基于改进灰色关联分析的仿真模型综合验证方法
|
摘要
灰色关联分析是仿真模型验证最有效的方法之一,但基于常规灰色关联分析进行仿真模型验证时存在着未考虑数据序列数值间的接近程度、给出的处理1组飞行试验序列与1组仿真实验序列的灰色关联度与靶场实际问题不符、无法获得模型的整体性能评价等问题,会引起决策风险较大。为此,提出一种基于改进灰色关联分析的仿真模型综合验证的方法。在灰色关联系数的计算中引入数据距离,从而使灰色关联度的计算值综合了时间序列几何形状的相似性和数值距离的接近性两个属性,提高了仿真模型验证的准确性。通过概率和计算能够处理1组飞行试验数据和多组仿真实验数据的关联分析问题,从而融合了试验过程的随机因素,在小样本飞行试验条件下充分利用了仿真实验信息,提高了仿真模型验证的可靠度。对不同的实际飞行试验样本赋予不同的重要性权重,从而得到仿真模型的整体性能评估。同时给出具体的基于改进灰色关联分析模型综合验证的操作过程,并证明改进灰色关联度模型满足灰色关联定理及相关性质。通过实例分析验证了该方法的合理性和有效性。
Grey relational analysis( GRA) is usually used to validate the simulation models because of its advantage in the field of time series relational analysis. The ordinary GRA stresses the similarity but ignores the proximity between two test time series while the proximity is part of model error. The grey relational degree given by a set of flight test sequences and a set of simulation test sequences is inconsistent with the practical problems of firing range. The ordinary GRA cannot be used in the overall performance evaluation of simulation model,which leads to a high risk of decision-making. An improved grey relational analysis is proposed to reduce the risk,in which the similarity and the proximity between the simula-tion test time series and the flight test time series are considered. At the same time it can analyze the time series which has not only one dimension but also more than one dimension by calculating probability sum,and so it fuses random factor of random process and makes full use of simulation test data with small sample flying test. Besides the new grey relational analysis improves the performance of GRA and has higher precision and reliability for the validation of simulation models. The proposed model can be used to solve the relational analysis problem with many characteristics of behavior,and the operational steps are listed in detail. Data test and case study are given to show the reasonability and validity of the improved method.
Grey relational analysis( GRA) is usually used to validate the simulation models because of its advantage in the field of time series relational analysis. The ordinary GRA stresses the similarity but ignores the proximity between two test time series while the proximity is part of model error. The grey relational degree given by a set of flight test sequences and a set of simulation test sequences is inconsistent with the practical problems of firing range. The ordinary GRA cannot be used in the overall performance evaluation of simulation model,which leads to a high risk of decision-making. An improved grey relational analysis is proposed to reduce the risk,in which the similarity and the proximity between the simula-tion test time series and the flight test time series are considered. At the same time it can analyze the time series which has not only one dimension but also more than one dimension by calculating probability sum,and so it fuses random factor of random process and makes full use of simulation test data with small sample flying test. Besides the new grey relational analysis improves the performance of GRA and has higher precision and reliability for the validation of simulation models. The proposed model can be used to solve the relational analysis problem with many characteristics of behavior,and the operational steps are listed in detail. Data test and case study are given to show the reasonability and validity of the improved method.
引文
[1]胡玉伟,马萍,杨明,等.基于改进灰色关联分析的仿真数据综合一致性检验方法[J].北京理工大学学报,2013,33(7):711-715.HU Yu-wei,MA Ping,YANG Ming,et al.A comprehensive consistency test method based on improved grey relational analysis for simulation results[J].Transactions of Beijing Institute of Technology,2013,33(7):711-715.(in Chinese)
[2]吴静,吴晓燕,陈永兴.基于改进灰色关联分析的仿真模型验证方法[J].系统工程与电子技术,2010,32(8):1677-1679.WU Jing,WU Xiao-yan,CHEN Yong-xing.Validation of simulation models based on improved grey relational analysis[J].Systems Engineering and Electronics,2010,32(8):1677-1679.(in Chinese)
[3]Naylor T H,Finger J M.Verification of computer simulation models[J].Management Science,1967,14(2):92-101.
[4]Kheir N A,Holmes W M.On validating simulation models of missile systems[J].Simulation,1978,30(4):117-128.
