A bivariate dependent degradation model based on artificial neural network supported stochastic process and Copula function

Abstract

In order to use the high ability of the artificial neural network (ANN) in data fitting, this paper introduces an ANN in stochastic process to describe the mean function for degradation modeling. Due to the fact that the existing method cannot handle the bivariate dependent degradation conditions, a bivariate dependent degradation model based on Copula function and ANN‐supported stochastic processes is proposed. Considering the random effects caused by individual difference, it is assumed that the unknown parameters in the stochastic processes and Copula functions are randomly distributed. Based on the maximum likelihood and moment estimation methods, a related statistical inference method for ANN training and parameter estimation is developed to use the bivariate dependent degradation model. An actual fatigue crack dataset is used to demonstrate the validity of the proposed method. The obtained results show that the dependent relationship between two degradation indicators should not be neglected, and it can be efficiently handled by the proposed method. Furthermore, the proposed degradation model can provide reliability and degradation intervals with enough precision due to the fact that it considers the random effects caused by individual difference.