A novel parameter-related wiener process model with its estimation of remaining useful life in degradation analysis

The Wiener process is widely used in the degradation modeling, life prediction, and maintenance decision of products in aerospace, high-speed rail and marine field. In the basic Wiener process model, the drift parameter represents the degradation rate and the diffusion parameter represents the degradation fluctuation, and they are independent of each other, which is not conform to the laws of physics and existing research experience. According to the physical knowledge and the widely known accelerated degradation test experience, when the environmental stress level increases, the degradation rate and degradation fluctuation of the product will increase accordingly. Thus, there is a positive correlation between the rate parameter and the diffusion parameter in the Wiener process model. Ignoring this positive correlation of the drift parameter and the diffusion parameter in Wiener process will lead to imprecise degradation modeling and life prediction results. In this paper, a novel parameter-related Wiener process model is proposed by considering the positive correlativity between the drift and the diffusion parameter. The statistical properties of the novel parameter-related Wiener process model are derived. The method proposed in this paper is demonstrated by applied to a set of ageing test data of rubber. First, the ageing path is simulated based on the proposed model. Then, the remaining useful life of the rubber is predicted using the novel parameter-related Wiener process model proposed in this paper. The predicted results are compared with those of the basic Wiener process model, with the following conclusions: 1) Model-10 and Model-12 are constructed theoretically by the novel thinking of the linear relationship between the drift and diffusion parameter. A novel class of parameterrelated Wiener process model is proposed in this paper by letting the drift and diffusion parameter have a positive relationship, which are Model-10 and Model-12. The random effect of the drift parameter is considered in the novel model. The reference is derived for the two models and they both have good statistical property for parameter estimation. 2) The proposed method is illustrated by a case study of rubber ageing data, and the proposed model is compared with the basic Wiener process model. The results show that Model-12 is precise in describing the ageing path as Model-0 does, and has a better RUL prediction effect than Model-0 in the latter third stage of the degradation process. And the remaining useful life (RUL) obtained from Model-10 is closer to the actual value than Model-0 over time. Thus, Model-10 is more accurate in RUL prediction. 3) For other novel points, this paper applies the Pearson correlation coefficient to test whether the actual degradation data suit the Model-10 and Model-12. After estimating the drift and diffusion parameter of degradation by maximum likelihood estimation (MLE), the Pearson correlation coefficient can be calculated to select the proper degradation model. And the Pearson correlation coefficient calculated from the ageing data of rubber proves that the parameter-related effect exists in the ageing process.