非線性動態稀疏識別法(The sparse identification of nonlinear dynamics method，簡稱為SINDy法)為Brunton等人於近年提出的數據驅動建模技術，此技術可透過分析動態數據逆向建立動態系統的非線性運動方程式，而本研究旨在探討SINDy法於結構系統非線性建模之應用及可行性。由於SINDy法適用於自治動態系統的數據驅動建模，因此有別於傳統的系統識別方法需要穩定的激振源驅動系統，此方法能夠透過分析結構自由振動響應而逆向建立系統之非線性模型。此外，SINDy法的另一項特點是允許使用者自行選定義非線性函數作為模型的基底，並透過稀疏回歸計算各個函數的權重，因此SINDy法具有自動抑制量測誤差並濾除不適用函數的特性。本研究分別將SINDy法應用於雙自由度的Duffing振盪子與T型樑結構中，並分別以數值模擬與實驗方法驗證SINDy於上述系統的建模準確性。

The sparse identification of nonlinear dynamics (SINDy) method is a data-driven nonlinear modelling technique for dynamic systems proposed by Brunton et al. in recent years. This study is the first application of the SINDy method to construct a dynamic model of structural systems. Since the SINDy method is suitable for data-driven modeling of autonomous dynamic systems, unlike traditional system identification methods that require a stable excitation to drive the system, this method can build a nonlinear model of the system by analyzing the free vibration response of the structure. Another feature of the SINDy method is that it can use a flexible nonlinear function as the base of the model and calculate the weights of each function through sparse regression. Therefore, the SINDy method has the characteristics of automatic suppression of measurement errors and inapplicable functions. In this study, the SINDy method is applied to a two-degree-of-freedom Duffing oscillator and a T-beam structure and is validated both numerically and experimentally.

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