Curvature Mode Research Articles

A Method for the Damage Detection of Pile Foundation in High-Pile Wharf Based on A Curvature Mode Deletion Model

As the top of the pile foundation in high-pile wharf is connected to the superstructure and most of the pile bodies are located below the water surface, traditional damage detection methods are greatly limited in their application to pile foundation in service. In the present study, a new method for pile foundation damage detection is developed based on the curve shape of the curvature mode difference (CMD) before and after damage. In the method, the influence at each node on the overall CMD curve shape is analyzed through a data deletion model, statistical characteristic indexes are established to reflect the difference between damaged and undamaged units, and structural damage is accurately detected. The effectiveness and robustness of the method are verified by a finite element model (FEM) of high-pile wharf under different damage conditions and different intensities of Gaussian white noise. The applicability of the method is then experimentally validated by a physical model of high-pile wharf. Both the FEM and the experimental results show that the method is capable of detecting pile foundation damage in noisy curvature mode and has strong application potential.

Structural damage identification based on the method of generalized uniform load surface curvature

In view of the fact that the lower-order structural modes can be obtained easily in practice and the structural parameters before damage are unknown, the generalized uniform load surface curvature method based on least squares polynomial fitting is proposed to detect structural damage. First of all, the modal flexibility curvature method and the uniform load surface curvature method derived from the modal flexibility curvature are analyzed theoretically, and then, combining with the concept of generalized modal flexibility matrix, the generalized uniform load surface curvature method is obtained, and the generalized uniform load surface curvature method based on least squares polynomial fitting is put forward finally. Second, taking the numerical simulation of a T-beam fixedly supported at both ends as an example, the damage identification effect of the four methods mentioned above is calculated and compared. The results show that the generalized uniform load surface curvature method based on least squares polynomial fitting needs only lower-order modal parameters after the structural damage, can well identify not only the damage location but also the damage degree of the single damage or the multiple damage, and presents small truncation errors. Compared to the other three methods, it has certain advantages. Finally, the damage of a T-shaped simply supported beam is identified by using the proposed method, which verifies the effectiveness of the method, and hence, this method has important practical application value.

Delamination Identification of Composites using Normalized Modal Curvature and Image Processing

Delamination Identification of Composites using Normalized Modal Curvature and Image Processing

Identification of modal strains in concrete beams at sub-microstrain amplitude excitation using fibre Bragg grating sensors mounted on a strain-amplifying transducer

Vibration-based damage identification is a non-destructive method that enables the health monitoring of civil infrastructures. It aims to detect the presence and location of damage by measuring changes in the vibration characteristics of these structures. Unfortunately, the most popular vibrational parameters – natural frequencies and modal displacements – have a low sensitivity to certain types of local damage. Modal strains and curvatures, on the other hand, can be sufficiently sensitive to local damage, but monitoring modal strains is challenging. Indeed, the strain amplitudes can be in the sub-microstrain range (<1 με) when considering ambient excitation which is too small for most conventional techniques. Here we show that such measurements can be successfully carried out in a quasi-distributed manner with fibre Bragg grating–based sensors that have been mounted on a dedicated strain-amplifying transducer. First, we report on lab-scale dynamic tests on a 5-m-long concrete beam, equipped with such transducers having a strain amplification of 62. Our results show that we can identify the first three bending modes while the average strain level on the beam was only 0.06 με. Second, we present the first field test for these transducers conducted on a high-speed railway viaduct. We have succeeded to obtain six strain modes of the viaduct from the data collected with fibre Bragg gratings on the transducers at an average strain level of 0.067 με. To the best of our knowledge, this is the first time that strain mode identification in operational conditions using strain-amplifying transducers was successful. This demonstration can be a starting point for the implementation of vibration-based damage identification in civil structures allowing the fulfilment of its long-standing promise.

Damage detection in girder bridges using modal curvatures gapped smoothing method and Convolutional Neural Network: Application to Bo Nghi bridge

This paper addresses a damage detection method based on changes in modal curvature combined with Convolutional Neural Network (CNN). The use of modal curvature for damage detection is very well known. Some methods require modal data of healthy structures as a reference, others do not. Gapped Smoothing Method (GSM) is a vibration-based damage detection methodology, which makes use of modal curvature for identifying the location of structural damage and does not require information of the intact structure. The Bo Nghi bridge is used as an illustrative example. This bridge consists of four T-shaped concrete simply supported girders. One single beam with the same length and cross-section of the bridge girder is modeled and used to extract numerical data to train the CNN. A CNN is trained by using images from the damage index of the GSM to classify the damage location in the numerical beam model. Finally, the finite element model of the bridge is built and used to model damage scenarios to test the trained CNN. The results indicate that the combination of GSM and CNN can be used for damage detection and localization.

