Damage In Plate Structures Research Articles

Quantitative characterization of fatigue damage in plate structures based on FSOM

For the problem of fatigue damage detection and damage degree assessment of plate structures, a quantitative damage assessment method based on the fast self-organizing feature mapping (FSOM) algorithm is proposed in this paper. The damage detection problem is transformed into a binary classification problem by extracting multidimensional damage features of the Lamb wave signal in plate to be detected and selecting damage sensitive features. Then, the FSOM network is used to identify the health state of the plate to be inspected, and the damage index is obtained by fusing the damage sensitive features using FSOM to quantitatively evaluate the damage level of the plate to be inspected. Simulation and experimental results show this method has a good dynamic tracking capability for the fatigue damage evolution of aluminum and composite plates, and can achieve quantitative assessment of fatigue damage of plate structures.

Damage assessment in plate structures using an enhanced Jaya algorithm

The article proposes a new method called enhanced Jaya (EJaya) to identify and evaluate damage in plate structures. The method uses a nonlinear optimization task to solve the inverse damage identification problem. The damage magnitudes of the plate elements are taken as design variables, and the objective function to be minimized uses the variations in the plate flexibility matrix and includes a penalization term to avoid false alarm detection. EJaya is developed by incorporating three modifications in the traditional Jaya algorithm: generating an initial population of candidate solutions using prior knowledge of the damage scenario, integrating a component that takes into account the individual distribution through the search space, and implementing a new local search technique. The simulation results show that EJaya is efficient in both solution quality and computational effort and can detect and evaluate damage even in large-sized problems and under noisy data conditions.

Application of the Lamb Wave Mode of Acoustic Emission for Monitoring Impact Damage in Plate Structures.

The impact acoustic emission (AE) of plate structures is a transient stress wave generated by local materials under impact force that contains the state information of the impacted area. If the impact causes damage, the AE from material damage will be superimposed on the impact AE. Therefore, this paper details the direct extraction of damage-induced AEs from impact AEs for the health monitoring of plate structures. The damage-induced AE was analysed based on various aspects, including the cut-off range and propagation speed characteristics of the Lamb wave mode, the correlation between the force direction and the Lamb wave mode, and the impact damage process. According to these features, the damage-induced AE wave packets were extracted and verified via impact tests on epoxy glass fibreboards. The results demonstrated the feasibility of the proposed method for determining whether an impact causes damage via the direct extraction of the damage-induced AE from the impact AE.

A Novel Two-Stage Structural Damage Identification Method Based on Superposition of Modal Flexibility Curvature and Whale Optimization Algorithm

A novel two-stage method is proposed to properly identify the location and severity of damage in plate structures. In the first stage, a superposition of modal flexibility curvature (SMFC) is adopted to locate the damage accurately, and the identification index of modal flexibility matrix is improved. The low-order modal parameters are used and a new column matrix is formed based on the modal flexibility matrix before and after the structure is damaged. The difference of modal flexibility matrix is obtained, which is used as a damage identification index. Meanwhile, based on SMFC, a method of weakening the “vicinity effect” is proposed to eliminate the impact of the surrounding elements to the damaged elements when damage identification is carried out for the plate-type structure. In the second stage, the objective function based on the flexibility matrix is constructed, and according to the damage location identified in the first stage, the actual damage severity is determined by the enhanced whale optimization algorithm (EWOA). In addition, the effects of 3% and 10% noise on damage location and severity estimation are also studied. By taking a simply supported beam and a four-side simply supported plate as examples, the results show that the method can accurately estimate the damage location and quantify the damage severity without noise. When considering noise, the increase of noise level will not affect the assessment of damage location, but the error of quantifying damage severity will increase. In addition, damage identification of a steel-concrete composite bridge (I-40 Bridge) under four damage cases is carried out, and the results show that the modified method can evaluate the damage location and quantify 5%–92% of the damage severity.

Damage Identification in Plate Structures Using Sparse Regularization Based Electromechanical Impedance Technique.

