Damage Detection In Plate-like Structures Research Articles

A rapid localization technique for detecting multiple damages in plate-like structures with unknown material properties

When using Lamb wave for damage detection in plate-like structures, factors such as unknown material properties, anisotropy and iterative operation for solving nonlinear equations make it difficult to accurately localize damages. This problem becomes even more difficult when multiple damages exist in the plate. To overcome these difficulties, a rapid technique for localizing multiple damages in plate-like structures without any prior knowledge of direction-dependent velocity profile is proposed in this paper. The time difference of arrival is obtained by performing cross-correlation processing on the damage features extracted from the received signal. Damage artifacts are removed using relative location determination and relative probability density analysis. Multi-damage localization at different locations were simulated. The proposed technique is validated experimentally for steel plates. Simulation and experimental results show that the proposed technique can realize multiple damage localization in plate-like structures with unknown material properties. With the help of L-shaped sensor clusters, damage locations for isotropic and anisotropic materials can be quickly predicted without solving nonlinear equations and without taking into account the dispersion effects. The results suggest that a suitable threshold range is set to 0.5–0.7 to remove damage artifacts.

Phased Array System for Damage Detection in Plate-Like Structures Based on Single Lamb Wave Mode Extraction

Phased Array System for Damage Detection in Plate-Like Structures Based on Single Lamb Wave Mode Extraction

Damage assessment using the Lamb wave factorization method

The Lamb wave technique has been widely used for damage detection in plate-like structures. However, for two-dimensional (2D) defects like corrosions or one-dimensional (1D) defects like cracks, conventional Lamb wave-based methodology usually selects the detection algorithm in terms of the damage type, which is restricted if the defect remains unknown. To address the issues, this paper proposes a damage assessment approach based on the Lamb wave factorization method, which is a general method that can adapt to the detection of both 2D and 1D defects. In the process, both the forward-scattered wave across the inspection area and the wave back-scattered from the defect are used for detection, so that the enclosed rich information can be fully exploited. To measure the wave field of defect, a transducer array is firstly set around the inspection area, whose transducers would take turns to excite the Lamb wave while others remain listeners. On the basis, the scattered waves of all directions are then extracted and transformed from the time domain to frequency domain. Under a certain frequency, the inspection area is next visualized by sampling the area and solving the inverse scattering problem using the spectral data at each sampling point. By fusing the results of different frequency together, the final image can be eventually obtained. The method is then numerically investigated and also validated through experiments. The results demonstrate that it can give out the outline description of 2D defect and the size evaluation of 1D defect accurately, thus being an effective tool for damage assessment.

An efficient Lamb wave-based virtual refined time-reversal method for damage localization in plates using broadband measurements

This study proposes a modified virtual time-reversal (VTR) algorithm for baseline signal-free damage detection in plate-like structures. The physical actuation and sensing of Lamb waves are performed using a broadband Gaussian excitation instead of the conventional narrowband modulated tone burst excitations. The forward response and the reconstructed signal due to the time-reversal process for a narrowband input signal are then constructed virtually using the broadband transfer function. The method eliminates the possibility of numerical errors encountered in the conventional VTR method based on narrowband excitations. It is also more efficient than the traditional VTR algorithm because it can probe at multiple excitation frequencies using a single measurement for each sensing path. This modified VTR algorithm is employed in the recently developed refined time-reversal method (RTRM), which uses an extended signal length of the reconstructed signal for computing damage index (DI) and probes the structure at the best reconstruction frequency. The new method is termed the virtual refined time-reversal method (VRTRM). The DIs based on the VRTRM are used in the reconstruction algorithm for probabilistic inspection of defects to achieve baseline signal-free localization of damages. The efficacy of the proposed VRTRM for damage localization is experimentally verified with the established technique RTRM. Experiments are performed in an aluminium plate equipped with a network of surface-bonded piezoelectric patch transducers to illustrate the conventional VTR’s pitfalls and the modified VTR’s accuracy for a single mass damage scenario. The results show that the proposed VRTRM is as accurate as the established technique RTRM in estimating the reconstructed signals and localizing a block mass damage. Finally, the VRTRM is shown to localize in a dual damage scenario with excellent accuracy. In contrast, the conventional main mode-based VTR method fails to localize the damages with or without single-mode tuning.

