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.     

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.     

Spurious mode distinguish by modal response contribution index in eigensystem realization algorithm

Modal identification process has played an important role for civil engineering structures. Among the identification methods, eigensystem realization algorithm is one of the most popular one. However, the noises in practical environment can influent the effectiveness of eigensystem realization algorithm, which can introduce spurious modes due to the overestimated physical order for the structure. This paper proposes a new index named the modal response contribution index (MRCI) for the eigensystem realization algorithm, which can determine the structural physical order and then distinguish spurious mode more precisely. First, the structural responses are divided into different modal response by the well‐known modal superposition theory. Then the square root summation of each modal response is obtained and named as MRCI. A modified stabilization diagram is also presented, which increases the row number of Hankel matrix with the determined order by MRCI. The straight lines formed by the stable points in the modified stabilization diagram designate the structural modal parameters. Finally, one numerical example and the monitoring data of a practical cable‐stayed bridge are employed. The results show that the proposed MRCI and modified stabilization diagram can identify the structural physical mode more precisely.     

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.     

Real-time wireless vibration monitoring for operational modal analysis of an integral abutment highway bridge

Remote structural health monitoring systems employing a sensor-based quantitative assessment of in-service demands and structural condition are perceived as the future in long-term bridge management programs. However, the data analysis techniques and, in particular, the technology conceived years ago that are necessary for accurately and efficiently extracting condition assessment measures from highway infrastructure have just recently begun maturation. In this study, a large-scale wireless sensor network is deployed for ambient vibration testing of a single-span integral abutment bridge to derive in-service modal parameters. Dynamic behavior of the structure from ambient and traffic loads was measured with accelerometers for experimental determination of the natural frequencies, damping ratios, and mode shapes of the bridge. Real-time data collection from a 40-channel single network operating with a sampling rate of 128 Hz per sensor was achieved with essentially lossless data transmission. Successful acquisition of high-rate, lossless data on the highway bridge validates the proprietary wireless network protocol within an actual service environment. Operational modal analysis is performed to demonstrate the capabilities of the acquisition hardware with additional correlation of the derived modal parameters to a Finite Element Analysis of a model developed using as-built drawings to check plausibility of the mode shapes. Results from this testing demonstrate that wireless sensor technology has matured to the degree that modal analysis of large civil structures with a distributed network is a currently feasible and a comparable alternative to cable-based measurement approaches.     

Optimal Sensor Placement for Mode Shapes Via Shannon's Sampling Theorem

Abstract: The feasibility of using Shannon's sampling theorem to reconstruct exact mode shapes of a structural system from a limited number of sampling points is investigated. Shannon's sampling theorem for the time domain is reviewed. The theorem is then extended to the spatial domain. Mode shapes are reconstructed from a limited amount of data, and the reconstructed mode shapes are compared with the exact mode shapes. On the basis of the results, simple rules are proposed for the placement of accelerometers in modal parameter extraction experiments. The feasibility of applying the rules and the extended Shannon's theorem to damage localization in a simple structure is demonstrated.     

Operational Modal Parameter Identification from Power Spectrum Density Transmissibility

Abstract: Operational modal analysis subjected to ambient or natural excitation under operational conditions has recently drawn great attention. In this article, the power spectrum density transmissibility (PSDT) is proposed to extract the operational modal parameters of a structure. It is proven that the PSDT is independent of the applied excitations and transferring outputs at the system poles. As a result, the modal frequencies and mode shapes can be extracted by combing the PSDTs with different transferring outputs instead of different load conditions where the outputs from only one load condition are needed. A five‐story shear building subjected to a set of uncorrelated forces at different floors is adopted to verify the property of PSDTs and illustrate the accuracy of the proposed method. Furthermore, a concrete‐filled steel tubular half‐through arch bridge tested in the field under operational conditions is used as a real case study. The identification results obtained from currently developed method have been compared with those extracted from peak‐picking method, stochastic subspace identification, and finite element analysis. It is demonstrated that the operational modal parameters identified by the current technique agree well with other independent methods. The real application to the field operational vibration measurements of a full‐sized bridge has shown that the proposed PSDTs are capable of identifying the operational modal parameters (natural frequencies and mode shapes) of a structure.     

