Estimation of loss coefficients of Nonlinear rubber using iterative H-infinity filter

Abstract

For automobile industry, rubber is widely used for noise isolation and vibration reduction. However, due to its distributed and nonlinear characteristics, it is hard to precisely estimate its characteristics such as the loss coefficient which is defined as the tangent of the phase delay between the fundamental components of the strain and the stress under sinusoidal driving. Moreover, even using a truncated finite-dimensional model, with rubber's nonlinearity, resonance of the testing mechanical system, and measurement noise, optimal estimation of the loss coefficient by using Kalman filter is not feasible in the presence of these uncertainties and non-Gaussian disturbances. Therefore, H-infinity filter is applied in this paper to robustly estimate the loss coefficient from the state-space perspective. As a state-space model for representing a sinusoidal signal has eigenvalues on the unit circle, the measured data is first processed by imposing a suitable exponential decay in order to ensure the stability of the H-infinity filter. Moreover, due to finite data length, an iterative H-infinity filter is developed to improve the accuracy of parameter estimates. At each iteration, estimation of disturbances by using the H-infinity filter is first performed by applying the previously estimated components of the desired signal. Then a robust estimation of the desired signal is made with respect to the measured signal which is subtracted by the estimated disturbance. Both simulation study and experimental test are conducted to verify the performance of the proposed iterative H. filter.