Belief-Rule-Base Inference Method Based on Gradient Descent With Momentum

The belief-rule-base (BRB) inference methodology using the evidential reasoning (ER) approach is widely used in different fields, such as fault diagnosis, system identification, and decision analysis. However, the calculation characteristic of the conventional rule activation weight makes the inference system have the rule zero activation problem. The difficulty of constructing partial derivatives restricts the optimization of parameters using the gradient method. Hence, this paper proposes a new belief rule structure and its gradient training method to solve the rule zero activation problem during the inference process and improve inference accuracy. The Gaussian function is applied to calculate the activation weight of the rule with the new structure. Its characteristics avoid the zero activation problem caused by the attribute reference value set in the original method. Based on the newly proposed method, the corresponding distance-sensitive parameter is set for each attribute, and the weight parameter of each rule is discarded. It simplifies the calculation of rule activation weights in the inference process and enables the partial derivatives of the parameters of the inference system to be easily constructed. In the parameter optimization, the momentum optimization gradient stochastic descent method is used to train the new BRB system, which improves the training speed and accuracy compared with the conventional methods. Experiments with nonlinear function fitting, oil pipeline leak detection, and classification of several public datasets are carried out to verify whether the new BRB system trained with momentum stochastic gradient descent (SGDM-BRB) has better performance than other conventional methods. The experimental results show that in the case of complete data, SGDM-BRB has higher accuracy and faster training speed than the conventional methods.