基于Kullback-Leibler距离离散度的加权代理模型
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摘要
复杂系统的仿真通常具有高维度、高计算量等特点,代理模型因其明晰的数学表达和良好的计算特性可用于逼近真实系统。加权模型对比单个代理模型来说,其稳定性和适应性更广。不同的代理模型其性能不一,根据特定指标,可以构造最优加权代理模型。基于代理模型预测分布以及Kullback-Leibler距离构造各子代理模型之间的离散度,并提出一种新的权函数构造方法。算例表明,该方法与最优子模型的精度相当,同时能提高对真实响应分布的逼近。
Surrogate methods( metamodels) are convenient to determine the mathematical relationship underlying the high dimensional complex systems,which are usually computationally expensive. Various stand-alone metamodels have been proposed in literature,and the ensemble of metamodels was being intensively studied recently to utilize the information reveals in construction of different metamodels. Compared with the stand-alone metamodels,the ensembled models were more robust and adaptable. The strategy of the ensemble by comparing the difference of the probability distribution of predictions was considered, where the Kullback-Leibler divergence was introduced to calculate the differences.Experiments show that the strategy has comparable accuracy in predictions with the most accurate stand-alone metamodel,and it can also perform better in recovering the distribution of the true response.
Surrogate methods( metamodels) are convenient to determine the mathematical relationship underlying the high dimensional complex systems,which are usually computationally expensive. Various stand-alone metamodels have been proposed in literature,and the ensemble of metamodels was being intensively studied recently to utilize the information reveals in construction of different metamodels. Compared with the stand-alone metamodels,the ensembled models were more robust and adaptable. The strategy of the ensemble by comparing the difference of the probability distribution of predictions was considered, where the Kullback-Leibler divergence was introduced to calculate the differences.Experiments show that the strategy has comparable accuracy in predictions with the most accurate stand-alone metamodel,and it can also perform better in recovering the distribution of the true response.
引文
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[2]Koziel S, Leifsson L. Surrogate based modelling and optimization[M]. USA:Springer-Verlag New York,2013.
[3]Meckesheimer M, Booker A J, Barton R R,et al.Computationally inexpensive metamodel assessment strategies[J]. AIAA Journal,2002,40(10):2053-2060.
[4]Myers R H,Montgomery D C,Vining G G,et al. Response surface methodology:a retrospective and literature survey[J].Journal of Quality Technology,2004,36(1):53-77.
[5]Friedman J H. Multivariate adaptive regression splines[J].The Annals of Statistics,1991,19(1):1-67.
[6]Rasmussen C E. Gaussian processes in machine learning[C]//Proceedings of Advanced Lectures on Machine Learning,2004:63-71.
[7]Seber G A F,Lee A J. Linear regression analysis[M]. USA:John Wiley&Sons,2012.
[8]Zerpa L E,Queipo N V,Pintos S,et al. An optimization methodology of alkaline surfactant polymer flooding processes using field scale numerical simulation and multiple surrogates[J]. Journal of Petroleum Science and Engineering,2005,47(3/4):197-208.
[9]Goel T,Haftka R T,Shyy W,et al. Ensemble of surrogates[J].Structural and Multidisciplinary Optimization,2007,33(3):199-216.
[10]Acar E, Rais-Rohani M. Ensemble of metamodels with optimized weight factors[J]. Structural and Multidisciplinary Optimization,2009,37(3):279-294.
[11]Hershey J R,Olsen P A. Approximating the Kullback Leibler divergence between Gaussian mixture models[C]//Proceedings of Acoustics, Speech and Signal Processing,2007:Ⅳ-317-Ⅳ-320.
[12]Wu Y T,Shin Y,Sue R H,et al. Safety-factor based approach for probability-based design optimization[C]//Proceedings of 42nd AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference,2001:AIAA-2001-1522.
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