Machine learning based novelty detection using modal analysis

Among many structural assessment methods, the change of modal characteristics is considered a well‐accepted damage detection method. However, the presence of environmental or operational variations may pollute the baseline and prevent a dependable assessment of the change. In recent years, the use of machine learning algorithms gained interest within structural health community, especially due to their ability and success in the elimination of ambient uncertainty. This paper proposes an end‐to‐end architecture to detect damage reliably by employing machine learning algorithms. The proposed approach streamlines (a) collection of structural response data, (b) modal analysis using system identification, (c) learning model, and (d) novelty detection. The proposed system aims to extract latent features of accessible modal parameters such as natural frequencies and mode shapes measured at undamaged target structure under temperature uncertainty and to reconstruct a new representation of these features that is similar to the original using well‐established machine learning methods for damage detection. The deviation between measured and reconstructed parameters, also known as novelty index, is the essential information for detecting critical changes in the system. The approach is evaluated by analyzing the structural response data obtained from finite element models and experimental structures. For the machine learning component of the approach, both principal component analysis (PCA) and autoencoder (AE) are examined. While mode shapes are known to be a well‐researched damage indicator in the literature, to our best knowledge, this research is the first time that unsupervised machine learning is applied using PCA and AE to utilize mode shapes in addition to natural frequencies for effective damage detection. The detection performance of this pipeline is compared to a similar approach where its learning model does not utilize mode shapes. The results demonstrate that the effectiveness of the damage detection under temperature variability improves significantly when mode shapes are used in the training of learning algorithm. Especially for small damages, the proposed algorithm performs better in discriminating system changes.     

Determination of the critical loading conditions for bridges under crossing trains

A procedure based on experimental and theoretical analyses to identify critical loading conditions on existing metallic railway bridges is presented. This method requires knowledge of the principal modal frequencies, and for this reason, a consolidated and simple procedure to study the bridge dynamics is herein explained. This consists of: preliminary studies; material and dynamic tests; and identification techniques to identify modal parameters and eventual non-linear behaviours. Generally the information collected can be used both to calibrate the bridge model and to obtain the refined frequency response function. In order to avoid high computational effort due to long time-history dynamic analyses by using the bridge model subjected to a series of train crossings, a new frequency domain approach for the identification of critical loading conditions is proposed. Evidence of the influence of the axle spacing and velocity of the vehicle on the dynamic magnification due to the train crossing is shown. The method is based on the construction of an excitation spectrum related to the train axle spacing and the velocity, given the weight of the vehicle. Comparison of the excitation spectrum with the frequency response function allows identification of the load patterns that bring the bridge to resonance conditions and might threaten bridge stability, bearing in mind continual changes in train technology.     

Moving train loads identification on a continuous steel truss girder by using dynamic displacement influence line method

This paper presents a dynamic displacement influence line method for moving load identification on bridge. The finite element model of Poyang Lake continuous truss bridge-train systems is established and the dispersed modal shapes are acquired by modal analysis. Multi-axle moving train loads are identified with simulated annealing genetic algorithm by minimizing the errors between the measured displacements and the reconstructed displacements from the identified moving loads. In the identification process, the dynamic displacement influence line technique is used to calculate the time history displacement responses of the bridge to avoid solving equations of motion of the bridge repetitively. Several important parameters of the bridge-train system are discussed to investigate their effects on the proposed method. The results demonstrate that the proposed method is an accurate and efficient method for moving train load identification on complex bridges.     

Vibration-based operational modal analysis of the Mikron historic arch bridge after restoration

This research presents finite element modelling, vibration-based operational modal analysis, and finite element model updating of a restored historic arch bridge. Mikron historic bridge, constructed on F?rt?na River in Rize, Turkey, is the subject of this case study. The General Directorate for Highways of Turkey repaired the bridge's main structural elements, arches, sidewalls, and filler material in 1998. To construct a 3D finite element model of the bridge, ANSYS finite element software estimated the analytical dynamic characteristics. Induced ambient vibrations such as human walking and wind excited the model bridge to allow measurement of the bridge's responses. Enhanced frequency domain decomposition in frequency domain and stochastic subspace identification in time domain methodologies extracted experimental dynamic characteristics. A comparison of the analytical and experimental results showed significant agreement between mode shapes, but some differences in natural frequencies appeared. Consequently, updating the finite element model of the bridge by changing boundary conditions minimised the differences between analytical and experimental natural frequencies. After the finite element model updating process, the differences between natural frequencies declined from 7% to 2%.     

