Multiple Damage Cases Research Articles

An efficient method for structural damage localization based on the concepts of flexibility matrix and strain energy of a structure

An efficient method is proposed here to identify multiple damage cases in structural systems using the concepts of flexibility matrix and strain energy of a structure. The flexibility matrix of the structure is accurately estimated from the first few mode shapes and natural frequencies. Then, the change of strain energy of a structural element, due to damage, evaluated by the columnar coefficients of the flexibility matrix is used to construct a damage indicator. This new indicator is named here as flexibility strain energy based index (FSEBI). In order to assess the performance of the proposed method for structural damage detection, two benchmark structures having a number of damage scenarios are considered. Numerical results demonstrate that the method can accurately locate the structural damage induced. It is also revealed that the magnitudes of the FSEBI depend on the damage severity.

A new flexibility-based damage index for structural damage detection

A new flexibility-based damage index has been proposed for structural damage detection. It is derived from the strain energy theory that the ratio of the flexural stiffness of the structure before and after damage is a function of the uniform load surface (ULS) curvature. The novelties of the proposed damage index lie in the following aspects: (1) the proposed method directly uses the deflection which is predicted from an advanced signal processing procedure, while the modal shape is approximately used to replace the deflection in the strain energy calculation for damage detection in the literature; (2) the scaling factor calculated during flexibility identification is used to weight each mode for damage detection, unlike the damage index in the literature equally weighting all modes for structural damage detection. Examples of a 12-story building model and a T-beam bridge model illustrate that the proposed damage index successfully detects structural damage locations in both the single- and multiple-damage cases.

Spatial Wavelet Approach to Local Matrix Crack Detection in Composite Beams with Ply Level Material Uncertainty

Wavelet coefficients based on spatial wavelets are used as damage indicators to identify the damage location as well as the size of the damage in a laminated composite beam with localized matrix cracks. A finite element model of the composite beam is used in conjunction with a matrix crack based damage model to simulate the damaged composite beam structure. The modes of vibration of the beam are analyzed using the wavelet transform in order to identify the location and the extent of the damage by sensing the local perturbations at the damage locations. The location of the damage is identified by a sudden change in spatial distribution of wavelet coefficients. Monte Carlo Simulations (MCS) are used to investigate the effect of ply level uncertainty in composite material properties such as ply longitudinal stiffness, transverse stiffness, shear modulus and Poisson’s ratio on damage detection parameter, wavelet coefficient. In this study, numerical simulations are done for single and multiple damage cases. It is observed that spatial wavelets can be used as a reliable damage detection tool for composite beams with localized matrix cracks which can result from low velocity impact damage.

A frequency response function change method for damage localization and quantification in a shear building under ground excitation

ABSTRACTA frequency response function change (FRFC) method to detect damage location and extent based on the change in the frequency response functions of a shear building under the effects of ground excitation was proposed in this paper. The damage identification equation was derived from the motion equations of the system before and after the occurrence of the damage. Efforts to make the FRFC method less model‐dependent were made. Intact system matrices, which could be estimated using the measured data without the need for an analytical model, and the frequency response functions were required for the FRFC method. The effects of measurement noise and model parameter error in the FRFC method were studied numerically. The proposed FRFC method was validated by experimental studies of a six‐story steel building structure with single and multiple damage cases. Copyright © 2012 John Wiley & Sons, Ltd.

Impedance-based structural health monitoring incorporating neural network technique for identification of damage type and severity

Impedance-based structural health monitoring (SHM) has come to the forefront in the SHM community because of its practical potential for real applications. In the impedance-based SHM technique, it is very important to select the optimal frequency range most sensitive to the expected structural damage, and more quantitative information on the structural damages might be needed compared to the conventional damage index. Therefore, this study proposes an innovative neural network (NN)-based pattern analysis tool (1) to identify damage-sensitive frequency ranges autonomously and (2) to provide detailed information such as the damage type and severity. The importance of selecting the optimal frequency range was first investigated experimentally using a simply-supported aluminum beam. The performance of the proposed NN-based approach was validated throughout damage identifications of loose bolts and notches on a bolt-jointed aluminum beam and a lab-scale pipe structure. Finally, the proposed NN-based algorithm was embedded into a wireless impedance sensor node to detect real damage in a full-scale bridge. Overall, the proposed approach incorporating a wireless impedance sensor node was used to evaluate the damage type and severity in multi-type and multiple structural damage cases.

