Unified Reliability Measure Method Considering Uncertainties of Input Variables and Their Distribution Parameters

Aleatoric and epistemic uncertainties can be represented probabilistically in mechanical systems. However, the distribution parameters of epistemic uncertainties are also uncertain due to sparsely available or inaccurate uncertainty information. Therefore, a unified reliability measure method that considers uncertainties of input variables and their distribution parameters simultaneously is proposed. The uncertainty information for distribution parameters of epistemic uncertainties could be as a result of insufficient data or interval information, which is represented with evidence theory. The probability density function of uncertain distribution parameters is constructed through fusing insufficient data and interval information based on a Gaussian interpolation algorithm, and the epistemic uncertainties are represented using a weighted sum of probability variables based on discrete distribution parameters. The reliability index considering aleatoric and epistemic uncertainties is calculated around the most probable point. The effectiveness of the proposed algorithm is demonstrated through comparison with the Monte Carlo method in the engineering example of a crank-slider mechanism and composite laminated plate.

Automated summary

In this study, a unified reliability measure method is proposed to consider uncertainties of input variables and their distribution parameters simultaneously, using evidence theory and Gaussian interpolation algorithm to construct probability density functions of uncertain distribution parameters of epistemic uncertainties, and representing epistemic uncertainties using a weighted sum. The effectiveness of this method has been demonstrated in engineering examples through comparison with the Monte Carlo method.