Adaptive reduced basis strategy for rare‐event simulations

Gallimard, Laurent

doi:10.1002/nme.6135

Cited by 10 publications

(13 citation statements)

References 50 publications

(103 reference statements)

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“…For higher percentages (6-sigma) much higher accuracy is needed, i.e., more sample points or other techniques have to be applied, e.g. importance sampling [27] or subset simulation [28].…”

Section: B Estimation Of the Yieldmentioning

confidence: 99%

Multi-Objective Yield Optimization for Electrical Machines using Machine Learning

Huber¹,

Fuhrländer²,

Schöps³

2022

Preprint

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This work deals with the design optimization of electrical machines under the consideration of manufacturing uncertainties. In order to efficiently quantify the uncertainty, blackbox machine learning methods are employed. A multiobjective optimization problem is formulated, maximizing simultaneously the reliability, i.e., the yield, and further performance objectives, e.g., the costs. A permanent magnet synchronous machine is modeled and simulated in commercial finite element simulation software. Four approaches for solving the multiobjective optimization problem are described and numerically compared, namely: ε-constraint scalarization, weighted sum scalarization, a multi-start weighted sum approach and a genetic algorithm.

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“…For higher percentages (6-sigma) much higher accuracy is needed, i.e., more sample points or other techniques have to be applied, e.g. importance sampling [27] or subset simulation [28].…”

Section: B Estimation Of the Yieldmentioning

confidence: 99%

Multi-Objective Yield Optimization for Electrical Machines using Machine Learning

Huber¹,

Fuhrländer²,

Schöps³

2022

Preprint

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“…For that reason, there is research on efficient yield estimation, using e.g. importance sampling [5], surrogate modeling [1,11,10] or hybrid approaches [8,3,4]. These hybrid approaches combine classic MC with surrogate methods, e.g.…”

Section: Definition Of the Yieldmentioning

confidence: 99%

Efficient yield optimization with limited gradient information

Fuhrländer¹,

Schöps²

2021

Preprint

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In this work an efficient strategy for yield optimization with uncertain and deterministic optimization variables is presented. The gradient based adaptive Newton-Monte Carlo method is modified, such that it can handle variables with (uncertain parameters) and without (deterministic parameters) analytical gradient information. This mixed strategy is numerically compared to derivative free approaches.

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“…Once an accurate surrogate model is available, it can then be used as an inexpensive substitute of Eq. (3) for an extensive MC analysis (6).…”

Section: Stochastic Collocation and Error Estimationmentioning

confidence: 99%

“…These methods determine the most probable point, which is the closest point from the parameter domain origin to the separating surface between the failure region and the safe region, and employ approximations of the limit state function around this point [4,5]. Investigations in the context of sampling have led to a sample size reduction, e.g., through importance sampling [6] or subset simulation [7,8]. Alternatively or complementarily, the computational effort has been reduced for each sample point, e.g., with surrogate based approaches.…”

Section: Introductionmentioning

confidence: 99%

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

Fuhrländer

Georg

Schöps

2020

Int. J. UncertaintyQuantification

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In this paper we present an algorithm for yield estimation and optimization consisting of Hessian-based optimization methods, an adaptive Monte Carlo (MC) strategy, polynomial surrogates, and several error indicators. Yield estimation is used to quantify the impact of uncertainty in a manufacturing process. Since computational efficiency is one main issue in uncertainty quantification, we propose a hybrid method, where a large part of a MC sample is evaluated with a surrogate model, and only a small subset of the sample is reevaluated with a high-fidelity finite element model. In order to determine this critical fraction of the sample, an adjoint error indicator is used for both the surrogate error and the finite element error. For yield optimization we propose an adaptive Newton-MC method. We reduce computational effort and control the MC error by adaptively increasing the sample size. The proposed method minimizes the impact of uncertainty by optimizing the yield. It allows one to control the finite element error, surrogate error, and MC error. At the same time it is much more efficient than standard MC approaches combined with standard Newton algorithms.

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Adaptive reduced basis strategy for rare‐event simulations

Cited by 10 publications

References 50 publications

Multi-Objective Yield Optimization for Electrical Machines using Machine Learning

Multi-Objective Yield Optimization for Electrical Machines using Machine Learning

Efficient yield optimization with limited gradient information

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

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