Damage identification in beams using discrete wavelet transforms

Researchers, over the years, have done extensive research on damage identification. In the recent years, there has been an increased impetus to conduct research on damage identification using wavelet transforms. In the present work, discrete wavelet transform (DWT) has been used to detect, locate and quantify damage in beam elements. A generalised method has been proposed to solve damage identification in beams with a single dominant crack. The proposed quantification methodology uses only the measurements made in the current (damaged) state of the beam structure. The generalised method has been proposed using a Damage Intensity Factor (DIF) to quantify damage in all beams with similar edge conditions. Formulae have also been proposed to help in quantifying the damage in simply supported and fixed beams. The proposed method has been validated using problems taken from the literature. The applicability of the proposed method to solve multiple damage cases has been demonstrated using literature problems.

A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization

A two-stage method is proposed here to properly identify the site and extent of multiple damage cases in structural systems. In the first stage, a modal strain energy based index ( MSEBI) is presented to precisely locate the eventual damage of a structure. The modal strain energy is calculated using the modal analysis information extracted from a finite element modeling. In the second stage, the extent of actual damage is determined via a particle swarm optimization (PSO) using the first stage results. Two illustrative test examples are considered to assess the performance of the proposed method. Numerical results indicate that the combination of MSEBI and PSO can provide a reliable tool to accurately identify the multiple structural damage.

Parameter subset selection based damage detection of aluminium frame structure

A three storey aluminium frame structure was tested in multiple damage cases. All damage scenarios, simulated by the localized stiffness changes, were associated with joint areas of the structure. Further, between damage tests the structure was returned to its healthy reference conditions and was again measured. In this paper, a parameter subset selection methodology is applied to an updated finite element model of the structure, together with a previously demonstrated approach employing concepts of model sensitivity subspace angles, first order model representation and mixed response residuals for damage detection. The objective of this paper is the evaluation of these methods on a real experimental structure with significant complexity, represented by an imprecise reference mathematical model and in the environment with uncertain reference structural state. The questions of symmetry, mixed response residuals and semi-localized parameterization are also addressed in this work.

Classification of multi-site damage using support vector machines

Pattern recognition is now well-known to be a powerful approach to addressing the higher levels of damage identification e.g. location and severity assessment of damage. However, a major problem in implementation for real structures is the need for training data associated with all possible damage states. Even if appropriate data were available for individual damage states, the combinatorial explosion in states which occurs when multiple simultaneous damages are present would usually prohibit a pattern recognition approach. One approach to the solution of this problem is to construct classifiers on the basis of single damage data which will generalise to multiple damage states; the current paper is a very preliminary step in this direction. In the first part, a comprehensive multiple damage feature database is established as the result of an experimental campaign on a full-sized aircraft wing structure; in the second part, a classifier based on the support vector machine paradigm is investigated. The paper also considers how data visualisation can shed light on which features are likely to generalise best from the single damage problem to the multiple damage case.

Dynamic reduction-based structural damage detection of transmission towers: Practical issues and experimental verification

Structural damage detection in large-scale three-dimensional spatial structures is a challenging problem. It is impractical to develop a general damage-detection method that is applicable to all types of structural systems and all kinds of damage. A practical and efficient structural damage detection method must consider the characteristics of the target structure and damage in the development stage. In 2009, Yin et al. [33] proposed a damage detection method for the health monitoring of transmission towers. The method was developed based on the dynamical finite element (FE) model reduction technique, which utilizes identified modal parameters, such as natural frequencies and mode shapes, with only a limited number of sensors. In Ref. [33], the proposed method was numerically verified by simulated noisy data from a three-dimensional transmission tower model for single and multiple damage cases. This paper discusses some practical issues related to the proposed method, such as sensor placement and computational efficiency. Rather than proposing a general sensor placement method, a set of preliminary sensor locations is determined based on engineering judgement. This set of sensor locations is then checked against the results of a sensitivity analysis to ensure that the measured data contain information for identifying all of the target damage scenarios. To reduce the required computational power, two simplified versions of the proposed method are presented. The proposed method is then verified with a scaled-down model of a transmission tower (2.4 m high) that was built at the Structural Vibration Laboratory (SVL) of the City University of Hong Kong. This paper reports the detailed experimental setup and the method of extracting the modal parameters from a series of free vibration tests with only a limited number of sensors. The verification results show that the proposed damage detection method identifies the damaged sub-structures in all of the experimental cases considered. It must be pointed out that the transmission tower structure, in its operating conditions, suffers from the effect of the forces transmitted from the cables it carries. The influence of this force on the damage identification result is great and can not be neglected in practice. In the present experimental case study, only a transmission tower-like structure without carrying the cables is investigated in laboratory conditions.

