遲滯系統：利用Bouc-Wen模式進行分析與識別

System with Hysteresis：Analysis and Identification Using Bouc-Wen Model

曹恆碩(Heng-Shuo Tsao)

指導教授 ： 羅俊雄

國立臺灣大學/工學院/土木工程學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.00223

摘要

在眾所皆知的模型中，我們最常使用的模式為Bouc、Wen與Baber等人所推導出的模式來模擬非線性系統。在這個模式中，非線性微分方程式包含了作用力、位移，以及未知的遲滯圈參數等。而遲滯圈參數的改變，對於模擬反應的結果有何關聯性，是我們值得去探討的。另外一方面，從模擬反應的結果去做訊號分析或是數值分析，是否也可以找出與遲滯圈參數的關聯性，亦是一門有趣的課題。最終，希望可以透過量測反應之特徵擷取分析，估計出非線性系統之非彈性行為，並且找出量測反應之特徵擷取部分與非線性物理特性之相關性。
本論文主要在探討Bouc-Wen 模式下，單自由度之非線性系統反應的分析結果與Bouc-Wen模式參數的關聯性。本文首先用Newmark’s β Method計算Bouc-Wen模式之非線性系統反應；然後，將輸入以及輸出資訊進行系統識別，識別方法有最小平方法（Least Square Method）以及推廣卡式過濾理論（Extended Kalman Filter）；而後再將輸入輸出資訊以及識別出的系統參數進行訊號分析，分析方法有頻率反應函數（Frequency Response Function）與其希爾伯特轉換（Hilbert Transform）、絕對能量方程式（Absolute Energy Equation）以及小波分析（Wavelet Analysis）。探討分析結果與遲滯圈參數變化之關聯性。
研究分析結果顯示：大部分所使用的分析方法皆可以觀察出與Bouc-Wen模式參數的關聯性。

關鍵字

遲滯圈參數 ； Bouc-Wen模式 ； 最小平方法 ； 推廣卡式過濾理論 ； 絕對能量方程式 ； 小波分析

並列摘要

One of the widely accepted models is a differential model of hysteresis proposed by Bouc, Wen, and Baber et al. In this model, the applied force and deformation are connected through a nonlinear differential equation containing unspecified loop parameters. We have the interested in the change of hysteresis loop parameters which have the relationship with the response of the Bouc-Wen Model. On the other hand, another interesting topic is taking the simulation response data to do signal analysis, or numerical analysis, whether the result have the relationship with the hysteresis loop parameters that are existed. To estimate the inelastic behavior of a nonlinear system through the analysis (feature extraction) of response measurements. Find the correlation between the features extracted from measurements and the physical nonlinear characteristics.
This study presents the response analysis result of a single degree of freedom nonlinear system that has the relationship with the hysteresis loop parameters in the Bouc-Wen Model. First, we used the Newmark’s β Method to calculate the nonlinear system response of the Bouc-Wen Model. Second, using the input and output data to identify the parameters of the nonlinear system. In this study, we use two kinds of the system identification method, one is the Least Square Method, and another is Extended Kalman Filter. Finally, we took the input data, output data, and parameters of the nonlinear system to do signal analysis. In this study, we used the Frequency Response Function and its Hilbert Transform, Absolute Energy Equation, and Wavelet Analysis for signal analysis.
As a result, most of the signal analysis result may observe the relationship with the parameters of the Bouc-Wen Model.

並列關鍵字

hysteresis loop parameters ； Bouc-Wen Model ； Least Square Method ； Extended Kalman Filter ； Absolute Energy Equation ； Wavelet Analysis

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