Simultaneous Discrete-Direct Methodology for Effective Treatment of Sparsely Sampled Sources of Aleatory Variability and Conservative Estimation of Tail Probabilities—Confirmation on a Weld Modeling Problem

Abstract Typically, in engineering projects, aleatory variability of materials, phenomena, and geometry/hardware can only be sampled very sparsely by replicate physical experiments or tests. This precludes accurate identification of the form and parameters of frequency distributions, or more generally, multidimensional random function models, of stochastically varying quantities for ensuing propagation through physics models. These difficult conditions are well handled with a new class of discrete-sample propagation and uncertainty processing approaches described and demonstrated in this paper, instead of trying to infer the random function models from the sparse sample data and then propagate the inferred functions and inference uncertainties. We explain the “Simultaneous Discrete Direct” (SDD) approach for aleatory uncertainty representation and propagation of multiple sources of sparsely sampled aleatory variability and apply SDD to a realistic and challenging test problem involving computationally expensive weld and structural response models. We perform random draws of N = 4 samples of each of five sources of known variability in the synthetic-reality test problem, propagate all samples with N = 4 model runs per the economical SDD approach, and use specialized 1D uncertainty quantification techniques to statistically process the N = 4 samples of each of 40 response quantities of the structural model into reliably conservative bounding estimates on 0.005 tail quantiles and probabilities. We perform 250 random trials to quantify the usefully high reliability/confidence of attaining conservative estimates. SDD is also simpler and less computationally expensive than frequency–distribution inference and propagation methods, so in general appears well suited for sparse-data conditions typical in engineering applications.