Low-cost simulation using model order reduction in structural health monitoring: Application of balanced proper orthogonal decomposition

In this paper, both two powerful methods in structural health monitoring, Lamb wave propagation and electromechanical impedance method, are modeled, implemented, and tested to inspect the plate-like structure using piezoelectric wafer active sensor (PWAS). In order to detect damage in structure, introducing a model for advanced signal processing algorithm is essential. A three-dimensional spectral finite element method has been applied to model Lamb wave propagation and electromechanical impedance in plate with attached PWAS. In reality, Lamb wave generation and electromechanical impedance in high frequencies lead to a high degree of freedom in modeling and consequently to a low speed simulation in frequency and time domains calculation. For us to overcome this problem, balanced proper orthogonal decomposition (BPOD) has been developed and used as model order reduction for these methods in structural health monitoring. The experimental tests are carried out on aluminum plate with two attached PWAS. The simulation results obtained by BPOD and full-order method are validated by comparison with experimental ones. The results show that the proposed and implemented model order reduction method (BPOD) leads to increase significantly simulation speed without any distortion in accuracy. For Lamb wave method, CPU time consuming using BPOD is reduced 5.8 times (frequencies 40 and 150kHz) comparing to full-order model application without any alteration of accuracy (less than 0.03 normalized voltage). For impedance method, the simulation time has been decreased 10 times less than using full-order model in frequency range 90-100kHz while the error of impedance real part remains less than 0.025.