摘要
系统识别的结果经常受到所选取的模型参数精确度的限制,模型参数的选取的过程中包含很多不确定的信息,这对系统识别结果有着非常大的影响。通过概率分布函数来描述非线性动力系统中模型参数,可以有效避免参数选取时所产生的误差。
大多数损伤识别技术是通过实际工程中测得的数据与桥梁结构模型进行对比,从而确定结构损伤的位置和程度。实际工程中,桥梁结构均体现出非线性性质,包括材料非线性,几何非线性和材料非线性情况。通过对结构损伤的位置和程度进行识别,可以对结构的剩余寿命进行评估。一般的结构损伤识别方法是从测量数据中提取结构的模态参数值,结构的损伤会引起模态参数值的变化,通过监测模态参数的变化趋势,可以分析出结构损伤的情况。桥梁结构损伤识别的方法很多,但是在实际中应用还有很多问题。很多学者对桥梁结构的损伤识别方法进行了系统研究,探求识别混凝土桥梁的振动模态参数的方法,减小环境噪声对识别结果的影响,提高模态参数识别结果的准确性和有效性。
基于贝叶斯框架下的相关向量机方法在信号处理中具有所需数据少,计算速度快和准确率高等优点。通过自相关判定方法消去响应向量中不相关项,可以大量降低运算次数,而又不会对结果造成太大的影响。本文通过对非线性理论的系统研究,建立了桥梁结构非线性有限元模型；并且根据贝叶斯模型方法,对有限元模型进行修正；然后对实际桥梁结构进行荷载试验并且对试验结果进行分析,通过相关向量机方法对结构损伤情况进行识别。本文的主要研究工作有：
根据材料非线性本构方程和几何非线性刚度矩阵,对双非线性平衡方程和非线性动力方程进行了推导。引入实际工程问题,建立了非线性桥梁结构有限元模型,并且描述了非线性对桥梁结构有限元模型的影响。
运用贝叶斯系统识别方法,计算非线性桥梁结构模型参数优化值和非线性结构模型参数的相对概率值。针对贝叶斯系统识别方法在概率密度函数选取过程中的局限性,通过随机模拟的方法,对先验概率密度函数进行迭代计算,得出模型参数修正概率密度函数。通过对杜芬运动方程和弹塑性振动模型的参数进行修正,验证贝叶斯方法在模型参数修正过程中的有效性。并且基于动力响应信号,对桥梁结构模型进行了修正。
介绍了相关向量机在回归和分类过程中的应用,引入核函数的概念,对相关向量机在响应信号分析中的应用进行了详细的阐述,提出相关向量机分析响应信号的流程。对Sinc函数和Ripley函数分别进行回归过程和分类过程计算,验证相关向量机的先进性。
创新性的将相关向量机方法应用于桥梁结构损伤识别过程中,提出选取桥梁结构模态参数变量函数△ψi/△ωi2和[△ψi△fi]做为输入函数进行相关向量机训练,根据训练的结果对桥梁结构的损伤进行识别。建立桥梁结构有限元损伤模型,对不同损伤组合模型的模态参数变化量进行训练,得出结构的损伤识别结果。对实际桥梁结构的荷载试验结果进行分析,将模态参数变量代入相关向量机进行训练,对桥梁结构进行损伤识别,通过与桥梁进行静力荷载试验结果对比,验证相关向量机对桥梁结构损伤识别的有效性。通过本文的研究,得出以下结论：
1、基于几何非线性平衡方程和材料非线性本构关系方程,推导出非线性耦合刚度矩阵。提出以非线性耦合刚度矩阵为增量,构建结构的材料非线性平衡方程。考虑材料非线性影响,将材料非线性刚度矩阵对应的弹性模量做为模型的基本参数,针对一座实际桥梁结构建立变截面连续梁桥结构模型。对双非线性连续梁桥结构模型进行加载,结果表明当集中力超过屈服荷载时,结构明显体现出材料非线性特征。
2、基于贝叶斯方法,对双非线性结构模型进行修正,可以降低模型参数选取时的误差,通过对杜芬运动方程和弹塑性振动模型的模型参数进行修正,验证贝叶斯方法在模型参数修正过程中的有效性。
3、对相关向量机训练方法进行详细的描述,并且给出相关向量机训练流程。分别通过相关向量机和支持向量机方法对Sinc函数进行回归,并且对Ripley二维混合数组进行分类,将训练结果进行比较,说明相关向量机在信号回归与分类过程中所需数据少,计算速度快和准确率高。
4、提出分别以双非线性桥梁结构模态参数变量函数△ψi/△ωi2和[△ψi△fi]为超参数,进行相关向量机训练,构建包含超参数的目标函数,通过训练结果对目标函数进行回归和分类,得到结构损伤识别结果。建立损伤结构有限元模型验证相关向量机训练方法在损伤识别过程中的有效性。将相关向量机损伤识别方法应用与实际工程中,与静载试验结果相比,基于相关向量机方法的损伤识别结果精确。说明基于相关向量机训练的损伤识别方法具有速度快,操作简便,准确率高等优点,具有实用价值。
Since the significant of response prediction, structure controlling and structural health monitoring, the problem of bridge structural system damage identification receives more attention recently. However, the research results always be restricted by the accuracy of the model parameters selection, and the parameters include lots of uncertain additional information during the model parameters selection. It will lead an adverse influence to the system damage identification. Adopt probability distribution function (PDF) to describe the nonlinear dynamic system model parameters, could avoid the errors while select the parameters effectively. The model parameters can be used to calculate the probability distribution function.
