Hybrid Uncertainty and Sensitivity Analysis of the Model of a Twin-Jet Aircraft

Abstract

International audienceThe mathematical models employed in the risk assessment of complex, safety-critical engineering systems cannot capture all the characteristics of the system under analysis, due to: (i) the intrinsically random nature of several of the phenomena occurring during system operation (aleatory uncertainty); (ii) the incomplete knowledge about some of the phenomena (epistemic uncertainty). In this work, we consider the model of a twin-jet aircraft, which includes twenty-one inputs and eight outputs. The inputs are affected by mixed aleatory and epistemic uncertainties represented by probability distributions and intervals, respectively. Within this context, we address the following issues: (A) improvement of the input uncertainty models (i.e., reduction of the corresponding epistemic uncertainties) based on experimental data; (B) sensitivity analysis to rank the importance of the inputs in contributing to output uncertainties; (C) propagation of the input uncertainties to the outputs; (D) extreme case analysis to identify those system configurations that prescribe extreme values of some system performance metrics of interest (e.g., the failure probability). All the tasks are tackled and solved by means of an efficient combination of: (i) Monte Carlo Simulation (MCS) to propagate the aleatory uncertainty described by probability distributions; (ii) Genetic Algorithms (GAs) to solve the numerous optimization problems related to the propagation of epistemic uncertainty by interval analysis, and (iii) fast-running Artificial Neural Network (ANN) regression models to reduce the computational time related to the repeated model evaluations required by uncertainty and sensitivity analyses

The Bhattacharyya distance: Enriching the P-box in stochastic sensitivity analysis

“…This task involves multiple uncertain parameter categories and multiple distribution formats, which provide a veritable challenge for SA in the uncertainty quantification background. In order to assess the results, three published works on the NASA UQ challenge problem, namely the papers by Patelli et al [7], Pedroni et al [24], and McFarland [25], are used as references to compare with the results of the current work.…”

“…Results in the references Results in the current work Patelli [7] Pedroni [24] McFarland [ The last three columns of Table 4 present the ranking results of the current work according to three different indices, namely the proportional index 𝑆𝑆 𝑚𝑚 (𝑝𝑝𝑝𝑝𝑝𝑝) , the variance-based index 𝑆𝑆 𝑚𝑚 (𝑣𝑣𝑚𝑚𝑝𝑝) , and the comprehensive index 𝑆𝑆 𝑚𝑚 (𝑐𝑐𝑝𝑝𝑚𝑚) . The index value is provided in parenthesis after each parameter in the table.…”

“…The second case study solves the SA task of the NASA UQ challenge problem [23]. Results of the current work are compared with previously published works [7,24,25] to demonstrate the Bhattacharyya distance as a competent UQ metric in the proposed stochastic SA approach.…”

Generalization of non-intrusive imprecise stochastic simulation for mixed uncertain variables

“…The simplest procedure is to perform optimization for distribution parameters in the outer loop and then propagate the degraded category I model in the inner loop with, e.g., precise stochastic simulation method [11]. This strategy has been applied to the NASA Langley challenge problem with the utilization of genetic algorithm for outer loop optimization and Monte Carlo simulation for the inner loop analysis [12]. The second strategy is based on sampling in the outer loop so as to generate a set of interval samples for input variables, and then propagate each interval sample in the inner loop by, e.g., interval finite element analysis or optimization algorithms [13]- [15].…”

Application of Probabilistic and Nonprobabilistic Hybrid Reliability Analysis Based on Dynamic Substructural Extremum Response Surface Decoupling Method for a Blisk of the Aeroengine

“…Other researchers optimized structures and studied their sensitivity through probabilistic and nonprobabilistic hybrid reliability methodology as well [25][26][27][28][29][30][31]. For example, Luo and Zhang investigated an adhesive bonded steel-concrete composite beam with probabilistic and nonprobabilistic uncertainties and mathematically formulated the reliability-based optimization, incorporating mixed reliability constraints as a nested problem.…”