Non-Destructive Evaluation Method Based On Dynamic Invariant Stress Resultants

This paper proposes a vibration-based damage detection method designed for structural elements subjected to important vertical loads, as columns or pillars. The method is based on the relation existing between the energy stored in the pillar in several vibration modes and the corresponding natural frequencies. For a certain mode, this energy results as the sum of the energies stored in all pillar slices, being dependent on the rigidity and the squared of the corresponding mode shape curvature. This means that the energy distribution along the pillar is different for each mode. Thus, reducing the rigidity of one slice due to damage, the frequencies will decrease in different ways, depending on the slice location. This fact permits to contrive patterns able to characterize the effect of damage at any location along the pillar. Since the mode shapes (and the natural frequencies) are influenced by inertial forces, but in the meantime by the compression and shear forces induced by the top mass, the patterns have to be derived for each load case. The paper presents a simple mathematical expression able to predict frequency changes if damage occurs at any location along the pillar and for any top mass value. Patterns that characterize the damage location are consequently derived by using the squared mode shape curvatures of the healthy beam. The damage location becomes an inverse problem, it being found by interpreting the results of frequency measurements for the healthy and damaged state. The process of damage location is exemplified by numerical simulations.

Damage detection for beam-like structures using the normalized curvature of a uniform load surface

Fundamental mode shape and its derivatives in structural damage localization

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.

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.

A two-step method for damage identification in moment frame connections using support vector machine and differential evolution algorithm

Damage in structures can negatively affect their functionality and safety and leads to failure. Thus it is very important to monitor structures for occurrence, location and severity of damage. Structural health monitoring techniques provide information on the life expectancy of structures simultaneously detects and locates structural damage. Damage identification of structures based on vibration has always been important subjects and are being rapidly used to damage and location of structures. Artificial Neural Networks (ANNs) as a soft computing method using dynamic parameters of structures have been utilized increasingly for structural damage detection due to their excellent pattern recognition capability. Dynamic parameters of structure are easy to implement for damage identification and can directly linked to the topology of structure. This study presents the application of ANN for damage identification in steel beams using dynamic parameters. For identification of severity and location of damage, at first, five individual neural networks corresponding to mode 1 to mode 5 are considered. At the second step, a method based on neural network ensemble is proposed to combine the outcomes of the individual neural networks to a single network. Ensemble results were evaluated and discussed according to the differences between predicted output by ANN and desire data (target data) obtained from experimental modal analysis of structure.KeywordsArtificial neural networksMean square errorModal analysisDamage detectionNeural network ensemble

New Damage Identification Method for Operational Metro Tunnel Based on Perturbation Theory and Fuzzy Logic

Two major challenges associated with a vibration-based damage detection method using changes in natural frequencies are addressed: accurate modeling of structures and the development of a robust inverse algorithm to detect damage, which are defined as the forward and inverse problems, respectively. To resolve the forward problem, new physics-based finite element modeling techniques are developed for fillets in thin-walled beams and for bolted joints, so that complex structures can be accurately modeled with a reasonable model size. To resolve the inverse problem, a logistic function transformation is introduced to convert the constrained optimization problem to an unconstrained one, and a robust iterative algorithm using the Levenberg-Marquardt method is developed to accurately detect the locations and extent of damage. The new methodology can ensure global convergence of the iterative algorithm in solving under-determined system equations and deal with damage detection problems with relatively large modeling error and measurement noise. It is applied to various engineering structures including lightning masts, a space frame structure and one of its components, and a pipeline. The exact locations and extent of damage can be detected in the numerical simulation, and the locations and extent of damage can be successfully detected in experimental damage detection.

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.

The frequency-shift-based scheme is one of the popular structural damage detectionmethods used in the field. Assuming that the damage will cause structural parameter(e.g. mass or stiffness) changes, one can detect damage by observing natural frequencyvariations before and after damage occurs. One of the major limitations of thefrequency-shift-based damage detection approach is that the natural frequencies could beinsensitive to local and small parameter variations (damages) in the structure. To addressthis problem, the concept of sensitivity-enhancing control has been developed andexplored by researchers. Recently, an eigenstructure (dual eigenvalue–eigenvector)assignment-based approach has been proposed to advance the state of the artof sensitivity-enhancing control design for multiple degrees-of-freedom systems(Jiang et al 2007 Trans. ASME, J. Vib. Acoust. 129 771–83). While promisingfeatures have been shown, the approach has not been experimentally verified. Inaddition, such a scheme requires an accurate analytical model, which is in generaldifficult to obtain for complex structures. The purpose of this research is to advancethe state of the art by exploring an experimental-based sensitivity-enhancingcontrol approach for structural damage detection. That is, we aim at utilizingmathematical models identified from experimental measurement data for controllerdesign and system analysis, and hence eliminate the requirement of an accurateanalytical model. With the identified model, an eigenstructure assignment-basedoptimization scheme is utilized to design the closed-loop control to best enhance thenatural frequency sensitivity to structural damages. An experimental investigationbased on a test bed beam structure is conducted to demonstrate and verify theproposed method. Sensitivity-enhancing controls are designed to increase thefirst two natural frequency sensitivities to mass changes in the beam structure.Experimental results show that by applying the designed sensitivity-enhancing controls tothe beam structure, the natural frequency sensitivities to mass variations canbe significantly enhanced. Results also show that the damage locations can besuccessfully identified and the damage severity can be predicted by using the measuredfrequency changes of the closed-loop systems before and after damage occurrence.

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.

Global dynamic technique based on frequencies change is used to detect the damages/ cracks in structures. This technique is based on changes in natural frequencies. However, it is found that changes in frequencies are negligible even in major damage cases. Several researchers have used modes shape instead of frequencies to detect the damage/ crack in structure. It is true that mode shapes approach is better compared to frequencies based analysis for damage detection; however, it fetches excellent result, if real mode shape is used. Researchers are using theoretical/ numerical/ interpolated modes shape, which produce erroneous results. In this paper, a method is proposed to extract the real mode shape of structure experimentally using only one accelerometer and damage was detected successfully in the steel beam using this mode shape. An artificial damages were created in the steel beam in four stages and the mode shapes were determined after damage for each stage. The damage was also located and severity was predicted with the help of the extracted modes shape. It was found that location predicted by proposed method was almost correct. This technique is useful for sensitive structures.

The Reinforced Concrete (RC) systems are composed of different structural RC members such as beams, columns, shear walls, etc. Damage in RC members is found in the form of cracks, compression failure, reduction in effective area etc. Due to the presence of damages, there is a change in the dynamic behaviour. In the present work, the dynamic behaviour of undamaged and damaged RC multi-storey structures is studied with different damage locations in beams and columns at different stories. The damage is introduced by reducing Young’s modulus of concrete by 25%. The critical damage level is identified by using modal analysis. The damage severity in the columns and beams varied from 25% to 75%. The modal analysis and lateral load analysis are carried out to understand the dynamic behaviour of damaged structures. The Equivalent Static Method (ESM) is considered for earthquake analysis as per IS 1893 (Part −1): 2016. Analysis is done by using ETABS software. The natural frequency and time periods are considered as dynamic parameters. From the results, it has been observed that, there is a change in the natural frequency of the structural system with the introduction of damage of certain severity and at a particular location.