Damage Detection of Regular Civil Buildings Using Modified Multi-Scale Symbolic Dynamic Entropy

Based on the examination of the fundamental characteristics of structures, structural health monitoring (SHM) has received increased attention in recent years. Studies have shown that the SHM method using entropy analysis can precisely identify the damaged location of the structure, which is very helpful for the daily inspection or maintenance of civil structures. Although entropy analysis has shown excellent accuracy, it still consumes too much time and too many resources in terms of data processing. To improve the dilemma, in this study, modified multi-scale symbolic dynamic entropy (MMSDE) is adopted to identify the damaged location of the civil structure. A damage index (DI) based on the entropy diagram is also proposed to clearly indicate the damage location. A seven-story numerical model was created to verify the efficiency of the proposed SHM system. The results of the analysis of each case of damage show that the MMSDE curve for the damaged floor is lower than that for the healthy floor, and the structural damage can be correctly diagnosed by the damage index. Subsequently, a scaled-down steel benchmark experiment, including 15 damage cases, was conducted to verify the practical performance of the SHM system. The confusion matrix was used to further evaluate the SHM system. The results demonstrated that the MMSD-based system can quickly diagnose structural safety with reliability and accuracy. It can be used in the field of long-term structural health monitoring in the near future.     

Structural damage detection of controlled building structures using frequency response functions

If a building structure requires both a vibration control system and a health monitoring system, the integration of the two systems will be cost-effective and beneficial. One of the key problems of this integrated system is how to use control devices to enhance system identification and damage detection. This paper presents a new method for system identification and damage detection of controlled building structures equipped with semi-active friction dampers through model updating based on frequency response functions. The two states of the building are first created by adding a known stiffness using semi-active friction dampers. A scheme based on the frequency response functions of the two states of the building is then presented to identify stiffness parameters of structural members in consideration of structural connectivity and transformation information. By applying the proposed model updating scheme to the damaged building, a damage detection scheme is proposed based on the identified stiffness parameters of structural members of both the original and damaged buildings. The feasibility of the proposed schemes is finally demonstrated through a detailed numerical investigation in terms of an example building, in which the effects of measurement noise and excitation conditions are discussed. The numerical results clearly show that the proposed method can locate and quantify damage satisfactorily even though measurement noise is taken into consideration.     

GUW-based structural damage detection using WPT statistical features and multiclass SVM

Recently, guided ultrasonic waves (GUW) are widely used for damage detection in structural health monitoring (SHM) of different engineering structures. In this study, an intelligent damage detection method is proposed to be used in SHM applications. At first, GUW signal is de-noised by discrete wavelet transform (DWT). After that, wavelet packet transform (WPT) is employed to decompose the de-noised signal and the statistical features of decomposed packets are extracted as damage-sensitive features. Finally, a multiclass support vector machine (SVM) classifier is used to detect the damage and estimate its severity. The proposed method is employed for GUW-based structural damage detection of a thick steel beam. The effects of different parameters on the sensitivity of the method are surveyed. Furthermore, by comparing with some other similar algorithms, the performance of the proposed method is verified. The experimental results demonstrate that the proposed method can appropriately detect a structural damage and estimate its severity.     

Identification of embedded horizontal cracks in beams using measured mode shapes

Mode shapes (MSs) have been extensively used to detect structural damage. This paper presents two new non-model-based methods that use measured MSs to identify embedded horizontal cracks in beams. The proposed methods do not require any a priori information of associated undamaged beams, if the beams are geometrically smooth and made of materials that have no stiffness discontinuities. Curvatures and continuous wavelet transforms (CWTs) of differences between a measured MS of a damaged beam and that from a polynomial that fits the MS of the damaged beam are processed to yield a curvature damage index (CDI) and a CWT damage index (CWTDI), respectively, at each measurement point. It is shown that the MS from the polynomial fit can well approximate the measured MS and associated curvature MS of the undamaged beam, provided that the measured MS of the damaged beam is extended beyond boundaries of the beam and the order of the polynomial is properly chosen. The proposed CDIs of a measured MS are presented with multiple resolutions to alleviate adverse effects caused by measurement noise, and cracks can be identified by locating their tips near regions with high values of the CDIs. It is shown that the CWT of a measured MS with the n-th-order Gaussian wavelet function has a shape resembling that of the n-th-order derivative of the MS. The crack tips can also be located using the CWTs of the aforementioned MS differences with second- and third-order Gaussian wavelet functions near peaks and valleys of the resulting CWTDIs, respectively, which are presented with multiple scales. A uniform acrylonitrile butadiene styrene (ABS) cantilever beam with an embedded horizontal crack was constructed to experimentally validate the proposed methods. The elastic modulus of the ABS was determined using experimental modal analysis and model updating. Non-contact operational modal analysis using acoustic excitations and measurements by two laser vibrometers was performed to measure the natural frequencies and MSs of the ABS cantilever beam, and the results compare well with those from the finite element method. Numerical and experimental crack identification can successfully identify the crack by locating its tips.     