This paper proposes a novel structural damage quantification approach using a sparse regularization based electromechanical impedance (EMI) technique. Minor structural damage in plate structures by using the measurement of only a single surface bonded lead zirconate titanate piezoelectric (PZT) transducer was quantified. To overcome the limitations of using model-based EMI based methods in damage detection of complex or relatively large-scale structures, a three-dimensional finite element model for simulating the PZT–structure interaction is developed and calibrated with experimental results. Based on the sensitivities of the resonance frequency shifts of the impedance responses with respect to the physical parameters of plate structures, sparse regularization was applied to conduct the undetermined inverse identification of structural damage. The difference between the measured and analytically obtained impedance responses was calculated and used for identification. In this study, only a limited number of the resonance frequency shifts were obtained from the selected frequency range for damage identification of plate structures with numerous elements. The results demonstrate a better performance than those from the conventional Tikhonov regularization based methods in conducting inverse identification for damage quantification. Experimental studies on an aluminum plate were conducted to investigate the effectiveness and accuracy of the proposed approach. To test the robustness of the proposed approach, the identification results of a plate structure under varying temperature conditions are also presented.

Structural damage detection in plates using a deep neural network–couple sparse coding classification ensemble method

The present study aims at identifying damages in plate structures by applying a pattern recognition–based damage detection technique using the frequency response function. The large number of degrees of freedom is one of the crucial obstacles in the way of accurately identifying damages in plate structures. On the other hand, frequency response functions include many details that dramatically lower the computing speed and enlarge the memory needed for storing data, hampering the application of this method. Furthermore, this study performs principal component analysis as an authoritative feature extraction method with the purpose of reducing the dimensions of the measured frequency response function data and generating distinct feature patterns. Also, because there has been no individual optimal classifier applicable to all problems, an ensemble comprising two powerful classifiers containing couple sparse coding classification and deep neural networks is used to predict the structure damage. This study evaluates the accuracy of damage detection by the proposed method in square-shaped structural plates with the lengths of 1 m and 2 m under different damage scenarios, namely, single and multiple element.

A modified damage index probability imaging algorithm based on delay-and-sum imaging for synthesizing time-reversed Lamb waves

Imaging for damage in plate structure by Lamb waves is one of the most effective methods in the field of structural health monitoring. In order to improve the accuracy of damage localization, a novel method is proposed to modify damage exponent probability imaging algorithm based on delay-and-sum imaging by using time reversal Lamb waves. A new probability distribution function is introduced to improve the damage index probability method and is combined with delay-and-sum method for damage localization. Experimental results on aluminum plate show that the hybrid algorithm achieves better accuracy of damage location and imaging quality than the conventional delay-and-sum method.

Comparisons of wavelets and contourlets for vibration-based damage identification in the plate structures

The objective of the present study is to compare a new approach based on contourlet transform and a traditional method based on wavelet transform to demonstrate curve damages in plate structures. The contourlet transform approach, as a novel two-dimensional development of wavelet transform, was extended to deal with inherent restrictions of wavelets. According to previous studies, wavelets have indicated poor performance to detect curve damages due to its basic elements. Therefore, this study utilized contourlet transform as a new method having an efficient performance to display this kind of discontinuities. In this research, contourlet transform and wavelet transform have been applied to a plate using four fixed boundary conditions including circle damages with arbitrary specifications and location in order to demonstrate their performance in damage identification. Comparing damage shape attained from contourlet transform and wavelet transform, it was revealed that contourlet transform could be utilized as an accessible and useful technique to detect damage with curvature.

Damage detection of a thin plate using pseudo local flexibility method

The virtual forces of the original local flexibility method are restricted to inducing stress on the local parts of a structure. To circumvent this restriction, we developed a pseudo local flexibility (PLFM) method that can successfully detect damage to hyperstatic beam structures using fewer modes. For this study, we further developed the PLFM so that it could detect damage in plate structures. We also devised the theoretical background for the PLFM with non-local virtual forces for plate structures, and both the lateral and rotary degree of freedom (DOF) measurements were considered separately. This study investigates the effects of the number of modes, the actual location that sustained damage, multiple damage locations, and noise in modal parameters for the damage detection results obtained from damaged numerical plates. The results revealed that the PLFM can be used for damage detection, localization, and quantification for plate structures, regardless of the use of the lateral DOF and/or rotary DOF.