Wireless Monitoring of a Multispan Bridge Superstructure for Diagnostic Load Testing and System Identification

Abstract: This article focuses on the deployment of a wireless sensor system (WSS) developed at Clarkson University for structural monitoring purposes. The WSS is designed specifically for diagnostic bridge monitoring, providing independent conditioning for accelerometers, strain transducers, and temperature sensors in addition to high‐rate wireless data transmission and is capable of supporting large‐scale sensor arrays. A three‐span simply supported structure was subjected to diagnostic load testing as well as ambient vibration monitoring. A total of 90 wireless and several wired sensors, including accelerometers and strain transducers were used in the deployment. Strain measurements provided capacity and demand characteristics of the structure in the form of neutral axis locations, load distributions, and dynamic allowances which ultimately produced an inventory and operating load rating for the structure. Additionally, modal characteristics of the structure, including natural frequencies and mode shapes, were derived from measured accelerations and discussed briefly.     

采用二维梁修正模型的钢梁-混凝土板组合桥梁的承载力分析

通过试验对钢梁-混凝土板组合桥梁的结构鉴定、基于修正模型的承载力、承载力对分析模型的敏感性进行分析。基于振型、频率、振型阶次等动力性能及静力变形,建立修正模型。用二维梁模型成功模拟了纵梁间横向荷载传递机理、扭转变形及斜桥影响。算得的承载力结果与三维有限元分析接近,而简化的一维杆模型误差却很大。在模型修正的不同阶段,将模型参数分组,这样能提高收敛速度和成功率。虽然可认为横向支撑不参加工作,但在承载力分析中它们却是临界杆。横向支撑的破坏改变了纵梁间的传力机理,可能导致内梁的过早破坏。     

Modal Identification Study of Vincent Thomas Bridge Using Simulated Wind-Induced Ambient Vibration Data

Abstract:   In this article, wind-induced vibration response of Vincent Thomas Bridge, a suspension bridge located in San Pedro near Los Angeles, California, is simulated using a detailed three-dimensional finite element model of the bridge and a state-of-the-art stochastic wind excitation model. Based on the simulated wind-induced vibration data, the modal parameters (natural frequencies, damping ratios, and mode shapes) of the bridge are identified using the data-driven stochastic subspace identification method. The identified modal parameters are verified by the computed eigenproperties of the bridge model. Finally, effects of measurement noise on the system identification results are studied by adding zero-mean Gaussian white noise processes to the simulated response data. Statistical properties of the identified modal parameters are investigated under an increasing level of measurement noise. The framework presented in this article will allow us to investigate the effects of various realistic damage scenarios in long-span cable-supported (suspension and cable-stayed) bridges on changes in modal identification results. Such studies are required to develop robust and reliable vibration-based structural health monitoring methods for this type of bridge, which is a long-term research objective of the authors.     

Load rating of concrete-deck-on-steel-stringer bridges using field-calibrated 2D-grid models

This paper presents and discusses issues related to structural identification, calibrated model-based load rating, and sensitivity of rating to the analytical model, along with experimental studies conducted on an existing concrete-deck-on-steel-stringer bridge. The proposed model-updating procedure uses collected dynamic data (mode shapes, modal frequencies, and order of modes) as well as static deformed shape information. Two-dimensional (2D) grid models were developed to successfully simulate the transverse load transfer mechanisms between girders, torsional flexibility, and effects of skewed bridge architecture. The rating results obtained from the 2D-grid models were close to 3D-FEM-based evaluation, while simplified 1D bar models had serious shortcomings. Grouping the parameters of the analytical model at different stages of model calibration enhanced the speed and convergence success of the objective function. Although cross-braces are considered as non-structural members, they have been found to be the most critical members of the selected bridge during rating studies. Failure of cross-braces deemed to alter the load transfer mechanism between girders and possibly resulting in the premature failures of interior girders.     

