基于贝叶斯统计推理的结构损伤识别方法研究
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摘要
随着科技的发展,大跨结构与高耸复杂建筑日益增多,这些结构在建造和使用过程中的损伤识别问题成为当前土木工程领域的热点问题。而利用结构振动特性来进行结构损伤识别的方法被认为是解决这一难题的有效途径之一。
本文首先简述了当前结构损伤识别领域的研究现状,介绍了不同的结构损伤识别方法,并比较了各种方法的优缺点;接着论述了贝叶斯统计推理的算法与基本原理,阐述贝叶斯原理在结构损伤识别中应用的可行性,与传统损伤识别方法相比,贝叶斯统计推理方法通过不同途径可实现结构在线参数识别与结构损伤模式识别。
卡尔曼滤波器(KF)的本质是利用递归算法获得贝叶斯推理的最优解,因此,KF是贝叶斯统计推理方法最直观的表达形式。利用传统KF将动力学系统的运动微分方程转换到状态空间中,然后将待识别的参数同结构的响应—并作为系统的状态向量进行识别。
传统的KF要求系统的状态方程和观测方程都是线性的,然而,现实中许多工程系统往往不能简单的用线性系统来描述。扩展卡尔曼滤波(EKF)采取对非线性系统近似线性化的处理方法,解决了非线性系统滤波问题。而EKF方法具有采用线型化模型不能准确反应结构系统的缺陷,同时不适用于非高斯噪声状况的识别,因此识别效果较差。采用卡尔曼滤波器与扩展卡尔曼滤波器(EKF)对线性和非线性系统进行结构参数的损伤识别,对实验结果进行分析,发现非线性结构参数识别会造成结果发散。揭示了卡尔曼滤波器的固有缺陷。
卡尔曼滤波在线性高斯模型下能得到最优估计,但在非线性非高斯模型下则无法应用。在这种情况下,粒子滤波(PF)因其适用面广而备受关注。PF是一种基于蒙特卡罗模拟和递推贝叶斯估计的滤波方法。PF和其他预测性滤波一样,可以通过模型方程由测量空间递推得到状态空间。它采用粒子描述状态空间,用由粒子及其权重组成的离散随机测度来近似真实的状态后验分布,并且根据算法递推更新离散随机测度。它可以处理模型方程为非线性、噪声分布为非高斯分布的问题,适合应用于结构损伤识别领域。而传统粒子滤波的缺点是粒子数量固定,不能结合系统进行粒子数量的调节。
由于传统PF中粒子数量取值为固定值,在计算过程中需要采取较大的粒子数量才能保证结构参数识别精度,不利于非平稳系统的结构系统参数识别。文中提出了采用自适应PF方法进行非平稳结构参数的损伤识别。该方法利用系统后验概率密度与当前粒子集概率密度的KL距离准则更新采样粒子数量,具有根据非平稳系统实时状态自适应调节粒子数量的优点(结构非稳定状态采取较多粒子进行识别,在结构平稳状态采用较少的粒子进行识别),改进了传统PF方法不能调节粒子数量的缺点,能在保证识别精度的同时大大降低识别过程的计算量,因此该方法比传统PF方法更适合进行在线的结构系统参数识别。数值仿真结果证明了此方法在结构损伤在线识别中的有效性。
贝叶斯概率神经网络(PNN)采用贝叶斯统计理论描述测量数据,因此贝叶斯概率神经网络在有噪声情况下的结构损伤模式识别具有巨大潜力。而小波分析的数据处理能力可以对振动数据进行详尽刻划,结合小波分析与PNN,提出小波概率神经网络对结构损伤模式进行识别,分析小波函数,小波尺度,噪声水平等因素对识别结果的影响,损伤识别结果证明小波神经网络具有抗噪声能力强,识别精度高的优点,在结构损伤模式识别方面具有巨大的潜力。
本论文基于贝叶斯统计推断理论针对结构系统参数识别与损伤模式识别问题进行了研究,最后对全文的主要工作和研究成果进行总结,并指出了课题中有待进一步改进和研究的问题。
More and more long span structures and high buildings are constructed with science and technique development; it is a hot topic in civil engineering field for structural damage identification in construction and employment. It is an effective approach to solve structural damage identification problem based on the structural dynamic parameters.
The state of arts of researches about structural damage identification is depicted in this dissertation, and the different structural damage identification methods are introduced; the characters of different methods are analyzed. Then the rationale of Bayesian statistics reasoning algorithm is depicted, and the feasibility using Bayesian theory for structural damage identification is expatiated. Compared with traditional damage identification methods, Bayesian statistics reasoning can realize structural parameters identification and structural damage pattern identification by different approachs.
The essence of Kalman filtering (KF) is to gain the most optimal solution using recursion algorithm; therefore, KF is the most intuitionistic expression of Bayesian statistics reasoning method. Traditional KF is utilized to identify structural parameters by transformation from dynamic system differential equation to state space, and combining structural parameters and responses in system state vectors in this dissertation.