Damage detection in plate structures using frequency response function and 2D-PCA

One of the suitable structural damage detection methods using vibrational characteristics are damage-index-based methods. In this study, a damage index for identifying damages in plate structures using frequency response function (FRF) data has been provided. One of the significant challenges of identifying the damages in plate structures is high number of degrees of freedom resulting in decreased damage identifying accuracy. On the other hand, FRF data are of high volume and this dramatically decreases the computing speed and increases the memory necessary to store the data, which makes the use of this method difficult. In this study, FRF data are compressed using two-dimensional principal component analysis (2D-PCA), and then converted into damage index vectors. The damage indices, each of which represents a specific condition of intact or damaged structures are stored in a database. After computing damage index of structure with unknown damage and using algorithm of lookup tables, the structural damage including the severity and location of the damage will be identified. In this study, damage detection accuracy using the proposed damage index in square-shaped structural plates with dimensions of 3, 7 and 10 meters and with boundary conditions of four simply supported edges (4S), three clamped edges (3C), and four clamped edges (4C) under various single and multiple-element damage scenarios have been studied. Furthermore, in order to model uncertainties of measurement, insensitivity of this method to noises in the data measured by applying values of 5, 10, 15 and 20 percent of normal Gaussian noise to FRF values is discussed.

An Algorithm for Identifying a Crack Within a Measured Displacement Field

This paper discusses an algorithm for the detection of crack damage in plate structures based on the governing differential equation (GDE) of in-plane displacement of a plate. A state-of-the-art 3D scanning laser Doppler vibrometer, which is able to provide very accurate measurements of a three-dimensional displacement field, was utilized to implement the algorithm. To evaluate the GDE from the measured displacements, a 2D Savitzky–Golay differentiating filter was used. The potential of this algorithm for detecting a crack was compared against another two algorithms which are based on displacement measurements. The first is an algorithm based on the error in smoothed to measured displacements and the other uses surface strains normalized by their mean. To investigate the efficiency of the algorithms in detecting crack damage, a number of PMMA plate specimens were fabricated with a range of crack lengths extending from a V-notch and tested under a cyclic, quasi-static, uni-axial load. For each algorithm, the crack location could be positively identified. However, the two algorithms based on the error in smoothed to measured displacements and surface strains normalized by their mean were found to be dependent on the direction of the applied load, whereas, theoretically the algorithm based on the GDE of in-plane displacement would work regardless of the direction of the applied load.

Nonlinear Dynamical Analysis of a Breathing Crack Plate Based on Structural Intensity Method

A Breathing crack is one of the most common damage in plate structures. When a plate vibrates, the breathing crack will produce the open and closing movement, and the structure has nonlinear dynamic response characteristics. In this paper, the contact nonlinearity of a plate structure with a breathing crack is considered, and the nonlinear vibration of the breathing cracked plate is analyzed. The structural intensity is studied under dynamic excitation and the surface structural intensity vector field of the structure is determined. The position and shape of the crack are identified by the structural intensity maps, which provide a theoretical basis for the damage identification of cracked structures with a breathing crack.

Optimizing location of damage within an enclosed area defined by an algorithm based on the Lamb wave response data

In the present study, experiments are carried out on an Aluminium (Al) plate with and without damage, using Lamb waves and an array of four Piezoelectric Wafer (PW) transducers bonded onto it. The PW transducers are used to actuate and sense Lamb waves. These transducers are very compact, cheap, and can be easily bonded onto the structure. The responses recorded from the experiments, are further analyzed using a new algorithm developed by the authors, in order to localize the damage. The damage location is obtained as a small enclosed area formed by the intersection of various curves generated by an algorithm proposed by the authors. The damage location is further refined within this enclosed area using the optimization methods. Three different types of damages are considered in the present work. The case of multiple damage localization is also reported here. The results obtained by the algorithm are in excellent agreement with the actual location of damage. Thus, the present method has the capability of locating single as well as multiple damages in plate structures using minimal number of transducers.

Lamb-Wave-Based Tomographic Imaging Techniques for Hole-Edge Corrosion Monitoring in Plate Structures.

This study presents a novel monitoring method for hole-edge corrosion damage in plate structures based on Lamb wave tomographic imaging techniques. An experimental procedure with a cross-hole layout using 16 piezoelectric transducers (PZTs) was designed. The A0 mode of the Lamb wave was selected, which is sensitive to thickness-loss damage. The iterative algebraic reconstruction technique (ART) method was used to locate and quantify the corrosion damage at the edge of the hole. Hydrofluoric acid with a concentration of 20% was used to corrode the specimen artificially. To estimate the effectiveness of the proposed method, the real corrosion damage was compared with the predicted corrosion damage based on the tomographic method. The results show that the Lamb-wave-based tomographic method can be used to monitor the hole-edge corrosion damage accurately.

