Damage identification in structural elements through curvature mode shapes and nonlinear energy operator

Vibration-based Structural Health Monitoring (SHM) is a non-destructive method and is widely used in recent years. To measure the vibration response of the structure under impact load, uniaxial/triaxial accelerometers, displacement, and velocity meters are used. Many works use modal parameters extracted from vibration such as frequency, mode shape, and modal curvature to detect damage. Among these parameters, modal curvature is proved very sensitive to damage. Modal strains (or curvatures) can be derived from displacement mode shape using the central difference method, but this procedure may contain cumulative errors. In this paper, direct modal strain measurement will be used. A steel slab equipped with strain transducers is set up in the laboratory. The strain response will be recorded and analysed directly to find the modal strains. From direct modal strain measurements, the damage location will be identified. Two damage scenarios are examined to verify the method.KeywordsStructural Health Monitoring (SHM)Strain measurementDirect modal strainCurvatures

Although much effort has been made to explore the characteristics of composite lattice truss core sandwich structures, little work has been undertaken into non-destructive evaluation (NDE) and structure health monitoring (SHM). This paper presents a baseline-free NDE method to determine the debonding of truss bar in composite lattice truss core sandwich structures. The method is proposed based on the uniform load surface (ULS) curvature and developed according to the combination of gapped smoothing method (GSM) and Teager energy operator (TEO), which is denoted as GSM-TEO method. The effects of truss bar on the vibration and wave motion characteristics of composite lattice truss core sandwich structures are firstly investigated, and then, experiment and numerical simulation are conducted to assess the performance of the proposed method. Results verify the method is reliable and applicable for damage localization in composite lattice truss core sandwich structures. doi: 10.12783/SHM2015/74

Laminated composite structures performance and behavior can be affected by damage that is not always visible on the surface. The need to monitor the health of these structures has continuously increased, which can be achieved in a fast and cost-effective way by numerical simulations. This paper presents an efficient two-step approach for damage identification in laminated composite plates. The first step uses mode shape and its derivatives (mode shape curvature) to locate the damages based on modal data. The proposed indicator utilizes modal analysis information extracted from finite element analysis. Then, a new metaheuristic Sunflower Optimization method (SFO) is employed to assess the correct severity of induced damages. This technique considers the damage detection problem as an inverse problem with minimization of an objective function. Numerical examples considering laminated composite plate with one and two induced damaged sites (delamination) are considered. The results indicate that the proposed method not only successfully identifies the location and severity of multi-damage cases in the composite structures, but also provides a better efficiency in terms of time saving and computational costs.

Vibration-based nondestructive damage detection relying on modal curvatures has been investigated in various applications. An intrinsic deficiency of a modal curvature is its susceptibility to the noise inevitably present in a measured mode shape. This adverse effect of noise is likely to mask actual features of damage, resulting in false results of damage detection. To circumvent this deficiency, a Teager energy operator (TEO), aided by a wavelet transform, is adopted for the treatment of mode shapes to produce a new algorithm for damage identification. After wavelet-transform- based preprocessing to separate the effective components of modal curvatures from noise interference, a TEO is employed as a singularity detector, acting on the separated effective components, to reveal and characterize the features of damage. The capacity of the TEO is demonstrated analytically in cases of cracked beams. The applicability of the algorithm is experimentally validated using a scanning laser vibrometer to acquire mode shapes of an aluminum beam bearing a crack. The analytical and experimental results show that the TEO, aided by wavelet transforms, has stronger sensitivity to slight damage and greater robustness to noise than modal-curvature- and wavelet-transform-based damage detection methods.

Damage within a structure refers to changes in both its geometric and material characteristics, resulting in a drop in the stiffness that impacts the structure’s performance adversely. This decrease in stiffness causes alterations in modal parameters, including natural frequencies and mode shapes. Utilizing modal analysis allows for the extraction of modal frequencies and mode shapes, facilitating the analysis of mode shape curvature to detect structural damage. In recent years, artificial neural networks (ANNs) have achieved significant application, mainly for their exceptional capability in pattern recognition, which proves invaluable for identifying structural damage. This article proposes a novel method based on mode shape curvature and ANNs for detecting damage in beam-like structures. Experimental study is conducted to analysis damaged and undamaged structural modal behaviours. A feed-forward neural network with two hidden layers, trained on damage indices from mode shape data, is used to accurately pinpoint damage locations within the structure. The proposed approach for damage detection is validated and proves its ability to precisely pinpoint the location of damage. The results of this study demonstrate that ANNs trained with modal curvatures hold significant promise for identifying structural damage, enabling early detection in beam-like structures and contributing to ensuring their safe operation.

Many composite materials and structures are susceptible to defects, which can significantly reduce the strength of structures and may grow to failure. To avoid the catastrophic failure of structures, development of a reliable method of structural health monitoring is one of the most important keys in maintaining the integrity and safety of structures. Dynamic response-based damage detection offers a simple procedure as an alternative to the conventional nondestructive evaluation techniques. However, this technique depends on the quality of measured data for its identification accuracy. In this article, experimental aspects of dynamic response-based damage detection technique on carbon/ epoxy composites are addressed. Smart piezoelectric materials are used as sensors or actuators to acquire the curvature modes of structures. These materials are surface-bonded to the beams. An impulse hammer is used as an actuating source as well. Four types of damage detection algorithms are evaluated for several possible damage configurations with two different excitation sources. The quality of damage identification with the four different detection algorithms is discussed. These experimental damage identification techniques using curvature modes and piezoelectric materials can be effectively used in damage detection and health monitoring of composite structures.

