60 research outputs found
Sensitivity analysis of expensive black-box systems using metamodeling
Simulations are becoming ever more common as a tool for designing complex
products. Sensitivity analysis techniques can be applied to these simulations
to gain insight, or to reduce the complexity of the problem at hand. However,
these simulators are often expensive to evaluate and sensitivity analysis
typically requires a large amount of evaluations. Metamodeling has been
successfully applied in the past to reduce the amount of required evaluations
for design tasks such as optimization and design space exploration. In this
paper, we propose a novel sensitivity analysis algorithm for variance and
derivative based indices using sequential sampling and metamodeling. Several
stopping criteria are proposed and investigated to keep the total number of
evaluations minimal. The results show that both variance and derivative based
techniques can be accurately computed with a minimal amount of evaluations
using fast metamodels and FLOLA-Voronoi or density sequential sampling
algorithms.Comment: proceedings of winter simulation conference 201
Metamodel-based importance sampling for structural reliability analysis
Structural reliability methods aim at computing the probability of failure of
systems with respect to some prescribed performance functions. In modern
engineering such functions usually resort to running an expensive-to-evaluate
computational model (e.g. a finite element model). In this respect simulation
methods, which may require runs cannot be used directly. Surrogate
models such as quadratic response surfaces, polynomial chaos expansions or
kriging (which are built from a limited number of runs of the original model)
are then introduced as a substitute of the original model to cope with the
computational cost. In practice it is almost impossible to quantify the error
made by this substitution though. In this paper we propose to use a kriging
surrogate of the performance function as a means to build a quasi-optimal
importance sampling density. The probability of failure is eventually obtained
as the product of an augmented probability computed by substituting the
meta-model for the original performance function and a correction term which
ensures that there is no bias in the estimation even if the meta-model is not
fully accurate. The approach is applied to analytical and finite element
reliability problems and proves efficient up to 100 random variables.Comment: 20 pages, 7 figures, 2 tables. Preprint submitted to Probabilistic
Engineering Mechanic
Solving optimisation problems in metal forming using FEM: A metamodel based optimisation algorithm
During the last decades, Finite Element (FEM) simulations of metal forming processes have\ud
become important tools for designing feasible production processes. In more recent years,\ud
several authors recognised the potential of coupling FEM simulations to mathematical opti-\ud
misation algorithms to design optimal metal forming processes instead of only feasible ones.\ud
This report describes the selection, development and implementation of an optimisa-\ud
tion algorithm for solving optimisation problems for metal forming processes using time\ud
consuming FEM simulations. A Sequential Approximate Optimisation algorithm is pro-\ud
posed, which incorporates metamodelling techniques and sequential improvement strate-\ud
gies for enhancing the e±ciency of the algorithm. The algorithm has been implemented in\ud
MATLABr and can be used in combination with any Finite Element code for simulating\ud
metal forming processes.\ud
The good applicability of the proposed optimisation algorithm within the ¯eld of metal\ud
forming has been demonstrated by applying it to optimise the internal pressure and ax-\ud
ial feeding load paths for manufacturing a simple hydroformed product. Resulting was\ud
a constantly distributed wall thickness throughout the ¯nal product. Subsequently, the\ud
algorithm was compared to other optimisation algorithms for optimising metal forming\ud
by applying it to two more complicated forging examples. In both cases, the geometry of\ud
the preform was optimised. For one forging application, the algorithm managed to solve\ud
a folding defect. For the other application both the folding susceptibility and the energy\ud
consumption required for forging the part were reduced by 10% w.r.t. the forging process\ud
proposed by the forging company. The algorithm proposed in this report yielded better\ud
results than the optimisation algorithms it was compared to
Design and analysis of computer experiments for stochastic systems
Ph.DDOCTOR OF PHILOSOPH
Otimização eficiente global dirigida por metamodelos combinados : novos caminhos abertos pela aproximação por mínimos quadrados
Orientador: Alberto Luiz SerpaTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: O presente trabalho representa a compilação dos resultados anteriores dessa pesquisa no campo de metamodelos combinados e otimização eficiente global (EGO), os quais foram sumetidos para publicação em periódicos especializados. Recentemente foi implementado nesse trabalho de doutorado o algoritmo LSEGO que é uma abordagem para conduzir algoritmos tipo EGO, baseando-se em metamodelos combinados através da aproximação por mínimos quadrados (metamodelos combinados LS). Através dos metamodelos combinados LS é possível estimar a incerteza da aproximação usando qualquer tipo de metamodelagem (e não somente do tipo kriging), permitindo estimar a função de expectativa de melhora para a função objetivo. Nos experimentos computacionais anteriores em problemas de otimização sem restrições, a abordagem LSEGO mostrou-se como uma alternativa viável para conduzir otimização eficiente global usando metamodelos combinados, sem se restringir a somente um ponto adicional por ciclo de otimização iterativa. Na presente tese o algoritmo LSEGO foi extendido de modo a tratar também problemas de otimização com restrições. Os resultados de testes numéricos com problemas analíticos e de referência e também em um estudo de caso de engenharia em escala industrial mostraram-se bastante promissores e competitivos em relação aos trabalhos similares encontrados na literaturaAbstract: In this work we review and compile the results of our previous research in the fields of ensemble of metamodels and efficient global optimization (EGO). Recently we implemented LSEGO that is an approach to drive EGO algorithms, based on LS (least squares) ensemble of metamodels. By means of LS ensemble of metamodels, it is possible to estimate the uncertainty of the prediction by using any kind of model (not only kriging) and provide an estimate for the expected improvement function. In previous numerical experiments with unconstrained optimization problems, LSEGO approach has shown to be a feasible alternative to drive efficient global optimization by using multiple or ensemble of metamodels, not restricted to kriging approximation or single infill point per optimization cycles. In the present work we extended the previous LSEGO algorithm to handle constrained optimization problems as well. Some numerical experiments were performed with analytical benchmark functions and also for industry scale engineering problems with competitive resultsDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutor em Engenharia Mecânic
Convergence Analysis of Stochastic Kriging-Assisted Simulation with Random Covariates
We consider performing simulation experiments in the presence of covariates.
Here, covariates refer to some input information other than system designs to
the simulation model that can also affect the system performance. To make
decisions, decision makers need to know the covariate values of the problem.
Traditionally in simulation-based decision making, simulation samples are
collected after the covariate values are known; in contrast, as a new
framework, simulation with covariates starts the simulation before the
covariate values are revealed, and collects samples on covariate values that
might appear later. Then, when the covariate values are revealed, the collected
simulation samples are directly used to predict the desired results. This
framework significantly reduces the decision time compared to the traditional
way of simulation. In this paper, we follow this framework and suppose there
are a finite number of system designs. We adopt the metamodel of stochastic
kriging (SK) and use it to predict the system performance of each design and
the best design. The goal is to study how fast the prediction errors diminish
with the number of covariate points sampled. This is a fundamental problem in
simulation with covariates and helps quantify the relationship between the
offline simulation efforts and the online prediction accuracy. Particularly, we
adopt measures of the maximal integrated mean squared error (IMSE) and
integrated probability of false selection (IPFS) for assessing errors of the
system performance and the best design predictions. Then, we establish
convergence rates for the two measures under mild conditions. Last, these
convergence behaviors are illustrated numerically using test examples
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