Null subspace-based damage detection of structures using vibration measurements

A damage detection method of mechanical system based on subspace identification concepts and statistical process techniques is presented. The aim is to propose a method that is sensitive to small-sized structural damages and suitable for on-line monitoring. Measured time-responses of structures subjected to artificial or environmental vibrations are assembled to form the Hankel matrix, which is further factorised by performing singular-value decomposition to obtain characteristic subspaces. It may be demonstrated that the structural responses are mainly located in the active subspace defined by the first principal components, which is orthonormal to the null subspace defined by the remaining principal components. If no structural damage occurs, the orthonormality relation between the subspaces remains valid with small residues when consecutive data sets are compared, and these residues may be evaluated by the proposed damage indicators. The method is validated using an experimental mock-up of an airplane subjected to different levels of damages simulated. It is also applied in environmental vibration testing of a street lighting device to monitor structural fatigue evolution.     

A probabilistic damage identification approach for structures with uncertainties under unknown input

To avoid the false positives of damages in the deterministic identification method induced by uncertainties in measurement noise, a probabilistic method is proposed to identify damages of the structures with uncertainties under unknown input. The proposed probabilistic method is developed from a deterministic simultaneous identification method of structural physical parameters and input based on dynamic response sensitivity. The deterministic simultaneous identification method is first derived. The effect of uncertainties caused by measurement noise on the identified parameters is then investigated. The statistical parameters of the identified structural parameters are calculated. The damage index is derived from the statistical parameters of the physical parameters of intact and damaged structure. The probability of identified damage, defined as the probability of identified structural stiffness smaller than that of intact structure, is further derived using the probability method. A twelve-story building and a nine-bay three-dimensional frame structure are, respectively, analyzed numerically and experimentally using the proposed method. The research results indicate that the probabilistic simultaneous identification method for damage and input can decrease the false positives of damages in contrast with the deterministic method under intensive measurement noise, and it can also achieve an accurate identification for structural unknown input.     

基于自适应技术的结构参数与输入同步反演

发展一种基于遗传优化算法的自适应追踪技术,结合输入未知条件下的二次误差平方和方法,利用事件中的加速度响应数据实现结构参数与输入的同步反演,判断并追踪结构损伤,包括损伤发生的时间、位置和程度。三自由度迟滞非线性系统数值仿真结果表明,该方法能够精确有效地追踪结构参数的变化,并同步反演结构的未知输入。此外,对三自由度基础隔振结构模型进行了多工况实验研究。结果表明,所发展方法能够实时有效地追踪结构时变物理参数、反演结构未知基底激励,进而精准地获取结构的损伤信息。     

基于广义模式搜索算法的框架结构损伤检测新方法研究

基于单自由度体系推导的统计矩理论,针对无模型方法识别结构损伤距离实际应用差距较大等问题,结合融入广义模式搜索算法,提出一种以融合位移四阶矩和加速度八阶矩为指标的全新框架结构两步层递式快速损伤检测方法。所提广义搜索模式算法结合无模型快速损伤定位理论形成的全新损伤诊断方法,利用融合位移四阶矩和加速度八阶矩作为指标,对12层框架结构数值模型有无噪声工况进行数值模拟,与标准结果偏差均在3%以内,证明了该方法的精确性及抗噪性效果。并与相同指标下的统计矩二范数优化方法和类贝叶斯思想方法进行对比,验证了该新方法相较其他方法在损伤检测精度、稳定程度及快速检测计算时间上的优越性。通过12层标准框架振动台试验数据,选取3个典型工况分别进行损伤诊断,并与实测报告分析对比,其结果表明该方法相对于其他方法更能反映试验工况累积而表现出来的单元损伤程度变化,凸显了新方法在工程检测中的可靠性。     

高耸类结构抗侧刚度突变位置统计矩比值检测方法研究

提出一种时域内的高耸类结构抗侧刚度突变位置快速检测方法。首先在高耸类结构同一竖直线上等高度间距布设测点,获取结构各高度测点在水平方向的同步动力响应;其次计算出响应信号二阶统计矩,并将相邻测点响应二阶统计矩作比,绘出该比值随测点高度变化的关系曲线;最后根据曲线突变位置判断结构抗侧刚度突变节段所在位置。本文基于单自由度结构统计矩理论,推导了多自由度结构体系响应统计矩与结构节段抗侧刚度的映射关系,首次结合矩阵摄动法论证了利用结构响应二阶统计矩比值曲线判段结构抗侧刚度突变节段位置的可行性,考虑实际工程应用中存在的诸多影响因素,利用数值模拟论证分析不同高耸结构在不同激励形式及30、40 dB噪音影响下所提方法的适用性,最后结合现场风电塔筒的实测响应数据进行分析研究。研究结果表明利用结构位移响应二阶统计矩作为检测指标,通过高耸结构相邻测点响应统计矩比值曲线,能够初步判断高耸类结构抗侧刚度突变位置,无需进行高耸结构抗侧刚度突变前后数据指标对比,有助于在实际高耸类结构检测工程中得到应用。     