[5]宁小磊,赵娜,吕永佳,等.基于阵灰色关联分析的仿真模型验证方法研究[J].弹箭与制导学报,2014,34(3):203-205.NING Xiao-lei,ZHAO Na,LYU Yong-jia,et al.Study of validation of simulation model based on matrix gray relational analysis[J].Journal of Projectiles,Rockets,Missiles and Guidance,2014,34(3):203-205.(in Chinese)
[6]刘藻珍.基于飞行试验数据的仿真模型验证方法的研究[J].系统仿真学报,2002,14(3):281-284.LIU Zao-zhen.Simulation validation based on the data of the aero experimentation[J].Journal of System Simulation,2002,14(3):281-284.(in Chinese)
[7]吴静,吴晓燕,滕江川,等.基于连续隐马尔可夫模型的仿真模型验证[J].兵工学报,2012,33(3):367-372.WU Jing,WU Xiao-yan,TENG Jiang-chuan,et al.Simulation model validation based on continuous hidden Markov model[J].Acta Armamentarii,2012,33(3):367-372.(in Chinese)
[8]魏华梁,刘藻珍.交叉谱估计及其在导弹系统仿真模型验证中的应用[J].系统仿真学报,1997,9(3):116-121.WEI Hua-liang,LIU Zao-zhen.Cross spectral estimation and its application in missile systems simulation validation[J].Journal of System Simulation,1997,9(3):116-121.(in Chinese)
[9]Kheir N A,Holmes W M.On validating simulation models of missile systems[J].Simulation,1978,30(4):117-128.
[10]Montgomery D C,Conard R G.Comparison of simulation and flight-test data for missile systems[J].Simulation,1980,34(2):63-72.
[11]李伟,焦松,陆凌云,等.基于特征差异的仿真模型验证及选择方法[J].自动化学报,2014,40(10):2134-2144.LI Wei,JIAO Song,LU Ling-yun,et al.Validation and selection of simulation model based on the feature differences[J].Acta Automatica Sinica,2014,40(10):2134-2144.(in Chinese)
[12]Sargent R G.Verification and validation of simulation models[C]∥Proceedings of the 2009 Winter Simulation Conference.Austin,TX,US:IEEE,2009:162-176.
[13]Gu H,Song B F.Study on effectiveness evaluation of weapon systems based on grey relational analysis and TOPSIS[J].Journal of Systems Engineering and Electronics,2009,20(1):106-111.
[14]白瑞阳,吴晓燕,张玉新,等.Gabor变换在仿真模型验证中的应用[J].弹箭与制导学报,2014,34(4):187-188.BAI Rui-yang,WU Xiao-yan,ZHANG Yu-xin,et al.Application of Gabor transform in validation of simulation model[J].Journal of Projectiles,Rockets,Missiles and Guidance,2014,34(4):187-188.(in Chinese)
[15]柳世考,刘兴堂,张文.利用相似度对仿真系统可信度进行定量评估[J].系统仿真学报,2002,14(2):143-145.LIU Shi-kao,LIU Xing-tang,ZHANG Wen.Fixed quantity evaluation to reliability of simulation system with similar degree[J].Journal of System Simulation,2002,14(2):143-145.(in Chinese)
[16]刘飞,马萍,杨明,等.复杂仿真系统可信度量化研究[J].哈尔滨工业大学学报,2007,39(1):1-3.LIU Fei,MA Ping,YANG Ming,et al.Research on credibility quantification of complex simulation systems[J].Journal of Harbin Institute of Technology,2007,39(1):1-3.(in Chinese)
[17]曲晓慧,乔新勇,陈玫,等.基于灰色关联分析的柴油机状况评估[J].兵工学报,2005,26(4):557-559.QU Xiao-hui,QIAO Xin-yong,CHEN Mei,et al.Condition evaluation for diesel engine based on grey relation analysis[J].Acta Armamentarii,2005,26(4):557-559.(in Chinese)
[18]胡方,黄建国,褚福照.基于粗糙集的武器系统灰色关联评估模型[J].兵工学报,2008,29(2):253-256.HU Fang,HUANG Jian-guo,CHU Fu-zhao.Grey relation evaluation model of weapon system based on rough set[J].Acta Armamentarii,2008,29(2):253-256.(in Chinese)
[19]孙勇成,周献中,李桂芳,等.基于灰色关联分析的仿真模型及其改进[J].系统仿真学报,2005,17(3):522-524.SUN Yong-cheng,ZHOU Xian-zhong,LI Gui-fang,et al.Validation of simulation models based on grey relational analysis and improvement[J].Journal of System Simulation,2005,17(3):522-524.(in Chinese)
[20]王曙钊,刘兴堂,段锁力.利用灰色关联度理论对仿真模型的评估研究[J].空军工程大学学报,2007,8(1):73-76.WANG Shu-zhao,LIU Xing-tang,DUAN Suo-li.Research on simulation model evaluation using grey correlation degree[J].Journal of Air Force Engineering University,2007,8(1):73-76.(in Chinese)
[2]吴静,吴晓燕,陈永兴.基于改进灰色关联分析的仿真模型验证方法[J].系统工程与电子技术,2010,32(8):1677-1679.WU Jing,WU Xiao-yan,CHEN Yong-xing.Validation of simulation models based on improved grey relational analysis[J].Systems Engineering and Electronics,2010,32(8):1677-1679.(in Chinese)
[3]Naylor T H,Finger J M.Verification of computer simulation models[J].Management Science,1967,14(2):92-101.
[4]Kheir N A,Holmes W M.On validating simulation models of missile systems[J].Simulation,1978,30(4):117-128.