The state equations and measurement equations of traditional KF are linear. Many engineering systems are not linear systems in reality. The extended Kalman filtering (EKF) method adopts the method to linearize the non-linear system approximately, and the problem of non-linear system filtering is solved. But the EKF method has the disadvantages that the linearization of system is only approximative, and it should have Gaussian noise hypothesis in system. Therefore, the EKF method has low identification precision. KF method and EKF method are adopted to identify structural parameters of liner/non-liner structural system in this paper, and the result of non-liner structural system identification is not converged in experiment. The facts have proved that KF method and EKF method have intrinsic limitation.
The KF can get the optimal estimate in the Linear-Gaussian model, but it can not be applied in the nonlinear and non-Gaussian model. In this case, Particle filtering (PF) method is studied abroad for its wide application. The PF is a filter method based on Monte-Carlo simulation and recursive Beyesian estimation. As other predictive filters, state space is recursively got from measure space with system model by using the PF. It uses particles to describe the state space. The discretely random measure composed by particles and associated weights approximates to the true posterior state distribution, and is updated by recursion of the algorithm. The PF can resolve the problem of nonlinear model equations and non-Gaussian noise distribution, and is suitable for the structural damage identification fields. The traditional PF method has the disadvantages that the particle numbers is fixed, and the PF can not adjust the particle number in system identification.
Since the particle numbers are fixed in particle filtering process, in order to guarantee the precision of system identification, the large particle numbers must be used which is not beneficial to the parameter identification of non-stationary system. An adaptive particle filtering (APF) method is proposed to identify non-stationary structural system parameters damage identification. In the APF, the sampling particle numbers are updated by the K-L distance rule between the system posterior probability density and current probability density of sampling particles set; it reduces the computations greatly in system identification by adaptive adjusting particle numbers by the state of non-stationary system (It adopts large particle numbers in non-stationary system state, vice versa.), hence it has a good time tracking ability, and it is more suitable for tracking the non-stationary system than the conventional PF. The numerical simulations confirm the effectiveness of the proposed method for the online structural damage identification.
The Bayesian probabilistic neural network (PNN) describes measurement data in Bayesian statistics theory; it shows great ability of structural damage pattern recognition with noisy conditions. By combining wavelet analysis with PNN, a wavelet probabilistic neural network (WPNN) is proposed for structural damage identification in the dissertation; and the effect factors to damage identification result of wavelet function, wavelet scales and noise level etc. were analyzed. The identification result shows that the WPNN has high identification accuracy and noise-resistant and, huge structural damage pattern identification future.
This dissertation focuses on structural system parameters identification and damage pattern identification problems based on Bayesian statistics reasoning theory, and at last, the main contributions and conclusions of this dissertation are summarized and some problems which need further research are put forward.
本文首先简述了当前结构损伤识别领域的研究现状,介绍了不同的结构损伤识别方法,并比较了各种方法的优缺点;接着论述了贝叶斯统计推理的算法与基本原理,阐述贝叶斯原理在结构损伤识别中应用的可行性,与传统损伤识别方法相比,贝叶斯统计推理方法通过不同途径可实现结构在线参数识别与结构损伤模式识别。
卡尔曼滤波器(KF)的本质是利用递归算法获得贝叶斯推理的最优解,因此,KF是贝叶斯统计推理方法最直观的表达形式。利用传统KF将动力学系统的运动微分方程转换到状态空间中,然后将待识别的参数同结构的响应—并作为系统的状态向量进行识别。
传统的KF要求系统的状态方程和观测方程都是线性的,然而,现实中许多工程系统往往不能简单的用线性系统来描述。扩展卡尔曼滤波(EKF)采取对非线性系统近似线性化的处理方法,解决了非线性系统滤波问题。而EKF方法具有采用线型化模型不能准确反应结构系统的缺陷,同时不适用于非高斯噪声状况的识别,因此识别效果较差。采用卡尔曼滤波器与扩展卡尔曼滤波器(EKF)对线性和非线性系统进行结构参数的损伤识别,对实验结果进行分析,发现非线性结构参数识别会造成结果发散。揭示了卡尔曼滤波器的固有缺陷。
卡尔曼滤波在线性高斯模型下能得到最优估计,但在非线性非高斯模型下则无法应用。在这种情况下,粒子滤波(PF)因其适用面广而备受关注。PF是一种基于蒙特卡罗模拟和递推贝叶斯估计的滤波方法。PF和其他预测性滤波一样,可以通过模型方程由测量空间递推得到状态空间。它采用粒子描述状态空间,用由粒子及其权重组成的离散随机测度来近似真实的状态后验分布,并且根据算法递推更新离散随机测度。它可以处理模型方程为非线性、噪声分布为非高斯分布的问题,适合应用于结构损伤识别领域。而传统粒子滤波的缺点是粒子数量固定,不能结合系统进行粒子数量的调节。
由于传统PF中粒子数量取值为固定值,在计算过程中需要采取较大的粒子数量才能保证结构参数识别精度,不利于非平稳系统的结构系统参数识别。文中提出了采用自适应PF方法进行非平稳结构参数的损伤识别。该方法利用系统后验概率密度与当前粒子集概率密度的KL距离准则更新采样粒子数量,具有根据非平稳系统实时状态自适应调节粒子数量的优点(结构非稳定状态采取较多粒子进行识别,在结构平稳状态采用较少的粒子进行识别),改进了传统PF方法不能调节粒子数量的缺点,能在保证识别精度的同时大大降低识别过程的计算量,因此该方法比传统PF方法更适合进行在线的结构系统参数识别。数值仿真结果证明了此方法在结构损伤在线识别中的有效性。
贝叶斯概率神经网络(PNN)采用贝叶斯统计理论描述测量数据,因此贝叶斯概率神经网络在有噪声情况下的结构损伤模式识别具有巨大潜力。而小波分析的数据处理能力可以对振动数据进行详尽刻划,结合小波分析与PNN,提出小波概率神经网络对结构损伤模式进行识别,分析小波函数,小波尺度,噪声水平等因素对识别结果的影响,损伤识别结果证明小波神经网络具有抗噪声能力强,识别精度高的优点,在结构损伤模式识别方面具有巨大的潜力。
本论文基于贝叶斯统计推断理论针对结构系统参数识别与损伤模式识别问题进行了研究,最后对全文的主要工作和研究成果进行总结,并指出了课题中有待进一步改进和研究的问题。