Crack Detection in Plate-Like Structures Using Modal Strain Energy Method considering Various Boundary Conditions

Among vibration-based damage detection methods, one of the effective approaches for damage localization is the modal strain energy method. In this paper, the modal strain energy method is developed for damage detection in plate-like structures with various boundary conditions. Firstly, the theory of the modal strain energy method is briefly outlined. In order to overcome the limitation of measuring points, a central difference method is newly employed to compute the partial differential terms in the modal strain energy formula. Finite element analysis is conducted on an aluminum thin plate to obtain the mode shapes before and after the occurrence of damage. Feasibility of the proposed method is verified by investigating plates with different types of boundary conditions. A damage index is presented to identify the location and extent of crack in the plate-like structures. The analytical results show that the proposed method accurately identifies the crack in the plate structure with various types of boundary conditions by using appropriate mode shapes and damage threshold.

Mean local frequency-wavenumber estimation through synthetic time-reversal of diffuse Lamb waves

Inspection of the elastic properties of plate-like structures is an important and challenging problem in many engineering disciplines. There exist multiple non-destructive inspection techniques based on active ultrasonic transducers to tackle this problem. In recent years, the usefulness of passively induced waves has also been explored. It has been shown that the diffuse waves, often referred to as coda waves, carry profound information about the elastic properties of the supporting medium. They can effectively probe the volume of a medium due to multiple scattering and long propagation paths. Moreover, the measured diffuse field can be synthetically focused using the correlation of wavefield’s time histories. The local elastic properties of the medium can be inferred from the focal spot size.In this work, we demonstrate the algorithm of mean local frequency-wavenumber estimation through synthetic focusing of diffuse Lamb waves. We provide theoretical foundations for expanding the concept of mean frequency estimation in purely temporal signals to mean wavenumber estimation in a spatiotemporal Lamb wave field. The applicability of this approach for the damage detection in plate-like structures is demonstrated on aluminum and carbon fiber reinforced polymer (CFRP) plates with localized defects. Test samples are excited with sequences of white noise signals, to create optimal diffuse field conditions, and wavefield is captured using a Scanning Laser Doppler Vibrometer (SLDV). We show that the spatial maps of mean wavenumber allow for precise localization and sizing of damage.

Damage Sensitive PCA-FRF Feature in Unsupervised Machine Learning for Damage Detection of Plate-Like Structures

Damage detection is important in maintaining the integrity and safety of structures. The vibration-based Structural Health Monitoring (SHM) methods have been explored and applied extensively by researchers due to its non-destructive manner. The damage sensitivity of features used can significantly affect the accuracy of the vibration-based damage identification methods. The Frequency Response Function (FRF) was used as a damage sensitive feature in several works due to its rich yet compact representation of dynamic properties of a structure. However, utilizing the full size of FRFs in damage assessment requires high processing and computational time. A novel reduction technique using Principal Component Analysis (PCA) and peak detection on raw FRFs is proposed to extract the main damage sensitive feature while maintaining the dynamic characteristics. A rectangular Perspex plate with ground supports, simulating an automobile, was used for damage assessment. The damage sensitivity of the extracted feature, i.e. PCA-FRF is then evaluated using unsupervised [Formula: see text]-means clustering results. The proposed method is found to exaggerate the shift of damaged data from undamaged data and improve the repeatability of the PCA-FRF. The PCA-FRF feature is shown to have higher damage sensitivity compared to the raw FRFs, in which it yielded well-clustered results even for low damage conditions.

Output-Only Damage Detection in Plate-Like Structures Based on Proportional Strain Flexibility Matrix.

