基于SVM的多自由度结构非线性模型检验及参数确定
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摘要
文章提出了一种基于支持向量机(support vector machine,SVM)的非线性结构模型验证和参数确定方法。首先建立了基于结构动力响应和外激励载荷的恢复力曲面;然后利用恢复力曲面得到刚度边际谱、阻尼边际谱及非线性指标,采用主成分分析法提取结构非线性指标,利用降维指标作为训练数据训练SVM分类器,用于检测存在的非线性;最后,采用正则化最小二乘法确定了结构非线性模型参数。在数值模拟中,采用1个非线性单自由度系统和1个非线性多自由度系统来验证该方法的有效性。数值仿真结果表明,该方法是一种有效的、噪声鲁棒性强的非线性模型验证和结构参数确定方法。
This paper proposes a novel method for nonlinear model validation and parameter calibration of nonlinear structures by using restoring force surface and support vector machine(SVM) method. In this study, the restoring force surface is established based on the structural dynamic responses and external excitation loads. Then the marginal spectrum and nonlinear indices are calculated by the obtained restoring force surface. Afterwards, the principal component analysis method is performed to extract the structural nonlinear indices, and the reduced dimension index is then employed as the training data to train SVM classifier which is used to detect the existed nonlinearity. Finally, the regularized least-square algorithm is conducted to update structural parameters. In the numerical simulation, a nonlinear single-degree-of-freedom system and a nonlinear multiple-degree-of-freedom system are used to verify the effectiveness of the proposed method. The numerical simulation results demonstrate that the method has great robustness against noise and is effective for nonlinear model validation and parameter calibration.
This paper proposes a novel method for nonlinear model validation and parameter calibration of nonlinear structures by using restoring force surface and support vector machine(SVM) method. In this study, the restoring force surface is established based on the structural dynamic responses and external excitation loads. Then the marginal spectrum and nonlinear indices are calculated by the obtained restoring force surface. Afterwards, the principal component analysis method is performed to extract the structural nonlinear indices, and the reduced dimension index is then employed as the training data to train SVM classifier which is used to detect the existed nonlinearity. Finally, the regularized least-square algorithm is conducted to update structural parameters. In the numerical simulation, a nonlinear single-degree-of-freedom system and a nonlinear multiple-degree-of-freedom system are used to verify the effectiveness of the proposed method. The numerical simulation results demonstrate that the method has great robustness against noise and is effective for nonlinear model validation and parameter calibration.
引文
[1]WANG Z C,XIN Y,XING J F,et al.Hilbert low-pass filter of non-stationary time sequence using analytical mode decomposition[J].Journal of Vibration and Control,2015,23(15):2444-2469.
[2]WANG Z C,WU F,REN W X.Stationarity test of vibration signals with surrogate data and time-frequency analysis[J].Advances in Structural Engineering,2016,20(8):1143-1154.
[3]SHI Z Y,LAW S S.Identification of linear time-varying dynamical system using Hilbert transform and EMD method[J].Journal of Applied Mechanics,2007,74(2):223-230.
[4]KERSCHEN G,WORDEN K A,VAKAKIS F,et al.Past,present and future of nonlinear system identication in structural dynamics[J].Mech Syst Signal Process,2006,20(3):505-592.
[5]ADAMS D E,ALLEMANG R J.Survey of nonlinear detection and identification techniques for experimental vibrations[C]//Proceedings of the International Seminal on Modal Analysis(ISMA).Leuven:[s.n.],1998:269-281.
[6]VANHOENACKER K,SCHOUKENS J,SWEVERS J,et al.Summary and comparing overview of techniques for the detection of non-linear distortions[C]//Proceedings of the International Seminal on Modal Analysis(ISMA).Leuven:[s.n.],2012:1241-1256.
[7]KRAGH K A,THOMSEN J J,TCHERNIAK D.Experimental detection and quantification of structural nonlinearity using homogeneity and Hilbert transform methods[C]//Proceedings of the International Conference on Noise and Vibration Engineering.[S.l.:s.n.],2010:3173-3188.
[8]GOGE D,SINAPIUS M,FULLERRUG U,et al.Detection and description of non-linear phenomena in experimental modal analysis via linearity plots[J].International Journal of Non-linear Mechanics,2005,40:27-48.
[9]HOSSEINI S M,JOHANSEN T A,FATEHI A.Comparison of nonlinearity measures based on time sceries analysis for nonlinearity detection,modeling,identication and control[J].A Norwegian Research Bulletin,2011,32(4):123-140.
[10]MASRI S F,CAUGHEY T K.A nonparametric identification technique for nonlinear dynamic problem[J].Journal of Applied Mechanics,1979,46(3):433-447.
