Classification correction of polynomial response surface methods for accurate reliability estimation

Abstract

Abstract In recent years, Meta models are widely used to reduce the computational cost of the reliability analysis by predicting the system responses using a surrogate model. This study shows that for complex problems, the surrogate model of some regression-based Meta models such as Response Surface Method (RSM) not only fails to properly predict the system response but also fails to classify the employed experimental samples (samples that used to construct surrogate model). Therefore, the current application of these approaches would not be sensible for many real-world problems. Accordingly, it is proved that the standard reliability formulation requires modification for proper handling of Meta models in reliability analysis and a refining term – in this study named as classification error removal term (CERT)- should be added to the well-known failure probability integral for removing the errors of the employed surrogate model. Then, the original failure probability integral is rewritten based on the proposed proposition and subsequently based on RSM and an importance sampling-based design of experiments. Thus, a mathematically exact formulation is presented for solving complex reliability problems. In the proposed formulation, CERT only reuses the results of experimental samples and therefore the proposed method does not require further function call compare to the conventional RSM-based reliability approaches. Solving high dimensional/complex reliability problems involving a real-world shell and tube heat exchanger system shows efficiency, accuracy, and robustness of the proposed method for solving real-world engineering problems.