Pipe crack identification based on the energy method and committee of neural networks

A crack identification method using an equivalent bending stiffness for cracked beam and committee of neural networks is presented. The equivalent bending stiffness is constructed based on an energy method for a straight thin-walled pipe, which has a through-the-thickness crack, subjected to bending. Several numerical analysis for a steel cantilever pipe using the equivalent bending stiffness are carried out to extract the natural frequencies and mode shapes of the cracked beam. The extracted modal properties are used in constructing a training patterns of a neural network. The input to the neural network consists of the modal properties and the output is composed of the crack location and size. Multiple neural networks are constructed and each individual network is trained independently with the different initial synaptic weights. Then, the estimated crack locations and sizes from different neural networks are averaged. Crack detection is carried out for 16 damage cases using the proposed method, and the identified crack locations and sizes agree reasonably well with the exact values.     

基于AEEMD和改进DATA-SSI算法的桥梁结构模态参数自动化识别

模态参数作为桥梁结构最重要的动力参数之一,在实际运用中,可通过监测其变化情况来辨识结构的使用性能,精确地参数识别对保障桥梁健康运营具有十分重要的意义。鉴于此,该文对现阶段常用的振动信号降噪处理算法和模态参数识别算法进行了相应的改进。一方面,提出一种新的信号自适应分解与重构算法,即自适应总体平均经验模态分解算法（AEEMD）,该算法相比总体平均经验模态分解算法（EEMD）而言,能够根据信号的自身特征自动化确定添加白噪声的幅值标准差和集成平均次数|能更好地处理端点效应|同时还能够保证所得本征模态函数之间不存在模态混叠现象|最终实现有效IMF分量的自动化筛选和信号重构。另一方面,将多维数据聚类分析算法引入随机子空间算法中,并以频率值、阻尼比以及振型系数为因子建立判别矩阵,以智能化区分虚假模态和真实模态,最终实现模态参数自动化识别。文章最后分别用模拟信号和实际桥梁测试信号对所提算法的有效性进行验证,结果表明,该文所提算法能运用于实际桥梁结构的模态参数自动化识别。     

Monitoring the dynamic characteristics of an urban bridge before,during and after widening

The dynamic characteristics of a multi-span pre-stressed concrete urban bridge before, during and after widening operations have been studied. The widening operations have been carried out by adding two new bridges on the either sides of the old bridge. The decks of the new bridges have been structurally separated from the old one by two longitudinal joints on the either side of the old bridge. The dynamic characteristics have been extracted from operational modal tests in three phases during different stages of the widening operations. The dynamic interaction between the new parts and the old part of the bridge has also been investigated. The results show that after the completion of the widening works, and when the whole bridge was placed in service condition, this interaction affects the natural frequencies of almost all the vibration modes of the bridge. It was also found that the longitudinal joints were unable to effectively isolate the new parts from the old part. Finally, in order to achieve a consistent behaviour in the first bending mode of the new and old bridges, a geometrical index has been introduced. This index includes both the effects of stiffness and mass properties of the bridge deck. In widening projects, where the span lengths, material properties and support conditions of the two bridges are taken the same, adopting equal geometrical indices leads to almost equal values of the natural frequencies and similar mode shapes in the first bending mode. The proposed index can be used in the initial design stage for such projects.     

Modal Response‐Based Visual System Identification and Model Updating Methods for Building Structures

This article proposes a new system identification (SI) method using the modal responses obtained from the dynamic responses of a structure for estimating modal parameters. Since the proposed SI method visually extracts the mode shape of a structure through the plotting of modal responses based on measured data points, the complex calculation process for the correlation and the decomposition for vibration measurements required in SI methods can be avoided. Also, without dependence on configurations of SI methods inducing variations of modal parameters, mode shapes and modal damping ratios can be stably extracted through direct implementation of modal response. To verify the feasibility of the proposed method, the modal parameters of a shear frame were extracted from modal displacement data obtained from a vibration test, and the results were compared with those obtained from the existing frequency domain SI method. The proposed method introduces the maximum modal response ratio of each mode computed by modal displacement data, and from this, the contribution of each mode and each measured location to the overall structural response is indirectly evaluated. Moreover, this article proposes a model updating method establishing the error functions based on the differences between the analytical model and measurement for the natural frequencies and the modal responses reflecting both mode shape and modal contribution. The validity of the proposed method is verified through the response prediction and modal contributions of the models obtained from model updating based on dynamic displacement from a shaking table test for a shear‐type test frame.     