Blind Modal Identification in Frequency Domain Using Independent Component Analysis for High Damping Structures with Classical Damping

Output‐only modal identification methods are practical for large‐scale engineering. Recently, independent component analysis (ICA) which is one of the most popular techniques of blind source separation (BSS) has been used for output‐only modal identification to directly separate the modal responses and mode shapes from vibration responses. However, this method is only accurate for undamped or lightly damped structures. To improve the performance of ICA for high damping structures, this article presents an extended ICA‐based method called ICA‐F, which establishes a BSS model in frequency domain. First, the basic idea of BSS and ICA applied in modal identification is introduced in detail. The free vibration responses and the correlation functions of ambient responses can be cast into the frequency‐domain BSS framework just by mapping the time history responses to frequency domain through fast Fourier transform (FFT). Then, an ICA‐based method in frequency domain called ICA‐F is proposed to accurately extract mode shapes and modal responses for both light and high damping structures. A simulated 3 degree of freedom mass‐spring system and a 4‐story simulated benchmark model developed by the IASC‐ASCE Task Group in Health Monitoring are employed to verify the effectiveness of the proposed method. The results show that the proposed method can perform accurate modal identification for both light and high damping structures. Finally, the IASC‐ASCE experimental benchmark structure is also utilized to illustrate the proposed method applied to practical structure.     

Hybrid Time‐Frequency Blind Source Separation Towards Ambient System Identification of Structures

Abstract: Ambient system identification in noisy environments, in the presence of low‐energy modes or closely‐spaced modes, is a challenging task. Conventional blind source separation techniques such as second‐order blind identification (SOBI) and Independent Component Analysis (ICA) do not perform satisfactorily under these conditions. Furthermore, structural system identification for flexible structures require the extraction of more modes than the available number of independent sensor measurements. This results in the estimation of a non‐square modal matrix that is spatially sparse. To overcome these challenges, methods that integrate blind identification with time‐frequency decomposition of signals have been previously presented. The basic idea of these methods is to exploit the resolution and sparsity provided by time‐frequency decomposition of signals, while retaining the advantages of second‐order source separation methods. These hybrid methods integrate two powerful time‐frequency decompositions—wavelet transforms and empirical mode decomposition—into the framework of SOBI. In the first case, the measurements are transformed into the time‐frequency domain, followed by the identification using a SOBI‐based method in the transformed domain. In the second case, a subset of the operations are performed in the transformed domain, while the remaining procedure is conducted using the traditional SOBI method. A new method to address the under‐determined case arising from sparse measurements is proposed. Each of these methods serve to address a particular situation: closely‐spaced modes or low‐energy modes. The proposed methods are verified by applying them to extract the modal information of an airport control tower structure located near Toronto in Canada.     

Real-time structural health monitoring of a supertall building under construction based on visual modal identification strategy

This paper presents a real-time structural health monitoring technique for a supertall building under construction, Lotte World Tower (LWT), the tallest building in Korea. To evaluate the state and safety of the supertall building under construction, this study presents a visual modal identification method to identify mode shape and damping ratio based on modal responses from the monitoring system. In the method, mode shape and damping are visually identified from the time history plotting of well-filtered modal responses in real time. Since the presented method does not include a kind of complex calculation for measured data required in the previous SI methods, it can avoid time consuming in system identification (SI) as well as variation in value of modal parameter extracted from measurement. An ambient vibration test on the LWT under construction was performed in 2015. Using the test data, the presented method identified the mode shapes and damping of the LWT visually with small variations without any complicated computations. Further, this study presents a model updating method with a simplified pseudo frame model to construct a baseline model for the LWT under construction using measured modal responses. The validity of the updated model for the LWT was verified through estimations of mode shape and structural responses.     

Experimental study of modal parameter identification in a simulated ambient-excited structure

Structure modal parameter online identification was used to monitor the structural health as evidenced by changes in the vibration characteristics. The natural excitation technique and the eigensystem realization algorithm were combined to identify the modal parameters in the time domain of a structure excited by simulated ambient vibrations. The mass-normalized mode shapes were obtained from the eigen-sensitivity analysis. The experimental modal analysis was performed on a two-story steel braced frame model excited by simulated ambient vibrations and hammer impacts. The mass-normalized mode shapes were acquired by changing the structural mass and by eigen-sensitivity analysis. From finite element analysis results and the experimental data, it is shown that this method is effective. __________ Translated from Journal of Tsinghua University (Science and Technology Edition), 2006, 46(6): 769–772 [译自: 清华大学学报 (自然科学版)]     

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.     

A modal-based Kalman filtering framework for mode extraction and decomposition of damped structures

The mode shape is one of the important modal parameters that enables to visualize the intrinsic behavior of a structure as well as the quantity of interest by extracting or separating modal response from measurements. In this study, a new output-only framework is proposed to extract modes using a modal-based Kalman filter defined in the modal space and identify the mode shape by manipulating the correlation between the separated modes and the measured responses. It is also shown that the proposed framework can be extended to estimate the mode shapes of a non-classically damped structure in state space when the state variable is constructed from the measured responses and applied to the modal-based Kalman filter. The mode shape estimation framework proposed in this study was verified by numerical simulations and full-scale measurements. From the verification examples and their results, it was noted that the proposed modal identification framework is not influenced by the presence of noise, and it can be applied to identify the state-space mode shapes of non-classically damped systems as well as systems with very closely distributed modes such as buildings equipped with tuned mass dampers.     

