應用含外變數的非線性自我迴歸模型估算非線性系統之線性模態參數

Abstract

由於現實生活中的力學系統都含有非線性因子，其中的差別僅在於非線性程度的多寡，因此自然界的振動現象皆為非線性振動。而非線性系統之振盪頻率是隨著振幅而改變，且對於真實系統來說皆有阻尼存在，因此使得估計其非線性振盪頻率更加困難；但系統之自然振頻是系統本質上的，不受到其他因素影響，因此本文提出一套識別流程直接估計非線性系統之線性模態參數。 本文首先透過單自由度以及三自由度的非線性具阻尼系統以數值模擬的方式模擬其輸出入響應資料，對此輸出入響應以系統識別技術中的含外變數的非線性自我迴歸模型(NARX model)結合伏爾泰拉級數(Volterra series)針對非線性振動系統之輸出響應做分析，主要用來檢驗本文所提出的識別程序於結構振動問題上的可行性。分析過程中並以時間歷時圖、功率頻譜密度圖、時譜圖及模態穩定圖來輔助觀察分析。最後探討兩組不同結構的實驗例，一為懸臂鋼樑，另一為機車車架結構，懸臂鋼樑主要用於檢驗自由響應資訊之系統識別。機車車架結構則分別為衝擊錘激振以及強迫激振儀激振作用下的結構系統識別，以檢驗NARX方法於未知雜訊干擾及複雜結構下的能力。由數值以及實驗資料識別結果顯示，本文所採用之識別技術能有效的從結構振動量測資料中萃取出線性模態參數。

Since the real mechanical systems have nonlinear factors, the only differences are the extent of nonlinearity, so the vibration phenomenon actually are nonlinear. Since the real system has damping, so the oscillation frequency of non-linear system change with amplitude. Thus it’s difficult to estimate the oscillation frequency of a non-linear systems. However, the natural frequency of any system is natural and is not influenced by other factors. This article purposes a set of identification process to estimate the linear modal parameters of nonlinear systems. At first in this thesis, it is to simulate the output response on both a single and three degrees of freedom of the non-linear systems with damping by using numerical simulation. We can compute the output response of a nonlinear vibration system using system identification techniques by the mathematical model of Nonlinear AutoRegressive with eXogenous inputs model combined with Volterra series to estimate the linear modal parameters of nonlinear systems. Besides, in the analytic process, it also utilizes power spectral density diagram, time frequency analysis diagram and modal stabilization diagram to assist the reach. Finally, NARX method is applied to the two experimental examples, cantilever beam and framed structure of motorcycle. cantilever beam used to test the free response of the system identification information. Framed structure of motorcycle were excitation by hammer and shaker to discuss the identification ability of NARX method under some noise disturbance. By comparing the numerical and the experimental data, for system identificationtechnique involved can work well to estimate the linear modal parameters of nonlinear systems