噪声影响下基于改进损伤识别因子和遗传算法的结构损伤识别

提出了一种考虑噪声影响的基于改进损伤识别因子和遗传算法的结构损伤识别方法。首先,介绍了结构损伤识别的参数化思想,并提出了一种考虑不同模态信息和权重系数的损伤识别因子。然后,在选择算子、交叉算子、变异算子以及自适应交叉和变异等方面对遗传算法进行了改进,并在无噪声情况下,对一简支梁和连续梁进行了损伤识别,识别效果非常好,验证了方法的正确性和有效性。随后,分别考虑了随机噪声和高斯白噪声对简支梁进行损伤识别,发现该方法在噪声水平不是很高的情况下,识别效果很好。最后,在一钢框架基准有限元模型基础上,考虑了四种损伤工况进行了损伤识别,识别结果较好,该方法能够很好地应用于结构的损伤识别和健康监测。     

运用BP-AdaBoost模型识别随机车载作用下大跨斜拉桥拉索损伤

为了有效地进行大跨结构的损伤识别,提出随机车载作用下利用BP-AdaBoost(Back Propagation neural network,Adaptive Boosting)模型对大跨斜拉桥拉索进行损伤识别的方法。该方法首先依据交通调查数据,建立随机交通荷载模型,再运用提升框架,对结构损伤前后的振动测试信号进行提升小波包分解,将小波包信号分量能量累积变异值作为特征值,识别斜拉索损伤位置,然后以此建立BP-AdaBoost模型,利用AdaBoost算法和BP神经网络相结合的方法对大跨斜拉桥拉索的损伤程度进行识别,并研究噪声对该算法的影响。数值分析结果表明,该方法有较强的抗噪声干扰能力,在随机车载作用下,运用BP-AdaBoost模型能够有效识别大跨斜拉桥拉索损伤。     

基于时间序列模型自回归系数灵敏度分析的结构损伤识别方法

该文在分析了时间序列模型的自回归系数对结构单元刚度灵敏度的基础上,提出了一种采用随机载荷作用下结构的时域响应数据进行损伤识别的新方法。该方法首先根据随机载荷作用下的结构响应拟合适用的时序模型;然后建立基于自回归系数的损伤灵敏度矩阵,通过该矩阵可以建立由单元损伤导致的自回归系数的变化与损伤系数变化之间的关系;最后通过求解损伤系数向量来识别损伤位置和损伤程度。对一悬臂梁结构损伤识别的数值结果表明:在计入1%和2%测量噪声的情况下,该方法仅利用单个传感器的时域测量数据,就能够较好地识别单个单元和多个单元损伤;如果对基于多个传感器的识别结果进行综合,识别结果则更加准确、可靠。     

基于频率变化识别结构损伤的摄动有限元方法

在结构有限元计算模型中定义了单元的损伤识别参数,将摄动理论与振动理论相结合导出结构振动特征值的一、二阶摄动方程,并由此建立了结构的一、二次损伤识别方程,给出了两种方程在欠定情况下求解损伤识别参数的优化算法。该方法仅使用在役结构固有频率测量值就能识别出结构的损伤位置和损伤程度,以及结构的老化程度,避免了使用模态振型识别结构损伤,因测量精度不高或自由度不足带来的误差。通过一座连续梁桥损伤识别的数值仿真结果,证明了该方法的有效性和实用性。该方法可用于大型结构的损伤识别或健康监测。     

基于位移平均曲率差的桥梁结构损伤识别方法研究EI北大核心CSCD

针对结构损伤识别受外界随机荷载干扰较大的问题,提出了归一化位移均值波形的平均曲率差法。该方法将多样本组的位移响应均值作为损伤特征函数,初步消除噪声的影响;再将位移均值曲线的曲率归一化处理,并求解曲率差值,大大降低随机荷载的影响;最后以相邻测点的平均曲率差为损伤识别指标判断损伤单元。以简支梁桥和自锚式悬索桥为算例,从理论和数值模型两方面对提出方法进行验证。结果表明,所提方法既能对任一移动荷载作用下的结构进行损伤识别,也适用于随机荷载作用下的结构损伤识别。该研究还分析了不同程度噪声对识别效果的影响,从分析结果可以看出,所提方法具有较好的抗噪性能。     

