面向响应准确度的参数不确定性模型确认方法
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摘要
针对参数不确定性模型中概率与区间混合不确定性情况的模型确认问题,提出了面向响应准确度的模型确认方法,并阐明了确认过程的具体实施步骤。根据响应数值结果的非精确累积分布函数和响应试验结果的经验分布函数求解模型确认准则参数,并评估模型确认结果。对于不满足评估要求的模型,建立以待修正区间不确定性参数总置信水平最大为优化目标,以模型确认评估标准和模型参数初始值为约束条件的优化模型,运用遗传算法求解优化问题,并得到模型参数修正值。将模型确认方法应用在圣地亚热传导问题中,结果表明:所提方法可明显提高预测精度和响应准确度,结果真实可信。
Aiming at the problems of model validation for mixed uncertainty cases of probability and interval in parameter uncertainty models, a model validation method was proposed for response accuracy, and the specific implementation steps were described for the validation processes.Model validation criterion parameters were obtained by using the imprecise cumulative distribution function of response numerical results and empirical distribution function of response test results, then the model validation results were assessed. For the model that didn't satisfy the evaluation requirements, an optimization model was established, the maximum total confidence level of interval uncertainty parameters to be corrected was taken as the optimization object, the assessment standard of model validation and initial values of model parameters were used as constraint conditions, finally the optimization model was solved by the genetic algorithm and the corrected values of model parameters were obtained.The model validation method was applied to the Sandia thermal challenge problem, the results show that the proposed method may significantly improve the forecast accuracy and response accuracy, the results are credible.
Aiming at the problems of model validation for mixed uncertainty cases of probability and interval in parameter uncertainty models, a model validation method was proposed for response accuracy, and the specific implementation steps were described for the validation processes.Model validation criterion parameters were obtained by using the imprecise cumulative distribution function of response numerical results and empirical distribution function of response test results, then the model validation results were assessed. For the model that didn't satisfy the evaluation requirements, an optimization model was established, the maximum total confidence level of interval uncertainty parameters to be corrected was taken as the optimization object, the assessment standard of model validation and initial values of model parameters were used as constraint conditions, finally the optimization model was solved by the genetic algorithm and the corrected values of model parameters were obtained.The model validation method was applied to the Sandia thermal challenge problem, the results show that the proposed method may significantly improve the forecast accuracy and response accuracy, the results are credible.
引文
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[14]何成,陈国平,何欢.径向基模型的不确定性模型区间修正与确认[J].机械工程学报,2013,49(11):128-134.HE Cheng,CHEN Guoping,HE Huan.Interval Verfication and Validation of Uncertainty Model of Radial Basis Model[J].Journal of Mechanical Engineering,2013,49(11):128-134.
[15]肖钊,韩旭,杨刚.基于区间技术的模型确认方法及应用[J].机械工程学报,2014,50(14):177-184.XIAO Zhao,HAN Xu,YANG Gang.Model Validation and Its Application Based on Interval Techniques[J].Chinese Journal of Mechanical Engineering,2014,50(14):177-184.
[16]方圣恩,林友勤,夏樟华.考虑结构参数不确定性的随机模型修正方法[J].振动、测试与诊断,2014,34(5):832-837.FANG Shengen,LIN Youqin,XIA Zhanghua.Considering the Uncertainty of Structural Parameters of Stochastic Model Verfication Method[J].Journal of Vibration Measurement and Diagnosis,2014,34(5):832-837.
[17]姜东,费国庆,吴邵庆.基于区间分析的不确定性结构动力学模型修正方法[J].振动工程学报,2015,28(3):352-358.JIANG Dong,FEI Guoqing,WU Shaoqing.A Verfication Method for Uncertainty Structural Dynamic Model Based on Interval Analysis[J].Journal of Vibration Engineering,2015,28(3):352-358.
[18]LIU Y,CHEN W,ARENDT P D,et al.Toward a Better Understanding of Model Validation Metrics[J].Journal of Mechanical Design,2011,133(7):1-13.
[19]MOORE R E.Methods and Applications of Interval Analysis[M].London:Prentice-Hall Inc,1979.
