Modal Curvature Difference Research Articles

Wooden Beams Modal Damage Identification Parameters Based on Strain

This study completely investigates the damage detection problem based on strain modal characteristics using simply supported wooden beams as the research object. First, modal analysis was performed, and finite element models of both damaged and undamaged timber beams were created using ABAQUS. Second, a number of strain modal characteristics (strain modal, strain modal difference, and strain modal curvature difference) were used to identify the damage to the wooden beam construction. Lastly, the modal parameters of the wooden beam under various damage scenarios were ascertained using damage identification experiments, and the test results were contrasted with those obtained from a numerical simulation. The findings showed that, while each of the three damage identification indices has a distinct identification effect, they can all locate the damage to wooden beams. Strain mode curvature difference > strain mode difference > strain mode is the order of them. The results of this study can be used as a reference to identify damage to timber beams in the future.

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.

Numerical investigation on crack identification using natural frequencies and mode shapes of a drilling riser during deployment and retrieval

Deployment and retrieval of drilling risers are among the most highly stressed marine operations processes, and allowable imperfections or missed-inspection cracks are likely to expand into limited defects, making crack identification essential during the deployment and retrieval of risers. This study's main objective is to investigate the performances of natural frequencies and modal shapes on crack identification in a drilling riser during installation and retrieval. First, a computation code is programmed to extract the natural frequencies and modal shapes of the intact and cracked risers, and its validity is verified by two numerical methods, i.e., precise integration method and differential transformation method in the literature. Second, the crack-identification ability of natural frequencies versus crack depth and riser-suspension length is studied in detail. An approach using the normalized fourth derivative of modal shapes is developed for crack identification compared with the traditional modal-curvature and modal-curvature difference approaches. Finally, the cracks near the middle span and both ends of the risers are identified, respectively, during the deployment. From the research on crack identification during installation, several conclusions and suggestions are drawn to provide some valuable references for the safety of drilling and production operations.

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.

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 of Bridge Based on Chebyshev Polynomial Fitting and Fuzzy Logic without Considering Baseline Model Parameters

The paper presents an effective approach for damage identification of bridge based on Chebyshev polynomial fitting and fuzzy logic systems without considering baseline model data. The modal curvature of damaged bridge can be obtained through central difference approximation based on displacement modal shape. Depending on the modal curvature of damaged structure, Chebyshev polynomial fitting is applied to acquire the curvature of undamaged one without considering baseline parameters. Therefore, modal curvature difference can be derived and used for damage localizing. Subsequently, the normalized modal curvature difference is treated as input variable of fuzzy logic systems for damage condition assessment. Numerical simulation on a simply supported bridge was carried out to demonstrate the feasibility of the proposed method.

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

The localization of stiffness variation in damaged beams through modal curvatures, i.e., second derivative of mode shapes, is studied by exploiting a perturbative solution of the Euler–Bernoulli equation. It is shown that for low order modes the difference between undamaged and damaged modal curvatures has only one distinct peak if the damage is localized in a narrow region. This phenomenon is independent of the presence of experimental noise and of the technique used to reconstruct the curvature mode shapes from the displacement mode shapes. Broader damages cause the modal curvature difference to have several peaks outside the damage region that could result in a false damage localization. The same effect is present at higher modes for both narrow and broad damages. As a result, modal curvatures can be effectively used to localize structural damages only once they have been properly filtered. Here the perturbative solution is used to introduce an effective damage measure able to localize correctly narrow and broad damages and also single and multiple damages cases.

Research Based on Modal Curvature and Wavelet Transform for Identifying Damage of Reticulated Shell Structures

In this paper, a research is carried on to identify damage of reticulated shell structures based on the combination of modal curvature method and wavelets transform method. Take a scaled model of the reticulated shell structure as an example to analyze, the cross section of one member supposed to have a slight damage of stiffness reduction. In order to locate the damage, modal curvatures of the structure are taken as damage indexes to perform continuous wavelet transform. Results of the numerical analysis indicate that the difference of wavelet transform coefficients of modal curvature can be used to locate damage roughly, while the wavelet transform coefficients of modal curvature difference can be used to locate damage more precisely with easier and more reliable data processing. So it is clear that the damage identification based on modal curvature and wavelet transform is quite effective.

Damage Identification of Multi-Box Steel-Concrete Composite Bridges Based on Modal Curvature Difference Method

Based on the data from dynamic analysis of a 40m-span multi-box steel-concrete composite bridge and the difference value of its modal curvature before and after the structural damage, this paper detects the damage locations in steel-concrete composite bridge by modal curvature difference method (MCDM). Here we adopt the updated finite element model in last work as analytical model, taking concrete density and elastic modulus as updating parameters and modal frequency+MAC as reference data. The results indicate that the modal curvature difference method can well locate the damages in steel-concrete composite bridge, especially the damage in concrete. But the change rate of frequency as damage index is insensitive to the bridge damage and the method can’t be applied solely for practical.

Damage Detection of Plane Member Structures Based on Modal Curvature Difference Method

Modal curvature difference (MCD) method is an effective damage detection technique for beams but not very feasible for plane member structures, because the MCD of each member is difficult to calculate with the structural modal shapes which are expressed in a global coordinate system. By improving MCD method, this paper develops a general and convenient damage detection method for plane member structures. The new method introduces coordinate transformation technique to settle the calculation difficulty of MCD. To validate the availability of the method, the finite element damage model of a typical structure is built up, and detection effects on the case of single member damage and multiple member damages are studied respectively. The results show that the improved method is especially suitable for the damage detection of plane member structures.