[11]MASRI S F,SASSI H,CAUGHEY T K.Nonparametric identification of nearly arbitrary nonlinear systems[J].Journal of Applied Mechanics,1982,49(5):619-628.
[12]MASRI S F,MILLER R K,SAND A F,et al.Identification of nonlinear vibrating structures:part I:formulation[J].Journal of Applied Mechanics,1987,109(9):918-922.
[13]MASRI S F,MILLER R K,SAND A F,et al.Identification of nonlinear vibrating structures:partⅡ:application[J].Journal of Applied Mechanics,1987,109(9):923-929.
[14]BENEDETTINI F,CAPECCHI D,VESTRONI F.Identification of hysteretic oscillators under earthquake loading by nonparametric models[J].Journal of Engineering Mechanics,1995,121(5):606-612.
[15]NI Y Q,KO J M,WONG C W.Nonparametric identification of nonlinear hysteretic systems[J].Journal of Engineering Mechanics,1997,125(2):206-215.
[16]张茂雨.支持向量机方法在结构损伤识别中的应用[D].上海:同济大学,2007.
[17]武魏娜.土木工程结构参数识别时域法研究[D].天津:天津大学,2006.
[18]刘杰.动态载荷识别的计算反求技术研究[D].长沙:湖南大学,2011.
[2]WANG Z C,WU F,REN W X.Stationarity test of vibration signals with surrogate data and time-frequency analysis[J].Advances in Structural Engineering,2016,20(8):1143-1154.
[3]SHI Z Y,LAW S S.Identification of linear time-varying dynamical system using Hilbert transform and EMD method[J].Journal of Applied Mechanics,2007,74(2):223-230.
[4]KERSCHEN G,WORDEN K A,VAKAKIS F,et al.Past,present and future of nonlinear system identication in structural dynamics[J].Mech Syst Signal Process,2006,20(3):505-592.
[5]ADAMS D E,ALLEMANG R J.Survey of nonlinear detection and identification techniques for experimental vibrations[C]//Proceedings of the International Seminal on Modal Analysis(ISMA).Leuven:[s.n.],1998:269-281.
[6]VANHOENACKER K,SCHOUKENS J,SWEVERS J,et al.Summary and comparing overview of techniques for the detection of non-linear distortions[C]//Proceedings of the International Seminal on Modal Analysis(ISMA).Leuven:[s.n.],2012:1241-1256.
[7]KRAGH K A,THOMSEN J J,TCHERNIAK D.Experimental detection and quantification of structural nonlinearity using homogeneity and Hilbert transform methods[C]//Proceedings of the International Conference on Noise and Vibration Engineering.[S.l.:s.n.],2010:3173-3188.
[8]GOGE D,SINAPIUS M,FULLERRUG U,et al.Detection and description of non-linear phenomena in experimental modal analysis via linearity plots[J].International Journal of Non-linear Mechanics,2005,40:27-48.
[9]HOSSEINI S M,JOHANSEN T A,FATEHI A.Comparison of nonlinearity measures based on time sceries analysis for nonlinearity detection,modeling,identication and control[J].A Norwegian Research Bulletin,2011,32(4):123-140.
[10]MASRI S F,CAUGHEY T K.A nonparametric identification technique for nonlinear dynamic problem[J].Journal of Applied Mechanics,1979,46(3):433-447.
[11]MASRI S F,SASSI H,CAUGHEY T K.Nonparametric identification of nearly arbitrary nonlinear systems[J].Journal of Applied Mechanics,1982,49(5):619-628.
[12]MASRI S F,MILLER R K,SAND A F,et al.Identification of nonlinear vibrating structures:part I:formulation[J].Journal of Applied Mechanics,1987,109(9):918-922.
[13]MASRI S F,MILLER R K,SAND A F,et al.Identification of nonlinear vibrating structures:partⅡ:application[J].Journal of Applied Mechanics,1987,109(9):923-929.
[14]BENEDETTINI F,CAPECCHI D,VESTRONI F.Identification of hysteretic oscillators under earthquake loading by nonparametric models[J].Journal of Engineering Mechanics,1995,121(5):606-612.
[15]NI Y Q,KO J M,WONG C W.Nonparametric identification of nonlinear hysteretic systems[J].Journal of Engineering Mechanics,1997,125(2):206-215.
[16]张茂雨.支持向量机方法在结构损伤识别中的应用[D].上海:同济大学,2007.
[17]武魏娜.土木工程结构参数识别时域法研究[D].天津:天津大学,2006.
[18]刘杰.动态载荷识别的计算反求技术研究[D].长沙:湖南大学,2011.