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Moment-Constrained Maximum Entropy Method for Expanded Uncertainty Evaluation

The probability distribution is often sought in engineering for the purpose of expanded uncertainty evaluation and reliability analysis. Although there are various methods available to approximate the distribution, one of the commonly used ones is the method based on statistical moments (or cumulants). Given these parameters, the corresponding solution can be reliably approximated using various algorithms. However, the commonly used algorithms are limited by only four moments and assume that the corresponding distribution is unimodal. Therefore, this paper analyzes the performance of a relatively new and an improved parametric distribution fitting technique known as the moment-constrained maximum entropy method, which overcomes these shortcomings. It is shown that the uncertainty (or reliability) estimation quality of the proposed method improves with the number of moments regardless of the distribution modality. Finally, the paper uses case studies from a lighting retrofit project and an electromagnetic sensor design problem to substantiate the computational efficiency and numerical stability of the moment method in design optimization problems. The results and discussions presented in the paper could guide engineers in employing the maximum entropy method in a manner that best suits their respective systems.