Utilizing mode shape curvature and artificial neural networks for structural damage assessment in beam-like structures

Support vector machine (SVM) is a machine learning algorithm based on statistical learning theory, and it has recently been established as a powerful tool for classification and regression problems. This paper presents a novel SVM-based approach for damage location identification in beam-like structures. The curvature mode shapes are used as inputs of the SVM. The proposed approach involves two steps. The first step uses support vector classification to obtain the structural damage probability distribution. The second step uses support vector regression to identify the precise damage location after reconstructing the training set. Furthermore, a series of simulations in the cantilever beams involving different damage scenarios (at different location and different extent), have been conducted to verify this method. In order to check the robustness of the input used in the analysis and to simulate the experimental uncertainties, artificial random noise has been generated numerically and added to noise-free data during the training of the SVM. The results show that this approach is a promising method for damage diagnosis

In this paper, a new damage indicator based on mode shape data is introduced to identify damage in beam structures. In order to construct the indicator proposed, the mode shape, mode shape slope and mode shape curvature of a beam before and after damage are utilized. Mode shape data of the beam are first obtained here using a finite element modeling and then the slope and curvature of mode shape are evaluated via the central finite difference method. In order to assess the robustness of the proposed indicator, two test examples including a simply supported beam and a two-span beam are considered. Numerical results demonstrate that using the proposed indicator, the location of single and multiple damage cases having different characteristics can be accurately determined. Moreover, the indicator shows a better performance when compared with a well-known indicator found in the literature.

This study proposes a method for localizing and quantifying fatigue damage in beam-like structures by utilizing energy dissipation as a sensitive feature. A scheme was developed to generate complete responses of the beam under random moving loads by combining individual responses from different moving load velocities, simulating real-world conditions and augmenting the training data set. The input load is assumed to be an approximate form of white noise. The responses were collected from three different beams using accelerometers evenly distributed along the length of beams. The Dissipation Spectrum (DS) was then calculated from the generated random response. The proposed approach is a two-step process: first, a Feedforward Neural Network (FNN) analyzes the correlation coefficients between DS at multiple locations on the beam, achieving 96–100% accuracy in damage localization; second, a 1D Convolutional Neural Network (1D-CNN) quantifies the damage level using the DS specifically from the localized damage, yielding an 80–100% accuracy in severity estimation. This two-step process, using correlations of DS for localization and local DS for quantification, has established a dependable method for structural health monitoring, offering a promising approach for engineering applications, particularly those requiring high sensitivity to early-stage fatigue damage.

It is very important to monitor the occurrence of damage of various structures. By early detection of damage and by taking the proper corrective measures the failure of damage could be avoided. When damage occurs in structure it results in change in stiffness properties of the structure which in turn result in change in modal properties like natural frequency, mode shape change, mode shape curvature and strain energy of a structure. These parameters are used as an input to train the artificial neural network(ANN). The efficiency of the ANN to predict the damage at single and multiple damage cases using the change in natural frequency and strain energy was evaluated in this study. The efficiency of individual modes and combination of frequency and strain energy to detect damage is also considered in this study. The modal parameters were obtained by carrying out modal analysis using ANSYS 2021 R1 software and the ANN was developed using MATLAB software. The results indicated that the strain energy accurately predict the damage location and varies linearly with severity of damage. It is better to use combination of frequency and strain energy as indicator to detect damages.

Fundamental mode shape and its derivatives in structural damage localization

Damage detection in structural elements using curvature mode shape technique has become a research focus of increasing interest during the last few years. A noticeable deficiency of curvature mode shape, however, is its susceptibility to measurement noise, easily impairing its advantage of sensitivity to damage. To overcome this drawback, a nonlinear operator called Teager Energy Operator (TEO) is incorporated. The efficacy of TEO is analytically verified through modal curvatures in a steel reinforced concrete cantilever beam with an induced damage (stiffness loss) along its length. The applicability of the proposed curvature mode shape technique is experimentally validated for detecting simulated damage (mass attached) in an aluminum plate from mode shapes acquired by a non-contact Scanning Laser Doppler Vibrometer (SLDV). Normal responses (out of plane flexure response) are measured with SLDV. The excitation is given with the help of a data-physics exciter based on the frequencies obtained from the free vibration tests using a roving hammer attached with a forced transducer. The proposed algorithm is to compute a robust nonlinear operator - TEO using the attained curvature, dynamic rotation and displacement mode shapes. This algorithm has been successfully implemented and tested for detecting damages on beam and plate elements, using finite element simulations as well as laboratory experiments. It is anticipated that the suggested approach facilitates damage localization in a comparatively fast and accurate manner.

