Abstract
In recent years, the rapid growth of computing technology has enabled identifying mathematical models for vibration systems using measurement data instead of domain knowledge. Within this category, the method Sparse Identification of Nonlinear Dynamical Systems (SINDy) shows potential for interpretable identification. Therefore, in this work, a procedure of system identification based on the SINDy framework is developed and validated on a single-mass oscillator. To estimate the parameters in the SINDy model, two sparse regression methods are discussed. Compared with the Least Squares method with Sequential Threshold (LSST), which is the original estimation method from SINDy, the Least Squares method Post-LASSO (LSPL) shows better performance in numerical Monte Carlo Simulations (MCSs) of a single-mass oscillator in terms of sparseness, convergence, identified eigenfrequency, and coefficient of determination. Furthermore, the developed method SINDy-LSPL was successfully implemented with real measurement data of a single-mass oscillator with known theoretical parameters. The identified parameters using a sweep signal as excitation are more consistent and accurate than those identified using impulse excitation. In both cases, there exists a dependency of the identified parameter on the excitation amplitude that should be investigated in further research.
Highlights
Mathematical model building, especially the construction of governing equations, is a significant problem for a large variety of dynamic systems, such as vibration systems [1], biological systems [2], and fluid mechanical systems [3]
Sci. 2022, 12, 747 tests, we review how SINDy-Least Squares method Post-Least Absolute Shrinkage and Selection Operator (LASSO) (LSPL) performs at discovering the governing equation of a simple vibration system, which is fundamental for further research dealing with complex systems with more than one Degree of Freedom (DoF)
Data Analysis and Results Due to the advantages of LSPL over Least Squares method with Sequential Threshold (LSST) mentioned in Section 3, LSPL was selected to experimentally identify the oscillator using the signals from the measurement
Summary
Mathematical model building, especially the construction of governing equations, is a significant problem for a large variety of dynamic systems, such as vibration systems [1], biological systems [2], and fluid mechanical systems [3]. The models of vibration systems can be identified with various approaches, such as iterative model updating [14], the Polynomial NonLinear State Space (PNLSS) model [15], Volterra series [16], the Wiener and Hammerstein model [17,18], artificial neural networks [19,20], and equation-free model building [21]. These methods usually build “black-box” or “grey-box”
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