DAMAGE DETECTION OF THE Z24 BRIDGE USING CONTROL CHARTS

Structural health monitoring of the Z24 Bridge in Switzerland was studied using the measurement data from three damage configurations. Changes in the modal parameters were used to detect possible damage to the structure. The identification of the modal parameters from the response data was automated using the stochastic subspace identification technique and the stabilisation diagram. Damage detection was performed using control charts, one of the primary techniques of statistical process control. An advantage of control charts is that they can be automated for on-line structural health monitoring. Univariate and multivariate Shewhart, x, CUSUM, and EWMA control charts were studied with different features including natural frequencies, mode shapes, and damping ratios. The sensitivity of the control chart to damage was substantially increased by further dimensionality reduction applying the principal component analysis.     

结构损伤诊断的改进静力方法

利用柔度分解技术,提出一种改进的静力方法用于工程结构损伤诊断中。通过在结构静力反应方程中引入柔度分解式,得到求解柔度扰动参数的线性方程组。由该线性方程组首先计算出各单元柔度扰动参数,再根据柔度扰动参数和刚度扰动参数(损伤参数)之间的关系式,即可计算出各单元损伤参数,据此即可评估结构的损伤状况。所提方法避免了已有方法中需要求解非线性方程组的缺点,无论损伤程度大小如何,均不需要进行迭代运算即可获得精度良好的计算结果。以一个桁架结构为例对所提方法进行验证。结果表明:无论损伤程度大小如何,所提方法只需经过一次计算即可获得精度较高的识别结果,避免多次迭代,显示该方法在计算上的优越性。     

Recursive fuzzy c-means clustering for recursive fuzzy identification of time-varying processes

In this paper we propose a new approach to on-line Takagi-Sugeno fuzzy model identification. It combines a recursive fuzzy c-means algorithm and recursive least squares. First the method is derived and than it is tested and compared on a benchmark problem of the Mackey-Glass time series with other established on-line identification methods. We showed that the developed algorithm gives a comparable degree of accuracy to other algorithms. The proposed algorithm can be used in a number of fields, including adaptive nonlinear control, model predictive control, fault detection, diagnostics and robotics. An example of identification based on a real data of the waste-water treatment process is also presented.     

Effects of noise on transfer entropy estimation for damage detection

Recent research has shown that transfer entropy can be effectively employed as a feature for nonlinearity detection and linear damage identification. However, computation of transfer entropy requires the estimation of non-parametric one-, two-, and three-dimensional probability density functions. Therefore, small random perturbations caused by noise could lead to large variances in transfer entropy estimates. In this paper, we evaluate the effect of input and output noise on estimation of transfer entropy, and how noise, in turn, affects the capability of transfer entropy as a damage detector in a structural health monitoring (SHM) application. A damage index from the transfer entropy is computed from the response of a simulated multi-degree-of-freedom oscillator subject to linear and nonlinear stiffness changes in the presence of various noise influences. Damage indices are also evaluated for an experimental frame structure. Based on the computational study, we find that input noise lessens the sensitivity of the damage feature by diminishing the ability of the non-parametric density estimators to produce low variance transfer entropy estimations. Despite this reduced capability, an input that has no deterministic component can still detect a 25% stiffness loss in the computational example employed. Output noise has a greater impact on the feature's ability to accurately estimate the transfer entropy, such that a signal-to-noise threshold of approximately 30 dB leads to a greatly diminished ability to detect damage. Despite these noise effects, all damage cases tested on an experimental frame structure were detectable using the transfer entropy damage index.     