Damage detection and localization from linear and nonlinear global vibration features in concrete slabs subjected to localized thermal damage

In this study, different alternatives to detect and localize damage from linear and nonlinear vibration responses were investigated. These alternatives were compared on two concrete slabs subjected to different damage extents. Linear and nonlinear modal test configurations were considered. The variations of linear resonant frequencies, modal assurance criterion values, and nonlinear hysteretic parameters were used to detect damage. Then, the modal shapes were used to locate damage positions. The maximum principal curvatures derived from the original modal shape displacements between damaged and undamaged states made it possible to spot the damaged zones. Damage localization was further enhanced by weighting the principal modal shape curvature differences for every mode by their respective variations of the nonlinear hysteretic parameter. Finally, damage localization was achieved using different outlier identification techniques.

Numerical, statistical and experimental investigation on damage quantification in beams from modal curvature

In the task of locating and quantifying damage in beams from experimentally-obtained modal data, one-dimensional models are attractive due to their simplicity and apparent generality. However, stress concentration and neutral axis change near cracks make the assumptions of classical beam theory invalid. Notwithstanding, empirical equivalences with some analytical basis have been stated in the past, which led to some successes in detection and localization, although with uncertain grade of generality in quantification. In the present work, a method for quantifying damage in simply supported beams from modal curvature is analytically developed, highlighting the hypotheses upon which it relies. Then, a wide variety of cases (thousands) are parametrically modeled by using solid finite elements. The considered universe involves different materials; section types; crack locations, positions and sizes; sensor positions and locations; and beam dimensions. From the modal analysis results, damage indicators that are based on modal curvature are tested for their damage-quantification capability. Finally, this large data set is statistically assessed by using data mining techniques. Thus, interesting conclusions are found about the limitations and advantages of this damage-quantification method. Also, useful recommendations are provided for defining suitable positions and locations of sensors in beams. Finally, a series of experimental tests demonstrates the performance of the method under non-ideal conditions.

A composite beam integrating an in-situ FPCB sensor membrane with PVDF arrays for modal curvature measurement

This research develops a novel composite beam integrating a flexible printed circuit board (FPCB) sensor membrane with polyvinylidene fluoride (PVDF) arrays for accurately extracting modal curvature in a convenient way, which can be easily used in the potential aerospace applications of in-situ structure damage detection or structure health monitoring. The proposed composite beam structure consists of a metal beam, a FPCB sensor membrane and a periodic array of identical rectangular PVDF films. Specifically, a periodic array of identical rectangular PVDF films is encapsulated in the FPCB sensor membrane, and the FPCB sensor membrane is integrated with the metal beam. Since the lead wire, sensors, the protective layer of sensor and the host beam structure are of one-piece construction in the proposed structure, the proposed structure has the self-sensing function that the discrete curvature of modal shapes of the metal beam can be directly obtained by using the experiment modal analysis (EMA) method and no other sensors. Results show that the proposed structure has good self-sensing performance and can directly extract the modal curvature information without any numerical differential calculation. In addition, the proposed structure restrains surrounding noise and improves the stability of the sensor array signal since the sensor array is encapsulated with the metal beam under the same condition.

Model-free damage localization of structures using wavelet based grey relational analysis

Damage detection of real-life civil structures is generally performed under a condition of poor information, mainly referring to our insufficient knowledge of structures, uncertainties and limited sensors. Moreover, most damage detection methods require the numerical or mathematical models of a structure, whose stiffness parameters are sought by inverse solutions such as model updating. However, ill-conditioning problems are often found when updating complex structures. Hence, a model-free damage localization strategy has been proposed incorporating wavelet packet transform with grey relation analysis. First acceleration response signals are decomposed into different frequency subbands using wavelet packet transform. The wavelet packet energies of specific frequency subbands corresponding to fundamental modal frequencies are extracted and then normalized by the total energy of all the accelerometers. After that, wavelet packet energy curvatures are constructed and incorporated with grey relation analysis to propose a wavelet grey correlation coefficient. Damage locations are determined according to magnitude changes in these coefficients. Lastly, the feasibility of the proposed method has been successfully verified against an experimental steel beam. The validation also found that direct damage localization based on mode shapes or modal curvatures could not provide effective judgment.

