Data-Driven Initial Gap Identification of Piecewise-Linear Systems Using Sparse Regression and Universal Approximation Theorem

This paper proposes a method for identifying an initial gap in piecewise-linear (PWL) systems from data. Piecewise-linear systems appear in many engineered systems such as degraded mechanical systems and infrastructures and are known to show strong nonlinearities. To analyze the behavior of such piecewise-linear systems, it is necessary to identify the initial gap, at which the system behavior switches. The proposed method identifies the initial gap by discovering the governing equations using sparse regression and calculating the gap based on the universal approximation theorem. A key step to achieve this is to approximate a piecewise-linear function by a finite sum of piecewise-linear functions in sparse regression. The equivalent gap is then calculated from the coefficients of the multiple piecewise-linear functions and their respective switching points in the obtained equation. The proposed method is first applied to a numerical model to confirm its applicability to piecewise-linear systems. Experimental validation of the proposed method has then been conducted with a simple mass-spring-hopping system, where the method successfully identifies the initial gap in the system with high accuracy.