A new model order reduction method based on global kernelk-means clustering: Application in health monitoring of plate using Lamb wave propagation and impedance method

Abstract

In this paper, a new method based on global kernel k-means clustering (GKKMC) has been developed as model order reduction to model electromechanical impedance and Lamb wave in a plate structure. First, a model, based on the spectral finite element method, is developed to simulate piezoelectric wafer active sensor (PWAS) induced electromechanical impedance and Lamb wave propagation. Second, the related coupled electromechanical field equations are solved in 3 dimensions, then an electric voltage signal is applied to PWAS actuator, and finally the produced voltage in PWAS sensor is calculated. In reality, high frequency impedance and Lamb wave simulation in a plate need high degrees of freedom, which leads to a very slow simulation in time and frequency domain calculations. To overcome this problem, GKKMC as a model order reduction approach is proposed and applied. For this purpose, in Lamb wave modeling, a time snapshot method based on the Rayleigh damping effect has been introduced. This proposed method not only has a high accuracy and less time to simulate the problem but also needs lower memory than a full order model. A comparison between the results obtained by GKKMC, the conventional balanced proper orthogonal decomposition method, and a full order method with experimental results have been carried out demonstrating a good agreement. The results show that using this new model order reduction based on GKKMC, simulation time speedups can be reached up to 6 times faster compared with applying a conventional balanced proper orthogonal decomposition method.