Multi-fidelity information fusion based on prediction of kriging

In this paper, a novel kriging-based multi-fidelity method is proposed. Firstly, the model uncertainty of low-fidelity and high-fidelity models is quantified. On the other hand, the prediction uncertainty of kriging-based surrogate models(SM) is confirmed by its mean square error. After that, the integral uncertainty is acquired by math modeling. Meanwhile, the SMs are constructed through data from low-fidelity and high-fidelity models. Eventually, the low-fidelity (LF) and high-fidelity (HF) SMs with integral uncertainty are obtained and a proposed fusion algorithm is implemented. The fusion algorithm refers to the Kalman filter’s idea of optimal estimation to utilize the independent information from different models synthetically. Through several mathematical examples implemented, the fused SM is certified that its variance is decreased and the fused results tend to the true value. In addition, an engineering example about autonomous underwater vehicles’ hull design is provided to prove the feasibility of this proposed multi-fidelity method in practice. In the future, it will be a helpful tool to deal with reliability optimization of black-box problems and potentially applied in multidisciplinary design optimization.

[1]  L. Romera,et al.  Crushing analysis and multi-objective crashworthiness optimization of GFRP honeycomb-filled energy absorption devices , 2014 .

[2]  George E. Apostolakis,et al.  Including model uncertainty in risk-informed decision making , 2006 .

[3]  Liang Gao,et al.  A hybrid variable-fidelity global approximation modelling method combining tuned radial basis function base and kriging correction , 2013 .

[4]  William A Link,et al.  Model weights and the foundations of multimodel inference. , 2006, Ecology.

[5]  T. J. Mitchell,et al.  Exploratory designs for computational experiments , 1995 .

[6]  Alexander I. J. Forrester,et al.  Multi-fidelity optimization via surrogate modelling , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[7]  Vassili Toropov,et al.  Design optimization of supersonic jet pumps using high fidelity flow analysis , 2012 .

[8]  George E. P. Box,et al.  Empirical Model‐Building and Response Surfaces , 1988 .

[9]  Andy J. Keane,et al.  Engineering Design via Surrogate Modelling - A Practical Guide , 2008 .

[10]  Tom Dhaene,et al.  Inverse modelling of an aneurysm’s stiffness using surrogate-based optimization and fluid-structure interaction simulations , 2012 .

[11]  Andy J. Keane,et al.  Recent advances in surrogate-based optimization , 2009 .

[12]  Zhenghong Gao,et al.  Research on multi-fidelity aerodynamic optimization methods , 2013 .

[13]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[14]  Theresa Dawn Robinson,et al.  Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping , 2008 .

[15]  Enrico Zio,et al.  Two methods for the structured assessment of model uncertainty by experts in performance assessments of radioactive waste repositories , 1996 .

[16]  Enrico Zio,et al.  An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability , 2014, Reliab. Eng. Syst. Saf..

[17]  Zhong-Hua Han,et al.  A New Cokriging Method for Variable-Fidelity Surrogate Modeling of Aerodynamic Data , 2010 .

[18]  Raphael T. Haftka,et al.  Sensitivity-based scaling for approximating. Structural response , 1993 .

[19]  Guangyao Li,et al.  Multi-fidelity optimization for sheet metal forming process , 2011 .

[20]  S. Koziel,et al.  A Space-Mapping Framework for Engineering Optimization—Theory and Implementation , 2006, IEEE Transactions on Microwave Theory and Techniques.

[21]  Raphael T. Haftka,et al.  Surrogate-based Analysis and Optimization , 2005 .

[22]  Karen Willcox,et al.  A Bayesian-Based Approach to Multifidelity Multidisciplinary Design Optimization , 2010 .

[23]  Vladimir Balabanov,et al.  Multi-Fidelity Optimization with High-Fidelity Analysis and Low-Fidelity Gradients , 2004 .

[24]  Slawomir Koziel,et al.  Multi-Objective Design of Antennas Using Variable-Fidelity Simulations and Surrogate Models , 2013, IEEE Transactions on Antennas and Propagation.

[25]  Shapour Azarm,et al.  A Kriging Metamodel Assisted Multi-Objective Genetic Algorithm for Design Optimization , 2008 .

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

[27]  Xiaoqian Chen,et al.  A surrogate based multistage-multilevel optimization procedure for multidisciplinary design optimization , 2011, Structural and Multidisciplinary Optimization.

[28]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007 .

[29]  Vassili Toropov,et al.  Metamodel-based collaborative optimization framework , 2009 .

[30]  Yoel Tenne,et al.  A framework for memetic optimization using variable global and local surrogate models , 2009, Soft Comput..

[31]  Leifur Þ. Leifsson,et al.  Surrogate-Based Aerodynamic Shape Optimization by Variable-Resolution Models , 2013 .

[32]  Wei Chen,et al.  A New Variable-Fidelity Optimization Framework Based on Model Fusion and Objective-Oriented Sequential Sampling , 2007, DAC 2007.

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

[34]  Farrokh Mistree,et al.  Kriging Models for Global Approximation in Simulation-Based Multidisciplinary Design Optimization , 2001 .

[35]  Xi Yang,et al.  Aerodynamic and heat transfer design optimization of internally cooling turbine blade based different surrogate models , 2011 .

[36]  M. B. Yelten,et al.  Demystifying Surrogate Modeling for Circuits and Systems , 2012, IEEE Circuits and Systems Magazine.

[37]  Christopher J. Roy,et al.  Verification and Validation in Scientific Computing , 2010 .

[38]  Vijayan K. Asari,et al.  Tracking and Recognizing Multiple Faces Using Kalman Filter and ModularPCA , 2011, Complex Adaptive Systems.

[39]  Andy J. Keane,et al.  Combustor Design Optimization Using Co-Kriging of Steady and Unsteady Turbulent Combustion , 2011 .

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

[41]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .