the system identification process. The proposed approach is verified and analyzed with numerical simulations for a mass–spring–damper model of 5 degrees of freedom. The results reported in time response analysis and frequency response analysis allow us to realize the effect of settings accordingly for the system identification improvement. The results analysis was extended to simulate and compare the Pseudo Random Binary Sequence with Gaussian white noise excitation, and the system was also submitted to the presence of measurement noise.

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

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.

An Eigensystem Realization Algorithm for Modal Parameter Identification of a Vertical-Shaft High-Speed Centrifugal Machine

In this paper, we utilize the observer/Kalman filter identification (OKID) and the eigensystem realization algorithm (ERA) techniques to identify the modal parameters of a centrifugal machine. To this end, we use an experimental setup to generate a pseudo-impulse input and collect output measurements which are corrupted by noise. We use the pseudo-impulse input and the OKID to find the Markov parameters of the system. Then we form the Hankel matrix of the system and determine the singular values of the system. A minimum-order, state-space model of the system is realized through the Markov parameters and then the natural frequency, damping ratio, mode shapes, and modal amplitudes at the sensor location are estimated by the ERA. We find three models for three separate cases and validate all the three identified models with the measured data and the Waterfall plot. The identified models are useful for designing passive or active vibration suppression control and fault detection systems. The results confirm that OKID/ERA is a reliable time-domain method for identifying the modal parameters of vertical centrifuge machines.

Modal identification for superstructure using virtual impulse response

In civil engineering, structural modes are identified with the assumption of stationary white noise, which cannot be satisfied in practical engineering. This article proposes a new method, which contains the virtual impulse response and eigensystem realization algorithm. The formulation of virtual impulse response is derived from the inverse Fourier transform of the ratio of the cross-power to auto-power spectral density functions of the measurement responses, which is based on the concept of frequency response function. During the formulation derivation, a single point excitation is only considered. Frequency response function would not change with different excitations and responses, which means that the excitation cannot influence frequency response function. The impulse response is pointed out to only represent the behavior of superstructure. After obtaining impulse responses, eigensystem realization algorithm is then performed to identify the modes of superstructure. The proposed method is validated by a numerical example. The results show that virtual impulse response can have much better free decayed behavior than natural excitation technique and identify very precise modal parameters for superstructure.