An Improved Fault-Tolerant Objective Function and Learning Algorithm for Training the Radial Basis Function Neural Network

As the concept of artificial neural networks is based on the mechanism of the human brain, it is essential that a trained artificial neural network should exhibit certain amount of fault-tolerant ability. In this paper, we propose a fault-tolerant learning method for training radial basis function (RBF) networks that may contain the coexistence of the stuck-at-zero node fault and the stuck-at-one node fault. First, we provide a formulation for evaluating the mean square error of the faulty RBF networks. Next an objective function, together with an algorithm for training the fault-tolerant RBF networks, is developed. Subsequently, we derive a mean prediction error (MPE) formula to estimate the test set error of the faulty RBF networks. With the MPE formula, we can estimate the RBF width that leads to near-optimal fault-tolerant capability. Finally, simulations are conducted to demonstrate the feasibility of our method, as well as its compliance with the theoretical outcome.