A Rational Design Approach to Gaussian Process Modeling for Variable Fidelity Models

Computer models and simulations are essential system design tools that allow for improved decision making and cost reductions during all phases of the design process. However, the most accurate models tend to be computationally expensive and can therefore only be used sporadically. Consequently, designers are often forced to choose between exploring many design alternatives with less accurate, inexpensive models and evaluating fewer alternatives with the most accurate models. To achieve both broad exploration of the design space and accurate determination of the best alternatives, surrogate modeling and variable accuracy modeling are gaining in popularity. A surrogate model is a mathematically tractable approximation of a more expensive model based on a limited sampling of that model. Variable accuracy modeling involves a collection of different models of the same system with different accuracies and computational costs. We hypothesize that designers can determine the best solutions more efficiently using surrogate and variable accuracy models. This hypothesis is based on the observation that very poor solutions can be eliminated inexpensively by using only less accurate models. The most accurate models are then reserved for discerning the best solution from the set of good solutions. In this paper, a new approach for global optimization is introduced, which uses variable accuracy models in conjuction with a kriging surrogate model and a sequential sampling strategy based on a Value of Information (VOI) metric. There are two main contributions. The first is a novel surrogate modeling method that accommodates data from any number of different models of varying accuracy and cost. The proposed surrogate model is Gaussian process-based, much like classic kriging modeling approaches. However, in this new approach, the error between the model output and the unknown truth (the real world process) is explicitly accounted for. When variable accuracy data is used, the resulting response surface does not interpolate the data points but provides an approximate fit giving the most weight to the most accurate data. The second contribution is a new method for sequential sampling. Information from the current surrogate model is combined with the underlying variable accuracy models’ cost and accuracy to determine where best to sample next using the VOI metric. This metric is used to mathematically determine where next to sample and with which model. In this manner, the cost of further analysis is explicitly taken into account during the optimization process.Copyright © 2011 by ASME

[1]  Christiaan J. J. Paredis,et al.  Model-Based Optimization of a Hydraulic Backhoe using Multi-Attribute Utility Theory , 2009 .

[2]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[3]  高正红,et al.  APPLICATION OF VARIABLE-FIDELITY MODELS TO AERODYNAMIC OPTIMIZATION , 2006 .

[4]  L. Schmit,et al.  Some Approximation Concepts for Structural Synthesis , 1974 .

[5]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[6]  G. G. Wang,et al.  Metamodeling for High Dimensional Simulation-Based Design Problems , 2010 .

[7]  Ning Qin,et al.  Variable-fidelity aerodynamic optimization for turbulent flows using a discrete adjoint formulation , 2004 .

[8]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[9]  John E. Renaud,et al.  Multilevel Variable Fidelity Optimization of a Morphing Unmanned Aerial Vehicle , 2004 .

[10]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[11]  Christiaan J. J. Paredis,et al.  Variable Fidelity Modeling as Applied to Trajectory Optimization for a Hydraulic Backhoe , 2009, DAC 2009.

[12]  Kok Wai Wong,et al.  Surrogate-Assisted Evolutionary Optimization Frameworks for High-Fidelity Engineering Design Problems , 2005 .

[13]  Barry L. Nelson,et al.  Stochastic kriging for simulation metamodeling , 2008, 2008 Winter Simulation Conference.

[14]  Andrew P. Sage,et al.  Introduction to systems engineering , 2000 .

[15]  D. Ginsbourger,et al.  A Multi-points Criterion for Deterministic Parallel Global Optimization based on Gaussian Processes , 2008 .

[16]  Jerome Sacks,et al.  Designs for Computer Experiments , 1989 .

[17]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[18]  Ashwin P. Gurnani,et al.  A constraint-based approach to feasibility assessment in preliminary design , 2006, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[19]  J. F. Rodríguez,et al.  Sequential approximate optimization using variable fidelity response surface approximations , 2000 .

[20]  Christiaan J. J. Paredis,et al.  A Process-Centric Problem Formulation for Decision-Based Design , 2009 .

[21]  Kemper Lewis,et al.  Feasibility Assessment in Preliminary Design Using Pareto Sets , 2005, DAC 2005.

[22]  Wei Chen,et al.  Decision Making in Engineering Design , 2006 .

[23]  John E. Renaud,et al.  Update Strategies for Kriging Models for Use in Variable Fidelity Optimization , 2005 .

[24]  G. Hazelrigg.  Systems Engineering: An Approach to Information-Based Design , 1996 .

[25]  S Kafandaris,et al.  The Economic Value of Information , 2001, J. Oper. Res. Soc..

[26]  Christiaan J. J. Paredis,et al.  An agent-based approach to the design of rapidly deployable fault-tolerant manipulators , 1996 .

[27]  Barry L. Nelson,et al.  Stochastic kriging for simulation metamodeling , 2008, WSC 2008.

[28]  A. O'Hagan,et al.  Predicting the output from a complex computer code when fast approximations are available , 2000 .

[29]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[30]  P. A. Newman,et al.  Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models , 2001 .

[31]  Søren Nymand Lophaven,et al.  DACE - A Matlab Kriging Toolbox , 2002 .

[32]  Michael S. Eldred,et al.  Formulations for Surrogate-Based Optimization Under Uncertainty , 2002 .

[33]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[34]  R. A. Miller,et al.  Sequential kriging optimization using multiple-fidelity evaluations , 2006 .

[35]  Henry P. Wynn,et al.  Screening, predicting, and computer experiments , 1992 .

[36]  Deborah L Thurston,et al.  A formal method for subjective design evaluation with multiple attributes , 1991 .

[37]  Robert T. Clemen,et al.  Making Hard Decisions: An Introduction to Decision Analysis , 1997 .

[38]  P. A. Newman,et al.  Optimization with variable-fidelity models applied to wing design , 1999 .

[39]  George A. Hazelrigg,et al.  A Framework for Decision-Based Engineering Design , 1998 .

[40]  John W. Bandler,et al.  Review of the Space Mapping Approach to Engineering Optimization and Modeling , 2000 .

[41]  M. Stein,et al.  A Bayesian analysis of kriging , 1993 .

[42]  R. Lewis,et al.  An Overview of First-Order Model Management for Engineering Optimization , 2001 .