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.     

Identification of Parametric Variations of Structures Based on Least Squares Estimation and Adaptive Tracking Technique

An important objective of health monitoring systems for civil infrastructures is to identify the state of the structure and to detect the damage when it occurs. System identification and damage detection, based on measured vibration data, have received considerable attention recently. Frequently, the damage of a structure may be reflected by a change of some parameters in structural elements, such as a degradation of the stiffness. Hence it is important to develop data analysis techniques that are capable of detecting the parametric changes of structural elements during a severe event, such as the earthquake. In this paper, we propose a new adaptive tracking technique, based on the least-squares estimation approach, to identify the time-varying structural parameters. In particular, the new technique proposed is capable of tracking the abrupt changes of system parameters from which the event and the severity of the structural damage may be detected. The proposed technique is applied to linear structures, including the Phase I ASCE structural health monitoring benchmark building, and a nonlinear elastic structure to demonstrate its performance and advantages. Simulation results demonstrate that the proposed technique is capable of tracking the parametric change of structures due to damages.     

Improved Damage Localization and Quantification Using Subset Selection

Because a structure’s modal parameters (natural frequencies and mode shapes) are affected by structural damage, finite- element model updating techniques are often applied to locate and quantify structural damage. However, the dynamic behavior of a structure can only be observed in a narrow knowledge space, which usually causes nonuniqueness and ill-posedness in the damage detection problem formulation. Thus, advanced optimization techniques are a necessary tool for solving such a complex inverse problem. Furthermore, a preselection process of the most significant damage parameters is helpful to improve the efficiency of the damage detection procedure. A new approach, which combines a parameter subset selection process with the application of damage functions is proposed herein to accomplish this task. Starting with a simple 1D beam, this paper first demonstrates several essential concepts related to the proposed model updating approach. A more advanced example considering a 2D model is then considered. To determine the capabilities of this approach for more complex structures, a trust region-based optimization method is adopted to solve the corresponding nonlinear minimization problem. The objective is to provide an improved robust solution to this challenging problem.     

Time Domain Backcalculation of Pavement Structure Material Properties Using 3D FEM with Ritz Vectors

The three‐dimensional finite element (3D FE) methods have been used increasingly to evaluate the bearing capacity of pavement structures. In this evaluation, layer moduli are backcalculated from measured surface deflections of the pavement structure. However, backcalculation requires repetitive computation to improve the parameter values in an iterative manner, and thus it is time consuming when 3D finite elements are used for the analysis. In this article, an effective method is developed to estimate layer moduli and damping coefficients in the time domain. The pavement is modeled using 3D finite elements. Gauss‐Newton and singular value decomposition methods are employed to backcalculate the unknown parameters. Ritz vectors are used to reduce the size of the matrices required for the analysis. Numerical simulations verify the effectiveness and accuracy of the Ritz vector method.     

Statistical Sensitivity Analysis of Lattice Space Structures

This paper presents a statistical sensitivity analysis for shape distortions of space structures. The approach is based on a statistical shape‐distortion analysis on the structural errors and an adjoint method of sensitivity analysis. The statistical shape‐distortion analysis allows the stochastic errors to be represented by member‐length tolerances. The sensitivity analysis is performed to predict the effects of member‐length errors for lattice space antennas on the surface accuracy. The formulas presented in this paper give an effective approach to predict the effects of member‐length errors on the shape distortions, to obtain effective structural elements to correct the shape distortions, and to design tolerance errors of the structural elements. Numerical examples for statically determinate and indeterminate two‐dimensional truss beams have been demonstrated to identify the members contributing most to the errors. These results show that the errors of the longitudinal elements of the structure are important for designing accurate truss structures. Moreover, the validity and effectiveness of the present approach have been investigated.     

Integrated Simulation of Machine Tool and Process Interaction for Turning

The interaction between process and machine tool behaviour can lead to process instabilities in terms of self‐excited vibrations where the energy of the machine tool oscillation is generated by process excitation. The regenerative chatter effects lead to wavy surfaces on the work‐piece. This effect has been simulated for turning processes with an integrated simulation approach, which couples a time domain simulation model for the machine tool and the workpiece with an analytical turning model. In this paper a procedure is illustrated for coupling an FEA‐based 3‐dimensional turning model with the time domain model for the machine tool under consideration of the resulting workpiece surface. In comparison to an analytical approach for calculating the mechanical tool load, the 3D‐FEA‐model has the potential to determine the resulting cutting forces for even complex‐shaped tool geometries, e.g. a complicated chip breaker or a varying cutting edge radius on the main or minor cutting edge. As a matter of the huge model size the calculation time in particular for 3‐dimensional problems is comparatively long to analytical cutting force models. Therefore, in this paper an approach to reduce the calculation time by using characteristic diagrams for the calculated process forces in the FEA‐model is presented. The research has also been focused on the current major problem in the FEA‐based modelling that the thrust and feed forces are generally underestimated in the simulation.     