For engineering structures, strain flexibility-based approaches have been widely used for structural health monitoring purposes with prominent advantages. However, the applicability and robustness of the method need to be further improved. In this paper, a novel damage index based on differences in uniform load strain field (ULSF) is developed for plate-like structures. When estimating ULSF, the strain flexibility matrix (SFM) based on mass-normalized strain mode shapes (SMSs) is needed. However, the mass-normalized strain mode shapes (SMSs) are complicated and difficult to obtain when the input, i.e., the excitation, is unknown. To address this issue, the proportional strain flexibility matrix (PSFM) and its simplified construction procedure are proposed and integrated into the frames of ULSF, which can be easily obtained when the input is unknown. The identification accuracy of the method under the damage with different locations and degrees is validated by the numerical examples and experimental examples. Both the numerical and experimental results demonstrate that the proposed method provides a reliable tool for output-only damage detection of plate-like structures without estimating the mass-normalized strain mode shapes (SMSs).

Pattern recognition framework using asynchronous discrete binary data for condition and damage assessment in plate-like structures

Recent advances in energy harvesting technologies have led to the evolution of self-powered structural health monitoring techniques that are energy-efficient. Concurrent to the emergence of self-powered sensing has been the development of power-efficient data communication protocols. One such technology is an energy-aware pulse communication architecture that employs ultrasonic pulses through the material substrate for information forwarding. This results in limited discrete binary data that raises the need for new data analysis methods for structural health monitoring purposes. A pattern recognition framework that allows interpretation of the resulting asynchronous discrete binary data for condition and damage assessment in plate-like structures is presented in this article. The proposed pattern recognition framework is based on integration of image-based pattern recognition using anomaly detection, a pattern anomaly measure, a focal density concept, and the k-nearest neighbor algorithm. Using numerical simulations, damage indication parameters were determined from the strain response of dynamically loaded plates. Simulated test cases considering different levels of damage severity, single and multiple damage regions, loading conditions, and measurement noise were studied to evaluate the effectiveness and robustness of the strategy. Furthermore, the effect of sensor density on the proposed strategy was explored. Results demonstrate satisfactory performance and robustness of the proposed pattern recognition framework for localized damage detection in plate-like structures using limited and low-resolution discrete binary data.

A novel time reversal sub-group imaging method with noise suppression for damage detection of plate-like structures

In this paper, a new time reversal imaging (TRI) algorithm with noise suppression is developed for the application of imaged based structural damage detection of plate-like structures. The conventional TRI method suffers from performance degradation in high noise condition. The proposed method addresses the aforementioned issues. First, an array of detection transducers is used and is divided into several subgroups. Then, the echo signals of the subgroups are time reversed and reemitted via numerical computation. Finally, the cross-correlation functions of the summation of refocused time reversed signals in each subgroup are obtained to locate damages. The time reversed signals at the reference time are irrelevant to the noise, meanwhile, the multiple refocused signals in each subgroup are first added and then cross-correlated. Therefore, the proposed method can effectively suppress noise. To validate the effectiveness of proposed method, 2 experiments were performed. The 2 experiments involved 2 aluminum plate specimens. Each specimen was equipped with 4 surface-bonded lead zirconate titanate transducers. One specimen involved a simulated damage (an addition of a mass), and the other one involved an actual through-hole damage. The experimental performances of the proposed method are compared to those of the conventional TRI method. The imaging results demonstrated that the damage on both specimens was clearly displayed with high spatial resolution by the proposed method even under the low signal-to-noise ratio condition. On the contrary, the location of the damage computed by the conventional TRI method was submerged in noise and cannot be distinguished.

Application of Extreme Learning Machine to Damage Detection of Plate-Like Structures

An effective method for damage detection of plate structures using the extreme learning machine (ELM) is proposed in this study. With the ELM, the mode shapes and natural frequencies of a damaged plate are treated as the input and the damage states in the plate elements as the output. The proposed method was applied to two numerical examples, namely, a cantilever and a plate with four-fixed supports containing one or several damages with and without noise in the modal data. The results obtained reveal that the methodology can be used as an effective technique for the damage identification of plate structures using the modal data and ELM.

