Nonlinear mechanical system identification method using auto-regression time series analysis

Abstract

In this paper, we discussed the geometrically nonlinear system identification technology using auto regressive time series analysis. We focused on the transient response from large amplitude to small amplitude. In addition, we assumed that the transient response contains structural non-stationary. We derived the regression formula of instantaneous frequencies and amplitudes using method of averaging. We formulated estimation method of instantaneous frequencies using Kalman filter and auto-regressive model. In numerical simulation, we conducted the identification of load-deformation relationship. In the result, our proposed method could identify the load-deformation relationship in a high degree of accuracy. On the other hand, we conducted the verification of accuracy using least-square method. In this case, accuracy of our proposed method was higher than accuracy of least-square method. We conducted the identification experiment using geometrically nonlinear system. In tensile test, we observed the hard spring characteristic in our experimental system. In addition, we got the free damping oscillation. In the result of an identification experiment, our estimation result was in good agreement with experimental data. On the other hand, we tried the identification test using least-square method. But, we could not reconstruct load-deformation relationship. Therefore, we confirmed availability of our proposed method in low length data.

Keywords

• system identification
• nonlinear vibration
• learning
• diagnostics
• modeling