Curvature Mode Research Articles

Rail base flaw detection and quantification based on the modal curvature method and the back propagation neural network

Due to the development of railways towards high speed and heavy load, a high-precision all-around system for rail flaw detection at the earliest stage is in huge demand. In the published literature, flaws in the rail head and web have already become the primary objective of much research. Fruitful conclusions have been satisfactorily drawn to guide different engineering practices. Unfortunately, flaws developed at the rail base are often overlooked. According to field investigations, the ignorance of this element might sometimes be the main suspect to explain certain derailments and severe accidents. Hence, an efficient technology for detecting rail base flaws is required. This paper investigates the application of the modal curvature method and a neural network. Firstly, the detection and quantification algorithms of rail base flaws are presented. Secondly, a series of numerical studies is introduced on a free rail and a fastened rail, respectively. Modal test results are utilized for verifying the numerical models. Finally, by using the trained neural network, the base flaws are detected and quantified. The proposed algorithm provides a new research idea for the area of rail detection.

Non-destructive performance assessment of bonded surface connections by changes in curvature mode shape

Joining processes have gained increasing relevance and their effectiveness appears as a necessity in the production of lightweight structures. Many researchers have been investigating affordable testing solutions to assess joint performance. Herein, an easy-to-apply non-destructive technique, based on vibration analysis, is presented and evaluated by a purely numerical approach. Changes in the curvature mode shape of beam-like structures are measured and related to the extension of bonded areas of the connected parts. The preliminary results, achieved by modal analysis, provide a first proof-of-concept of the proposed technique and of its increased sensitivity compared to techniques based on frequency response functions.

An extendable Space-Time Curvature Mode model

Einstein calculated the curvature of space-time from a Field equation based on an equation of motion derived by the variation of a geodetic path and a second rank Metric tensor. In this study a Space-Time Curvature Mode (STCM) model is calculated from a series of coupled Field equations derived from the variation of a Taylor series expansion of a Lagrangian potential of the STCM. The Taylor series expansion coefficients are Metric tensors of increasing rank. The STCM model can be extended to any number of Field equations. The coupled Field equations of the STCM describe the warping of space-time by masses and energy fields, and the effect of the curved space-time on the motion of masses and energy fields. This results in a description of space coordinates that have locally positive and negative slopes as a function of the time coordinate and can describe a Universe with at times an accelerating expansion and at later times a contracting Universe. This study replaces the postulated concepts of Einstein’s Cosmological constant and postulated concepts of Dark Mass and Dark Energy. It is shown that the Hamiltonian is conserved.

Magnetic field back reaction on the matter power spectrum

At lowest order comoving magnetic fields which are frozen-into the expanding cosmic fluid do not evolve in time. At next-to-leading order the induction equation is sourced by the interaction term between the baryon velocity and the magnetic field amplitude which leads to a non-trivial evolution of the comoving magnetic field. Moreover, it induces non-trivial cross correlations between the adiabatic curvature mode and the magnetic mode. This cross correlation together with the evolution of the induced matter perturbation leads to interesting effects on the total matter power spectrum at small scales.

Model-independent approach to effective sound speed in multi-field inflation

For any physical system satisfying the Einstein’s equations, the comoving curvature perturbations satisfy an equation involving the momentum-dependent effective sound speed, valid for any system with a well defined energy-stress tensor, including multi-fields models of inflation. We derive a general model-independent formula for the effective sound speed of comoving adiabatic perturbations, valid for a generic field-space metric, without assuming any approximation to integrate out entropy perturbations, but expressing the momentum-dependent effective sound speed in terms of the components of the total energy-stress tensor. As an application, we study a number of two-field models with a kinetic coupling between the fields, identifying the single curvature mode of the effective theory and showing that momentum-dependent effective sound speed fully accounts for the predictions for the power spectrum of curvature perturbations. Our results show that the momentum-dependent effective sound speed is a convenient scheme for describing all inflationary models that admit a single-field effective theory, including the effects of entropy pertubations present in multi-fields systems.

Corrosion Damage Identification of Towering Steel Headframe Based on Parametric Modeling and Data Fusion

The mine hoisting headframe is a typical towering truss structure, and its damage is complicated after long-term service, which affects the safety of the structure. To achieve rapid identification of corrosion damage on a towering steel headframe, the degradation law of headframe under different damage was analyzed via parametric modeling method and verified via field measurement. The results show that the influence range of element corrosion damage is localized, and a 50% corrosion rate of the bottom column will lead to a collapse risk of the headframe. After that, the single index method, of superimposed curvature mode difference and modal flexibility difference curvature, is used to identify corrosion damage of headframe column. The results indicate that the single index method is susceptible to interference in the undamaged position and leads to error identification. The improved multi-index data fusion damage identification method based on D-S evidence matrix is proposed, through which the multi-position damages in headframe structure can be identified accurately. Compared to the one-stage fusion method, the improved two-stage fusion method is more robust, with an increase of 42.9% in identification accuracy, and a reduction of 75% in misjudgment.