基于二重切比雪夫多项式的多自由度系统SMA非线性恢复力识别

针对真实结构在动力荷载作用下恢复力模型难以用准确参数化形式描述问题,将结构非线性恢复力作为结构损伤及非线性行为的直接描述,提出基于二重切比雪夫多项式模型的多自由度体系非线性恢复力时域识别方法,实现结构质量信息完全未知及激励完整、非完整两种情况下多自由度系统非线性恢复力识别。通过带理想双旗形恢复力模型形状记忆合金(SMA)阻尼器两自由度数值模型的数值模拟与安装SMA阻尼器的钢框架模型动力实验结果验证该方法的识别效果,并与基于幂多项式模型方法进行对比。数值模拟验证中同时考虑测量噪声对识别结果影响。结果表明,该方法能对结构质量分布及在动力荷载作用下非线性恢复力进行有效识别,为结构在动力荷载作用下损伤发生、发展过程监测及结构耗能的定量评估提供方法。     

混凝土桥梁损伤识别的理论与试验研究

针对目前桥梁损伤识别理论受到测量误差、环境随机因素与模型误差等影响识别精度低的缺点,利用数理统计与随机分析的基本理论,提出进行混凝土桥梁裂缝等损伤识别的新理论方法;该方法首先寻找监测响应量的主要影响因素作为原因量,其次建立原因量与响应量的统计模型,最后利用预测模型进行判别是否发生损伤;利用该方法可以有效地考虑环境随机因素、测量误差等不确定因数,避免结构分析的计算模型误差,因而可以有效地提高进行损伤识别的精度;两根钢筋混凝土小梁模型试验证实了本理论的正确性。     

基于部分加速度测量的结构Bouc-Wen非线性恢复力及质量识别

结构非线性行为识别是结构灾后损伤评估的关键。扩展卡尔曼滤波(Extended Kalman Filter,EKF)有助于解决结构动力响应测量不完备的问题,但一般要求结构质量已知。针对仅部分加速度响应已知和结构质量未知情况下结构非线性恢复力的识别问题,提出一种结合EKF和最小二乘算法的结构非线性恢复力及质量识别的迭代算法。该方法基于质量估计值和部分自由度上的加速度响应测量,通过EKF预测完整响应时程,再利用最小二乘法识别修正质量分布,循环迭代至收敛,最后基于质量收敛值实现物理参数(刚度、阻尼、非线性)的识别,进而得到非线性恢复力。以一个含Bouc-Wen磁流变阻尼器的多自由度体系的数值模型为例,考虑4种不同的质量初始误差,通过数值模拟验证该方法识别结构质量及非线性恢复力的有效性。同时考虑加速度测量噪声的影响,证明了该方法的鲁棒性。     

基于缩聚模态应变能与频率的结构损伤识别

在结构损伤识别中,测试振型往往是不完整的,这阻碍了结构损伤识别技术的应用效率。提出了一种采用缩聚应变能与频率相结合的损伤识别定性与定量方法。采用基于Neumann 级数展开的方法对有限元模型进行缩聚,定义了单元缩聚模态应变能,并证明了缩聚模态应变能的变化对损伤的敏感性;将单元缩聚应变能变化率作为标识量来识别损伤的位置;在损伤位置初步判定的基础上,采用特征值灵敏度法求解损伤程度。以一简支钢梁为例证明了所提出的方法。结果表明:在测量模态数据有误差的情况下也能较好地给出损伤识别结果。     

基于时域响应灵敏度分析的板结构损伤识别

提出了一种基于响应灵敏度分析的有限元模型修正法,对平板结构的局部损伤进行识别。在正问题研究中,将结构的局部损伤模拟为板结构单元杨氏模量的减少,建立了板结构的有限元动力学方程,利用直接积分法获得了结构强迫振动响应。在损伤识别反问题中,基于响应灵敏度分析,直接利用结构的动态响应进行有限元模型修正和损伤识别。算例表明,本文方法能有效识别板类结构的局部损伤,具有需要测点数目少,损伤识别精度高,对模拟的测量噪声不大敏感的优点。     