Enhanced Realization∕Identification of Physical Modes

Physical structures are often sufficiently complicated to preclude constructing an accurate mathematical model of the system dynamics from simple analysis using the laws of physics. Consequently, determination of an accurate model requires utilization of (generally noisy) output measurements from dynamic tests. In this paper, we present a robust method for constructing accurate, structural‐dynamic models from discrete time‐domain measurements. The method processes the measurements in order to determine the number of modes present, the damping and frequency of each mode, and the mode shape. The structure may be highly damped. Although the mode‐shape identification is more sensitive to measurement noise than the order, frequency, and damping identification, the method is considerably less sensitive to noise than other leading methods. Accurate detection of the modal parameters and mode shapes is demonstrated for modes with damping ratios exceeding 15%.     

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.     

Damage Detection based on Single-Input-Single-Output Measurements

A methodology is presented for detecting damage of structural systems maintaining a linear response. A single frequency response function measured at several frequencies along with a correlated analytical model of the undamaged structure are used to detect and assess damage. The method is directed toward situations where the number of damaged elements is generally known to be limited. A computationally efficient method of recalculating a single receptance is presented. Numerical results for a two-dimensional structural frame are presented to validate and assess the proposed approach. Issues for the development of the approach are discussed.     

Model-Based Damage Identification in a Continuous Bridge Using Vibration Data

Damage often causes changes in the dynamic characteristics of a structure such as frequencies and mode shapes. Vibration-based damage identification techniques utilize the changes in the dynamic characteristics of a structure to determine the location and extent of damage in the structure. Such techniques are applied in this study to the Crowchild Bridge, a steel-free deck continuous bridge located in western Canada. While the numerical models of the bridge are correlated with the measured dynamic characteristics, computer simulation is used to study the identification of a number of different damage patterns, and the effects of measurement errors and incomplete mode shapes on the quality of results are evaluated. The effectiveness of some selected damage identification techniques is examined; the potential difficulties in identifying the damage are outlined; and areas of further research are suggested. A three-dimensional finite-element model and a simple two-dimensional girder model of the bridge have been constructed to study the usefulness of the selected damage identification methods. Another promising damage detection method proposed here is based on the application of neural networks that combines a vibration-based method.     

3D Finite Element Model for Asphalt Concrete Response Simulation

An extensive experimental, analytical, and numerical investigation on the response of asphalt concrete is currently in progress at Delft University of Technology. The objectives of this Asphalt Concrete Response (ACRe) project are: (a) the formulation and finite element implementation of a three‐dimensional, strain‐rate sensitive, temperature‐ and loading history‐dependent constitutive model, and (b) the development of the necessary experimental set‐ups, testing procedures, and data analysis methods for determination of the model parameters. These objectives are strongly interrelated: on the one hand, the model dictates what should be measured in a test, while on the other hand, the response observed in the tests sets the requirements for the model. As a result, model development/verification and experimental testing have been progressing in parallel throughout the project. In this contribution both the finite element and the experimental aspects of the project will be presented. The constitutive model has been implemented in the finite element system INSAP. The system has been used to simulate the initiation and propagation of damage in two flexible pavement structures due to repeated loading. The simulations illustrate the influence of geometry and material characteristics on the development of damage.     

Damage Diagnosis Using Experimental Ritz Vectors

This paper describes an experimental study on the use of Ritz vectors for damage detection of a grid-type bridge model. A new procedure to extract Ritz vectors from experimental modal analysis is proposed and demonstrated using the test structure. The extracted Ritz vectors are then used for the damage detection of the test structure using a Bayesian probabilistic approach. Using appropriate load patterns, Ritz vectors can be made more sensitive to damage than modal vectors. The results indicate that the use of load-dependent Ritz vectors produce better damage diagnoses than the modal vectors. The Bayesian probabilistic approach is shown to give better diagnostic results than commonly used deterministic methods.     

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.     

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.     

Nonlinear Identification of Lumped-Mass Buildings Using Empirical Mode Decomposition and Incomplete Measurement

Most structures exhibit some degrees of nonlinearity such as hysteretic behavior especially under damage. It is necessary to develop applicable methods that can be used to characterize these nonlinear behaviors in structures. In this paper, one such method based on the empirical mode decomposition (EMD) technique is proposed for identifying and quantifying nonlinearity in damaged structures using incomplete measurement. The method expresses nonlinear restoring forces in semireduced-order models in which a modal coordinate approach is used for the linear part while a physical coordinate representation is retained for the nonlinear part. The method allows the identification of parameters from nonlinear models through linear least-squares. It has been shown that the intrinsic mode functions (IMFs) obtained from the EMD of a response measured from a nonlinear structure are numerically close to its nonlinear modal responses. Hence, these IMFs can be used as modal coordinates as well as provide estimates for responses at unmeasured locations if the mode shapes of the structure are known. Two procedures are developed for identifying nonlinear damage in the form of nonhysteresis and hysteresis in a structure. A numerical study on a seven-story shear-beam building model with cubic stiffness and hysteretic nonlinearity and an experimental study on a three-story building model with frictional magnetoreological dampers are performed to illustrate the proposed method. Results show that the method can quite accurately identify the presence as well as the severity of different types of nonlinearity in the structure.     