Detection of transversal cracks in prismatic cantilever beams with weak clamping using machine learning

Because our infrastructure is aging and approaching the end of its intended functioning time, the detection of damage or loosening of joints is a topic of high importance in structural health monitoring. The most desired way to assess the health of engineering structures during operation is to use non-destructive vibration-based methods that can offer a global evaluation of the structure’s integrity. A comparison of using different modal data for training feedforward backpropagation neural networks for detecting transverse damages in beam-like structures that can also be affected by imperfect boundary conditions is presented in the current paper. The different RFS, RFSmin, and DLC training datasets are generated by applying an analytical method, previously developed by our research team, that uses a known relation, based on the modal curvature, severity estimation of the transverse crack, and the estimated severity for the weak clamping. The obtained dataset values are employed for training three feedforward backpropagation neural networks that will be used to locate transverse cracks in cantilever beams and detect if the structure is affected by weak clamping. The output from the three ANN models is compared by plotting the calculated error for each case.

Construction of Biologic Microscopic Image Segmentation Model Based on Smoothing of Fourth-Order Partial Differential Equation.

In order to solve the problem of microscopic image noise, a biological microscopic image segmentation model based on the smoothing of the fourth-order partial differential equation was proposed. Based on the functional description of image smoothness by directional curvature mode value, a fourth-order PDE image denoising model is derived, which can effectively reduce noise while preserving edges. The result of this method is piecewise linear image, and the gradient at the edge of the target has a step. Using the feature of noise reduction, a new geodesic active contour model is proposed. The experiment result shows that when the variance of Gaussian white noise is 15, the enhancement and denoising effects of the proposed method are 80.35% and 69.84 higher than those of the original vibration filtering method and L. Alvarez method. In terms of time, the proposed method is 1.3075 seconds slower than the original vibration filtering method and 17.5754 seconds faster than the L. Alvarez method. When the variance of Gaussian white noise is 25, the enhancement and denoising effects of the proposed method are 97.79% and 81.16 higher than those of the original vibration filtering method and L. Alvarez method. In terms of time, the proposed method is 1.3246 seconds slower than the original vibration filtering method and 17.5796 seconds faster than the L. Alvarez method. Conclusion. The new model is not only stable but also has strong ability of contour extraction and fast convergence.

A detection method integrating modal deflection curvature difference and natural frequency for structural stiffness degradation

A detection method integrating modal deflection and natural frequency is proposed to locate and quantify the damage of the beam. A damage identification index using modal deflection curvature difference is developed to locate damage. Note that the modal deflection is derived from the flexibility matrix and virtual force. A damage quantification equation is established by the transfer matrix method, which includes the parameters of natural frequencies, damage coefficients and damage location. Since the damage location parameters are determined by the proposed damage identification index, the damage coefficients of the damaged segments can be determined from the natural frequencies according to the damage quantification equation. The proposed damage detection method is verified numerically and experimentally. The results indicate that the proposed method can well locate and quantify the local damage of beams, especially for the beams with non-uniform damage degradation. The proposed damage localization index is more appropriate to locate damage than the index using modal flexibility curvature (MFC) or modal flexibility curvature matrix (MFCM).

Damage recognition of glass fiber composite bi-directional corrugated sandwich cylindrical panels via non-contacted vibration method

It has always been one of the important issues and challenges of current concern on the damage identification of fiber-reinforced composite sandwich structures. In this work, a damage index based on the modal flexibility curvature change rate (MFCCR) method considering the effect of curvature is proposed to study the damage recognition of glass fiber composite bi-directional corrugated sandwich cylindrical panels (BCSCPs). A series of composite BCSCPs without and with different kinds of defects is designed and fabricated. A non-contacted vibration experiment is carried out to investigate the modal characteristics of the specimens with different configurations. Numerical structural parametric analyses are also conducted to verify the feasibility of the present damage recognition method. It is found that the position of the defect can be successfully detected by using the MFCCR damage index focus on the sensitive area, and can be applied for more than one damage position existing on the models. Some conclusions are given, which can provide references for damage identification of such complex structures.