[5]宁小磊,赵娜,吕永佳,等.基于阵灰色关联分析的仿真模型验证方法研究[J].弹箭与制导学报,2014,34(3):203-205.NING Xiao-lei,ZHAO Na,LYU Yong-jia,et al.Study of validation of simulation model based on matrix gray relational analysis[J].Journal of Projectiles,Rockets,Missiles and Guidance,2014,34(3):203-205.(in Chinese)
[6]刘藻珍.基于飞行试验数据的仿真模型验证方法的研究[J].系统仿真学报,2002,14(3):281-284.LIU Zao-zhen.Simulation validation based on the data of the aero experimentation[J].Journal of System Simulation,2002,14(3):281-284.(in Chinese)
[7]吴静,吴晓燕,滕江川,等.基于连续隐马尔可夫模型的仿真模型验证[J].兵工学报,2012,33(3):367-372.WU Jing,WU Xiao-yan,TENG Jiang-chuan,et al.Simulation model validation based on continuous hidden Markov model[J].Acta Armamentarii,2012,33(3):367-372.(in Chinese)
[8]魏华梁,刘藻珍.交叉谱估计及其在导弹系统仿真模型验证中的应用[J].系统仿真学报,1997,9(3):116-121.WEI Hua-liang,LIU Zao-zhen.Cross spectral estimation and its application in missile systems simulation validation[J].Journal of System Simulation,1997,9(3):116-121.(in Chinese)
[9]Kheir N A,Holmes W M.On validating simulation models of missile systems[J].Simulation,1978,30(4):117-128.
[10]Montgomery D C,Conard R G.Comparison of simulation and flight-test data for missile systems[J].Simulation,1980,34(2):63-72.
[11]李伟,焦松,陆凌云,等.基于特征差异的仿真模型验证及选择方法[J].自动化学报,2014,40(10):2134-2144.LI Wei,JIAO Song,LU Ling-yun,et al.Validation and selection of simulation model based on the feature differences[J].Acta Automatica Sinica,2014,40(10):2134-2144.(in Chinese)
[12]Sargent R G.Verification and validation of simulation models[C]∥Proceedings of the 2009 Winter Simulation Conference.Austin,TX,US:IEEE,2009:162-176.
[13]Gu H,Song B F.Study on effectiveness evaluation of weapon systems based on grey relational analysis and TOPSIS[J].Journal of Systems Engineering and Electronics,2009,20(1):106-111.
[14]白瑞阳,吴晓燕,张玉新,等.Gabor变换在仿真模型验证中的应用[J].弹箭与制导学报,2014,34(4):187-188.BAI Rui-yang,WU Xiao-yan,ZHANG Yu-xin,et al.Application of Gabor transform in validation of simulation model[J].Journal of Projectiles,Rockets,Missiles and Guidance,2014,34(4):187-188.(in Chinese)
[15]柳世考,刘兴堂,张文.利用相似度对仿真系统可信度进行定量评估[J].系统仿真学报,2002,14(2):143-145.LIU Shi-kao,LIU Xing-tang,ZHANG Wen.Fixed quantity evaluation to reliability of simulation system with similar degree[J].Journal of System Simulation,2002,14(2):143-145.(in Chinese)
[16]刘飞,马萍,杨明,等.复杂仿真系统可信度量化研究[J].哈尔滨工业大学学报,2007,39(1):1-3.LIU Fei,MA Ping,YANG Ming,et al.Research on credibility quantification of complex simulation systems[J].Journal of Harbin Institute of Technology,2007,39(1):1-3.(in Chinese)
[17]曲晓慧,乔新勇,陈玫,等.基于灰色关联分析的柴油机状况评估[J].兵工学报,2005,26(4):557-559.QU Xiao-hui,QIAO Xin-yong,CHEN Mei,et al.Condition evaluation for diesel engine based on grey relation analysis[J].Acta Armamentarii,2005,26(4):557-559.(in Chinese)
[18]胡方,黄建国,褚福照.基于粗糙集的武器系统灰色关联评估模型[J].兵工学报,2008,29(2):253-256.HU Fang,HUANG Jian-guo,CHU Fu-zhao.Grey relation evaluation model of weapon system based on rough set[J].Acta Armamentarii,2008,29(2):253-256.(in Chinese)
[19]孙勇成,周献中,李桂芳,等.基于灰色关联分析的仿真模型及其改进[J].系统仿真学报,2005,17(3):522-524.SUN Yong-cheng,ZHOU Xian-zhong,LI Gui-fang,et al.Validation of simulation models based on grey relational analysis and improvement[J].Journal of System Simulation,2005,17(3):522-524.(in Chinese)
[20]王曙钊,刘兴堂,段锁力.利用灰色关联度理论对仿真模型的评估研究[J].空军工程大学学报,2007,8(1):73-76.WANG Shu-zhao,LIU Xing-tang,DUAN Suo-li.Research on simulation model evaluation using grey correlation degree[J].Journal of Air Force Engineering University,2007,8(1):73-76.(in Chinese)