Least-Squares Estimation with Unknown Excitations for Damage Identification of Structures

System identification and damage detection for structural health monitoring of civil infrastructures have received considerable attention recently. Time domain analysis methodologies based on measured vibration data, such as the least-squares estimation and the extended Kalman filter, have been studied and shown to be useful. The traditional least-squares estimation method requires that all the external excitation data (input data) be available, which may not be the case for many structures. In this paper, a recursive least-squares estimation with unknown inputs (RLSE-UI) approach is proposed to identify the structural parameters, such as the stiffness, damping, and other nonlinear parameters, as well as the unmeasured excitations. Analytical recursive solutions for the proposed RLSE-UI are derived and presented. This analytical recursive solution for RLSE-UI is not available in the previous literature. An adaptive tracking technique recently developed is also implemented in the proposed approach to track the variations of structural parameters due to damages. Simulation results demonstrate that the proposed approach is capable of identifying the structural parameters, their variations due to damages, and unknown excitations.     

Adaptive Quadratic Sum-Squares Error for Structural Damage Identification

The ability to detect damages online, based on vibration data measured from sensors, will ensure the reliability and safety of structures. Innovative data analysis techniques for the damage detection of structures have received considerable attention recently, although the problem is quite challenging. In this paper, we proposed a new data analysis method, referred to as the quadratic sum-squares error (QSSE) approach, for the online or almost online identification of structural parameters. Analytical recursive solution for the proposed QSSE method, which is not available in the previous literature, is derived and presented. Further, an adaptive tracking technique recently proposed is implemented in the proposed QSSE approach to identify the time-varying system parameters of the structure, referred to as the adaptive quadratic sum-squares error. The accuracy and effectiveness of the proposed approach are demonstrated using both linear and nonlinear structures. Simulation results using the finite-element models demonstrate that the proposed approach is capable of tracking the changes of structural parameters leading to the identification of structural damages.     

Natural Excitation Technique and Eigensystem Realization Algorithm for Phase I of the IASC-ASCE Benchmark Problem: Simulated Data

A benchmark study in structural health monitoring based on simulated structural response data was developed by the joint IASC–ASCE Task Group on Structural Health Monitoring. This benchmark study was created to facilitate a comparison of various methods employed for the health monitoring of structures. The focus of the problem is simulated acceleration response data from an analytical model of an existing physical structure. Noise in the sensors is simulated in the benchmark problem by adding a stationary, broadband signal to the responses. A structural health monitoring method for determining the location and severity of damage is developed and implemented herein. The method uses the natural excitation technique in conjunction with the eigensystem realization algorithm for identification of modal parameters, and a least squares optimization to estimate the stiffness parameters. Applying this method to both undamaged and damaged response data, a comparison of results gives indication of the location and extent of damage. This method is then applied using the structural response data generated with two different models, different excitations, and various damage patterns. The proposed method is shown to be effective for damage identification. Additionally the method is found to be relatively insensitive to the simulated sensor noise.     

Damage Detection Utilizing the Damage Index Method to a Benchmark Structure

This paper addresses the first generation benchmark problem on structural health monitoring developed by the ASCE Task Group on Structural Health Monitoring. The focus of the problem is a four-story model of an existing physical model at the University of British Columbia where simulated data are used for the system identification. Modal parameters were extracted using the frequency domain decomposition method. Rather than relying on data from the undamaged structure, a new proposed methodology based on ratios between stiffness and mass values from the eigenvalue problem is presented to identify the undamaged state of the structure. Once the structural identification is complete, the damage index method is used to detect the location and severity of damage. By not relying on undamaged structure information, this approach may be applicable to existing structures that may already incorporate some amount of damage.     

Vibration Testing at Meazza Stadium: Reliability of Operational Modal Analysis to Health Monitoring Purposes