Structural Damage Identification Method of Girder Bridges Based on Multilevel Data Fusion Theory

The single index based on modal strain energy and modal curvature is proved to be effective for damage localization, while its recognition accuracy is not satisfied and can not directly reflect damage degree. Therefore, multilevel data fusion methods are proposed here with three new indexes of modal strain energy dissipation rate (DR), change rate of cross-model modal strain energy (CR), and difference of modal curvature ratio (RD). Firstly, first-level, second-level, and third-level data fusion methods are deduced based on Bayes theory, weighted average criterion, and BP neural network, respectively. The first three order modes data of each index are fused in the first level, and their results are further fused between indexes in the second level, which will be applied for damage position judgement; moreover, results of the second level as input are last fused in the third level in order to predict structural damage degree. Secondly, a simply supported beam and a three-span continuous girder models are simulated to verify effectiveness of multilevel data fusion indexes. It can be concluded that the recognition results agree well with man-made damage cases whatever the positions or degrees are. Finally, a test study on a simply supported steel beam with different damage forms is carried out. The results show that the proposed multilevel data fusion methods have good abilities of sensitivity and anti-interference, are fault-tolerant, have robustness, and would provide certain effective experience for actual damage identification.

Directional wavelet modal curvature method for damage detection in plates

Abstract Vibration-based damage detection using the 2D modal curvature has become a research focus. However, the traditional methods based on modal curvature lack the sensitivity to direction of the damage. To address this problem, a directional 2D Morlet wavelet modal curvature is proposed in this paper. The directional wavelet modal curvatures show the following merits: robust to noise interference and sensitive to direction of damage. By the numerical simulation, the efficiency of the proposed method is demonstrated in the plate-like structure.

Advances in the characterization of aerosol optical properties using long-term data from AERONET in Buenos Aires

We present a complete characterization of aerosols in Buenos Aires based on their optical and microphysical properties from a long-term record (19-years) of AERONET V3 observations at the CEILAP-BA site. The baseline climatology indicates that the city has low mean aerosol load (0.11 ± 0.1) and mean Ångström exponent (α) of 1.11 (±0.4). The long-term trend of the monthly median aerosol optical thickness (AOT) is not significant whereas monthly α medians show a significant negative trend. Atmospheric turbidity increases in August and September (40%). Annual and monthly particle size distributions show predominance of the coarse mode. This apportionment can change under particular conditions, e.g., showing increased fine mode load in August and September.The thresholds of α and AOT proposed for four aerosol types allowed a satisfactory classification of aerosols. The relationship between AOT and α clearly illustrated the major contribution to extinction of finer particles under more turbid conditions. This feature—not evident in the baseline climatology— is consistent with the presence of smoke from regional biomass burning. Sporadic intrusions of coarse particles (dust/ash) from remote sources also enhance extinction. The analysis of the interrelations among aerosol properties (fine mode fraction of AOT, volume concentration, spectral curvature, and size distribution) supports these findings. The aerosols seem to undergo aging and/or hydration processes as shown by the relationships among AOT, extinction due to the fine mode, spectral curvature, and aerosol fine mode radius. This comprehensive analysis revealed details associated with the contributions from local and remote anthropogenic and/or natural sources.

Multiple damage detection in a cantilever beam using baseline-free operational modal analysis

Operational Modal Analysis (OMA) or output-only modal analysis allows obtaining modal parameters in operational conditions, i.e., without external excitation. While being more challenging than traditional or Experimental Modal Analysis (EMA), OMA allows to monitor the structural health of a structure in cases where EMA is not practical or feasible. This article presents an introduction to an OMA technique based on Frequency Domain Decomposition (FDD) and its mathematical formalism, and demonstrates its potential for detecting damage in a cantilever beam. A transient dynamic Finite-Element Analysis (FEA) under white noise excitation has been performed in ANSYS Workbench to obtain the acceleration responses of the system. The numerical accelerometers signals along the beam are used for the OMA analysis and multiple cracks are analyzed at different positions along the beam. The technique used for damage detection is Curvature Mode Shape (CMS) analysis, using only the information of the damaged structure, making it a baseline-free method. The technique is shown to be capable of correctly detecting and locating the different damages analyzed.

NOVEL APPROACH TO EXTRACT DENSE FULL-FIELD DYNAMIC PARAMETERS OF LARGE-SCALE BRIDGES USING SPATIAL SEQUENCE VIDEO

This study proposes the use of a high-speed camera as a holographic visual sensor to obtain the dense full-field dynamic parameters of the main beam of a bridge by the field of view through uniaxial rotation photography. Based on the basic principle that the frequency and mode of a structure are inherent characteristics, the mode coordinates obtained from each field of view are unified, normalized, and matched according to the same name pixels to obtain the dense fullfield dynamic parameters of the entire bridge. The frequency and first three order modes of a self-anchored suspension test bridge are collected by the method proposed in this study. The frequency comparison between the accelerometers and dial gauges is within 3%, and the mode shapes are more holographic and more realistic than those obtained by limited measuring points. In addition, the difference in the curvature mode under various damage conditions obtained by limited measurement points is compared with that obtained by the method proposed in this study. Results shows that the dense full-field modal curvature difference can reflect the change in the damage location even in a low order, which means the sensitivity of the change of damage location in low-order modal.

