Efficient robust design via Monte Carlo sample reweighting

Abstract The need for yield estimation strategies in the design stage is a priority recognized by industry. Yield estimates can be employed to assess the manufacturability of a design, and allow for modification to produce a robust design. Therefore, low yield of products can be avoided and costs for manufacturing can be reduced. This paper presents an accurate and time-efficient yield estimation approach for use with simulation models. We use a metamodel-based method, which is time-efficient compared to crude Monte Carlo yield estimation using the original simulation code. The approach employs a boundary-focused experiment design, which overcomes the inaccuracy of yield estimates that can occur when using a metamodel method. The results of two examples demonstrate the effectiveness of this new approach.

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Statistical Inference from a Markov Chain Monte Carlo Sample

Understanding Computational Bayesian Statistics ◽

10.1002/9780470567371.ch7 ◽

2009 ◽

pp. 159-178

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Statistical Inference ◽

Monte Carlo Sample

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Robust designs accounting for model uncertainty in longitudinal studies with binary outcomes

Statistical Methods in Medical Research ◽

10.1177/0962280219850588 ◽

2019 ◽

Vol 29 (3) ◽

pp. 934-952

Author(s):

Jérémy Seurat ◽

Thu Thuy Nguyen ◽

France Mentré

Keyword(s):

Monte Carlo ◽

Longitudinal Studies ◽

Robust Design ◽

Fisher Information ◽

Model Uncertainty ◽

Fisher Information Matrix ◽

Information Matrix ◽

Average Power ◽

Binary Outcomes ◽

Mixed Effect

To optimize designs for longitudinal studies analyzed by mixed-effect models with binary outcomes, the Fisher information matrix can be used. Optimal design approaches, however, require a priori knowledge of the model. We aim to propose, for the first time, a robust design approach accounting for model uncertainty in longitudinal trials with two treatment groups, assuming mixed-effect logistic models. To optimize designs given one model, we compute several optimality criteria based on Fisher information matrix evaluated by the new approach based on Monte-Carlo/Hamiltonian Monte-Carlo. We propose to use the DDS-optimality criterion, as it ensures a compromise between the precision of estimation of the parameters, and hence the Wald test power, and the overall precision of parameter estimation. To account for model uncertainty, we assume candidate models with their respective weights. We compute robust design across these models using compound DDS-optimality. Using the Fisher information matrix, we propose to predict the average power over these models. Evaluating this approach by clinical trial simulations, we show that the robust design is efficient across all models, allowing one to achieve good power of test. The proposed design strategy is a new and relevant approach to design longitudinal studies with binary outcomes, accounting for model uncertainty.

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Robust Design Optimization Under Mixed Uncertainties With Stochastic Expansions

Journal of Mechanical Design ◽

10.1115/1.4024230 ◽

2013 ◽

Vol 135 (8) ◽

Cited By ~ 11

Author(s):

Yi Zhang ◽

Serhat Hosder

Keyword(s):

Monte Carlo ◽

Robust Optimization ◽

Objective Function ◽

Design Optimization ◽

Robust Design ◽

Optimization Technique ◽

Response Surfaces ◽

Robust Design Optimization ◽

Stochastic Expansions ◽

Mixed Uncertainties

The objective of this paper is to introduce a computationally efficient and accurate approach for robust optimization under mixed (aleatory and epistemic) uncertainties using stochastic expansions that are based on nonintrusive polynomial chaos (NIPC) method. This approach utilizes stochastic response surfaces obtained with NIPC methods to approximate the objective function and the constraints in the optimization formulation. The objective function includes a weighted sum of the stochastic measures, which are minimized simultaneously to ensure the robustness of the final design to both inherent and epistemic uncertainties. The optimization approach is demonstrated on two model problems with mixed uncertainties: (1) the robust design optimization of a slider-crank mechanism and (2) robust design optimization of a beam. The stochastic expansions are created with two different NIPC methods, Point-Collocation and Quadrature-Based NIPC. The optimization results are compared to the results of another robust optimization technique that utilizes double-loop Monte Carlo sampling (MCS) for the propagation of mixed uncertainties. The optimum designs obtained with two different optimization approaches agree well in both model problems; however, the number of function evaluations required for the stochastic expansion based approach is much less than the number required by the Monte Carlo based approach, indicating the computational efficiency of the optimization technique introduced.

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Optimisation and Robust Design in Aero Engine Development

Volume 1: 30th Design Automation Conference ◽

10.1115/detc2004-57400 ◽

2004 ◽

Author(s):

Alexander Karl ◽

Stephan Lisiewicz ◽

Winfried-Hagen Friedl ◽

Janet Worgan ◽

Gordon May

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Response Surface ◽

Robust Design ◽

Design Methods ◽

Surface Model ◽

Widespread Application ◽

Deterministic Optimization ◽

Aero Engine ◽

Engine Development

Recent developments in computer capabilities and software enabled the application of deterministic optimization and Robust Design methods in real world aero engine development programs. This paper describes the methods used and shows several applications of this technology. The first example is the application of a Monte-Carlo simulation to support design decisions in the HP turbine casing air system. Here the main goal was to achieve a robust design addressing the variation of build tolerances on flow areas. The variation of parameters as mass flows, pressures and temperatures based on 5000 permutations of the base model give a high confidence level for achieving reliable system behavior for a large population of engines. In addition, dependencies of result parameters on input variations indicate the main levers for system improvement. A second example is the optimization of compressor discs. Here the main emphasis was on the influence of manufacturing tolerances and on the best method to evaluate these tolerances for longer running analysis tasks. Therefore, results of a full Monte-Carlo simulation are compared with results based on two surrogate models, a response surface and a Taylor series expansion. As a final example the optimization of a HP turbine disc for which a Design of Experiment has been performed to generate a response surface model is discussed. Using the response surface data the life variability due to assumptions in the thermal modeling have been quantified and used to adjust the constraints for the subsequent deterministic optimization for weight of the HP turbine. Using deterministic optimization and especially Robust Design methods a considerable decrease in development time and cost as well as an increased product quality and reliability have been achieved. However, deterministic optimization methods alone normally drive designs on to the constraint boundaries, leading to “cliff-edge” designs. Therefore, the application of Robust Design methods is required to increase the product reliability. These methods still require a considerable computing effort, so the widespread application is just starting.

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