Damage detection of shear buildings using deflections obtained by modal flexibility

This paper presents a vibration-based damage detection method for shear buildings usingthe damage-induced deflections estimated by modal flexibility from ambient vibrationmeasurements. This study intends to provide a basis for the damage detectionproblem of more complex building structures by investigating a rather idealizedstructure, a shear building. From analytical investigations on the damage-inducedinter-story deflection (DI-ID) of shear buildings, it was shown that the DI-IDoccurs only at damaged floors and not at intact floors as long as a proper load isapplied to the building. To simplify the damage detection procedure a new loadconcept, the positive shear inspection load (PSIL), was proposed, defined as aload producing positive shear forces at all floors. It was shown that an excessiveDI-ID under a PSIL indicates the existence of damage to the building and thatthe floors with excessive DI-ID are the damaged floors. A simple damage indexZi isproposed based on outlier analysis to account for measurement noise. Numerical and experimentalstudies on a 5-story shear building were carried out for two damage scenarios with 10% columnEI reductions. The proposed method was found to identify the damage locations successfullyfor the multiple damage case as well as the single damage case, with no false-positive orfalse-negative detections. For the purpose of comparison, damage detection was alsoconducted using the damage index method and the mode shape curvature method. Themode shape curvature method was found to be the most sensitive metric, but it showedfalse-positive detections on an undamaged floor. The damage index method had nofalse-positive detections, but it was found to miss some damage in the multiple damagecase.

Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic

Uncertainties associated with the structural model and measured vibration data may lead to unreliable damage detection. In this paper, we show that geometric and measurement uncertainty cause considerable problem in damage assessment which can be alleviated by using a fuzzy logic-based approach for damage detection. Curvature damage factor (CDF) of a tapered cantilever beam are used as damage indicators. Monte Carlo simulation (MCS) is used to study the changes in the damage indicator due to uncertainty in the geometric properties of the beam. Variation in these CDF measures due to randomness in structural parameter, further contaminated with measurement noise, are used for developing and testing a fuzzy logic system (FLS). Results show that the method correctly identifies both single and multiple damages in the structure. For example, the FLS detects damage with an average accuracy of about 95 percent in a beam having geometric uncertainty of 1 percent COV and measurement noise of 10 percent in single damage scenario. For multiple damage case, the FLS identifies damages in the beam with an average accuracy of about 94 percent in the presence of above mentioned uncertainties. The paper brings together the disparate areas of probabilistic analysis and fuzzy logic to address uncertainty in structural damage detection.

Dynamic reduction-based structural damage detection of transmission tower utilizing ambient vibration data

This paper reports a feasibility study of utilizing ambient vibration data measured from a limited number of sensors in the structural damage detection of transmission towers, which are large-scaled three-dimensional spatial structures. To develop a practical and efficient structural damage detection methodology, the characteristics of transmission towers are considered in the development stage, including the most common types of damage, accessible locations for installing sensors, the technique needed to identify a reliable set of modal parameters utilizing ambient vibration data, a method to divide the transmission tower into sub-structures for structural damage detection, a way to formulate the damage detection problem, and the corresponding solution method. The proposed methodology is numerically verified by simulated noisy data from a three-dimensional transmission tower sample under both single and multiple damage cases. Very encouraging results are obtained, showing that the proposed methodology can identify the damaged sub-structure by estimating the ‘equivalent’ stiffness reduction even in the presence of both measurement noise and modeling error.

Experimental validation of modal strain energies based damage identification method for a composite sandwich beam

A vibration-based damage identification method, based on changes in modal strain energies before and after occurrence of damage, is presented for a composite sandwich beam. Experiments were performed to obtain the natural frequencies and mode shapes for validation of the presented method. The observed changes in modal strain energies were used for the prediction of existence and location of damage in a composite sandwich beam. Subsequently, these changes were also used to predict damage extents in the two stages. In the first stage, the proposed method is used to approximate the damage extents in the face and core. These were updated to obtain more accurate values of damage extent at the second stage by using the model updating theory. Experimental and numerical results were presented to demonstrate and verify the effectiveness of this method for several single and multiple damage cases. These damage cases also include interactive damage modes. Results indicate that the proposed method is capable of identifying the location and extent of damage in the faces and core of a composite sandwich beam.