Changes in Frequency and Mode Shapes Due to Damage in Steel-Concrete Composite Beam.

This study presents an analysis of changes in the vibration frequency and mode of vibration of a composite beam due to damage. A steel–concrete composite beam was considered, for which numerical analysis (RFE model) and experimental tests were conducted. Two levels of damage were introduced to the beam. To determine the changes in the mode of vibration before and after the damage, the modal assurance criterion (MAC) and its partial variation (PMAC) were applied. The curvature damage factor (CDF) was used to determine the changes in the modal curvature. The natural frequencies were sensitive to the introduced damage. The results show that the MAC is not effective in determining the location of damage in the connection plane. Two different coefficients were introduced to locate the damage. The PMAC was used for sections of subsequent modes of vibration and allowed effectively locating the damage. The CDF considered simultaneous changes in the curvatures of all vibration modes and was effective in locating the damage in the connection plane.

Improvement on modal curvatures methods for multiple damage identification in beams

PurposeThe purpose of this paper is to present a study on the application of four damage factors to several single and multiple damage scenarios of aluminium beams. Each one of these damage factors is defined by the information given by modal curvatures of the beams.Design/methodology/approachThe methodology consisted of a first experimental stage in which the modal rotations were measured with shearography and a subsequent numerical analysis in order to obtain the modal curvatures. To this end, three finite difference formulae were applied. The modal curvatures were then used to calculate the damage factors.FindingsIt was found that the profile of the damage factors varies according to the finite difference formula used. In view of the findings, the differences among the damage factors analysed are highlighted and some final recommendations to improve damage identifications via modal curvature-based are presented.Originality/valueTo the best of the authors’ knowledge, the application and comparison of several finite difference formulae and corresponding optimal sampling has not been carried out before. With the proposed approach, it is possible to identify multiple damages, which is still a great challenge. The post-processing of shearography measurements with a numerical method, which is inherently a multidisciplinary approach, is also a substantial improvement upon other type of approaches found in the literature.

Wavelet-based damage localization and severity estimation of experimental RC beams subjected to gradual static bending tests

In this paper, the modal curvatures of experimental and numerical reinforced concrete (RC) beams were analyzed by wavelet transform to find the locations and severities of damages. Two RC beam specimens were selected from previous research works that were gradually damaged under four-point static bending tests, and following each loading step, modal tests were performed to achieve their dynamic parameters. Then, based on the selected experimental RC beams, numerical models including single, double and triple damage scenarios, as slots at different locations with constant width and different depths, were simulated to propose proper damage indices. By utilizing Shannon entropy, normalizing and applying threshold on the resulted wavelet coefficient of modal curvatures at undamaged and damaged states, two damage indices were proposed, in which one of them uses just the damaged modal data to conduct damage localization whereas the second one needs both damaged and undamaged modal data to estimate damage severities as long as damage locations. The results show that the second proposed damage index has the ability to assess the increasing trend of damage in different levels in addition to correctly detection the locations of all damage scenarios in numerical models. Moreover, regarding the experimental RC beams, the second proposed damage index could successfully detect the damaged degree of freedoms and the corresponding severities at different loading steps in both specimens. The predicted crack propagation trend by the proposed damage indices were consistence with the experimental observations.

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 Detection on a Beam with Multiple Cracks: A Simplified Method Based on Relative Frequency Shifts

Identifying cracks in the incipient state is essential to prevent the failure of engineering structures. Detection methods relying on the analysis of the changes in modal parameters are widely used because of the advantages they present. In our previous research, we found that eigenfrequencies were capable of indicating the position and depth of damage when sufficient vibration modes were considered. The damage indicator we developed was based on the relative frequency shifts (RFS). To calculate the RFSs for various positions and depths of a crack, we established a mathematical relation that involved the squared modal curvatures in the healthy state and the deflection of the healthy and damaged beam under dead mass, respectively. In this study, we propose to calculate the RFS for beams with several cracks by applying the superposition principle. We demonstrate that this is possible if the cracks are far enough from each other. In fact, if the cracks are close to each other, the superposition method does not work and we distinguish two cases: (i) when the cracks affect the same beam face, the frequency drop is less than the sum of the individual frequency drops, and (ii) on the contrary, cracks on opposite sides cause a decrease in frequency, which is greater than the sum of the frequency drop due to individual damage. When the RFS curves are known, crack assessment becomes an optimization problem, the cost function being the distance between the measured RFSs and all possible RFSs for several vibration modes. Thus, the RFS constitutes a benchmark that characterizes damage using only the eigenfrequencies. We can accurately locate multiple cracks and estimate their severity through experiments and thus prove the reliability of the proposed method.