In the last years an increasing interest has been devoted to all the topics related to the security and safety of people. Particular attention has been paid to health monitoring of large civil structures hosting many people, such as high-rise buildings and stadiums. Some extraordinary events, such as the Millennium Bridge oscillations in London, excited by pedestrians, or the Bruce Springsteen concert at the Ullevi Stadium in which coordinated jumps from the crowd caused serious damage to the structure, and drew attention toward a deeper and more careful study of all those problems related to the dynamic behavior of civil structures and their interaction with crowds. Research on these topics is also aimed, among others, at developing techniques allowing for a continuous monitoring of the structure, starting from a set of measurements that can be performed continuously, 24?h a day, without the need to stop the structure's functionality. The vast scientific literature confirms the possibility of relating structural health to the evolution of modal parameters, often reaching the aim of localizing any eventual damage, a task otherwise impossible with different techniques. This paper shows part of a long lasting project involving Politecnico di Milano in the setting up of a permanent health monitoring system at the G. Meazza Stadium in Milan. The aim of this project was the evaluation of the actual health state of the structures constituting the stands of the stadium and the deployment of a permanent monitoring system to record the vibration levels reached in all substructures during each event. Evaluation of the actual structure condition was performed by the use of ambient vibration, which was also checked against traditional experimental modal analysis, performed by using an inertial force given by a hydraulic actuator and a detailed measurement mesh. This offered the chance to exploit all possible information concerning natural frequencies, modal shapes, and damping factors. This task is extremely time consuming and expensive, therefore, it cannot be repeated very often. The possibility of using the data coming from the permanent monitoring system, which is about to be installed, is then an attractive perspective to improve structural diagnosis. It is expected that using operational modal analysis techniques will mean knowledge of the excitation applied to the structure will not be required. The parameter estimation obtained by this technique is usually affected by a spread, given both by the uncertainty of the adopted identification techniques and the influence of external parameters, such as crowd loading or temperature. As damage identification is related to changes of the modal parameters, the evaluation of their normal spread is fundamental to fix a threshold in order to identify possible worrysome situations. This paper deals with the identification of the spread in the modal parameter estimation of one of the grandstands of the so-called 3° ring of the G. Meazza Stadium in Milan, performed analyzing data collected over more than one year. Vibration data have been recorded during different events, such as soccer matches and concerts. The considered data came from a set of sensors similar to that which is to be installed for the permanent monitoring system, to check about the possibility to use the monitoring system as a diagnostic tool for the structure. A study was also carried out to identify critical aspects in the sensors’ choice and their placement, in order to provide useful information about the design of the permanent monitoring system. The presented results can be used to determine confidence intervals out of which changes in the modal properties can be considered anomalous, and so, worthy of being deeply investigated to assess structural integrity.     

Structural Health Monitoring and Damage Assessment Using Frequency Response Correlation Criteria

Two frequency response correlation criteria, namely the global shape correlation (GSC) function and the global amplitude correlation (GAC) function, are established tools to quantify the correlation between predictions from a finite-element (FE) model and measured data for the purposes of FE model validation and updating. This paper extends the application of these two correlation criteria to structural health monitoring and damage detection. In addition, window-averaged versions of the GSC and GAC, namely WAIGSC and WAIGAC, are defined as effective damage indicators to quantify the change in structural response. An integrated method of structural health monitoring and damage assessment, based on the correlation functions and radial basis function neural networks, is proposed and the technique is applied to a bookshelf structure with 24 measured responses. The undamaged and damaged states, single and multiple damage locations, as well as damage levels, were successfully identified in all cases studied. The ability of the proposed method to cope with incomplete measurements is also discussed.     

Hilbert-Huang Based Approach for Structural Damage Detection

When measured data contain damage events of the structure, it is important to extract the information of damage as much as possible from the data. In this paper, two methods are proposed for such a purpose. The first method, based on the empirical mode decomposition (EMD), is intended to extract damage spikes due to a sudden change of structural stiffness from the measured data thereby detecting the damage time instants and damage locations. The second method, based on EMD and Hilbert transform is capable of (1) detecting the damage time instants, and (2) determining the natural frequencies and damping ratios of the structure before and after damage. The two proposed methods are applied to a benchmark problem established by the ASCE Task Group on Structural Health Monitoring. Simulation results demonstrate that the proposed methods provide new and useful tools for the damage detection and evaluation of structures.     

Electromechanical Impedance-Based Structural Health Monitoring with Evolutionary Programming

An impedance-based structural health monitoring technique is presented. By analyzing the in-plane vibration of a thin lead–zirconate–titanate (PZT) patch, the electromechanical impedance of the PZT patch is predicted. The force impedances of a beam and a plate with damage are calculated by Ritz method using polynomial as shape functions. The damage is then identified from the changes of the impedance spectra caused by the appearance of damage. A hybrid evolutionary programming is employed as a global search technique to back-calculate the damage. A specially designed fitness function is proposed, which is able to effectively reduce the inaccuracy in representing the real structure using analytical or numerical models. Experiments are carried out on a beam and a plate to verify the numerical predictions. The results demonstrate that the proposed method is able to effectively and reliably locate and quantify the damage in the beam and the plate.     

Integrated Procedure for Identification and Control of MDOF Structures

An integrated procedure based on a direct adaptive control algorithm is applied to structural systems for both vibration suppression and damage detection. The wider class of noncollocated actuator-sensor schemes is investigated through parameterized linear functions of the state variables that preserve the minimum phase property of the system. A larger number of mechanical parameters are shown to be identifiable in noncollocated configurations. Proper output selection allowing for model reference control and tracking error based parameters estimation under persistent excitation is described. Using full-state feedback, these capabilities are effectively exploited for oscillation reduction and health monitoring of uncertain multi-degree-of-freedom (MDOF) shear-type structures.     