随机结构弹性屈曲的递推求解方法

采用随机收敛的非正交的多项式展式表示未知的随机屈曲特征值和屈曲模态,利用摄动技巧,建立了随机结构弹性屈曲的递推求解方法。算例表明,和基于泰勒展开的摄动随机有限元方法相比,方法的结果能在较宽的随机涨落范围内更好地逼近蒙特卡洛模拟结果,即使只采用前四阶非正交多项式展式,逼近的结果仍然较好。     

随机结构重特征值分析的递推随机有限元法

利用递推随机有限元方法研究了具有随机参数结构的重特征值问题。采用随机收敛的非正交多项式展式表示未知的随机重特征值和随机特征向量，建立了和摄动法类似的一系列确定的递推方程，通过求解这些速推方程，得到了重特征值的统计值。算例表明，同基于二阶泰勒展开的摄动随机有限元法相比，递推随机有限元法的结果能在较宽的随机涨落范围内更好地逼近蒙特卡洛模拟结果。     

Recursive approach for random response analysis using non-orthogonal polynomial expansion

Using non-orthogonal polynomial expansions, a recursive approach is proposed for the random response analysis of structures under static loads involving random properties of materials, external loads, and structural geometries. In the present formulation, non-orthogonal polynomial expansions are utilized to express the unknown responses of random structural systems. Combining the high-order perturbation techniques and finite element method, a series of deterministic recursive equations is set up. The solutions of the recursive equations can be explicitly expressed through the adoption of special mathematical operators. Furthermore, the Galerkin method is utilized to modify the obtained coefficients for enhancing the convergence rate of computational outputs. In the post-processing of results, the first- and second-order statistical moments can be quickly obtained using the relationship matrix between the orthogonal and the non-orthogonal polynomials. Two linear static problems and a geometrical nonlinear problem are investigated as numerical examples in order to illustrate the performance of the proposed method. Computational results show that the proposed method speeds up the convergence rate and has the same accuracy as the spectral finite element method at a much lower computational cost, also, a comparison with the stochastic reduced basis method shows that the new method is effective for dealing with complex random problems.     

A perturbation method for stochastic meshless analysis in elastostatics

A stochastic meshless method is presented for solving boundary‐value problems in linear elasticity that involves random material properties. The material property was modelled as a homogeneous random field. A meshless formulation was developed to predict stochastic structural response. Unlike the finite element method, the meshless method requires no structured mesh, since only a scattered set of nodal points is required in the domain of interest. There is no need for fixed connectivities between nodes. In conjunction with the meshless equations, classical perturbation expansions were derived to predict second‐moment characteristics of response. Numerical examples based on one‐ and two‐dimensional problems are presented to examine the accuracy and convergence of the stochastic meshless method. A good agreement is obtained between the results of the proposed method and Monte Carlo simulation. Since mesh generation of complex structures can be a far more time‐consuming and costly effort than the solution of a discrete set of equations, the meshless method provides an attractive alternative to finite element method for solving stochastic mechanics problems. Copyright © 2001 John Wiley & Sons, Ltd.     

Gaussian process emulators for the stochastic finite element method

This paper explores a method to reduce the computational cost of stochastic finite element codes. The method, known as Gaussian process emulation, consists of building a statistical approximation to the output of such codes based on few training runs. The incorporation of emulation is explored for two aspects of the stochastic finite element problem. First, it is applied to approximating realizations of random fields discretized via the Karhunen–Loève expansion. Numerical results of emulating realizations of Gaussian and lognormal homogeneous two‐dimensional random fields are presented. Second, it is coupled with the polynomial chaos expansion and the partitioned Cholesky decomposition in order to compute the response of the typical sparse linear system that arises due to the discretization of the partial differential equations that govern the response of a stochastic finite element problem. The advantages and challenges of adopting the proposed coupling are discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