More and more long span structures and high buildings are constructed with science and technique development; it is a hot topic in civil engineering field for structural damage identification in construction and employment. It is an effective approach to solve structural damage identification problem based on the structural dynamic parameters.
The state of arts of researches about structural damage identification is depicted in this dissertation, and the different structural damage identification methods are introduced; the characters of different methods are analyzed. Then the rationale of Bayesian statistics reasoning algorithm is depicted, and the feasibility using Bayesian theory for structural damage identification is expatiated. Compared with traditional damage identification methods, Bayesian statistics reasoning can realize structural parameters identification and structural damage pattern identification by different approachs.
The essence of Kalman filtering (KF) is to gain the most optimal solution using recursion algorithm; therefore, KF is the most intuitionistic expression of Bayesian statistics reasoning method. Traditional KF is utilized to identify structural parameters by transformation from dynamic system differential equation to state space, and combining structural parameters and responses in system state vectors in this dissertation.
The state equations and measurement equations of traditional KF are linear. Many engineering systems are not linear systems in reality. The extended Kalman filtering (EKF) method adopts the method to linearize the non-linear system approximately, and the problem of non-linear system filtering is solved. But the EKF method has the disadvantages that the linearization of system is only approximative, and it should have Gaussian noise hypothesis in system. Therefore, the EKF method has low identification precision. KF method and EKF method are adopted to identify structural parameters of liner/non-liner structural system in this paper, and the result of non-liner structural system identification is not converged in experiment. The facts have proved that KF method and EKF method have intrinsic limitation.
The KF can get the optimal estimate in the Linear-Gaussian model, but it can not be applied in the nonlinear and non-Gaussian model. In this case, Particle filtering (PF) method is studied abroad for its wide application. The PF is a filter method based on Monte-Carlo simulation and recursive Beyesian estimation. As other predictive filters, state space is recursively got from measure space with system model by using the PF. It uses particles to describe the state space. The discretely random measure composed by particles and associated weights approximates to the true posterior state distribution, and is updated by recursion of the algorithm. The PF can resolve the problem of nonlinear model equations and non-Gaussian noise distribution, and is suitable for the structural damage identification fields. The traditional PF method has the disadvantages that the particle numbers is fixed, and the PF can not adjust the particle number in system identification.
Since the particle numbers are fixed in particle filtering process, in order to guarantee the precision of system identification, the large particle numbers must be used which is not beneficial to the parameter identification of non-stationary system. An adaptive particle filtering (APF) method is proposed to identify non-stationary structural system parameters damage identification. In the APF, the sampling particle numbers are updated by the K-L distance rule between the system posterior probability density and current probability density of sampling particles set; it reduces the computations greatly in system identification by adaptive adjusting particle numbers by the state of non-stationary system (It adopts large particle numbers in non-stationary system state, vice versa.), hence it has a good time tracking ability, and it is more suitable for tracking the non-stationary system than the conventional PF. The numerical simulations confirm the effectiveness of the proposed method for the online structural damage identification.
The Bayesian probabilistic neural network (PNN) describes measurement data in Bayesian statistics theory; it shows great ability of structural damage pattern recognition with noisy conditions. By combining wavelet analysis with PNN, a wavelet probabilistic neural network (WPNN) is proposed for structural damage identification in the dissertation; and the effect factors to damage identification result of wavelet function, wavelet scales and noise level etc. were analyzed. The identification result shows that the WPNN has high identification accuracy and noise-resistant and, huge structural damage pattern identification future.
This dissertation focuses on structural system parameters identification and damage pattern identification problems based on Bayesian statistics reasoning theory, and at last, the main contributions and conclusions of this dissertation are summarized and some problems which need further research are put forward.
引文
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