New model for system behavior prediction based on belief rule based systems

To predict the behavior of a complex engineering system, a model can be built and trained using historical data. However, it may be difficult to obtain a complete and accurate set of data to train the model. Consequently, the model may be incapable of predicting the future behavior of the system with reasonable accuracy. On the other hand, expert knowledge of a qualitative nature and partial historical information about system behavior may be available which can be converted into a belief rule base (BRB). Based on the unique features of BRB, this paper is devoted to overcoming the above mentioned difficulty by developing a forecasting model composed of two BRBs and two recursive learning algorithms, which operate together in an integrated manner. An initially constructed forecasting model has some unknown parameters which may be manually tuned and then trained or updated using the learning algorithms once data become available. Based on expert intervention which can reflect system operation patterns, two algorithms are developed on the basis of the evidential reasoning (ER) algorithm and the recursive expectation maximization (EM) algorithm with the former used for handling judgmental outputs and the latter for processing numerical outputs, respectively. Using the proposed algorithms, the training of the forecasting model can be started as soon as there are some data available, without having to wait until a complete set of data are all collected, which is critical when the forecasting model needs to be updated in real-time within a given time limit. A numerical simulation study shows that under expert intervention, the forecasting model is flexible, can be automatically tuned to predict the behavior of a complicated system, and may be applied widely in engineering. It is demonstrated that if certain conditions are met, the proposed recursive algorithms can converge to a local optimum. A case study is also conducted to show the wide potential applications of the forecasting model.