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Metamodels, also known as surrogate models, can be used in place of computationally expensive simulation models to increase computational efficiency for the purposes of design optimization or design space exploration. Metamodel-based design optimization is especially advantageous for ship design problems that require either computationally expensive simulations or costly physical experiments. In this paper, three metamodeling methods are evaluated with respect to their capabilities for modeling highly nonlinear, multimodal functions with incrementally increasing numbers of independent variables. Methods analyzed include kriging, radial basis functions (RBF), and support vector regression (SVR). Each metamodeling technique is used to model a set of single-output functions with dimensionality ranging from one to ten independent variables and modality ranging from one to twenty local maxima. 58715
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The number of points used to train the models is increased until a predetermined error threshold is met. Results show that each of the three methods has its own distinct advantages. Los metamodelos, también conocimos como modelos substitutos, pueden ser utilizados en lugar de modelos cuyas simulaciones tienen un costo computacional muy alto, incrementado con esto la eficiencia en procesos de optimización de diseños o en el diseño de exploraciones espaciales. La optimización de diseños basados en metamodelos es especialmente ventajosa en problemas de diseño relacionado con vehículos marinos en los cuales se requieran simulaciones con un alto costo computacional o bien de experimentos con una alta inversión en equipos. En este artículo se evalúan tres métodos para el desarrollo de metamodelos. La evaluación de estos métodos es desarrollada teniendo en cuenta la capacidad de cada uno de ellos para modelar funciones multimodales no lineales con un número creciente de variables independientes. Dentro de los métodos analizados se encuentran el método de kriging, el método de funciones de base radiales, y el método de regresión con vector de apoyo. Cada una de las anteriores técnicas para la generación de metamodelos es utilizada para modelar un grupo de funciones de una salida con dimensiones variando desde uno hasta diez variables independientes y una modalidad variando entre uno y veinte máximos locales. El número de puntos utilizados para entrenar los modelos es incrementado hasta que el error alcanza una tolerancia predeterminada. Los resultados obtenidos muestran que cada uno de los tres modelos tiene sus propias ventajas distintivas. Key words: Metamodeling, kriging, radial basis functions, support vector regression, metamodel-based design optimization.Palabras claves: Desarrollo de metamodelos, kriging, funciones de base radiales, regresión con vector de apoyo, optimización de diseños basada en metamodelos.AbstractResumen1 Applied Research Laboratories. The University of Texas. Austin, TX. USA. e-mail: pbacklund@mail.utexas.edu2 The University of Texas. Austin, TX. USA. e-mail: david.shahan@mail.utexas.edu3 The University of Texas.
Austin, TX. USA. e-mail: ccseepersad@mail.utexas.eduDate received: May 19th, 2010. - Fecha de recepción: 19 de Mayo de 2010.Date Accepted: July 6, 2010. - Fecha de aceptación: 6 de Julio de 2010. Computer models of naval systems and other physical systems are often complex and computationally expensive, requiring minutes or hours to complete a single simulation run. While the accuracy and detail offered by a well constructed computer model are indispensable, the computational expenseof many models makes it challenging to use them for design applications. For example, objective functions for ship hull design problems commonly include payload, ship speed, motions, and calm-water drag (Percival et al., 2001). In many cases, computational fluid dynamics (CFD) models are used as tools to analyze performance characteristics of candidate designs (Periet al., 2001). Unfortunately, CFD simulations tend to be computationally expensive and time consuming to execute and therefore limit a designer’s ability to explore a broad range of configurations or interface the simulation with design optimization algorithms that require numerous, iterative solutions.To remedy this situation, metamodel scan bedeveloped as surrogates of the computer model to provide reasonable approximations in a fraction of the time. Metamodels are developed using a set of training points from a base model. Once built, the metamodel is used in place of the base model to predict model responses quickly and repeatedly. For example, a metamodel built using a set of training points from a CFD model could enable ship designers to find satisfactory hull forms more rapidly than by using the base model alone. Other possible applications of metamodels to ship design problems include optimization of marine energy systems (Dimopouloset al., 2008), propeller design (Watanabe et al., 2003), and marine vehicle maneuvering problems (Racine and Paterson, 2005). In this paper, the focus will be on designing thermal systems for ship applications.The best metamodeling method for a particular application depends on the needs of the project and the nature of the base model that is to be approximated. Five common criteria for evaluating metamodels include:•