[20]茆诗松,王静龙,濮晓龙.高等数理统计[M].北京:高等教育出版社,2006.MAO Shisong,WANG Jinglong,PU Xiaolong.Advanced Mathematical Statistics[M].Beijing:Higher Education Press,2006.
[21]FERSON S,HAJAGOS J.Arithmetic with Uncertain Numbers:Rigorous and(often)Best Possible Answers[J].Reliability Engineering&System Safety,2004,85(1):135-152.
[22]FERSON S,KREINOVICK V,GINZBURG L R,et al.Constructing Probability Boxes and Dempstershafer Structures[R].Livermore:Sandia National Laboratories,2003.
[23]Ferson S,Oberkampf W L,Ginzburg L.Model Validation and Predictive Capability for the Thermal Challenge Problem[J].Computer Methods in Applied Mechanics and Engineering 2008,197:2408-2430.
[24]GOLDBERG D E.Genetic Algorithms in Search,Optimization and Machine Learning[M].New Jersey:Addison-Wesley,1989:19-89.
[25]DOWDING K J,PILCH M,HILLS R G,et al.Formulation of the Thermal Problem[J].Computer Methods in Applied Mechanics and Engineering,2008,197(29/32):2385-2389.
[26]BRANDYBERRY M D.Thermal Problem Solution Using a Surrogate Model Clustering Technique[J].Computer Methods in Applied Mechanics and Engineering,2008,197(29/32):2390-2407.
[27]MCFARLAND J,MAHADEVAN S.Multivariate Significance Testing and Model Calibration under Uncertainty[J].Computer Methods in Applied Mechanics and Engineering,2008,197(29/32):2467-2479.
[28]RUTHERFORD B M.Computational Modeling Issues and Methods for the“Regulatory Problem”in Engineering Solution to the Thermal Problem[J].Computer Methods in Applied Mechanics and Engineering,2008,197(29/32):2480-2489.
[2]姜潮,李文学,王彬,等.一种针对概率与非概率混合结构可靠性的敏感性分析方[J].中国机械工程,2013,24(19):2577-2583.JIANG Chao,LI Wenxue,WANG Bin,et al.A Sensitivity Analysis Method for Probabilistic and Nonprobabilistic Hybrid Structures[J].China Mechanical Engineering,2013,24(19):2577-2583.
[3]American Institute of Aeronautics and Astronautics,AIAA-G-077-1998,Guide for the Verification and Validation of Computational Fluid Dynamics Simulations[S].Reston:AIAA,1998.
[4]American Society of Mechanical Engineers.ASMEV&V 10-2006,Guide for Verification and Validation in Computational Solid Mechanics[S].New York:ASME,2006.
[5]American Society of Mechanical Engineers.ASMEV&V 10.1-2012,an Illustration of the Concepts of Verification and Validation in Computational Solid Mechanics[S].New York:ASME,2012.
[6]OBERKAMPF W L,ROY C J.Verification and Validation in Scientific Computing[M].New York:Cambridge University Press,2010.
[7]XIONG Y,CHEN W,TSUI K,et al.A Better Understanding of Model Updating Strategies in Validating Engineering Models[J].Computer Methods in Applied Mechanics and Engineering,2009,198(15):1327-1337.
[8]KENNEDY M C,OHAGAN A.Bayesian Calibration of Computer Models[J].Journal of the Royal Statistical Society Series B-statistical Methodology,2001,63(3):425-464.
[9]HILLS R G,DOWDING K J.Multivariate Approach to the Thermal Challenge Problem[J].Computer Methods in Applied Mechanics and Engineering,2008,197(29):2442-2456.
[10]BRANDYBERRY M D.Thermal Problem Solution Using a Surrogate Model Clustering Technique[J].Computer Methods in Applied Mechanics and Engineering,2008,197(29):2390-2407.
[11]LIU F,BAYARRI M J,BERGER J Q,et al.ABayesian Analysis of the Thermal Challenge Problem[J].Computer Methods in Applied Mechanics and Engineering 2008,197(29/32):2121-2136.
