多自由度结构动力可靠度分析的小波方法
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摘要
该文发展了基于小波分析的局部平稳法在多自由度结构动力可靠度中的应用。首先,基于广义谐和小波和随机过程的局部平稳小波模型,发展了线性多自由度结构系统在各时间-频率子域上激励功率谱与响应功率谱之间的关系,并计算得到了在一般随机动力激励下结构随机动力响应功率谱密度和各阶谱矩。随后,根据随机动力激励和响应的高斯假定及超越过程的Markov假定,得到了线性多自由度结构在均匀/非均匀调制随机激励下层间位移的动力可靠度指标。结构动力可靠度的Monte Carlo模拟显示了所提方法的可靠性与计算高效性。
A wavelet-based local stationary approach for the dynamic reliability determination of linear MDOF systems is presented. First, based on the generalized harmonic wavelet and the local stationary wavelet model of the stochastic process, an evolutionary power spectrum(EPS) density relationship between a full non-stationary excitation and response is developed. Based on the response EPS, the moments of the response EPS are calculated for the reliability determination. Finally, based on the Gaussian assumption for the linear response and Markovian assumption for the crossing event, the probability of the drift displacement remaining below a certain limit is calculated. Monte Carlo simulations demonstrate the reliability and computational efficiency of the proposed approach.
A wavelet-based local stationary approach for the dynamic reliability determination of linear MDOF systems is presented. First, based on the generalized harmonic wavelet and the local stationary wavelet model of the stochastic process, an evolutionary power spectrum(EPS) density relationship between a full non-stationary excitation and response is developed. Based on the response EPS, the moments of the response EPS are calculated for the reliability determination. Finally, based on the Gaussian assumption for the linear response and Markovian assumption for the crossing event, the probability of the drift displacement remaining below a certain limit is calculated. Monte Carlo simulations demonstrate the reliability and computational efficiency of the proposed approach.
引文
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[17]Corotis R B,Vanmarcke E H,Cornell A C.First passage of nonstationary random processes[J].Journal of the Engineering Mechanics Division,1972,98(2):401―414.
[18]Vanmarcke E H.On the distribution of the first-passage time for normal stationary random processes[J].Journal of applied mechanics,42(1975):215―220.
[19]Barbato M,Conte J P.Structural reliability applications of nonstationary spectral characteristics[J].Journal of Engineering Mechanics,2010,137(5):371―382.
[20]Li J,Chen J B.Stochastic Dynamics of Structures[M].Singapore:John Wiley&Sons,2009:285―308.
[21]曹晖,赖明,白绍良.地震地面运动局部谱密度的小波变换估计[J].工程力学,2004,21(5):109―115.Cao Hui,Lai Ming,Bai Shaoliang.Estimation of local spectral density of earthquake ground motion based on wavelet transform[J].Engineering Mechanics,2004,21(5):109―115.(in Chinese)
[22]周广东,丁幼亮,李爱群,孙鹏.基于小波变换的非平稳脉动风时变功率谱估计方法研究[J].工程力学,2013,30(3):89―97.Zhou Guangdong,Ding Youliang,Li Aiqun,Sun Peng.Estimation method of evolutionary power spectrum for non-stationary fluctuating wind using wavelet transforms[J].Engineering Mechanics,2013,30(3):89―97.(in Chinese)
[2]Roberts J B,Spanos P D.Random vibration and statistical linearization[M].New York:Dover,2003:1―16.
[3]朱位秋.随机振动[M].北京:科学出版社,1992:474―558.Zhu Weiqiu.Random vibration[M].Beijing:Science Press,1992:474―558.(in Chinese)
[4]李桂青,曹宏.结构动力可靠度及其应用[M].北京:地震出版社,1993:26―82.Li Guiqiing,Cao Hong.Structure dynamic reliability and its application in engineering[M].Beijing:Earthquake Press,1993:16―82.(in Chinese)
[5]Crandall S H.First-crossing probabilities of the linear oscillator[J].Journal of Sound and Vibration,1970,12(3):285―299.
[6]Chen J B,Li J.Dynamic response and reliability analysis of non-linear stochastic structures[J].Probabilistic Engineering Mechanics,2005,20(1):33―44.
[7]Daubechies I.Ten lectures on wavelets[M].Philadelphia:Society for Industrial and Applied Mathematics,1992:1―16.
[8]Basu B.Wavelet-based stochastic seismic response of a duffing oscillator[J].Journal of Sound and Vibration,2001,245(2):251―260.
[9]Basu B,Gupta V K.Seismic response of SDOF systems by wavelet modeling of nonstationary processes[J].Journal of Engineering Mechanics-ASCE,1998,124(10):1142―1150.
[10]Tratskas P,Spanos P D.Linear multi-degree-of-freedom system stochastic response by using the harmonic wavelet transform[J].Journal of Applied Mechanics,2003,70(5):724―731.
[11]Spanos P D,Kougioumtzoglou I A.Harmonic wavelets based statistical linearization for response evolutionary power spectrum determination[J].Probabilistic Engineering Mechanics,2012,27(1):57―68.
[12]Nason G P,von Sachs R,Kroisandt G.Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum[J].Journal of The Royal Statistical Society Series B-Statistical Methodology,2000,62(2):271―295.
[13]Newland D E.Harmonic and musical wavelets[J].Proceedings of the Royal Society of London.Series A:Mathematical and Physical Sciences,1994,444(1922):605―620.
[14]Newland D E.Harmonic wavelet analysis[J].Proceedings of the Royal Society of London.Series A:Mathematical and Physical Sciences,1993,443(1917):203―225.
[15]Priestley M.Power spectral analysis of non-stationary random processes[J].Journal of Sound And Vibration,1967,6(1):86―97.
[16]Spanos P D,Kougioumtzoglou I A.Harmonic wavelet-based statistical linearization of the Bouc-Wen hysteretic model[C]//Faber,Kohler and Nishijima.Proceedings of the 11th International Conference on Applications of Statistics and Probability in Civil Engineering,ICASP.London:Taylor&Francis Group,2011:2649―2656.
[17]Corotis R B,Vanmarcke E H,Cornell A C.First passage of nonstationary random processes[J].Journal of the Engineering Mechanics Division,1972,98(2):401―414.
[18]Vanmarcke E H.On the distribution of the first-passage time for normal stationary random processes[J].Journal of applied mechanics,42(1975):215―220.
[19]Barbato M,Conte J P.Structural reliability applications of nonstationary spectral characteristics[J].Journal of Engineering Mechanics,2010,137(5):371―382.
[20]Li J,Chen J B.Stochastic Dynamics of Structures[M].Singapore:John Wiley&Sons,2009:285―308.
[21]曹晖,赖明,白绍良.地震地面运动局部谱密度的小波变换估计[J].工程力学,2004,21(5):109―115.Cao Hui,Lai Ming,Bai Shaoliang.Estimation of local spectral density of earthquake ground motion based on wavelet transform[J].Engineering Mechanics,2004,21(5):109―115.(in Chinese)
[22]周广东,丁幼亮,李爱群,孙鹏.基于小波变换的非平稳脉动风时变功率谱估计方法研究[J].工程力学,2013,30(3):89―97.Zhou Guangdong,Ding Youliang,Li Aiqun,Sun Peng.Estimation method of evolutionary power spectrum for non-stationary fluctuating wind using wavelet transforms[J].Engineering Mechanics,2013,30(3):89―97.(in Chinese)
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