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. • A new finite element model updating approach is developed for identifying the local damages in plate structures. • Dynamic response sensitivity with respect to damage parameter is introduced in time domain. • The proposed method is effective and accurate for local damage identification. • Small local damages in the plate can be identified.

Damage detection and denoising in two-dimensional structures using curvelet transform by wrapping method

The main objectives of this study are to present a vibration-based damage identification method and also a denoising mode shape approach applicable to two-dimensional structures using curvelet transform. For this purpose, the curvelet transform via wrapping method is employed. The reliability of the proposed technique is demonstrated through a verification study by comparing the results of numerical and those of the experimental data in plate structures. Two case studies, one-story and three-story shear walls assuming damages at arbitrary locations, are examined in which different noise levels are included. Good agreement between the simulated and assumed damage in both example is demonstrated. The results confirm the robustness and high performance of the proposed method in detecting the damage in plate structure and eliminating the noises.

Reference-free crack detection using transfer impedances

A new concept of reference-free damage detection methodology is developed using transfer impedances to detect crack damage in a plate-like structure without using previously collected baseline data. Conventional impedance-based damage detection techniques have been shown to be vulnerable to other types of changes such as temperature variation that may not be relevant to defects of interest. One of the potential disadvantages of the conventional techniques is frequent false-alarms due to these undesirable variations that may occur in field applications. In order to reduce these false-alarms, this paper proposes a new methodology that utilizes transfer impedances obtained between two pairs of collocated PZT patches instead of the electromechanical impedance obtained at one PZT patch. The proposed technique utilizes Lamb mode conversion effects caused by the presence of crack damage in plate structures. Furthermore, an instantaneous damage classification is carried out by comparing mode conversion energy among several combinations of measured signals without any user-specified threshold or relying on the baseline data. The feasibility of the proposed reference-free methodology using transfer impedances is investigated via a series of experiments conducted on an aluminum plate.

Development of scanning damage index for the damage detection of plate structures using modal strain energy method

This work presents a novel approach of nondestructive detection of damage in plate structures by using experimental modal analysis (EMA) and modal strain energy method (MSEM). An aluminum alloy 6061 thin plate with a surface crack is investigated in this study. EMA is conducted on the plate to obtain the mode shapes before and after damage. The modal displacements of each mode shape are then used to compute the modal strain energy. For all measured mode shapes, a damage index is defined by using the ratio of modal strain energies of the plate before and after damage. In fact, small damage causes very little change in system response, but it is an essential early warning of structure damage. As the second-order derivatives, modal strain energy is much more sensitive to the small change of structural response than frequencies and mode shapes. It is therefore feasible to approach the small damage by using a damage index defined by fractional MSE of the structure before and after damage. In this study, a scanning damage index (SDI) is developed by moving damage indices obtained from the local area throughout the structure as if a scanning sensor is used to inspect the structure. The damage indices in overlap areas are added up and the summation may intensify the signals of damage in the plate. Limited by the numbers of measured point, a differential quadrature method is employed to calculate the partial differential terms in strain energy formula. Experimental results show that SDI well identifies a surface crack location by using only few measured mode shapes of the aluminum plate. This novel approach provides a flexible, cost-effective, and nondestructive damage evaluation in either local or global structure. Its applicability to different types of structures and different sizes of damage is to be experimentally validated in the future work.

Development of nondestructive damage detection algorithms for plate structures

The objective of this paper is to develop appropriate algorithms to locate and size damage in plate structures. Two methods, one using the changes in the compliance distribution and the other using the changes in the modal strain energy, are presented in this paper. A damage index, used to identify possible locations and corresponding severities of local damage, is defined and expressed in terms of modal displacements that are obtained numerically from mode shapes of the undamaged and the damaged structures. The possible damage locations in the structure are determined by the application of damage indicators according to previously developed decision rules. Each of the two methods is demonstrated using a numerical example of a simply supported plate with simulated damage.