Assessment and design of an engineering structure with polymorphic uncertainty quantification

Abstract

Engineers are faced with the challenge of supporting decision making under uncertainty. Engineering decisions often depend on model‐based predictions of the performance of the engineering system of interest. Input uncertainties of models can be categorized into two distinct types: aleatory (random/irreducible) or epistemic (reducible). Polymorphic uncertainty quantification (UQ) can be used to treat aleatory and epistemic uncertainties in a unified framework. The polymorphic UQ framework employs probability theory to model aleatory variables and alternative approaches (interval, fuzzy, Bayesian probabilistic, and combinations thereof) to model epistemic variables. This paper compares different polymorphic UQ approaches with respect to their ability to support a simple engineering decision. The comparison is based on a test‐bed example, whereby aleatory variables are defined in terms of probability distributions and epistemic variables are described based on limited information (sparse data or intervals). Two challenges related to common engineering decisions (safety assessment and reliability‐based design) serve as a basis for the comparison. Five independent research groups applied different models to describe the epistemic parameters based on a subjective interpretation of the given information. The comparison of the results reveals a strong influence of both the subjective choices on the models of the epistemic variables and the chosen basis for assessing the performance of the structure on the obtained decision outcomes.

Yield Optimization Based on Adaptive Newton-Monte Carlo and Polynomial Surrogates

“…These uncertainties are often classified as aleatory. The setting could be generalized by interpreting the computed yield to be conditioned on epistemic uncertainties and by further quantifying these uncertainties as outlined, for instance, in [20,21]. However, since the focus of the present work is on adaptivity and error control in the context of yield estimation, this will not be considered here.…”

On data-based estimation of possibility distributions

“…Papaioannou et al pose a benchmark problem for the quantification of polymorphic uncertainties in [35]. Therein, the probability of the failure of a wide flange steel column is investigated under aleatory as well as epistemic uncertainties, and several approaches to its solution in different frameworks are provided and compared.…”

“…The problem itself is based on Example 2 in [36] and considers a column which is "subjected to a compressive load P consisting of two components P = P p + P e , where P p denotes the permanent load and P e the environmental load." [35] A complete solution to the problems posed therein would go beyond the scope of this paper. However, an exemplary analysis on the basis of possibility theory with an emphasis on estimation problems shall be pursued in the following.…”

“…Its probability distribution is unknown, yet 20 measurements from consecutive years are provided to enable an estimation thereof, see Table 1. For simplicity, all approaches in [35] assume the load to follow a Gumbel distribution for which only the location and the scale parameter need to be identified. This is accomplished by several variants of Bayesian inference and maximum likelihood estimation.…”

“…in the high residual probability P res (20, •). Under this approach, the possibilistic answer to Challenge 1 in [35], posing the question if a failure probability below 1.3 • 10 −6 can be guaranteed, has to be a clear 'no', since the system will always fail for an environmental load which is high enough. Yet, the estimated possibility distribution for all but the lowest levels of confidence γ does not render this event improbable enough with a sufficiently low possibility.…”