Earthquake analysis of reinorced concrete minarets using ambient vibration test results

This paper describes a Turkish style reinforced concrete minaret, its finite element model, modal testing, finite element model updating and earthquake behaviour, before and after model updating. The minaret of a mosque located in Trabzon, Turkey is selected as an application. A three‐dimensional (3D) model of the minaret and its modal analysis is performed to obtain analytical frequencies and mode shapes using ANSYS finite element program. The ambient vibration tests are conducted on the minaret under natural excitations such as wind effects and human movement. The output‐only modal parameter identification is carried out by Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods in Operational Modal Analysis software and in doing so, dynamic characteristics (natural frequencies, mode shapes and damping ratios) are determined. A 3D finite element model of the minaret is updated to minimize the differences between analytical and experimental modal properties by changing some uncertain modelling parameters such as material properties and boundary conditions. The earthquake behaviour of the minaret is investigated using 1992 Erzincan earthquake before and after finite element model updating. Maximum differences in the natural frequencies are reduced from 21% to 8%, and good agreement is found between analytical and experimental natural frequencies. In addition to this, it is realized that finite element model updating is effective on the earthquake behaviour of the minaret. Copyright © 2008 John Wiley & Sons, Ltd.     

基于振型参数的装配式桥梁损伤识别研究

利用结构动力特性的振型参数对桥梁进行快速损伤诊断和定位,可以提高结构性能评价与损伤诊断的效率。本文以装配式预应力混凝土T梁为算例,通过定义位移振型和曲率振型的桥梁损伤识别指标进行损伤识别,计算结果表明采用位移振型和曲率振型的方法进行损伤识别和定位效果较好。     

A Two‐Step Model Updating Algorithm for Parameter Identification of Linear Elastic Damped Structures

A Frequency Response Functions (FRFs)‐based two‐step algorithm to identify stiffness, mass, and viscous damping matrices is developed in this work. The proposed technique uses the difference between the experimentally recorded FRF and their analytical counterparts by minimizing the resultant error function at selected frequency points. In the first step, only mass and stiffness matrices are updated while keeping the uncalibrated viscous damping matrix constant. In the second step, the damping matrix is updated via changes on the selected unknown modal damping ratios. By using a stacking procedure of the presented error function that combines multiple data sets, adverse effects of noise on the estimated modal damping ratios are decreased by averaging the FRF amplitudes at resonant peaks. The application of this methodology is presented utilizing experimentally obtained data. The presented algorithm can perform an accurate structural identification via model updating, with a viscous damping matrix that captures the variation of the modal damping ratios with natural frequencies as opposed to other conventional proportional damping matrix formulations.     

珠江大桥动力特性测试与分析

利用频域中的单模态识别法(SDOFI)对珠江大桥——大跨度预应力砼连续刚构桥的现场环境振动试验数据进行桥梁动力特性识别。利用ANSYS建立了全桥三维有限元模型并进行了理论模态分析。     

Mobile Impact Testing for Structural Flexibility Identification with only a Single Reference

In contrast to the traditional impact test method requiring a number of sensors to measure the entire structure, a mobile impact test method sequentially measuring segments of the structure and the related data processing strategy is proposed. Especially, only a single reference node is required when integrating measurements of the segments to identify the flexibility characteristic of the entire structure. Equations are first derived to adjust the magnitudes of mode shapes of the substructure to a same scaling level. Then the phase angle concept is utilized to determine the coherent signs of mode shapes for structural flexibility identification. The advantage of the proposed method is that it outputs the same flexibility identification results as the traditional impact test method, whereas it only requires a single reference no matter how many segments of the structure are divided, thus it significantly speeds up the impact test and makes it be an ideal approach for rapid testing of short/middle span bridges. Numerical and experiment examples investigated successfully verify the effectiveness of the proposed method for structural flexibility identification.     

Statistical Regularization for Identification of Structural Parameters and External Loadings Using State Space Models

A novel numerical approach is presented, in the time domain, to simultaneously identify structural parameters and unmeasured input loadings using incomplete output measurement only. The identification problem is formulated as an optimization process, wherein the objective function is defined as the discrepancy between the measured and the predicted data, and is solved by a damped Gauss‐Newton method. Because the proposed algorithm is a time domain technique, forward analyses are required to obtain predicted system responses so as to compute the discrepancy. Therefore, we propose an input force estimation scheme in the identification process to complete the task of input‐output forward analyses, for the case of output‐only measurement. The relationship between the unknown input loadings and the output measurement is established through a state space model, which basically formulates an ill‐posed least squares problem. A statistical Bayesian inference‐based regularization technique is presented to solve such a least squares problem. Finally, the proposed approach is illustrated by both numerical and experimental examples using output‐only measurements of either acceleration or strain time histories. The results clearly show the robustness and the applicability of the proposed algorithm to simultaneously identify structural parameters and unmeasured input loadings with a high accuracy.     

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.