Neural Networks and Principal Component Analysis for Identification of Building Natural Periods

This paper deals with an application of neural networks for computation of fundamental natural periods of buildings with load-bearing walls. The analysis is based on long-term tests performed on actual structures. The identification problem is formulated as the relation between structural and soil basement parameters, and the fundamental period of building. The principal component analysis for compression of input data is also used. Backpropagation neural networks are applied in the analysis. Results of neural network identification of natural periods are compared with data from experiments. The application of the proposed neural networks enables us to identify the natural periods of the buildings with quite satisfactory accuracy for engineering practice. The compression of the input data to principal components by principal component analysis makes it possible to design much smaller neural networks than those without data compression with no greater increase of the neural approximation errors. It appears that this technique would also be very useful in damage detection and health monitoring of structures.     

Structural Damage Detection Using Dynamic Properties Determined from Laboratory and Field Testing

Studies have shown that experimentally determined dynamic properties can be used to identify the characteristics of a structure. In this paper, a damage detection technique is developed and demonstrated using system identification, finite-element modeling, and a modal update process. The proposed approach, SFM, provides a rapid estimate of damage locations and magnitudes. The proposed methodology is applied to three case studies. The first is a numerical simulation using computer generated data. The second is an ASCE benchmark problem for structural health monitoring, where the results can be compared to other researchers. The third is a full-scale highway bridge that was field tested using a forced vibration shaking machine. In this case study, the bridge was shaken in several states of damage and the proposed methodology was utilized to detect and determine the location and extent of the damage. It was found that, using the collected data, the SFM approach was able to consistently predict the location of damage as well as estimate the magnitude of the damage.     

Application of Wavelet Approach for ASCE Structural Health Monitoring Benchmark Studies

This paper presents an application of wavelet analysis for damage detection and locating damage region(s) for the ASCE structural health monitoring benchmark data. The response simulation data were generated basically by a FEM program provided by the ASCE Task Group on Health Monitoring for a four-story prototype building structure subjected to simulated stochastic wind loading. Damage was introduced in the middle of response by breaking one or more structure elements such as interstory braces. Wavelets were used to analyze the simulation data. It was found that structural damage due to sudden breakage of structural elements and the time when it occurred can be clearly detected by spikes in the wavelet details. The damaged region can be determined by the spatial distribution pattern of the observed spikes. The effects of measurement noise and the severity of damage were investigated. The results in this paper illustrate a great promise of wavelet analysis for structural health monitoring, especially for an on-line application.     

Damage Identification Using Electromagnetic Waves Based on Born Imaging Algorithm

Reconstructing damage geometry with computationally efficient and effective algorithms is of primary importance in establishing a robust structural health monitoring (SHM) system. In this paper, Born imaging algorithm is proposed for three-dimensional (3D) damage imaging of reinforced concrete structures using electromagnetic waves. This algorithm is derived in time domain for inhomogeneous isotropic and lossy structures. In order to reduce the computational cost of the algorithm, different imaging conditions are introduced. Numerical simulations in a 2D transverse magnetic case for a reinforced concrete slab with multiple damages are performed to test the effectiveness of the algorithm. In this simulated study, sensor data, incident field, and back-propagated field are computed via a finite difference time-domain method. It is concluded that the proposed imaging algorithm is capable of efficiently identifying the damages’ geometries and may be employed in a SHM system.     

Structural Health Monitoring by Recursive Bayesian Filtering

A new vision of structural health monitoring (SHM) is presented, in which the ultimate goal of SHM is not limited to damage identification, but to describe the structure by a probabilistic model, whose parameters and uncertainty are periodically updated using measured data in a recursive Bayesian filtering (RBF) approach. Such a model of a structure is essential in evaluating its current condition and predicting its future performance in a probabilistic context. RBF is conventionally implemented by the extended Kalman filter, which suffers from its intrinsic drawbacks. Recent progress on high-fidelity propagation of a probability distribution through nonlinear functions has revived RBF as a promising tool for SHM. The central difference filter, as an example of the new versions of RBF, is implemented in this study, with the adaptation of a convergence and consistency improvement technique. Two numerical examples are presented to demonstrate the superior capacity of RBF for a SHM purpose. The proposed method is also validated by large-scale shake table tests on a reinforced concrete two-span three-bent bridge specimen.     

Structural Health Monitoring by Piezo–Impedance Transducers. II: Applications

This paper, the second in a two-part series, presents a new methodology for structural identification and nondestructive evaluation by piezo–impedance transducers. The theoretical development and experimental validation of the underlying lead–zirconium–titanate (PZT)–structure interaction model was presented in the first part. In our newly proposed method, the damage in evaluated on the basis of the equivalent system parameters “identified” by the surface-bonded piezo–impedance transducer. As proof of concept, the proposed method is applied to perform structural identification and damage diagnosis on a representative lab-sized aerospace structural component. It is then extended to identify and monitor a prototype reinforced concrete bridge during a destructive load test. The proposed method was found to be able to successfully identify as well as evaluate damages in both the structures.     

