Abstract
Many non-probabilistic approaches have been widely regarded as mathematical tools for the representation of epistemic uncertainties. However, their heavy computational burden and low computational efficiency hinder their applications in practical engineering problems. In this article, a unified probabilistic representation approach for multiple types of epistemic uncertainties is proposed based on the cubic normal transformation method. The epistemic uncertainties can be represented using an interval approach, triangular fuzzy approach, or evidence theory. The uncertain intervals of four statistical moments, which contain mean, variance, skewness, and kurtosis, are calculated using the sampling analysis method. Subsequently, the probabilistic cubic normal distribution functions are conducted for sampling points of four statistical moments of epistemic uncertainties. Finally, a calculation procedure for the construction of probabilistic representation functions is proposed, and these epistemic uncertainties are represented with belief and plausibility continuous probabilistic measure functions. Two numerical examples and one engineering example demonstrate that the proposed approach can act as an accurate probabilistic representation function with high computational efficiency.
Highlights
There are various sources of uncertainties in real-world engineering conditions, such as loading uncertainties, material uncertainties, geometric and boundary uncertainties due to manufacturing tolerances, variation in operating environments, and differences in technical levels
In numerical example 2, the proposed methodology is applied to uncertainty propagation analysis for multiple types of epistemic uncertainties, and the probabilistic uncertainty result is similar to the results of the Monte Carlo simulation (MCS)
The time taken to evaluate the calculation of the uncertainty of the performance function using the proposed algorithm and MCS method was 4.75 and 14.67 s, respectively, and the computational efficiency was improved by 67.6%
Summary
There are various sources of uncertainties in real-world engineering conditions, such as loading uncertainties, material uncertainties, geometric and boundary uncertainties due to manufacturing tolerances, variation in operating environments, and differences in technical levels. Evidence theory uses belief assignment as its basis to describe uncertainty information, and it represents the variable uncertainty with the belief and plausibility measure function With these non-probabilistic uncertainty representation methods, epistemic uncertainty is quantified, propagated, and optimized in the reliability design of engineering products [24,25]. (2) The representation function of epistemic uncertainties is discontinuous, so repeated extreme analysis of epistemic uncertainties at discrete subintervals should be implemented, which reduces the computational efficiency in the reliability design of engineering products To resolve these issues effectively, a unified probabilistic uncertainty representation approach for multiple types of epistemic uncertainties is proposed based on the cubic normal distribution method. Multiple Types of Non-Probabilistic Representation Approaches for Epistemic Uncertainties
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