An efficient multi-stage optimization approach for damage detection in plate structures

The paper presents an efficient multi-stage optimization approach for damage detection in plate-like structures. In this approach, the damage identification process is achieved by minimizing an objective function established via flexibility changes of the structure. The vector of design variables represents correspondingly the damage extent of elements discretized by the finite element model. For analyzing the response of plate structures, the finite element model using 9-node quadratic quadrilateral elements is applied. For solving the optimization problem, a modified differential evolution (MDE) algorithm, which can help enhance the balance of global and local searches in each generation, is used for many stages of damage detection, in which the low damage variables in each stage are gradually eliminated after several generations to reduce the dimension of searching space and to increase the convergence rate of the problem. The efficiency of the proposed method is investigated through two numerical examples for isotropic and laminated composite plates. The obtained results indicate that the proposed method not only successfully detects the location and severity of multi-damage cases in the plate structures, but also show the better efficiency in term of computational cost.

Damage detection of plate-like structures using intelligent surrogate model

Cracks in plate-like structures are some of the main reasons for destruction of the entire structure. In this study, a novel two-stage methodology is proposed for damage detection of flexural plates using an optimized artificial neural network. In the first stage, location of damages in plates is investigated using curvature-moment and curvature-moment derivative concepts. After detecting the damaged areas, the equations for damage severity detection are solved via Bat Algorithm (BA). In the second stage, in order to efficiently reduce the computational cost of model updating during the optimization process of damage severity detection, multiple damage location assurance criterion index based on the frequency change vector of structures are evaluated using properly trained cascade feed-forward neural network (CFNN) as a surrogate model. In order to achieve the most generalized neural network as a surrogate model, its structure is optimized using binary version of BA. To validate this proposed solution method, two examples are presented. The results indicate that after determining the damage location based on curvature-moment derivative concept, the proposed solution method for damage severity detection leads to significant reduction of computational time compared with direct finite element method. Furthermore, integrating BA with the efficient approximation mechanism of finite element model, maintains the acceptable accuracy of damage severity detection.

Application of soft-thresholding on the decomposed Lamb wave signals for damage detection of plate-like structures

Effective application of the Lamb waves for structural health monitoring and damage identification intensively relies on the accurate damage-related feature extraction in the received signals. Most of existing signal processing methods extract the damage-related features from the time–frequency joint spectrum which requires a quite amount of effort. In this paper, the soft-thresholding process, based on different signal decomposition methods, is introduced to damage identification so that the damage-related signal features can be manifested more distinctively. By applying two popular signal decomposition methods (i.e., the discrete wavelet transform (DWT) and the empirical mode decomposition (EMD)), the signal of interest can be represented by a series of components with different frequencies. Since most noises exist in the high frequency range, it is feasible to alleviate noise by restricting the energy of high-frequency components. Finally, a denoised signal is synthesized using the corresponding reconstruction method. As an application, the soft-thresholding process is performed to detect a small crack on an isotropic aluminum plate under the white Gaussian noise contamination. The results, from both the numerical finite element simulation and experimental test, indicate that the soft-thresholding process is capable of effectively reducing the effect of noise, convincingly improving the sensitivity of damage identification, and discriminating relatively small damage.

Damage detection of plate-like structures based on residual force vector

Structural health monitoring is essential to maintain the structural integrity by predicting problems in an early time. This consequently could be reflected on extending the life time of structures. Nondestructive tests based on dynamic measures are usually fast and economic in detecting damages of structures. Various numerical techniques together with recording time histories are used for this purpose. This paper presents a numerical method for damage detection in plate-like structures. The modeling of damage was conducted commercially using the module of MatLab. Comparison of different mode shapes was used in the analysis to detect the location of local damage based on residual force vector. The technique utilized the node residual force vector to locate and evaluate the degree of the suspected damaged elements. In the current study, three configurations for plates were used. The study also concentrated on the efficiency of the new method in identifying damages of different degradation levels. The plates were subjected to different combinations of artificial damages applied at various positions on each plate. The study was not only able to identify the location but also the degree of damage in plates. It has been noted that identification of severe degradation was more precisely identified. As a result, the residual force method is the simplest damage quantification technique which approved to be accurate enough to be used in practical applications.