This paper presents an experimental study on the detection and localization of damage in a steel plate using vibration-based methods. Dynamic impulse tests were conducted on both undamaged and damaged plate to determine changes in modal parameters, such as eigenfrequencies and mode shapes. Several damage detection methods, including the Modal Assurance Criterion (MAC), Coordinate Modal Assurance Criterion (COMAC), Mode Shape Curvature (MSC), Mode Shape Curvature Square (MSCS), and Damage Index (DI), were applied. The results showed that while MAC and COMAC effectively detected damage, they did not provide information about the location. MSC and MSCS indices demonstrated improved damage localization, with the MSCS being particularly effective. The DI index provided the clearest and most accurate representation of the damage location. These findings highlight the potential of these methods for non-destructive testing and structural health monitoring.

This article presents an improved procedure for detecting single damage in beam-like structures. Many damage detection methods are based on the analysis of beam natural frequency shifts in damaged and intact states and its analytical modal curvatures. They identify the damage by constructing curves of damage coefficients along the beam and visually determining the point of their mutual intersection. However, for some cases, the absence of an unambiguous point of intersection of these curves or the low accuracy of its localization makes it difficultto use these methods. To accurately determine the mutual intersection of damage coefficient curves, this work proposes to use a subset of modes without one having its curvature close to zero at the site of the alleged damage. This approach greatly simplifies the determination of the point of intersection of the curves of damagecoefficients. An enhanced procedure for the numerical determination of this intersection point is also proposed,rather than the visual one used in existing methods. The effectiveness of the proposed technique was confirmedby numerical simulation followed by experimental verification.

On the basis of the theory that natural frequency changes and curvature mode shapes can be employed to determine the locations and degrees of damage of structures, a BP neural network technique with an improved input structure was developed. The two networks were used for diagnosis of structural damage, and structural damages were predicted using gray theory. The results showed that the gray theory to predict the structural damage neural network was applicable to irregular objects such injury problem diagnosis.

Detecting damage in structures based on the change in their dynamics or modal parameters (modal frequencies and mode shapes) has been extensively studied for three decades. The success of such a global, passive, vibration-based method in field applications, however, has long been hindered by the bottleneck of low spatial resolution vibration sensor measurements. The primary reason is that damage typically initiates and develops in local regions that need to be captured and characterized by very high spatial resolution vibration measurements and modal parameters (mode shapes), which are extremely difficult to obtain using traditional vibration measurement techniques. For example, accelerometers and strain-gauge sensors are typically placed at a limited number of discrete locations, providing low spatial resolution vibration measurements. Laser vibrometers provide high-resolution measurements, but are expensive and make sequential measurements that are time- and labor-consuming. Recently, digital video cameras—which are relatively low cost, agile, and able to provide high spatial resolution, simultaneous, pixel measurements—have emerged as a promising tool to achieve full-field, high spatial resolution vibration measurements. Combined with advanced vision processing and unsupervised machine algorithms, a new method has recently been developed to blindly and efficiently extract the full-field, high-resolution, dynamic parameters from the video measurements of an operating, output-only structure. This work studies the feasibility of performing damage detection using the full-field, very high spatial resolution mode shape (of the fundamental mode) blindly extracted from the video of the operating (output-only) structure without any knowledge of reference (healthy) structural information. A spatial fractal dimension analysis is applied on the full-field mode shape of the damaged structure to detect damage-induced irregularity. Additionally, the equivalence between the fractal dimension and the squared curvature (modal strain energy) of the mode shape curve, when of high spatial resolution, is mathematically derived. Laboratory experiments are conducted on bench-scale structures, including a building structure and a cantilever beam, to validate the approach. The results illustrate that using the full-field, very high-resolution mode shape enables detection of minute, non-visible, damage in a global, completely passive sensing manner, which was previously not possible to achieve.