[12]HASSELMAN T,YAP K,LIN C,et al.A Case Study in Model Improvement for Vehicle Crashworthiness Simulation[C]//23rd International Modal Analysis Conference.Orlando,2005:89-98.
[13]张保强,陈国平,郭勤涛.模型确认热传导挑战问题求解的贝叶斯方法[J].航空学报,2011,32(7):1202-1209.ZHANG Baoqiang,CHEN Guoping,GUO Qintao.A Bayesian Method for Solving the Problem of Heat Conduction Challenge[J].Journal of Aeronautics,2011,32(7):1202-1209.
[14]何成,陈国平,何欢.径向基模型的不确定性模型区间修正与确认[J].机械工程学报,2013,49(11):128-134.HE Cheng,CHEN Guoping,HE Huan.Interval Verfication and Validation of Uncertainty Model of Radial Basis Model[J].Journal of Mechanical Engineering,2013,49(11):128-134.
[15]肖钊,韩旭,杨刚.基于区间技术的模型确认方法及应用[J].机械工程学报,2014,50(14):177-184.XIAO Zhao,HAN Xu,YANG Gang.Model Validation and Its Application Based on Interval Techniques[J].Chinese Journal of Mechanical Engineering,2014,50(14):177-184.
[16]方圣恩,林友勤,夏樟华.考虑结构参数不确定性的随机模型修正方法[J].振动、测试与诊断,2014,34(5):832-837.FANG Shengen,LIN Youqin,XIA Zhanghua.Considering the Uncertainty of Structural Parameters of Stochastic Model Verfication Method[J].Journal of Vibration Measurement and Diagnosis,2014,34(5):832-837.
[17]姜东,费国庆,吴邵庆.基于区间分析的不确定性结构动力学模型修正方法[J].振动工程学报,2015,28(3):352-358.JIANG Dong,FEI Guoqing,WU Shaoqing.A Verfication Method for Uncertainty Structural Dynamic Model Based on Interval Analysis[J].Journal of Vibration Engineering,2015,28(3):352-358.
[18]LIU Y,CHEN W,ARENDT P D,et al.Toward a Better Understanding of Model Validation Metrics[J].Journal of Mechanical Design,2011,133(7):1-13.
[19]MOORE R E.Methods and Applications of Interval Analysis[M].London:Prentice-Hall Inc,1979.
[20]茆诗松,王静龙,濮晓龙.高等数理统计[M].北京:高等教育出版社,2006.MAO Shisong,WANG Jinglong,PU Xiaolong.Advanced Mathematical Statistics[M].Beijing:Higher Education Press,2006.
[21]FERSON S,HAJAGOS J.Arithmetic with Uncertain Numbers:Rigorous and(often)Best Possible Answers[J].Reliability Engineering&System Safety,2004,85(1):135-152.
[22]FERSON S,KREINOVICK V,GINZBURG L R,et al.Constructing Probability Boxes and Dempstershafer Structures[R].Livermore:Sandia National Laboratories,2003.
[23]Ferson S,Oberkampf W L,Ginzburg L.Model Validation and Predictive Capability for the Thermal Challenge Problem[J].Computer Methods in Applied Mechanics and Engineering 2008,197:2408-2430.
[24]GOLDBERG D E.Genetic Algorithms in Search,Optimization and Machine Learning[M].New Jersey:Addison-Wesley,1989:19-89.
[25]DOWDING K J,PILCH M,HILLS R G,et al.Formulation of the Thermal Problem[J].Computer Methods in Applied Mechanics and Engineering,2008,197(29/32):2385-2389.
[26]BRANDYBERRY M D.Thermal Problem Solution Using a Surrogate Model Clustering Technique[J].Computer Methods in Applied Mechanics and Engineering,2008,197(29/32):2390-2407.
[27]MCFARLAND J,MAHADEVAN S.Multivariate Significance Testing and Model Calibration under Uncertainty[J].Computer Methods in Applied Mechanics and Engineering,2008,197(29/32):2467-2479.
[28]RUTHERFORD B M.Computational Modeling Issues and Methods for the“Regulatory Problem”in Engineering Solution to the Thermal Problem[J].Computer Methods in Applied Mechanics and Engineering,2008,197(29/32):2480-2489.
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