Error and Uncertainty Analysis of Inexact and Imprecise Computer Models

Abstract

Computer simulations are routinely executed to predict the behavior of complex systems in many fields of engineering and science. These computer-aided predictions involve the theoretical foundation, numerical modeling, and supporting experimental data, all of which come with their associated errors. A natural question then arises concerning the validity of computer model predictions, especially in cases where these models are executed in support of high-consequence decision making. This article lays out a methodology for quantifying the degrading effects of incompleteness and inaccuracy of the theoretical foundation, numerical modeling, and experimental data on the computer model predictions. Through the method discussed in this paper, the validity of model predictions can be judged and communicated between involved parties in a quantitative and objective manner.

Robust system identification and model predictions in the presence of systematic uncertainty

“…However, learning the correct values of physical parameters is important for the understanding of the true behavior of the system and also for improving confidence in model extrapolation [10,16]. Extrapolation values are predictions out of the measurement context, such as fatigue life in the example of the beginning of this paper.…”

A Resource Allocation Framework for Experiment-Based Validation of Numerical Models

“…The bounds on the critical stress associated with glide and the lower bound of the critical stress associated with climb are determined according to Eqs. (9) and (10). The upper bound of the critical stress associated with climb is determined from Eq.…”

“…This incompleteness invariably causes systematic bias in predictions [3][4][5][6][7] and often leads to missing input parameters [8]. Imprecise model parameters, the second factor, are identified by the analyst; however, their precise values (or distributions) remain unknown [9,10]. These imprecise model parameters are typically the main contributors to the uncertainty in predictions.…”

Partitioned Analysis of Coupled Numerical Models Considering Imprecise Parameters and Inexact Models

“…Note that here the calibration parameters θ are treated as part of the decision variables of the optimization procedure. The aforementioned process for calibrating uncertain parameter values while simultaneously determining the discrepancy bias, discussed in great detail in Farajpour and Atamturktur (2013), is developed for a single model, and thus is not configured to be applicable for coupled numerical models (neither weakly nor strongly coupled models). The goal of the authors here is to extend the applicability of this previously developed uncertainty quantification approach beyond a single model.…”

“…The interactions between these constituents are typically complex in nature during this process, where the outputs of a constituent become inputs for another. Each constituent inherently contains uncertainty in the numerical calculation and solution of mathematical equations (numerical uncertainty), imprecision in model parameters (parameter uncertainty) and bias owing to incomplete physics principles (known as model form error or structural uncertainty) (Farajpour and Atamturktur 2013). When these constituents are coupled, the uncertainties and biases propagate between different scales and/or physics.…”