Variance based sensitivity analysis for Monte Carlo and importance sampling reliability assessment with Gaussian processes

Menz, Morgane; Dubreuil, Sylvain; Mitard, J.; Gogu, Christian; Bartoli, Nathalie; Chiron, Marie

doi:10.1016/j.strusafe.2021.102116

Cited by 31 publications

(5 citation statements)

References 44 publications

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“…Another way to fix this issue was proposed in the article [27]. The authors claimed that, in order to reduce the overall numerical cost of simulations such as the Monte Carlo method, a Gaussian process based on active learning methods could be used.…”

Section: Monte Carlo Methods and Alternative Optionsmentioning

confidence: 99%

Methods for the Calculation and Control of Launch Vehicle Drop Regions

et al. 2023

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The article aims at reviewing the drop regions (DR) of the launch vehicles (LV) separating parts (SP) and methods of their determination. The DRs include sea and land areas; going beyond them is associated with a number of environmental, economic, and political factors. Their combination dictates the need to ensure the safety of the people, transport, infrastructure, and environment from the negative impact of LV SPs and fuel residues. The Monte Carlo method is mostly used to determine the impact areas. It enables an estimation of the probability of the SPs of LVs falling in certain areas, constituting the DRs. These points are varied according to a set of different initial parameters. The methods of controlling the impact areas are contingently divided into engineering (based on a change in the design appearance of the LV), mathematical (which includes the changes in or optimization of the LV’s trajectory or its SP), and “soft landing” (implying the return of the LV’s to the spaceport or to a certain prepared area). The present analysis can be used as a starting point when choosing a method for determining and controlling the projected LVs and the SPs’ area of impact.

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Section: Monte Carlo Methods and Alternative Optionsmentioning

confidence: 99%

Methods for the Calculation and Control of Launch Vehicle Drop Regions

et al. 2023

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“…If the criterion on the quantile is not fulfilled, a local enrichment of the surrogate model is proposed. Local enrichment of surrogate model has proven to be efficient in order to increase the accuracy with respect to a given objective in various context such as optimization (see References 4,40 for example) and reliability (see References 41‐43 for example). In the present context the difficulties for the enrichment step come from the choice of the disciplinary surrogate model to enrich and the coupling between the disciplinary surrogate models.…”

Section: Detailed Description Of the Proposed Methodologymentioning

confidence: 99%

Disciplinary proper orthogonal decomposition and interpolation for the resolution of parameterized multidisciplinary analysis

Berthelin

Dubreuil

Salaün

et al. 2022

Numerical Meth Engineering

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This article proposes a new method for the resolution of parameterized coupled systems of equations, such as typical in multidisciplinary analysis (MDA).It is based on the use of disciplinary surrogate models within a multi-query context. The main idea is to replace the costly disciplinary solvers of the MDA by Proper Orthogonal Decomposition and Interpolation models. The main challenge we address is the high-dimensional coupling variables whose ranges are unknown. To overcome this issue, a training strategy is developed by uncoupling the disciplinary solvers from the MDA context. This new surrogate MDA called Disciplinary Proper Orthogonal Decomposition and Interpolation is iteratively enriched to solve the analysis with an estimation of the error made by the surrogate models. The disciplinary surrogate model which has the most influence on this error is determined by a sensitivity analysis and thus enriched. This approach allows to uncouple the disciplinary solvers during the training and enrichment phases. The approach is applied to various aeroelastic problems of an aircraft wing and allows to reduce by a factor of 5 the mean number of disciplinary solver calls needed for the resolution of the MDA.

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“…A more recent approach based on Karhunen-Loève decomposition of the covariance kernel with the Nyström method has been proposed in [18] where the paths can be sampled by generating independent standard Normal distributed samples. The different methods are documented in the tutorial Gaussian Process Trajectory Sampling [147].…”

Section: Contributions To Applicationsmentioning

confidence: 99%

High-dimensional multidisciplinary design optimization for aircraft eco-design

SAVES

2024

Preprint

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Nowadays, there is a significant and growing interest in improving the efficiency of vehicle design processes through the development of tools and techniques in the field of MDO. Specifically, in aerostructure design, aerodynamic and structural variables influence each other and have a joint effect on quantities of interest like weight or fuel consumption and, as such, MDO arises as a powerful tool for automatically making interdisciplinary trade-offs. In the aircraft design context, the process generally involves mixed continuous and categorical design variables. For instance, the size of an aircraft’s structural parts can be described using continuous variables, while discrete variables may include either integer variables, like the number of panels, or categorical variables, like cross-sections or material choices. The objective of this Philosophiae Doctor (Ph.D) thesis is to propose an efficient approach for optimizing a multidisciplinary black-box model when the optimization problem is constrained and involves a large number of mixed integer design variables (typically 100 variables). The targeted optimization approach, called EGO, is based on a sequential enrichment of an adaptive surrogate model and, in this context, GP surrogate models are one of the most widely used in engineering problems to approximate time-consuming high fidelity models. EGO is a heuristic BO method that performs well in terms of solution quality. However, like any other global optimization method, EGO suffers from the curse of dimensionality, meaning that its performance is satisfactory on lower dimensional problems, but deteriorates as the dimensionality of the optimization search space increases. For realistic aircraft design problems, the typical size of the design variables can even exceed 100 and, thus, trying to solve directly the problems using EGO is ruled out. The latter is especially true when the problems involve both continuous and categorical variables increasing even more the size of the search space. In this Ph.D thesis, effective parameterization tools are investigated, including techniques like partial least squares regression, to significantly reduce the number of design variables. Additionally, Bayesian optimization is adapted to handle discrete variables and high-dimensional spaces in order to reduce the number of evaluations when optimizing innovative aircraft concepts such as the “DRAGON” hybrid airplane to reduce their climate impact.

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Variance based sensitivity analysis for Monte Carlo and importance sampling reliability assessment with Gaussian processes

Cited by 31 publications

References 44 publications

Methods for the Calculation and Control of Launch Vehicle Drop Regions

Methods for the Calculation and Control of Launch Vehicle Drop Regions

Disciplinary proper orthogonal decomposition and interpolation for the resolution of parameterized multidisciplinary analysis

High-dimensional multidisciplinary design optimization for aircraft eco-design

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