基于试验模态参数的索-拱铁路桥的改进有限元模型

介绍基于模态参数的索-拱铁路桥的校准数值模型。基于扩大的频域分解法,采用只输出技术,通过扰动测试来确定自振频率,桥梁振动的整体和局部模态对应的振型及阻尼系数。采用一种遗传算法对数值模型进行改进,该算法可以在数值模型的15个参数中得到最优解。为了与模态匹配,采用了一种基于模态应变能计算的新技术。考虑到不同的初始种群,大量参数的稳定性证明了数值模型在优化范围内所采用优化算法的鲁棒性。通过一个混凝土的变形模量的特征试验和铁路运输下的动力试验,对改进的数值模型进行了验证。结果显示数值模拟结果与试验结果吻合较好。     

Variational mode decomposition based modal parameter identification in civil engineering

An out-put only modal parameter identification method based on variational mode decomposition (VMD) is developed for civil structure identifications. The recently developed VMD technique is utilized to decompose the free decay response (FDR) of a structure into to modal responses. A novel procedure is developed to calculate the instantaneous modal frequencies and instantaneous modal damping ratios. The proposed identification method can straightforwardly extract the mode shape vectors using the modal responses extracted from the FDRs at all available sensors on the structure. A series of numerical and experimental case studies are conducted to demonstrate the efficiency and highlight the superiority of the proposed method in modal parameter identification using both free vibration and ambient vibration data. The results of the present method are compared with those of the empirical mode decomposition-based method, and the superiorities of the present method are verified. The proposed method is proved to be efficient and accurate in modal parameter identification for both linear and nonlinear civil structures, including structures with closely spaced modes, sudden modal parameter variation, and amplitude-dependent modal parameters, etc.     

Response surface‐based finite‐element model updating of a historic masonry minaret for operational modal analysis

This study aimed to use the response surface (RS) method for finite element (FE) model updating, using operational modal analysis (OMA). The RS method was utilized to achieve better agreement between the numerical and field‐measured structure response. The OMA technique for the field study was utilized to obtain modal parameters of the selected historic masonry minaret. The natural frequencies and mode shapes were experimentally determined by the enhanced frequency domain decomposition (EFDD) method. The optimum results between the experimental and numerical analyses were found by using the optimization method. The central composite design was used to construct the design of experiments, and the genetic aggregation approach was performed to generate the RS models. After obtaining the RS models, an attempt was made to converge the natural frequency values corresponding to the five‐mode shapes with the frequency values identified by the experimental analysis. ANSYS software was used to perform 3D finite element (FE) modeling of the historic masonry minaret and to numerically identify the natural frequencies and mode shapes of the minaret. The results of the experimental, initial, and updated FE model were compared with each other. Significant differences can be seen when comparing the experimental and analytical results with the initial conditions.     

Modal Identification for High‐Rise Building Structures Using Orthogonality of Filtered Response Vectors

The modal parameters of civil structures (natural frequency, mode shape, and mode damping ratio) are used for structural health monitoring (SHM), damage detection, and updating the finite element model. Long‐term measurement has been necessary to conduct operational modal analysis (OMA) under various loading conditions, requiring hundreds of thousands of discrete data points for estimating the modal parameters. This article proposes an efficient output‐only OMA technique in the form of filtered response vector (frv)‐based modal identification, which does not need complex signal processing and matrix operations such as singular value decomposition (SVD) and lower upper (LU) factorization, thus overcoming the main drawback of the existing OMA technique. The developed OMA technique also simplifies parameters such as window or averaging, which should be designed for signal processing by the OMA operator, under well‐separated frequencies and loading conditions excited by white noise. Using a simulation model and a 4‐story steel frame specimen, the accuracy and applicability were verified by comparing the dynamic properties obtained by the proposed technique and traditional frequency‐domain decomposition (FDD). In addition, the applicability and efficiency of the method were verified by applying the developed OMA to measured data, obtained through a field test on a 55‐story, 214‐m‐tall high‐rise building.     