Mode shape curvature of multiple cracked beam and its use for crack identification in beam-like structures

The problem of using the modal curvature for crack detection is discussed in this paper based on an exact expression of mode shape and its curvature. Using the obtained herein exact expression for the mode shape and its curvature, it is demonstrated that the mode shape curvature is really more sensitive to crack than mode shape itself. Nevertheless, crack-induced change in the approximate curvature calculated from the exact mode shape by the central finite difference technique (Laplacian) is much greater in comparison with both the mode shape and curvature. It is produced by the fact, shown in this study, that miscalculation of the approximate curvature is straightforwardly dependent upon crack magnitude and resolution step of the finite difference approximation. Therefore, it can be confidently recommended to use the approximate curvature for multiple crack detection in beam by properly choosing the approximation mesh. The theoretical development has been illustrated by numerical results.

Deterministic deterioration modeling of wind turbines toward the failure identification – a modal curvature approach

ABSTRACT The amount of built wind resource has greatly increased since wind turbines have started to get installed offshore in order to power much of the world. Topics relating to wind turbine have encouraged researchers to put in greater efforts towards developing modeling methodologies, analytical theories, assessment techniques. Through the establishment of certain models and new findings, potential ideas regarding structural health monitoring and non-destructive evaluations may be proposed and worthy of exploration. Based on the spectral formulation of a Timoshenko member with the consideration of soil–structure interaction, the simulated model of a wind turbine was investigated in this work in order to quantify the various effects due to defects as well as foundation stiffness on the dynamic responses of the tower. This paper focuses on the analysis of the tower structure using the modal curvature data of the first vibration mode. Preliminary results show that the curvature index defined in the proposed method is capable of indicating not only the damaged region of the tower, but also the degree of stiffness softening that the foundation system may have encountered. The presented methodology demonstrates potential as a feasible analysis method to be applied in a vibration-based assessment scheme for the wind turbine tower.

Enhancing the curvature mode shape method for structural damage severity estimation by means of the distributed genetic algorithm

An important challenge in damage detection based on the curvature mode shape (CMS) method is recognizing damage severity in damaged structures. Here, an efficient approach is proposed based on the finite element (FE) method, which detects the existence, location and severity of damage using the distributed genetic algorithm in conjunction with CMS. First, using the mode shape of the structure, curvature is calculated at the nodes of the structure in the FE model. By comparing the curvature between the intact and damaged structures, the existence and location of damage are determined. Next, by defining an optimization problem, damage severity in the damaged elements is determined. Results of applying the proposed approach on beam and frame structures under various damage scenarios and an experimental set-up show that this method is very effective in damage detection of such structures. Furthermore, the performance and accuracy of the proposed method are examined for various noise levels.

Delamination Detection in Mono Composite Leaf Spring by Modal Curvature and Flexibility Approaches

The premature failure analysis of laminated composite structures through damage inspections at initial level has gained considerable importance in recent years. Delamination is one of the major failure mechanisms which occur due to low inter-laminar fracture toughness of the matrix in composite structures. Detection of delamination is crucial to ensure safety and reliable use of composites. In the paper, the modal curvature and flexibility methods have been applied for delamination detection in composite leaf spring through analytical and finite element approaches. First, finite element models of healthy and delaminated leaf spring are formulated to evaluate the Eigen value and Eigen vectors. Next, the absolute curvature difference and change in flexibility in both springs are determined after mass normalization. The presence, location and severity of delamination in a spring are found through change in absolute modal curvature and difference in local flexibilities. The modal curvature method precisely identifies the delamination location and its severity than the modal flexibility method.

Damage identification of bridge structures based on curvature mod

Based on the modal analysis theory of bridge dynamic characteristics, a pre-damaged reinforced concrete model beam is established by ANSYS as the object of analysis. The regularity of modal parameters such as displac, ement mode and curvature mode of the model beam at the preset damage location and different damage degree and the identification of modal parameters in structure damage are studied by finite element numerical analysis. Sensitivity. The results show that the displacement mode is difficult to identify the damage of the structure effectively, but the curvature mode can reflect the damage of the structure more accurately. The damage identification method based on the curvature mode can be applied to the damage diagnosis of the structure in practical engineering.

An Effective Approach for Damage Identification in Beam-Like Structures Based on Modal Flexibility Curvature and Particle Swarm Optimization

In this paper, a computationally simple approach for damage localization and quantification in beam-like structures is proposed. This method is in consonance with applying modal flexibility curvature (MFC) and particle swarm optimization (PSO) algorithm. Analytical studies in the literature have revealed that changes in the modal flexibility curvature can be considered as a sensitive and suitable criterion for identifying damage in the beam-like structures. Modal flexibility curvature can be calculated utilizing central difference approximation, based on entries of the modal flexibility matrix. The PSO algorithm, as a powerful optimization tool, is employed in order to minimize the error function which is formulated as an error function between the measured modal flexibility curvatures of the damaged structure and those calculated from the analytical structure. To demonstrate the efficiency of the method, two beam-like structures under different damage scenarios are studied. In addition, the robustness of presented method is investigated only when the first several modal data are available. It is observed that the proposed approach is able to localize and quantify various damage cases only by a few lower vibrational modes and also, it is low-sensitive to measurement noise.

