Hidden behavior prediction of complex systems under testing influence based on semi-quantitative information and belief rule base

Compared with the observable behavior, it is difficult to predict the hidden behavior of a complex system. In the existing methods for predicting the hidden behavior, a lot of testing data (usually quantitative information) are needed to be sampled. However, some complex engineering systems have the following characteristics: 1) The systems cannot be tested periodically, and the observable information is incomplete; 2) the change process of hidden behavior may be affected by the test; and 3) only part of quantitative information and qualitative knowledge (i.e., semiquantitative information) may be obtained. These characteristics all related to the test are named as testing influence for simplicity. Although a model and a corresponding optimal algorithm for training the model parameters have been proposed to predict the hidden behavior on the basis of semiquantitative information and belief rule base (BRB), the testing influence has not been considered. In order to solve the above problems, a new BRB-based model, which can use the semiquantitative information, is proposed under testing influence in this paper. In the newly proposed forecasting model, there are some parameters of which the initial values are usually assigned by experts and may not be accurate, which can lead to the inaccurate prediction results. As such, an improved optimal algorithm for training the parameters of the forecasting model is further developed on the basis of the expectation-maximization idea and the covariance matrix adaption evolution strategy (CMA-ES). By using the semiquantitative information, the proposed BRB-based model and the improved CMA-ES algorithm can operate together in an integrated manner so as to improve the forecasting precision. A case study is examined to demonstrate the ability and applicability of the newly proposed BRB-based forecasting model and the improved CMA-ES algorithm.