Advanced Probabilistic Neural Network for Reliability Estimation via Semi-supervised Learning

Abstract

In general, the accuracy of a classification-based surrogate model for reliability assessment can be improved by augmenting the training data with a large number of unlabeled data (data with unknown response) in Semi-Supervised Learning (SSL) methods. In this research, an improved Semi-Supervised Learning algorithm is proposed which involves the usage of Bayes rule. The prior probabilities are calculated using the Expectation-Maximization algorithm for all the contributing clusters. Bayes theorem is then used to relax the ‘spherical’ covariance assumption of Probabilistic Neural Networks (PNN). Individual contributions (posterior probabilities) of each ‘full’ covariance matrices are found by using the Bayes theorem. A Bayes decision criterion is used again in the final output layer of the PNN to classify test patterns into either the safe or the failure classes. The primary benefit of the proposed method comes from including unlabeled data for better estimation of Probability Density Functions of either class, which are then used for estimating the class labels of test patterns. This procedure does not require additional computational costs. The examples of an analytical problem and a ten bar truss problem demonstrate the efficacy of the proposed procedure in estimating the reliability of given systems The results reflect considerable improvements of the classifier performance for estimating reliability while maintaining sufficient accuracy.