Database enrichment for multi objective optimization Patricia Klotz Nathalie Bartoli† Laurence Cornez† Renaud Lecourt† and Nicolas Savary‡

Description

Database enrichment for multi-objective optimization Patricia Klotz?†, Nathalie Bartoli†, Laurence Cornez†, Renaud Lecourt† and Nicolas Savary‡ †ONERA - Toulouse France, ‡TURBOMECA - Bordes France Abstract The problem of optimization of complex phenom- ena is studied by using response surface approxi- mation. Design of experiments are elaborated for database generation of samples, but it can be im- proved to obtain more adapted response surfaces through a sequential enrichment based on bootstrap techniques. A multi-objective optimization is per- formed on a two phase flow configuration for the optimization of injection parameters in a Low Pre- mixed Prevaporized (LPP) injection system for a combustor chamber. keywords: multi-objective optimization, re- sponse surface, neural network, design of experi- ments, bootstrap 1 Introduction This paper outlines some optimization research done at ONERA within the context of an ON- ERA Internal project (PRF DOOM) and a Euro- pean project (INTELLECT D.M.). Because opti- mization requires a lot of computations, the use of response surface model (RSM) is a good solution to decrease CPU time. The set of points for fitting RSM to each objective function is provided by a de- sign of experiments. We use here Latin Hypercube Sampling (LHS) which combines deterministic and random sampling in order to reduce the variance of the RSM. The number of necessary points and their best location can be both improved.

• taking into


• sponse surface


• multi-objective optimization


• phase flow


• ac- cordingly


• results obtained


• rate

Sujets

• Bartoli
• Lecourt
• Cornez
• Savary
• Multi-objective optimization

Informations

• Publié par: pefav
• Nombre de lectures: 19
• Langue: English

Extrait

Database enrichment for multiobjective optimization

∗† †† †‡ Patricia Klotz, Nathalie Bartoli, Laurence Cornez, Renaud Lecourtand Nicolas Savary † ‡ ONERA  Toulouse France,TURBOMECA  Bordes France

Abstract the methodology of our approach and secondly some multiobjective results obtained on a test case The problem of optimization of complex phenom proposed by Turbomeca.We close by proposing fu ena is studied by using response surface approxi ture domains of investigation for response surface mation. Designof experiments are elaborated for improving. database generation of samples, but it can be im proved to obtain more adapted response surfaces through a sequential enrichment based on bootstrap description2 Method techniques. Amultiobjective optimization is per Artificial neural networks (ANN) offer a right com formed on a two phase flow configuration for the promise between accuracy of the response surface optimization of injection parameters in a Low Pre approximation and implementation.In particular, mixed Prevaporized (LPP) injection system for a non linearities and large parameters number are combustor chamber. easily taken into account.Multi Linear Perceptron keywords:remultiobjective optimization, (MLP) with supervised learning and one hidden sponse surface, neural network, design of experi layer are chosen for their reliability [4].The pro ments, bootstrap posed algorithm is carried out with a view to iter atively enriching databases for surrogate model by taking into account multiobjective approach.As 1 Introduction depicted in Fig.1, three main steps can be identi fied: This paper outlines some optimization research done at ONERA within the context of an ON 1. Bootstrapenrichment to add points where the ERA Internal project (PRF DOOM) and a Euro approximation error is maximized, pean project (INTELLECT D.M.).Because opti mization requires a lot of computations, the use of 2. Surrogate construction comprising for ANN response surface model (RSM) is a good solution the choice of the optimal parameters of the to decrease CPU time.The set of points for fitting MLP, RSM to each objective function is provided by a de 3. Optimizationto add interesting points which sign of experiments. We use here Latin Hypercube minimize the predominant response surface. Sampling (LHS) which combines deterministic and random sampling in order to reduce the variance of Each of these steps is described in the following. the RSM. The number of necessary points and their The size of the dataset is denoted byN, the dimen best location can be both improved. Our purpose is sion of the design space bypand the number of to define an economic way to design a RSM which objectives bym. will be used for optimization.We can notice that depending on type of surface, some RSM are more efficient than others, but unfortunately it can’t be 2.1 RSMconstruction predicted. Themethodology developed can be ap Considering the reduced number of points in the plied to all problems where computation time is de database, it is important to take into account all terminant. the points for the construction of the network rel In the sections that follow, at first, we shall present ative to one objective function.For this reason, ∗ Email: [e-mail] aKfold cross validation technique [7] is used to