A unified stochastic framework for robust topology optimization of continuum and truss-like structures

In this article, a unified framework is introduced for robust structural topology optimization for 2D and 3D continuum and truss problems. The uncertain material parameters are modelled using a spatially correlated random field which is discretized using the Karhunen–Loève expansion. The spectral stochastic finite element method is used, with a polynomial chaos expansion to propagate uncertainties in the material characteristics to the response quantities. In continuum structures, either 2D or 3D random fields are modelled across the structural domain, while representation of the material uncertainties in linear truss elements is achieved by expanding 1D random fields along the length of the elements. Several examples demonstrate the method on both 2D and 3D continuum and truss structures, showing that this common framework provides an interesting insight into robustness versus optimality for the test problems considered.     

刚度不确定性结构在基础随机激励下的振动响应谱分析

综合考虑动载荷和结构刚度的不确定性，建立了基础机激励下刚度不确定性结构的动力学递推方程组。将随机有限元法和随机振动理论相结合，推导了结构振动响应谱一阶、二阶变异量以及均值、方差的计算公式，建立了刚度不确定结构在基础随机激励下的振动响应谱分析方法。算例分析验证了本方法的有效性。     

Stochastic projection schemes for deterministic linear elliptic partial differential equations on random domains

We present stochastic projection schemes for approximating the solution of a class of deterministic linear elliptic partial differential equations defined on random domains. The key idea is to carry out spatial discretization using a combination of finite element methods and stochastic mesh representations. We prove a result to establish the conditions that the input uncertainty model must satisfy to ensure the validity of the stochastic mesh representation and hence the well posedness of the problem. Finite element spatial discretization of the governing equations using a stochastic mesh representation results in a linear random algebraic system of equations in a polynomial chaos basis whose coefficients of expansion can be non‐intrusively computed either at the element or the global level. The resulting randomly parametrized algebraic equations are solved using stochastic projection schemes to approximate the response statistics. The proposed approach is demonstrated for modeling diffusion in a square domain with a rough wall and heat transfer analysis of a three‐dimensional gas turbine blade model with uncertainty in the cooling core geometry. The numerical results are compared against Monte–Carlo simulations, and it is shown that the proposed approach provides high‐quality approximations for the first two statistical moments at modest computational effort. Copyright © 2010 John Wiley & Sons, Ltd.     

An improved perturbation method for stochastic finite element model updating

In this paper, an improved perturbation method is developed for the statistical identification of structural parameters by using the measured modal parameters with randomness. On the basis of the first‐order perturbation method and sensitivity‐based finite element (FE) model updating, two recursive systems of equations are derived for estimating the first two moments of random structural parameters from the statistics of the measured modal parameters. Regularization technique is introduced to alleviate the ill‐conditioning in solving the equations. The numerical studies of stochastic FE model updating of a truss bridge are presented to verify the improved perturbation method under three different types of uncertainties, namely natural randomness, measurement noise, and the combination of the two. The results obtained using the perturbation method are in good agreement with, although less accurate than, those obtained using the Monte Carlo simulation (MCS) method. It is also revealed that neglecting the correlation of the measured modal parameters may result in an unreliable estimation of the covariance matrix of updating parameters. The statistically updated FE model enables structural design and analysis, damage detection, condition assessment, and evaluation in the framework of probability and statistics. Copyright © 2007 John Wiley & Sons, Ltd.     

Weighted integral method in multi-dimensional stochastic finite element analysis

This paper, using the weighted integral method, proposes a new stochastic finite element method for estimating the response variability of multi-dimensional stochastic systems. Young's modules is considered to have spatial variation and is idealized as a multi-dimensional stochastic field. An essential feature of the proposed method is that the continuous stochastic field is rigorously taken care of by means of weighted integrations to construct element stiffness matrices, as the results, the issue involving the stochastic field is transformed into a problem involving only a few random variables. This may lead to substantial improvement in computational efficiency. Numerical examples show that the proposed SFEM is concluded as an efficient and accurate method.