Investigation of a System Identification Methodology in the Context of the ASCE Benchmark Problem

This article briefly presents the theory for a system identification and damage detection algorithm for linear systems, and discusses the effectiveness of such a methodology in the context of a benchmark problem that was proposed by the ASCE Task Group in Health Monitoring. The proposed approach has two well-defined phases: (1) identification of a state space model using the Observer/Kalman filter identification algorithm, the eigensystem realization algorithm, and a nonlinear optimization approach based on sequential quadratic programming techniques, and (2) identification of the second-order dynamic model parameters from the realized state space model. Structural changes (damage) are characterized by investigating the changes in the second-order parameters of the “reference” and “damaged” models. An extensive numerical analysis, along with the underlying theory, is presented in order to assess the advantages and disadvantages of the proposed identification methodology.     

Terrestrial Laser Scanning-Based Structural Damage Assessment

Terrestrial laser scanning (TLS) provides a rapid, remote sensing technique to model 3D objects. Previous work applying TLS to structural analysis has demonstrated its effectiveness in capturing simple beam deflections and modeling existing structures. This paper extends TLS to the application of damage detection and volumetric change analysis for a full-scale structural test specimen. Importantly, it provides a framework necessary for such applications, in combination with an analysis approach that does not require tedious development of complex surfaces. Intuitive slicing analysis methods are presented, which can be automated for rapid generation of results. In comparison with conventional photographic and surface analysis methods, the proposed approach proved consistent. Furthermore, the TLS data provided additional insight into geometric change not apparent using conventional methods. As with any digital record, a key benefit to the proposed approach is the resulting virtual test specimen, which is available for posttest analysis long after the original specimen is demolished. Uncertainties that can be introduced from large TLS data sets, mixed pixels and parallax in the TLS analysis are also discussed.     

Application of Neural Networks for Detection of Changes in Nonlinear Systems

A nonparametric structural damage detection methodology based on nonlinear system identification approaches is presented for the health monitoring of structure-unknown systems. In its general form, the method requires no information about the topology or the nature of the physical system being monitored. The approach relies on the use of vibration measurements from a “healthy” system to train a neural network for identification purposes. Subsequently, the trained network is fed comparable vibration measurements from the same structure under different episodes of response in order to monitor the health of the structure and thereby provide a relatively sensitive indicator of changes (damage) in the underlying structure. For systems with certain topologies, the method can also furnish information about the region within which structural changes have occurred. The approach is applied to an intricate mechanical system that incorporates significant nonlinear behavior typically encountered in the applied mechanics field. The system was tested in its “virgin” state as well as in “damaged” states corresponding to different degrees of parameter changes. It is shown that the proposed method is a robust procedure and a practical tool for the detection and overall quantification of changes in nonlinear structures whose constitutive properties and topologies are not known.     

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.     

Three-Dimensional Micromechanics-Based Constitutive Framework for Analysis of Pultruded Composite Structures

A new 3D micromechanics-based framework is proposed for the nonlinear analysis of pultruded fiber-reinforced polymeric composites. The proposed 3D modeling framework is a nested multiscale approach that explicitly recognizes the response of the composite systems (layers) within the cross section of the pultruded member. These layers can have reinforcements in the form of roving, continuous filament mat (CFM), and∕or woven fabrics. Different 3D micromechanical models for the layers can be used to recognize the basic response of the fiber and matrix materials. The framework is implemented with both shell and 3D finite elements. The 3D lamination theory is used to generate a homogenized nonlinear effective response for a through-thickness representative stacking sequence. The proposed modeling framework for pultruded composites is used to predict the stiffness and nonlinear stress-strain response of E-glass∕vinylester pultruded materials reinforced with roving and CFM. The roving layer is idealized using a 3D nonlinear micromechanics model for a unidirectional fiber-reinforced material. A simple nonlinear micromechanics model for the CFM layer is also applied. The proposed model shows very good predictive capabilities of the overall effective properties and the nonlinear response of pultruded composites, based on the in situ material properties, and the volume fractions of the constituents. Experimental data from off-axis tests of pultruded plates under uniaxial compression are used to verify the proposed model. The proposed framework can be easily incorporated within displacement-based finite-element models of composite structures.