Numerical and Experimental Study on the Application of Mode Shape Curvature for Damage Detection in Plate-Like Structures

The paper describes on-going research effort at detecting and localizing damage in plate-like structures using mode shape curvature based damage detection algorithm. The proposed damage index uses data on exclusively mode shape curvature from the damaged structure. This method was originally developed for beam-like structures. The article generalizes the method of plate-like structures characterized by two-dimensional mode shape curvature. To examine limitations of the method, several sets of simulated data are applied and the obtained results of the numerical detection of damage are validated by comparing them with the findings of the case of the experimental test. The simulated test cases include the damage of various levels of severity. In order to ascertain the sensitivity of the proposed method for noisy experimental data, numerical mode shapes are corrupted with different levels of random noise. Modal frequencies and corresponding mode shapes of an aluminium plate containing mill-cut damage are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer (SLV) for the experimental study.

Experimental Study of Multi-damage Detection in a Plate Based on Non-modal Method

Many published damage localization indices require structural modal identification and mathematical model of the undamaged structure. However, it is somewhat inconvenient for use in practical engineering. In this study, an efficient localization index has been presented, named as image flexibility of frequency response function, for damage detection in plate-like structures. In order to avoid the finite element model error, two-dimensional gapped smoothing method is employed without the need for the baseline data from a presumably undamaged structure. To assess the effectiveness of the proposed scheme, experimental studies on a multi-damage steel plate are carried out. Meanwhile, the effects of damage magnitude and boundary condition on detection results are also discussed. The results show the effectiveness and robustness of the non-modal method compared to those found in the literature.

Fractal dimension–based Lamb wave tomography algorithm for damage detection in plate-like structures

This study presents a new signal-processing technique that utilizes the fractal proprieties of guided ultrasonic waves for structural health monitoring in complex structures. In particular, we use the fractal dimension of Lamb waves as a damage-sensitive feature. In the last decade, a fractal analysis has been extensively used in image analysis problems, especially in the medical field. In this article, a damage index based on the fractal dimension of Lamb waves is proposed using a modified box-counting algorithm. The proposed damage index has been also combined with a tomographic imaging algorithm to identify damages in plate-like structures. The performance of the proposed approach is validated through experimental tests performed on an aluminum plate instrumented with eight circular piezoelectric (lead zirconate titanate) transducers.

Damage detection in plate-like structures using High-Order mode shape derivatives

This paper investigates the application and reliability of using high-order mode shape derivatives especially, the fourth derivative in damage detection of plate-like structures. Numerical analyses have been carried out for low- and high-order mode shapes of simply supported and cantilever steel plate models. Six scenarios of damages are studied for plate models to represent different damage characteristics. The influence of artificial noise on the damage identification using changes in fourth derivative of mode shapes has been investigated. Based on the numerical studies, it is shown that the fourth derivative of mode shape is promising in detecting and locating structural damage in plate-like structures since it is localized at the damage locations even for a small amount of damage using only one of the mode shapes. Both low- and high-order mode shapes give successful results. Also, damage indices of the fourth derivatives give smoother localization and consequently better damage identification than those of curvature of mode shapes. Furthermore, using high-order modes (which can be measured by advanced sensors) does not improve the results of damage identification using the fourth derivative. Unfortunately, damage detection using changes in fourth derivative of mode shapes is sensitive to measurement noise.

Vibration analysis of annular-like plates

The existence of eccentricity of the central hole for an annular plate results in a significant change in the natural frequencies and mode shapes of the structure. In this paper, the vibration analysis of annular-like plates is presented based on numerical and experimental approaches. Using the finite element analysis code Nastran, the effects of the eccentricity, hole size and boundary condition on vibration modes are investigated systematically through both global and local analyses. The results show that analyses for perfect symmetric conditions can still roughly predict the mode shapes of “recessive” modes of the plate with a slightly eccentric hole. They will, however, lead to erroneous results for “dominant” modes. In addition, the residual displacement mode shape is verified as an effective parameter for identifying damage occurring in plate-like structures. Experimental modal analysis on a clamped–free annular-like plate is performed, and the results obtained reveal good agreement with those obtained by numerical analysis. This study provides guidance on modal analysis, vibration measurement and damage detection of plate-like structures.