Enhanced Gaussian Process Metamodeling and Collaborative Optimization for Vehicle Suspension Design Optimization

Dynamic stability is a key performance metric of motor vehicles and has a direct impact on passenger experience and customer satisfaction. The desired vehicle dynamics behavior can be achieved by optimizing the design of vehicle suspensions. Two challenges are associated with this design optimization task. The first one arises from the large number (e.g., 40 or 50) of design variables in modern suspension systems. Such multitude of variables not only makes it expensive to build a training dataset for metamodeling purposes, but also renders accurate surrogate modeling extremely difficult. The second challenge is a lack of guideline for choosing a proper multidisciplinary design optimization (MDO) method for a single MDO problem such as one for vehicle suspension design. In this paper, an enhanced Gaussian process (GP) metamodeling technique is developed and several versions of the collaborative optimization (CO) method are compared via a vehicle suspension design problem. In our enhanced GP modeling method, the model parameters are efficiently estimated using the smoothing effect of the so-called nugget parameter to reduce the search space. In addition, various versions of the CO method are studied where the enhanced collaborative optimization (ECO) method is found to perform the best. A simplified ECO formulation is also investigated to provide insights for future engineering applications.

[1]  Brian Douglas Roth,et al.  Aircraft family design using enhanced collaborative optimization , 2008 .

[2]  Ilan Kroo,et al.  Enhanced Collaborative Optimization: Application to an Analytic Test Problem and Aircraft Design , 2008 .

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

[4]  Ann-Britt Ryberg,et al.  Metamodel-Based Multidisciplinary Design Optimization for Automotive Applications , 2012 .

[5]  Seung-Jin Heo,et al.  Robust design optimization of suspension system by using target cascading method , 2011 .

[6]  Panos Y. Papalambros,et al.  Analytical Target Cascading in Automotive Vehicle Design , 2001 .

[7]  Daniel W. Apley,et al.  Lifted Brownian Kriging Models , 2017, Technometrics.

[8]  Wei Chen,et al.  Lagrangian coordination for enhancing the convergence of analytical target cascading , 2006 .

[9]  T. Simpson,et al.  Use of Kriging Models to Approximate Deterministic Computer Models , 2005 .

[10]  Ilan Kroo,et al.  Development and Application of the Collaborative Optimization Architecture in a Multidisciplinary Design Environment , 1995 .

[11]  Natalia Alexandrov,et al.  Analytical and Computational Aspects of Collaborative Optimization for Multidisciplinary Design , 2002 .

[12]  I. Sobol.  On the distribution of points in a cube and the approximate evaluation of integrals , 1967 .

[13]  Pritam Ranjan,et al.  A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data , 2010, Technometrics.

[14]  Paul D. Arendt,et al.  A preposterior analysis to predict identifiability in the experimental calibration of computer models , 2016 .

[15]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[16]  Paul D. Arendt,et al.  Quantification of model uncertainty: Calibration, model discrepancy, and identifiability , 2012 .

[17]  Yves Deville,et al.  DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization , 2012 .

[18]  James O. Berger,et al.  A Framework for Validation of Computer Models , 2007, Technometrics.

[19]  Yang Li,et al.  A Descriptor-Based Design Methodology for Developing Heterogeneous Microstructural Materials System , 2014 .

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

[21]  Joaquim R. R. A. Martins,et al.  Multidisciplinary design optimization: A survey of architectures , 2013 .

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

[23]  Hugh A. Chipman,et al.  GPfit: An R Package for Fitting a Gaussian Process Model to Deterministic Simulator Outputs , 2013, 1305.0759.

[24]  Daniel W. Apley,et al.  Improving Identifiability in Model Calibration Using Multiple Responses , 2012, DAC 2011.

[25]  Angel-Victor DeMiguel,et al.  An analysis of collaborative optimization methods , 2000 .

[26]  Panos Y. Papalambros,et al.  Solving multiobjective optimization problems using quasi-separable MDO formulations and analytical target cascading , 2014 .

[27]  N. Cressie.  The origins of kriging , 1990 .

[28]  Wei Chen,et al.  An Efficient Algorithm for Constructing Optimal Design of Computer Experiments , 2005, DAC 2003.

[29]  Angel-Victor DeMiguel,et al.  Two decomposition algorithms for nonconvex optimization problems with global variables , 2001 .

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