SUMMARY

Traditionally design engineers have used the Factor of Safety method for ensuring that designs don’t fail in the field. Access to advanced computational tools and resources have made this process obsolete and new methods to introduce higher levels of reliability in an engineering systems are being investigated currently. However, even though high computational resources are available the computational resources required by reliability analysis procedures leave much to be desired. Furthermore, the regression based surrogate modeling techniques fail when there is discontinuity in the design space, caused by failure mechanisms, when the design is required to perform under severe externalities. Hence, in this research we propose efficient surrogate modeling techniques that will enable accurate estimation of a system’s response, even under discontinuity, while ensuring a drastic reduction in computational requirement. In Supervised Machine Learning, surrogate models can be trained with a set of training points for which the corresponding system responses are known. These labeled training points are computationally expensive to get since the responses have to be evaluated for a combination of uncertain design variables. These combinations of uncertain design variables, called unlabeled data, are available in plenty since the Probability Distribution Function (PDF) information for the uncertain design variables are assumed to be known. We propose the combination of a few labeled and a large number of unlabeled data in order to construct superior surrogate modeling techniques, which come under the category of Semi-Supervised Learning. This superior performance is gained by combining the efficiency of Probabilistic Neural Networks (PNN) for classification and Expectation-Maximization (EM) algorithm for treating the unlabeled data as labeled data with hidden labels. Representative examples will be demonstrated where the proposed algorithms are shown to be effective in cases of linear, non-linear and discontinuous failure domains. Furthermore, the applicability of the proposed algorithms during the conceptual design stages is validated by three reliability-based engineering design examples.