用于线性时变系统辨识的固定长度平移窗投影估计递推子空间方法

给出了一个新的用于线性时变参数结构系统模态参数识别的基于固定长度平移窗投影估计的递推子空间方法。首先推得基于平移窗投影估计的子空间跟踪算法,以代替奇异值分解,再推得系统数据矩阵的一阶修正形式,从而得到新的基于平移窗投影估计的递推子空间方法。该方法可有效地降低算法的计算量。最后通过刚度随时间变化的3自由度系统和一具有移动质量的机械臂系统的时变模态频率辨识仿真表明该方法可有效地辨识线性时变系统的伪模态参数。     

ON-LINE MODAL MONITORING OF AIRCRAFT STRUCTURES UNDER UNKNOWN EXCITATION

In this paper, we present the application of recently proposed subspace-based damage detection and isolation algorithms in on-line structural monitoring of an airplane structure under unknown excitation. The first step of the approach is a subspace-based modal analysis of the safe structure, using output-only measurements. The monitoring step consists in the computation of a χ²-variable, which reflects possible deviations of newly collected output-only data w.r.t. the reference (safe) modal behaviour. No re-identification of the possibly damaged structure is required. An on-line version of the detection algorithm is proposed. Monitoring certain critical modes can also be achieved through sensitivity tests. Experimental results for the proposed monitoring algorithms are reported, in the case of the Paris MS760 airplane, on which mass as well as stiffness changes are introduced. Moreover, the results of the output-only subspace-based modal analysis are compared with the modal appropriation method.     

基于贝叶斯思想的框架结构损伤检测方法研究* .txt

摘要：基于单自由度体系的统计矩理论,以位移四阶矩和加速度八阶矩为损伤指标,使用贝叶斯思想和Gibbs抽样相结合方法,提出一种框架结构损伤检测新方法。以理论分析为基础选取3种典型损伤指标,在信噪比40及30 dB环境噪音的不同损伤工况下,使用贝叶斯思想和Gibbs抽样相结合方法,对某12层标准框架数值模型的不同损伤指标进行了损伤识别效果的对比研究,并在此基础上与其他相似检测方法进行对比分析,发现使用贝叶斯思想和Gibbs抽样相结合的新方法,提出的损伤指标更适合框架结构损伤检测,与标准结果偏差均在5%以内。进一步分析12层标准框架振动台试验数据,选取3个典型振动工况中所有梁柱单元及前20个振动工况累积下的典型梁柱单元分别进行损伤检测,结果表明,所提方法避免了多次采样进行贝叶斯分析的局限性,且一定程度上能反映各损伤单元随振动台试验工况累积而表现出来的损伤程度变化,有助于推动所提方法在框架结构损伤检测中的实际应用。 .txt     

Differentiating damage effects in a structural component from the time response

This paper proposes an approach to differentiate the effect of local anomalies on the different load-resisting capacities of a structural component made of elastic isotropic material. The sensitivities of structural dynamic response with respect to different damage indices are derived. They are then used in a time-domain sensitivity-based algorithm for model updating using a gradient-based approach. A planar frame structure is studied in the numerical simulation. Results show that the proposed method can effectively locate and quantify the different types of damage effects, and the proposed method is insensitive to measurement noise. Laboratory verification was performed with a three-dimensional truss structure with the identified results clearly showing how much a local physical damage can change the different physical parameters that lead to the load-resisting capacities of a structural component.     

自适应卡尔曼滤波在无刷直流电机系统辨识中的应用

为了有效抑制量测噪声特性变化对系统辨识精度的影响以获得准确的无刷直流电机模型,提出了一种采用自适应卡尔曼滤波算法的无刷直流电机系统辨识方法。通过计算新息理论方差的极大似然最优估计,并将其引入卡尔曼滤波算法中修正滤波增益来抑制量测噪声特性变化对辨识结果的影响,使该滤波算法实现对模型参数的准确估计,提高辨识精度。实验结果表明,在量测噪声特性变化的情况下,该算法能够准确跟踪实际量测噪声特性的变化,参数估计平滑,相对于目前系统辨识广泛采用的带有遗忘因子的递推最小二乘算法,输出误差的均方根值减小了73.5%。该算法简单易行,计算量小,辨识结果可以很好地描述系统行为,便于在工程实践中应用。     

