Objectives Substantial epistemic and aleatory uncertainties coexist in the modeling and simulation (M&S) of ship non-contact underwater explosion (UNDEX). Such uncertainties can lead to large deviations between the numerical results and true experimental data for system response quantity (SRQ), which can deteriorate M&S performance. However, the uncertainty quantification (UQ) of non-contact UNDEX can improve the reliability and credibility of M&S.

Methods First, the D−S theory of evidence (DSTE) combined with subject matter expert (SME) opinion is utilized to obtain the basic belief assignment (BBA) function and value interval of the phenomenological parameters, which have no physical meaning and cannot be directly calibrated through physical experiments. In view of the constraints of engineering experience and knowledge structure of SME, the multiple source fusion and periodic fusion methods are used to further improve the objectivity of the epistemic UQ. Furthermore, the Monte Carlo method is applied to study the high-dimensional uncertainty propagation of the non-contact UNDEX of the ship. Finally, the double-loop method is applied in the mixed UQ when the ship non-contact UNDEX is disturbed by both aleatory uncertainty and epistemic uncertainty; to be specific, the phenomenological parameters are solved in the outer loop and the aleatory uncertainty is handled in the inner loop.

Results The results show that the range of epistemic uncertainty is shortened and the initial opinion of SME substantially altered. The BBA of epistemic uncertainty computed from altered DSTE becomes more accurate and objective. The credible confidence interval of SRQ and corresponding BBA function in the non-contact UNDEX calculation can be obtained from the double loop approach, and the results indicate that it agrees with the common sense.

Conclusion This study can provide guiding references for ship protection design and improve the explosive damage power of underwater weapons.