Load spectrum modeling for tracked vehicles based on variational Bayesian inference

Abstract

The load spectrum is the basis of performing the reliability and fatigue life analysis for the structures of tracked vehicles. In order to obtain the load spectrum, the load cycles should be extracted from the measured or simulated load time history using rainflow counting method. After that, the distribution of the load cycles can be modeled by a continuous distribution function. For the purpose of finding a common modeling method and effective parameters’ estimation method for the load spectrum, we used a mixture of multivariate Gaussian functions to model the probability density function of general load time history on the basis of extracted load cycles. Additionally, we proposed an approach for unknown parameters’ estimation based on variational Bayesian inference. This parameter estimation method can automatically infer the number of components from the observed data set. Numerical examples were given to illustrate the effectiveness of our proposed modeling method and unknown parameters’ estimation method. We compared the distributions of the load cycles reconstructed by the load spectrum models with those of the original load cycles. At the same time, we obtained the quantitative optimal results of the parameters for the load cases. The results showed that the mixture Gaussian functions can model complex distribution of the rainflow load cycles for tracked vehicles by choosing suitable number of components and suitable parameters of them, and the variational Bayesian inference is an effective unknown parameters’ estimation method for the mixture models which have latent variables.