Bayesian Probabilistic Inference for Nonparametric Damage Detection of Structures

This paper presents a Bayesian hypothesis testing-based probabilistic assessment method for nonparametric damage detection of building structures, considering the uncertainties in both experimental results and model prediction. A dynamic fuzzy wavelet neural network method is employed as a nonparametric system identification model to predict the structural responses for damage evaluation. A Bayes factor evaluation metric is derived based on Bayes’ theorem and Gaussian distribution assumption of the difference between the experimental data and model prediction. The metric provides quantitative measure for assessing the accuracy of system identification and the state of global health of structures. The probability density function of the Bayes factor is constructed using the statistics of the difference of response quantities and Monte Carlo simulation technique to address the uncertainties in both experimental data and model prediction. The methodology is investigated with five damage scenarios of a four-story benchmark building. Numerical results demonstrate that the proposed methodology provides an effective approach for quantifying the damage confidence in the structural condition assessment.     

基于微振动监测的AFT厂房结构–浆液耦合振动特性

AFT氧化风机房是脱硫工艺中的一种钢筋混凝土结构支撑钢罐的复合结构,结构产生的明显振动不利于正常生产运营,因此针对AFT结构进行现场监测和模拟计算。首先对AFT结构进行现场调查,基于一种AFT结构视频监测与局部监测相结合的方法对其进行监测,随后又提出简化搅拌机及氧化风作用的模拟方法,通过数值模拟对AFT结构振动特性进行研究。结果表明:对AFT结构进行视频监测可快速明确结构运动轨迹;局部监测结果表明搅拌机作用是结构振动的主要因素,氧化风的鼓入加剧了结构振动响应,因此造成了结构各柱间填充墙不同程度的损伤;将数值模拟结果与监测结果对比,验证了简化搅拌机及氧化风作用的计算方法,可为分析此类结构振动响应、损伤机制以及加固设计提供参考。      

Bayesian Probabilistic Approach to Structural Health Monitoring

A Bayesian probabilistic methodology for structural health monitoring is presented. The method uses a sequence of identified modal parameter data sets to compute the probability that continually updated model stiffness parameters are less than a specified fraction of the corresponding initial model stiffness parameters. In this approach, a high likelihood of reduction in model stiffness at a location is taken as a proxy for damage at the corresponding structural location. The concept extends the idea of using as indicators of damage the changes in structural model parameters that are identified from modal parameter data sets when the structure is initially in an undamaged state and then later in a possibly damaged state. The extension is needed, since effects such as variation in the identified modal parameters in the absence of damage, as well as unavoidable model error, lead to uncertainties in the updated model parameters that in practice obscure health assessment. The method is illustrated by simulating on-line monitoring, wherein specified modal parameters are identified on a regular basis and the probability of damage for each substructure is continually updated.     

Baseline Models for Bridge Performance Monitoring

A baseline model is essential for long-term structural performance monitoring and evaluation. This study represents the first effort in applying a neural network-based system identification technique to establish and update a baseline finite element model of an instrumented highway bridge based on the measurement of its traffic-induced vibrations. The neural network approach is particularly effective in dealing with measurement of a large-scale structure by a limited number of sensors. In this study, sensor systems were installed on two highway bridges and extensive vibration data were collected, based on which modal parameters including natural frequencies and mode shapes of the bridges were extracted using the frequency domain decomposition method as well as the conventional peak picking method. Then an innovative neural network is designed with the input being the modal parameters and the output being the structural parameters of a three-dimensional finite element model of the bridge such as the mass and stiffness elements. After extensively training and testing through finite element analysis, the neural network became capable to identify, with a high level of accuracy, the structural parameter values based on the measured modal parameters, and thus the finite element model of the bridge was successfully updated to a baseline. The neural network developed in this study can be used for future baseline updates as the bridge being monitored periodically over its lifetime.     

Vibration-based Damage Detection of Structures by Genetic Algorithm

Vibration-based methods are being rapidly applied to detect structural damage. The usual approaches incorporate sensitivity analysis and the optimization algorithm to minimize the discrepancies between the measured vibration data and the analytical data. However, conventional optimization methods are gradient based and usually lead to a local minimum only. Genetic algorithms explore the region of the whole solution space and can obtain the global optimum. In this paper, a genetic algorithm with real number encoding is applied to identify the structural damage by minimizing the objective function, which directly compares the changes in the measurements before and after damage. Three different criteria are considered, namely, the frequency changes, the mode shape changes, and a combination of the two. A laboratory tested cantilever beam and a frame are used to demonstrate the proposed technique. Numerical results show that the damaged elements can be detected by genetic algorithm, even when the analytical model is not accurate.