A Reliability-Metric-Based Validation Method for Multi-Output Models Under Random and Interval Mixed Uncertainty

Abstract

Conventional validation methods for multi-output models generally assume probabilistic descriptions of all input variables. In engineering applications, however, sparse data and limited knowledge may permit some inputs to be specified only by intervals, which limits the applicability of existing methods under random and interval mixed uncertainty. This challenge is prevalent in numerical simulation of various aerospace structural systems. A reliability-metric-based validation method for multi-output models under random and interval mixed uncertainty is proposed in this paper. The Mahalanobis distance (MD) is used to account for correlations among multiple responses, and interval analysis is introduced to construct an interval-valued MD. A conservative validation metric is then defined as the probability that the upper bound of the model–experiment MD is smaller than the lower bound of the MD corresponding to the engineering-tolerance vector. The metric therefore quantifies, from a reliability perspective, the probability that model predictions satisfy prescribed engineering tolerances. Because the coupling between random and interval uncertainties prevents a straightforward analytical solution, a baseline numerical procedure based on Monte Carlo simulation (MCS) is developed. Two numerical examples and two engineering examples demonstrate the applicability of the method. The results indicate that the proposed metric accommodates random and interval mixed uncertainty, accounts for correlations among multiple outputs, and provides a probabilistic measure of agreement between model predictions and experimental measurements. The method offers an interpretable basis for assessing the credibility of complex engineering simulation models.