Empirical method for structural damage location using dynamic analysis

Abstract This paper presents the use of numerical model techniques for identification and damage location adopting the Modal Curvature Difference (MCD) method as reference for the analysis of a simply supported concrete structure. Then, an empirical formulation to detect damages in this structure is proposed. In this method, called Acceleration Summation Difference (ASD), the difference of acceleration amplitude between intact and damaged structures are calculated for concrete plates simply supported on rubber bearings. During the analyses, the finite element models were developed using SAP2000® software. The results obtained depicted that it is possible to determine the approximate position of one or more damages in the structure, with some restrictions, and the proposed ASD method presented good correlation to localize the position of single or multiple damages.

Damage detection on hull girder of ship subjected to explosion loading

Considering the limitation of current direct measurement method for ship damage identification, an indirect damage identification method based on dynamic parameters is taken into account. A 1500-ton ship simplified as the hull girder is taken as the research object. Artificial neural network method, the coordinate modal confidence (COMAC) and modal curvature index are applied to identify the ship's damage under different conditions through numerical experiments. Migration matrix method is introduced to obtain the damage database. The damage identification accuracy of two indexes based on modal shapes is discussed. Results show that the neural network intelligent method based on frequency changes can well locate and quantify the damage of the ship structure. Damages were correctly located, and the average accuracy of damage severity reached 95.78%. For damage indexes based on modal shapes, COMAC requires less data to identify the damage and has high calculation efficiency, but there is a certain range of error. When used in conjunction with various modes of the index modal curvature, damage localization is relatively accurate. Both indicators based on modal shapes can reflect the damage degree to some extent, but can't accurately identify the specific extent of damage.

Vibration-based damage diagnosis of composite sandwich panels with bi-directional corrugated lattice cores

In this paper we design and fabricate a series of carbon fibre composite bi-directional corrugated sandwich panels (BCSPs) with and without defects. A modified damage index (MDI) based on modal flexibility curvature variation (MFCV) is proposed to identify the damage location of composite BCSPs numerically. A good agreement of natural frequencies and modal shapes is obtained between the numerical and the experimental results, which demonstrates that the adopted numerical models are reliable for the present structures. Results show that the proposed MDI method can accurately detect almost all of damages and effectively eliminate the influence of false peaks as much as possible, which demonstrate the present MDI method is better than the DI method for the damage location of the present structures, which could be useful for the non-destructive evaluation (NDE) of such kinds of composite sandwich structures.

Study of damage identification for bridges based on deep belief network

To solve the problem of poor anti-noise ability faced by traditional pattern recognition methods in damage identification field, a bridge damage identification method based on deep belief network was proposed. Taken the modal curvature difference as the damage index, three restricted Boltzmann machines were constructed for pre-training. Then, the Softmax classifier and neural network were used to identify the damage location and degree under the environmental cases of no noise, weak noise, and strong noise, respectively. Subsequently, the influence of incomplete measurement modal data on the method was studied. Finally, damage identification based on deep belief network was implemented to a continuous beam bridge and compared with that of the back propagation neural network. The results showed that the proposed method could be highly effective not only on damage location but also on degree identification. Compared with back propagation neural network, deep belief network method may possess better identification ability and stronger anti-noise ability. It also demonstrates good identification effect under the condition of incomplete measurement modal data.

Damage Identification Method of Beam Structure Based on Modal Curvature Utility Information Entropy

Generally, the damage of the structure will lead to the discontinuity of the local mode shape, which can be well reflected by the modal curvature of the structure, and the local information entropy of the beam structure will also change with the discontinuity of the mode. In this paper, based on the information entropy theory and combining the advantages of modal curvature index in damage identification of beam structure, the modal curvature utility information entropy index is proposed. The modal curvature curves of nondestructive structures were obtained by fitting the modal curvature curves of damage structures with the gapped smoothing technique to avoid dependence on the baseline data of nondestructive structures. The index comprehensively reflects the damage state of the structure by calculating mutual weight change matrix and the weight‐probability coefficient. The performance of the new index was verified by the finite element simulation and model test of simply supported beam, respectively. The results show that the modal curvature utility information entropy index takes advantage of the modal curvature index which is sensitive to damage and can overcome its shortcomings effectively. The index proposed can identify the damage location and damage degree accurately and has certain noise immunity, which provides an effective damage identification indicator for beam structures.