A reliable and effective damage detection technique is one of the significant tools to maintain the safety and integrity of structures. A dynamic response offers viable information for the identification of damage in the structures. However, the performance of such dynamics-based damage detection depends on the quality of measured data and the effectiveness of data processing algorithms. In this article, the experimentally measured data of two sensor systems, i.e., a surface-bonded piezoelectric sensor system and a noncontact scanning laser vibrometer (SLV) system, are studied, and their effectiveness in damage identification of composite laminated beams is compared. Three dynamics-based damage detection algorithms are evaluated using the data acquired from these two measurement systems. The curvature mode shape is selected as a parameter to locate damage due to its sensitivity. The piezoelectric sensors directly acquire the curvature mode shapes of the structures, while the SLV measures the displacement mode shapes. The difference in the measurement characteristics of these systems and their influence in the damage identification performance are addressed. The beam specimens are made of E-glass/epoxy composites, and several different types of damages are introduced in the beams (i.e., delaminations, and impact and saw-cut damages). This study provides a thorough assessment of the two sensor systems in damage detection of composite laminated beams and verifies the validity of dynamics-based damage detection methodology in locating the local defects in composite structures.

The use of modal curvatures for damage localization in beam-type structures

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 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.

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.

In this paper, the experimentally measured data of two sensor systems (i.e., a surface-bonded piezoelectric sensor system and a non-contact scanning laser vibrometer (SLV) system) are studied, and three dynamics-based damage detection algorithms are evaluated. The curvature mode shapes are selected as a parameter to locate damage due to its sensitivity. The piezoelectric sensors directly acquire the curvature mode shapes of the structures, while the SLV measures the displacement mode shapes. The beam specimens are made of E-glass/epoxy composites, and several different types of damages are introduced in the beams (i.e., delaminations, impact and saw cut damage). This study provides a thorough assessment of the two sensor systems to damage detection of laminated composite beams and verify the validity of dynamics-based damage detection methodology for locating the local defects in composite structures.

In this work, we present a two-step procedure for damage identification in beam structures exploiting modal curvature changes. The reconstruction of modal curvatures requires the knowledge of several mode shape components along the analyzed beam. This requirement is practically unachievable when mode shapes are identified via vibration-based monitoring using a limited number of accelerometers. To overcome this limitation, in the first step of the proposed procedure, we perform a mode shape expansion employing a reduced subset of measured modal components. The remaining measured components are used as control parameters to formulate a first hypothesis on damage location and extent. For this purpose, the expansion procedure is performed considering a number of possible damage scenarios, consisting of a location and a severity (loss of stiffness) of the damage. Using the Total modal assurance criterion (TMAC), we select the expanded modes with the highest degree of correspondence with the measured control components. These expanded modes are thus associated with a first guess of the damage location and severity. In the next step, this initial damage identification is verified through the computation of a modal curvature-based damage index. If the curvature-based damage identification confirms the previous identification, the damage location and extent are determined. The procedure can be easily extended to identify multiple simultaneously damaged elements. The approach is numerically validated using a benchmark beam modeled via finite elements, investigating the influence of different parameters such as noise, position of the control components and beam discretization on the identification success rate. Finally, the procedure is tested on two experimental specimens: a steel beam, with three different damage configurations and a concrete beam progressively damaged with multiple damage locations.

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.

Structural damage identification (SDI) serves as an indirect approach that has the potential to meet real‐time monitoring of structures. However, the identification accuracy and efficiency of some methods need to be improved, especially when there are some uncertain interfering factors or noise. This paper presents a new optimization algorithm and an improved objective function for inverse problems of SDI, offering an effective solution for bridge damage identification under uncertain noise interference and incomplete modal data. In this study, by hybridizing the whale optimization algorithm and the sand cat swarm optimization, a novel whale‐sand cat swarm optimization (W‐SCSO) method is proposed for SDI. The cubic chaotic mapping is introduced for initialization of the W‐SCSO method, and then the lens opposition‐based learning and the stochastic differential mutation are employed to enhance the search capability and convergence accuracy of the proposed algorithm. Besides, the mode shape curvature, the frequency change ratio, and the L 1/2 sparse regularization are used to improve the objective function. Four other existing state‐of‐the‐art methods are used to verify the performance of the proposed W‐SCSO method by the CEC2017 benchmark functions and a simply supported beam finite model. The comparative analysis highlights the feasibility and effectiveness of the proposed method in the considered cases. Moreover, an aluminum alloy simply supported beam was conducted for the SDI experiment to further prove the effectiveness of the improved method in practice. Simulation and experimental results show that the proposed method effectively locates and quantifies stiffness reduction in bridge structures, which maintains high accuracy in damage identification despite potential modal incompleteness and uncertain measurement noise interference.