Autoregressive model updating for modal analysis of non-stationary vibration systems

Abstract

Operational modal analysis (OMA) has recently become one of the most effective techniques to extract modal parameters (natural frequencies, damping ratios, and mode shapes) for practical vibrations under working conditions. Many good results have been observed in numerous domains, such as robotics, fluid-structure interaction, and bridges. Due to these applications being considered under working conditions, their modal parameters change over time. Hence, identifying the operational modal parameters in structures is a computationally complex and time-consuming procedure. In addition, collected non-stationary signals are usually mixed with heavy noise caused by operating conditions or changing environments. Consequently, problem resolution using least-squares is rank deficient. To mitigate these disadvantages in OMA, it is essential to develop updating algorithms. The main objective of this study is to develop novel algorithms to reduce the computational complexity, time burden, and matrix singularity for the modal identification of OMA. The proposed methods can be applied to slow-varying non-stationary vibration structures and are validated by experiments on the fluid-structure interaction. To achieve this, the research is conducted in two steps. The objective of the first step is to present a novel method for updating model parameters of autoregressive models and monitoring the change of modal parameters for slow-varying nonstationary vibration systems. This method avoids computational complexity and timeconsuming modal analysis for slow-varying non-stationary vibration systems. The sliding window technique is used to extract modal parameters for systems. For this objective, the Schur complement is applied to the sliding window to update model parameters in time and order. Numerical simulation and experiments on an emerging plate are effective ways to validate that the proposed approach enhances performance in terms of computational complexity and execution time. In addition, the proposed method is used to monitor and track the change of modal parameters for slow-varying non-stationary systems. Restrictions of the proposed approach are also discussed. The results of the first step have been accepted for publication in the Journal of Mechanical Systems and Signal Processing (MSSP). Based on the promising results regarding reduced computational complexity and execution time for modal analysis identification, the second step is also to develop an updating algorithm, which can be applied to structures under working conditions with only the output vibratory responses. In addition, the proposed method copes with the matrix singularity caused by operating conditions for operational modal analysis. The basic idea of this method consists of using a short-time sliding window (STSW) to identify modal parameters for slow-varying nonstationary vibration structures. This method uses the recursive multivariable least-squares method with singular value decomposition (SVD) to find the solutions in a data segment from each time window. The updating model identification is conducted by updating the SVD of the data matrix through the order and time from the previous computational window to monitor the modal parameters of the slow-varying non-stationary systems. Prospective applications are found in the modal analysis of the submerged hydraulic turbines excited by turbulent flows to extract and monitor the change of modal parameters. The results of this step have been submitted to the Journal of Mechanical Systems and Signal Processing (MSSP) for publication.

Date	20 Dec 2022
Original language	American English
Awarding Institution	École de technologie supérieure
Supervisor	Zhaoheng Liu (Supervisor) & Viet Hung Vu (Co-supervisor)