Vibrational wave analysis of infinite damaged beams using structure-borne power flow

In the view of structure-borne sound, vibrational wave analysis of infinite beam structures with a transverse open damage by means of vibrational power flow is investigated. In this paper, the damage is modeled as a joint of a local spring with a constant value that is deduced from the relationship between the strain energy and stress intensity factor in fracture mechanics, then the input power flow and transmitted power flow of perfect and dmaged beams are computed. The results show that the vibrational power flow of damaged beam is highly relative to the degree and location of damage.     

Structural damage evolution assessment using the regularised time step integration method

This paper presents an approach to identify both the location and severity evolution of damage in engineering structures directly from measured dynamic response data. A relationship between the change in structural parameters such as stiffness caused by structural damage development and the measured dynamic response data such as accelerations is proposed, on the basis of the governing equations of motion for the original and damaged structural systems. Structural damage parameters associated with time are properly chosen to reflect both the location and severity development over time of damage in a structure. Basic equations are provided to solve the chosen time-dependent damage parameters, which are constructed by using the Newmark time step integration method without requiring a modal analysis procedure. The Tikhonov regularisation method incorporating the L-curve criterion for determining the regularisation parameter is then employed to reduce the influence of measurement errors in dynamic response data and then to produce stable solutions for structural damage parameters. Results for two numerical examples with various simulated damage scenarios show that the proposed method can accurately identify the locations of structural damage and correctly assess the evolution of damage severity from information on vibration measurements with uncertainties.     

THE CHARACTERISTIC RECEPTANCE METHOD FOR DAMAGE DETECTION IN LARGE MONO-COUPLED PERIODIC STRUCTURES

An approach based on the concept of wave propagation to detect the structural damage in large mono-coupled periodic structures is presented in this paper. The free vibration analysis of a finite mono-coupled periodic structure with a single disorder has been conducted by the characteristic receptance method, and the sensitivity of the natural frequencies to the disorder in flexibility has been discussed. Based on the sensitivity analysis, the locations and magnitude of damage in large mono-coupled periodic systems have been estimated using measured changes in the natural frequencies. The paper also introduces a substructure-based method for improving the computational efficiency and the accuracy of damage detection in large mono-coupled periodic structures. Numerical results from two periodic mass-spring-structures show that the proposed method can provide good predictions of both the locations and magnitude of damage at one or more sites. Furthermore, the proposed method, in which a priori information about the nature such as stiffness of the undamaged structure is not needed, and only measurements of the change in a few of the structure's natural frequencies between the undamaged and damaged states are required, is particularly attractive in practice. However, some issues such as the role of noise in actual measurements, application to multi-coupled periodic structures with complex boundary conditions remain to be resolved before this approach becomes a truly variable method of structural damage assessment.     

Damage identification in beam type structures based on statistical moment using a two step method

This paper defines a novel damage index-strain statistical moment, and formulates the fourth strain statistical moment (FSSM) of beam-type structures under white noise excitation. Based on this newly defined strain statistical moment index and the least square optimization algorithm, a two-step damage identification method is proposed. This two-step method is operated like this: first use the difference curves of FSSMs before and after damage to locate damage elements; then for those identified damage elements, employ the model updating method based on the least square algorithm to assess their damage severity. Numerical studies on a simply supported beam and a two-span continuous beam are performed and the study results show that the newly defined index is effective to locate damages, even when the noise intensity is as high as 15 percent. Integrating with the least square-based model updating technique, the damage severities of beam-type structures can also be determined quantitatively. In this way, the proposed two-step method is verified and found to be capable of identifying damage positions and severities of beam-type structures and insensitive to measurement noise.     

Reference-free impedance-based crack detection in plates

Impedance-based damage detection techniques gained popularity among structural health monitoring (SHM) and nondestructive testing (NDT) communities due to their sensitivity to local damage and applicability to complex structures. In general, conventional impedance-based techniques identify damage by comparing “current” impedance signals with “baseline” ones obtained from the pristine condition of a structure. However, in-situ structures are often subject to changing temperature and loading conditions that can adversely affect measured impedance signals and cause false-alarms. In this paper, a “reference-free” impedance method, which does not require direct comparison of the current impedance signals with the previously obtained baseline impedance signals, is developed for crack detection in a plate-like structure. The proposed technique utilizes a single pair of PZTs collocated on the opposite surfaces of a structure to extract mode conversion produced by crack formation. Then, a reference-free damage classifier is developed and performed on the extracted mode conversion for instantaneous damage diagnosis. Numerical simulations and experimental tests have been conducted explicitly considering varying temperature and loading conditions to demonstrate the robustness of the proposed damage detection technique under varying operational and environmental conditions.     