Modeling Guided Waves for Damage Identification in Isotropic and Orthotropic Plates Using a Local Interaction Simulation Approach

In this paper, a numerical simulation technique based on the local interaction simulation approach (LISA)/sharp interface model (SIM) is used to study the propagation of Lamb waves in aluminum and orthotropic plates and wave interactions with damage. The LISA/SIM model allows for accurate and fast simulations of sharp changes in material properties across interfaces associated with damage or specimen boundaries. Damage in the form of holes and changes in density and/or stiffnesses are studied for three different plates. These local changes in density and stiffness have dimensions not exceeding the wave length of the interrogating wave form. Wave scatter from these damage sites is shown at different time instants and at specific spatial locations. Multiple site damage cases are studied for all the plate structures. The different scatter patterns associated with intersecting and nonintersecting surface cracks are also studied. Results obtained from a combination of single site damage cases are compared with the composite multiple site damage case to study the usability of commonly applied algorithms for identifying damage. The benefits of observing multiple directions of the displacement field are demonstrated. It is shown that the out-of-plane measurements give a clearer indication of damage sites than the in-plane measurements.

Damage localisation and severity evaluation of a beam-like timber structure based on modal strain energy and flexibility approaches

Timber bridges are often exposed to harsh environmental conditions, which, over time, can lead to deterioration resulting from decay, insect attack, weathering, and mechanical damage. In turn, this deterioration may lead to a loss of structural integrity that is detrimental to the structure and its users. Non-destructive evaluation (NDE) techniques provide effective means for assessment of current structural integrity status of given structures. As a global NDE technique, vibration-based damage identification techniques have received increasing attention for structural damage evaluation. Among them, there is a popular and promising damage identification method called the damage index method based on calculating the change of modal strain energy before and after damage. Despite its popularity, however, a systematic investigation on its capability and limitations in locating and quantifying damage is yet to be reported, especially for structures suffering multiple damage. In this paper, after reviewing the current NDE methods, the focus was set on the vibration-based NDE methods, in particular the damage index method. The investigation was based on finite element analysis (FEA) results of a timber beam by which the capability and limitation of the damage index was fully explored. As a result of the investigation, a new hybrid algorithm combining modified damage index (MDI) and change in flexibility algorithms is proposed for damage localisation and severity evaluation. The numerical results indicate that the proposed hybrid algorithms based on MDI method and flexibility have clear advantages in detecting damage locations and evaluating damage severities, especially for multiple damage cases.

Structural damage detection using neural network with learning rate improvement

In this research, we explore the structural damage detection using frequency response functions (FRFs) as input data to the back-propagation neural network (BPNN). Such method is non-model based and thus could have advantage in many practical applications. Neural network based damage detection generally consists of a training phase and a recognition phase. Error back-propagation algorithm incorporating gradient method can be applied to train the neural network, whereas the training efficiency heavily depends on the learning rate. While various training algorithms, such as the dynamic steepest descent (DSD) algorithm and the fuzzy steepest descent (FSD) algorithm, have shown promising features (such as improving the learning convergence speed), their performance is hinged upon the proper selection of certain control parameters and control strategy. In this paper, a tunable steepest descent (TSD) algorithm using heuristics approach, which improves the convergence speed significantly without sacrificing the algorithm simplicity and the computational effort, is investigated. A series of numerical examples demonstrate that the proposed algorithm outperforms both the DSD and FSD algorithms. With this as basis, we implement the neural network to the FRF based structural damage detection. The analysis results on a cantilevered beam show that, in all considered damage cases (i.e., trained damage cases and unseen damage cases, single damage cases and multiple-damage cases), the neural network can assess damage conditions with very good accuracy.

Comparative study of damage identification algorithms applied to a bridge: II. Numerical study

This paper extends the study of damage identification algorithms summarized in the accompanying paper `Comparative study of damage identification algorithms: I. Experiment' to numerical examples. A finite element model of a continuous three-span portion of the I-40 bridges, which once crossed the Rio Grande in Albuquerque, NM, was constructed. Dynamic properties (resonant frequencies and mode shapes) of the undamaged and damaged bridge that were predicted by the numerical models were then correlated with experimental modal analysis results. Once correlated with the experimental results, eight new damage scenarios were introduced into the numerical model including a multiple damage case. Also, results from two undamaged cases were used to study the possibility that the damage identification methods would produce false-positive readings. In all cases analytical modal parameters were extracted from time-history analyses using signal processing techniques similar to those used in the experimental investigation. This study provides further comparisons of the relative accuracy of these different damage identification methods when they are applied to a set of standard numerical problems.