A statistical approach for evaluating crack defects in structures under dynamic responses

Abstract: This article aims to identify multiple cracks of a structure under the act of moving load by using wavelet analysis based on displacement signal. Among many researches on this topic, the current study presents three new salient points. Firstly, the breakthrough is the combination of two independent algorithms in wavelet analysis of deflection signal’s static and dynamic elements using deep learning. The static elements allow determining quantity as well as location of defects in structures while the dynamic elements help to assess growth rate of defects during structural operation. Secondly, wavelet analysis is conducted based on deflection signal, which is rarely used but has a great deal of information proving the existence of cracks in a structure. This signal can also be applied to various types of structures such as plate, beam, bar and pivot. Thirdly, original signals are analyzed directly using wavelet analysis without any intermediate algorithm. This gives simpler and more accurate assessment of crack status, therefore, helps to increase sensitivity as well as data accuracy during identification process, especially for structures with multiple cracks. This study concurrently identifies all three criteria of defect assessment, namely: quantity, location and growth rate. In addition, the results have high potential for practical application to most structures.

Abstract: This research proposes a correlation coefficient for detecting and evaluating defects in beams, which brings about a positive outcome in terms of accuracy and efficiency. This parameter surpasses other parameters, such as natural frequency and damping coefficient, thanks to its sensitivity to structural changes. Our results show that although the damping coefficient had more variation than the natural frequency value in the same experiment, its changes were insufficient and unstable at different levels of defects. In addition, the proposed correlation coefficient parameter has a linear characteristic and always changes significantly according to increasing levels of defects. The results outweigh damping coefficient and natural frequency values. Furthermore, this value is always sensitive to measurement channels, which could be an important factor in locating defects in beams. The testing index is statistically evaluated by a normal distribution of the amplitude value of vibration measurement signals. Changes and shifts in this distribution are the basis for evaluating beam defects. Thus, the suggested parameter is a reliable alternative for assessing the defects of a structure.

Abstract: In this paper, we investigate changes in the mechanical properties of complex structures using a combination of the discrete model, Fast Fourier Transform (FFT) analysis and deep learning. The first idea from this research utilizes the discrete model from a perspective that is different from the finite element method (FEM) of previous works. As the method in this paper only models the mechanical properties of structures with finite degrees of freedom instead of dividing them into smaller elements, it reduces error in evaluation and produces more realistic results compared to the FEM model. Another advantage is how it allows the research to survey both parameters that affect the mechanical properties of structures—the overall stiffness (K) and the damping coefficient (c)—during vibration, while previous researches focus only on one of these two parameters. The second idea is to use FFT analysis to increase the sensitivity of the signal received during vibration. FFT analysis simplifies calculations, thereby reducing the effect of noise or errors. The sensitivity achieved in FFT analysis increases by 25% compared to traditional Fourier Transform (FT) analysis; moreover, the error in FFT analysis compared to experimental results is quite small, less than 2%. This shows that FFT is a suitable method to identify sensitive characteristics in evaluating changes in the mechanical properties. When FFT is combined with the discrete model, results are much better than those of several existing approaches. For the last idea, the manuscript applies deep learning (FFT-deep learning) in the noise reduction process for the original data. This makes the results much more accurate than in previous studies. The results of this research are shown through the monitoring of spans of the Saigon Bridge—the biggest and most important bridge in Ho Chi Minh City, Vietnam—during the past 11 years. The correspondence between the theoretically obtained result and the experimental one at the Saigon Bridge suggests a new area for development in evaluating and forecasting structural changes in the future.

Abstract: We propose a novel representative power spectrum density as a specific characteristic for showing responses of spans during a long operational period. The idea behind this method is to use the representative power spectrum density as a powerful tool to evaluate the stiffness decline of spans during their operation period. In addition, a new measurement method has been introduced to replace the traditional method of monitoring the health conditions of bridges through a periodic measurement technique. This helps to reduce costs when carrying out testing bridges. Besides, the proposed approach can be widely applied not only in Vietnam but also in many other underprivileged countries around the world. Obtained results show that, during the operational process of spans, there is not only a pure vibration evaluation such as bending vibration and torsion vibration tests but also a combination of various vibration types including bending-torsion vibration or high-level vibrations like first-mode bending and first-mode torsion. Depending on each type of structure and material properties, different types of vibrations will appear more or less during the operational process of spans under a random moving load. Furthermore, the representative power spectrum density is also suitable for evaluating and determining many different fundamental vibrations through the same measurement time as well as various measurement times.

Abstract: A continuous cracked beam vibration theory is developed for the lateral vibration of cracked Euler–Bernoulli beams with single-edge or double-edge open cracks. The Hu–Washizu–Barr variational formulation was used to develop the differential equation and the boundary conditions of the cracked beam as a one-dimensional continuum. The displacement field about the crack was used to modify the stress and displacement field throughout the bar. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack, found with fracture mechanics methods. The results of two independent evaluations of the lowest natural frequency of lateral vibrations for beams with a single-edge crack are presented: the continuous cracked beam vibration theory developed here, and a lumped cracked beam vibration analysis. Experimental results from aluminum beams with fatigue cracks are very close to the values predicted. A steel beam with a double-edge crack was also investigated with the above mentioned methods, and results compared well with existing experimental data.

Abstract: The differential equation and associated boundary conditions for a nominally uniform Bernoulli-Euler beam containing one or more pairs of symmetric cracks are derived. The reduction to one spatial dimension is achieved using integrations over the cross-section after plausible stress, strain, displacement and momentum fields are chosen. In particular the perturbation in the stresses induced by the crack is incorporated through a local function which assumes an exponential decay with distance from the crack and which includes a parameter which can be evaluated by experimental tests. Some experiments on beams containing cuts to simulate cracks are briefly described and the change in the first natural frequency with crack depth is matched closely by the theoretical predictions.

Abstract: The equation of motion and associated boundary conditions are derived for a uniform Bernoulli-Euler beam containing one single-edge crack. The generalized variational principle used allows for modified stress, strain and displacement fields that satisfy the compatibility requirements in the vicinity of the crack. The concentration in stress is represented by introducing a crack function into the beam's compatibility relations. A displacement function is also introduced to modify the in-plane displacement and its slope near the crack. Both functions are chosen to have their maximum value at the cracked section and to decay exponentially along the beam's longitudinal direction. The rate of exponential decay is evaluated from finite element calculations. The resulting equation of motion is solved for simply supported and cantilevered beams with single-edge cracks by a Galerkin and a local Ritz procedure, respectively. These theoretical natural frequencies and mode shapes match closely with experimental and finite element results. The possibility of determining the damage properties of cracked beams from changes in dynamic behavior is discussed.