Debonding detection of honeycomb sandwich structures using frequency response functions

A vibration-based non-destructive evaluation (NDE) method is proposed to determine the location and size of debonding in honeycomb sandwich beams. Although most of the existing vibration-based NDE methods need many measurement points, the method proposed here only utilizes the frequency response function (FRF) measured at one point. A parameterized damaged Timoshenko beam model is developed with the method of reverberation-ray matrix (MRRM) for the first time, and combined with the genetic algorithm (GA) to inverse the damage parameters from the measured FRF. The detection of a honeycomb sandwich beam can be divided into two steps: (1) identifying the equivalent elastic moduli and other parameters of the intact sandwich beam. (2) Identifying the debonding location and size of the damaged sandwich beam with the predetermined parameters. It is demonstrated experimentally that the method can inverse damage parameters with acceptable precision.     

Damage identification in plates using finite element model updating in time domain

A response sensitivity-based approach is presented for identifying the local damages in isotropic plate structures from the measured structural dynamic responses. The local damage is simulated by a reduction in the elemental Young's modulus of the plate. In the forward analysis, the forced vibration responses of the plate under external force are obtained from Newmark direct integration. In the inverse analysis, a response sensitivity-based finite element model updating approach is used to identify local damages of the plate in time domain. The damage identification results are obtained iteratively with the penalty function method with Tikhonov regularization using the measured structural dynamic responses. Two numerical examples are investigated to illustrate the correctness and efficiency of the proposed method. Both single damage and multiple damages cases are studied. The effects of measurement noise and measurement point on the identification results are investigated. Studies in this paper indicate that the proposed method is efficient and robust for both single and multiple damages for plate structures. Good identified results can be obtained from the short time histories of a few number of measurement points.     

Structural damage measure index based on non-probabilistic reliability model

Uncertainties in the structural model and measurement data affect structural condition assessment in practice. As the probabilistic information of these uncertainties lacks, the non-probabilistic interval analysis framework is developed to quantify the interval of the structural element stiffness parameters. According to the interval intersection of the element stiffness parameters in the undamaged and damaged states, the possibility of damage existence is defined based on the reliability theory. A damage measure index is then proposed as the product of the nominal stiffness reduction and the defined possibility of damage existence. This new index simultaneously reflects the damage severity and possibility of damage at each structural component. Numerical and experimental examples are presented to illustrate the validity and applicability of the method. The results show that the proposed method can improve the accuracy of damage diagnosis compared with the deterministic damage identification method.     

Statistical damage identification of structures with frequency changes

Model updating methods based on structural vibration data have being rapidly developed and applied to detect structural damage in civil engineering. But uncertainties existing in the structural model and measured vibration data might lead to unreliable damage detection. In this paper a statistical damage identification algorithm based on frequency changes is developed to account for the effects of random noise in both the vibration data and finite element model. The structural stiffness parameters in the intact state and damaged state are, respectively, derived with a two-stage model updating process. The statistics of the parameters are estimated by the perturbation method and verified by Monte Carlo technique. The probability of damage existence is then estimated based on the probability density functions of the parameters in the two states. A higher probability statistically implies a more likelihood of damage occurrence. The presented technique is applied to detect damages in a numerical cantilever beam and a laboratory tested steel cantilever plate. The effects of using different number of modal frequencies, noise level and damage level on damage identification results are also discussed.     

Time reversal of flexural waves in a beam at audible frequency

There has been very limited work on the application of time reversal to the propagation of audible frequency waves in mechanical structures. The present work concentrates on the application of time reversal to the focusing of audible range, flexural waves in an infinite beam, and to the detection of local heterogeneity in such a beam. Practical applications of time reversal of flexural waves in structures include vibration energy focusing, detection of vibratory or acoustic sources, and detection of defects in mechanical structures. An analytical model of flexural wave propagation in the beam as well as sensing and emission using piezoelectric transducers is presented. Time reversal experiments are conducted and compared to the model results in either a homogeneous beam or a beam with point mass heterogeneities. In the various situations tested, it is shown that time reversal effectively compensates the spreading in time of the impulse due to the dispersive propagation of flexural waves. One interesting aspect of this property is the generation of large amplitude impulsive responses in the beam using remote actuators. Finally, the "Decomposition de l'Operateur de Retournement Temporel" approach is examined to detect and localize point mass scatterers in the beam.     