某多层砌体教学楼环境振动试验及其模态分析

本文进行某多层砌体结构教学楼环境振动试验,利用基于传递率参数识别方法进行教学楼动力参数识别,并与该楼MI-DAS三维有限元模型理论计算结果进行比较,得出一些有价值的结论。     

Enhanced Hilbert–Huang transform and its application to modal identification

The well‐known Hilbert–Huang transform (HHT) consists of empirical mode decomposition to extract intrinsic mode functions (IMFs) and Hilbert spectral analysis to obtain time–frequency characteristics of IMFs through the Hilbert transform. There are two mathematical requirements that limit application of the Hilbert transform. Moreover, noise effects caused by the empirical mode decomposition procedure add a scatter to derivative‐based instantaneous frequency determined by the Hilbert transform. In this paper, a new enhanced HHT is proposed in which by avoiding mathematical limitations of the Hilbert spectral analysis, an additional parameter is employed to reduce the noise effects on the instantaneous frequencies of IMFs. To demonstrate the efficacy of the proposed method, two case studies associated with structural modal identification are selected. In the first case, through identification of a typical 3‐DOF structural model subjected to a random excitation, accuracy of the enhanced method is verified. In the second case, ambient response data recorded from a real 15‐story building are analyzed, and nine modal frequencies of the building are identified. The case studies indicate that the enhanced HHT provides more accurate and physically meaningful results than HHT and is capable to be an efficient tool in structural engineering applications. Copyright © 2012 John Wiley & Sons, Ltd.     

Rapid Impact Testing and System Identification of Footbridges Using Particle Image Velocimetry

The rapid impact testing of bridges contains unique advantages. For example, structural parameters, including frequency response function and structural flexibility matrix can be identified; however, additional impact‐testing instruments are required to excite a bridge, restricting the efficiency of the measurement strategy in terms of experimental cost and time. In this paper, a particle image velocimetry‐based method is proposed for the rapid impact testing and system identification of footbridges under pedestrian excitations. The proposed method has shown promising features: (1) pedestrian load is utilized for the impact excitation of footbridges, which is more convenient than the conventional impact‐testing method with additional excitation devices; (2) the human‐induced impact forces under varying jumping scenarios are calculated from image sequences of human motions acquired by a single camera with its noncontact and target‐less characteristics; and (3) both human‐induced impact forces (inputs) and structural responses (outputs) are employed to identify more modal parameters (i.e., scaling factors, modal mass, and structural flexibility). The robustness of the proposed method was successfully validated by a laboratory test of a simply supported beam and field testing of a cable‐stayed footbridge. The proposed method not only could improve the testing efficiency of footbridges, but also could obtain more modal parameters, which can be further utilized for deflection prediction, damage detection, and long‐term performance evaluation.     

Finite element model updating of a large structure using multi-setup stochastic subspace identification method and bees optimization algorithm

In the present contribution, operational modal analysis in conjunction with bees optimization algorithm are utilized to update the finite element model of a solar power plant structure. The physical parameters which required to be updated are uncertain parameters including geometry, material properties and boundary conditions of the aforementioned structure. To determine these uncertain parameters, local and global sensitivity analyses are performed to increase the solution accuracy. An objective function is determined using the sum of the squared errors between the natural frequencies calculated by finite element method and operational modal analysis, which is optimized using bees optimization algorithm. The natural frequencies of the solar power plant structure are estimated by multi-setup stochastic subspace identification method which is considered as a strong and efficient method in operational modal analysis. The proposed algorithm is efficiently implemented on the solar power plant structure located in Shahid Chamran university of Ahvaz, Iran, to update parameters of its finite element model. Moreover, computed natural frequencies by numerical method are compared with those of the operational modal analysis. The results indicate that, bees optimization algorithm leads accurate results with fast convergence.