基于指数窗截取递推最小二乘法的齿轮啮合刚度辨识算法研究

齿轮在机械传动系统中有着广泛应用,由于齿轮啮合过程中参与啮合的轮齿对数周期变化,因此,齿轮啮合刚度为时变参数,在啮合时会产生啮合振动。当齿轮副出现齿根裂纹时,啮合刚度会减小,齿轮啮合产生的系统振动响应也发生改变,通过振动响应辨识齿轮啮合刚度能够监测齿轮副的健康状态。针对齿轮啮合刚度的时变特征,提出了基于指数窗截取递推最小二乘(Exponential window recursive least square,EWRLS)算法和振动信号瞬时频率的齿轮啮合刚度辨识方法。进行啮合刚度辨识时,EWRLS算法将输入、输出齿轮的转速曲线分别作为辨识输入信号和观测信号,使用指数窗函数进行数据截断,使用递推最小二乘算法估计系统参数。为了计算输入、输出齿轮的转速曲线,使用经验模态分解(Empirical mode decomposition,EMD)方法将振动信号分解为具有不同变化频率的本征模态函数(Intrinsic mode function,IMF),并根据IMF的平均频率重构输入、输出齿轮的特征信号。通过Hilbert变换计算特征信号的瞬时频率曲线,从而获得各齿轮的转速曲线。使用仿真和实测信号对算法进行验证,结果表明,EWRLS算法能够辨识齿轮副的时变啮合刚度。     

基于伪传递函数的高耸结构损伤识别

基于传递函数可以反映结构输入输出相互关系（结构特性）的思想,提出了一种基于具有额外输入的自回归模型（autoregressive model with exogenous input,简称ARX模型）建立伪传递函数的损伤定位方法。首先,根据各自由度之间的关联性对其进行分组,选取其中一个自由度的响应作为参考通道即系统输出,将与其相关联的其他自由度响应信号作为系统输入,利用ARX模型,建立各分组在结构完好工况下的伪传递函数,将其作为基准伪传递函数;然后,利用基准伪传递函数对待识别工况的响应进行预测,计算其拟合度;最后,通过定义待识别工况与完好工况之间拟合度的差异作为损伤指标,对结构损伤进行识别。通过广州塔缩减模型算例分析表明,该方法在有噪声的情况下,可以很好地发现损伤并对结构损伤位置和损伤程度进行识别。     

采用EEMD和WPT的结构损伤特征提取方法

为了解决传统小波或小波包变换方法对结构损伤振动信号频率分辨率不高、易受邻近谐波交叠影响的问题,提出了一种基于聚类经验模式分解(EEMD)和小波包变换(WPT)的结构损伤特征提取方法.首先对原始信号进行EEMD分解,提取包含结构损伤信息的固有模式分量(IMF),再对其进行正交小波包分解,并计算小波包相对能量分布.该方法用于美国土木工程师学会(ASCE)提出的钢结构框架的损伤特征提取,结果表明:EEMD方法具有白噪声的剔除特性,可避免模式混叠的发生;不同检测节点处不同损伤工况的IMF小波包相对能量分布有显著的差异,可以作为一种理想指标表征结构损伤特征.     

线性时变动力系统参数识别方法与试验分析

根据时变频率的定义由时变动力系统的响应计算瞬时频率,由自由衰减响应或希尔伯特阻尼谱识别瞬时阻尼特性。采用2层框架结构数值模型验证了识别方法的可行性,进而应用于12层短肢剪力墙结构振动台实验及识别模型结构在试验过程中动力性能的时变特性。将识别所得瞬时阻尼比代入有限元模型中计算结构响应,并与常值阻尼比及实测结果进行了对比。结果表明,采用时变阻尼比的计算结果更接近实测响应,文中方法可以反映结构的时变动力特性。     

基于最小秩修正的结构损伤识别方法

提出一种改进的最小秩修正法.通过引入损伤定位向量,首先确定损伤单元的个数,再由最小秩修正法求解损伤程度.该方法较好地解决了运用最小秩修正法时必须采用正确的模态个数的问题.以一个平面桁架结构为例验证该方法,并对测量噪音的影响进行讨论.结果表明,所提方法是准确可靠的,且对测量噪音有很强的鲁棒性.     

基于递归理论的泵站压力管道运行状态监测

为了准确地识别建筑结构的模态参数,提出了一种基于多重信号分类算法（multiple signal classification,简称MUSIC）、经验小波变换（empirical wavelet transform,简称EWT）和同步提取小波变换（synchroextracting transform ,简称SET）的结构模态参数识别方法。首先,通过MUSIC-EWT对实测振动信号进行分解;其次,使用SET对单模态信号进行去噪处理;然后,采用自然环境激励技术（natural excitation technique,简称NExT）得到单模态信号的自由衰减响应;最后,利用Hilbert变换（hilbert transform,简称HT）和曲线拟合获得结构的自振频率和阻尼比。通过三层框架结构的数值模拟验证了该方法的准确性和鲁棒性。利用该方法对台风“达维”作用下广州中信广场的实测加速度数据进行分析,并将估计的结构模态参数和其他识别方法的分析结果进行对比,进一步证明了该方法的准确性和鲁棒性。