Joint Prediction of Continuous and Discrete States in Time-Series Based on Belief Functions

Forecasting the future states of a complex system is a complicated challenge that is encountered in many industrial applications covered in the community of prognostics and health management. Practically, states can be either continuous or discrete: Continuous states generally represent the value of a signal while discrete states generally depict functioning modes reflecting the current degradation. For each case, specific techniques exist. In this paper, we propose an approach based on case-based reasoning that jointly estimates the future values of the continuous signal and the future discrete modes. The main characteristics of the proposed approach are the following: 1) It relies on the K-nearest neighbor algorithm based on belief function theory; 2) belief functions allow the user to represent his/her partial knowledge concerning the possible states in the training data set, particularly concerning transitions between functioning modes which are imprecisely known; and 3) two distinct strategies are proposed for state prediction, and the fusion of both strategies is also considered. Two real data sets were used in order to assess the performance in estimating future breakdown of a real system.