Researchers, using the structural health monitoring method of bridge structure to identify the early damage and change. Recently, the structural damage identification methods are received much attention. After analysis for the structural modal parameters, we can identify the structure of injuries in position. However, the bridge structural always complex and with many parameters, determine the damage location structure is difficult, since the large amount of calculation.
Most damage identification methods are based on actual engineering in measured data and compared the bridge structure model to determine the location and degree of structural damage. Bridge structure model is established to identify the process, the influence is bigger. In practical engineering, bridge structures are embodied in nonlinear properties, including material nonlinearity and the geometrical nonlinearity. However, nonlinear system of bridge structure by the result of identification is often the selection of model parameters accuracy of model with the limit, the parameter selection, many uncertain factors were also included in the parameters, and the system identification results have very adverse effects. Using probability distribution function to describe the nonlinear dynamic system model parameters, can effectively avoid the errors when parameter selection.
Based on the location and severities of structural damage identification, the remaining life of structure could be assessed. General structural damage identification method was extracted from the measurement data of modal parameter value structure, the structure of the damage can cause modal parameter value change, so by monitoring the modal parameters change trend, also can reflect the structural damage.
Bridge structural damage identification methods are variously, but in practice and a lot of problems. Many scholars bridge structure damage identification method is studied systematically identifying concrete bridge, and to explore the vibration modal parameters method to identify and reduce the environmental noise affect the results of modal parameter identification, improve the accuracy and validity.
Bayesian theory in the concrete steps for damage identification from a large number of data including extract limited a regression variables or eigenvalue of feature extraction phase; Recognition input variables and the extraction of eigenvalue of the relationship between training phases; By means of the regression equations and boundary conditions on the structural damage assessment of prediction stage. Bayesian framework based on the relevance vector machine in signal processing method has the required data in less computing speed and accuracy, high yield. In response to the signal accord with Gaussian distribution under the condition of the autocorrelation determination methods, through the response is not relevant items in vector away, so that they could be massively reduce operation times, and won't cause too big for the results of influence. Based on the systematic study of nonlinear theory, a nonlinear finite element model of bridge structure and, depending on the Bayesian model modification method of finite element model, revised, amended bridge structure with nonlinear finite element model for the reference to the actual bridge structure, load test and the experimental results were analyzed, through the relevance vector machine method to identify structural damage situation. This dissertation main research work for:
According to material nonlinear constitutive equations and geometry nonlinear stiffness matrix, on the double nonlinear equilibrium equation and nonlinear dynamic equations are deduced. Introducing actual engineering problems, establish the nonlinear finite element model of bridge structure, and to describe the nonlinear finite element model of the influence of bridge structure.
Using bayesian system identification method, the double nonlinear bridge structure model parameters are updating. Through the limitations of the random simulation method of prior probability density function, iterative computation model parameters fixed probability density function.The Duffing equations of motion, and elastic-plastic vibration parameters of the model are employed, validation bayesian method in model parameters in the process of fixed effectiveness.
The Relevance Vector Machine in regression and classification is introduced, the kernel function is employed, to verify the Relevance Vector Machine application, the response signal of double nonlinear bridge model is adopted. Sine function and Ripley function are employed to verify the Relevance Vector Machine validation.
Apply the Relevance Vector Machine method in bridge structural damage identification process, put forward the bridge structure modal parameter selection and variable as input function for the Relevance Vector Machine, the result of training according to training of bridge structure damage identification. To verify the Relevance Vector Machine method, bridge structure finite element damage model is established, the modal parameter variation during the Relevance Vector Machine training will yeild structure damage identification results. Employ the actual bridge structure to analysis, the modal parameter variable generation into the Relevance Vector Machine trainning, through and bridge for the static load test results contrast to identify the damage of bridge structure, verify the Relevance Vector Machine structural damage identification method has effectiveness of the double nonlinear bridge structure. Through the above work, the conclusions are:
1. A double nonlinear coupling stiffness matrix is proposed based on geometric nonlinear balance equation and nonlinear constitutive relation. According to the least squares theory, the nonlinear coupling stiffness matrix is deduced. Consider the double nonlinear effects, to establish the bridge structure model of structure. By the results that the concentrated force beyond the yield load, the structure of the double nonlinear characteristics significantly reflects, with the increase of structural deformation.
2. Based on bayesian method, on the double nonlinear structure model, through Duffing motion equation and elastoplastic vibration parameters of the model are fixed, validation bayesian method in model parameters in the process of updating effectiveness.
3. The training methods of the relevance vector machine described in detail. Ramified through the relevance vector machine and support vector machine method to regression Sine function, and classification of Ripley function compared to the training, verify the relevance vector machine in signal regression and classification, the data in the process less computing speed and accuracy higher advantages.
4. Puts forward the double nonlinear bridge structure modal parameters variable function and for the relevance vector machine training for structural damage identification. Establishing the damage structure finite element model is validated the relevance vector machine training methods in the process of effectiveness in damage identification. Apply the Relevance Vector Machine damage identification method in practical engineering, compared with the static load test results. The relevance vector machine method damage identification results are accurately.
引文
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