This study tackles the challenge of operational damage identification on wind turbine blades and proposes a novel framework for damage detection and localization. A vibration-based scheme is proposed, which tracks the variability of the mode shape curvatures (MSCs) of the blade along its plane direction. The method consists of a training and a diagnostics stage. In the former, MSC information for a number of predefined modes is extracted over varying operational conditions in the healthy state of the blade and, via the implementation of the principal component analysis (PCA), a statistical characterization of each blade’s node is estimated. Then, during the diagnostics stage, the MSCs are assembled and the same PCA mapping is enforced. A corresponding damage index is established, in order to detect and localize damage, if it exists. In both stages, MSC extraction is based on the successful estimation of vector autoregressive moving average (VARX) models that rely on pressure excitation and distributed strain measurements.

This study presents a modal-based damage detection technique for framed structures. A framed structure is tested using a vibration-based method and the mode shapes corresponding to undamaged and damaged states of the structure are obtained. The damage to the framed structure is induced by reducing the stiffness of columns at a particular storey and tested using the shaking table. The corresponding finite element (FE) model was verified for its natural frequency with the experimental model. Moreover, a series of studies were performed by concentrating the damage to a smaller scale by including spot damage on the framed structure and varying the damage location and intensity. The model was analysed using finite element software for these tests and mode shape slope differences and mode shape curvature differences were generated. Derivatives of mode shape slopes were plotted and correlated with the damage location. Mode shape slope is discontinuous and becomes a maximum value close to the damaged location. Mode shape curvatures also show a maximum difference near the damaged location. Finite element model, as well as the experimental investigation, shows the competence of the proposed approach in structural damage identification.

Pulsed Nd:YAG laser has high intensity and high quality beam characteristics, which can be used to produce micro-grooves and micro-turning surface on advanced engineering ceramics. The present research attempts to develop mathematical models by using response surface methodology approach for correlating the machining process parameters and the process responses during laser micro-turning of aluminum oxide (Al2O3) ceramics. The process parameters such as laser average power, pulse frequency, workpiece rotating speed, assist air pressure and Y feed rate were varied during experimentation. The rotatable central composite design experimental planning has been used to design the experimentation. The performance measures considered are surface roughness (Ra) and micro-turning depth deviation. Multi-objective optimization has been carried out for achieving the desired surface roughness as well as minimum depth deviation during laser micro-turning operation. Further, an artificial neural network (ANN) model has been developed to predict the process criteria. Levenberg-Marquadt training algorithm is used for multilayer feed forward backpropagation neural network. The developed ANN model has 5-10-2 feed forward network. There are 5 neurons in the input layer, 10 neurons in the hidden layer and 2 neurons in the output layers corresponding to two output responses, respectively. The developed ANN model has been validated using data obtained by conducting additional set of experiments. It was found that the developed ANN model can predict the process criteria more accurately than response surface methodology (RSM) based developed models.

Identification of the mode shapes through monitoring is one of the key problems in damage diagnosis based on modal parameters especially for damaged structures. In order to obtain mode shapes of damaged structures easily and accurately, the mass‐stiffness combined perturbation (MSCP) method is proposed in this paper. To do so, the relationship between the stiffness perturbation mode shapes of damaged and intact structures is firstly derived and established. Then, the principle of similar frequency is applied to optimize the objective function of the most suitable mass perturbation model. Both numerical analyses and experimental tests on simple and complex structures demonstrate that the proposed MSCP method achieves higher precision than traditional mode shape identification methods. The additional advantages of the MSCP method include (i) lower requirement on the frequency analysis of only damaged structures and (ii) higher effectiveness for minor damage scenarios. In fact, the lower the damage, the higher the precision achieved by the MSCP method. As illustrated in the paper, the proposed technique has excellent applications in mode shapes identification and structural health monitoring.

This paper presents an innovative sensitivity equation to detect changes of stiffness parameters using mode shape data. Most of the sensitivity-based model updating methods use changes of mode shapes for structural model updating. However, the proposed method uses the mode shape data to estimate changes of the structural parameters directly. The proposed method sets up a relation between the change of structural parameters and the mode shapes of the damaged structure. The proposed formula uses the measured natural frequencies of the damaged structure and the mode shapes of the intact structure. The formulation yields to a set of accurate sensitivity equations. The proposed method is successfully applied to a plane truss and a frame structure using simulated error-contaminated mode shapes data. Results prove robustness of the proposed method against mode shape, natural frequency, and mass modeling errors. Copyright © 2016 John Wiley & Sons, Ltd.