A generalized flexibility matrix based approach for structural damage detection

In this paper, a new structural damage detection approach based on changes in the generalized flexibility matrix is presented. The generalized flexibility matrix is first introduced; its sensitivity and change are then used to detect structural damage location and damage extent. Compared with the original flexibility matrix based approach, the effect of truncating higher-order modes can be considerably reduced in this new approach. Finally, a numerical example for a simply supported beam is used to illustrate the effectiveness of this proposed method.     

Guided waves for autonomous online identification of structural defects under ambient temperature variations

Ultrasonic guided waves that are excited by piezoelectric transducers can be used for the autonomous online identification of structural defects in thin structures. The proposed technique in this paper continuously analyzes a damage metric which is defined as the maximum residual amplitude of the differential signal. A special focus is on the decision making to discriminate the undamaged from the damaged state of the structure where the appropriate detection thresholds are derived statistically from the inverse cumulative distribution function of the damage metric during an initial training phase. An integrated trend analysis by means of the moving average mitigates the impact of statistical outliers and reduces the probability of erroneous identifications.Long-term measurements under ambient temperature variations have been conducted on an aluminum and a composite plate to study the properties of the proposed novelty detection framework. In this process the temperature effect was compensated by the well-known combination of optimal baseline selection (OBS) and baseline signal stretch (BSS). In case of the aluminum structure two artificial cracks with different sizes have been identified reliably. Consistent results were found on the composite specimen where an impact damage was identified for different excitation frequencies.     

Damage localization in linear-form structures based on sensitivity investigation for principal component analysis

This paper addresses the problem of damage detection and localization in linear-form structures. Principal component analysis (PCA) is a popular technique for dynamic system investigation. The aim of the paper is to present a damage diagnosis method based on sensitivities of PCA results in the frequency domain. Starting from frequency response functions (FRFs) measured at different locations on the structure; PCA is performed to determine the main features of the signals. Sensitivities of principal directions obtained from PCA to structural parameters are then computed and inspected according to the location of sensors; their variation from the healthy state to the damaged state indicates damage locations. It is worth noting that damage localization is performed without the need of modal identification. Influences of some features as noise, choice of parameter and number of sensors are discussed. The efficiency and limitations of the proposed method are illustrated using numerical and real-world examples.     

FRF-based damage localization method with noise suppression approach

In this paper a noise-robust damage identification method is presented for localization of structural damage in presence of heavy noise influences. The method works based on Frequency Response Functions (FRFs) of the damaged structure without any prior knowledge of the healthy state. The main innovation of this study starts with convolving FRFs with Gaussian kernel to suppress the noise. Denoised signals are then used to develop shape signals according to the second derivative of the operational mode shapes at frequencies in the half-power bandwidth of the center resonant frequencies. The scheme is followed by normalization of shape signals to create a two-dimensional map indicating the damage pattern. The validation of the method was carried out based on simulated data and experimental measurements. The simulated data polluted with 10 percent random noise considering four different conditions: (i) un-correlated noise with Gaussian distribution (ii) noise with non-Gaussian exponential distribution (iii) noise with non-Gaussian Log-normal distribution and (iv) correlated colored noise. The robustness of the method was examined with respect to the damage severity with various damage conditions. Finally, damage detection experiments of a fixed–fixed steel beam are presented to illustrate the feasibility and effectiveness of the proposed method. According to the numerical and experimental investigations, it was demonstrated that the proposed approach presents satisfactory damage indices both in single and multiple damage states in presence of high level noise. Hence, the method can overcome the problems of output measurement noise and deliver encouraging results on damage localization.     

VIBRATION-BASED DAMAGE IDENTIFICATION USING RECONSTRUCTED FRFS IN COMPOSITE STRUCTURES

This work aims to establish a vibration-based damage identification method for fiber-reinforced laminated composites and their sandwich construction. This new on-line structural damage identification technique uses the structural dynamic system reconstruction method exploiting the frequency response functions (FRFs) of a damaged structure. To verify the effectiveness of this damage identification method, the frequency responses obtained by vibration testing of fatigue-damaged laminated composites and honeycomb sandwich beams with debonding are examined according to the extent of the damage via the fatigue-damage load cycle for laminated composites, and via the debonding extent for honeycomb sandwich beams. The changes of the peaks and valley of the FRFs according to the debonding extent and the fatigue load cycles are examined, and the area changes in the FRFs are also discussed as the damage index. The residual FRFs or the difference between intact and damaged FRFs are newly defined for application of the on-line damage identification method. Finally, the delamination extent for the sandwich beams and the fatigue damage level for the laminated composites can be easily identified in terms of the changes in natural frequencies and damping ratios of the reconstructed FRFs for these damaged composite structures.