No abstract

Damage detection based on modal parameter changes has become popular in the last few decades. Nowadays, there are robust and reliable mathematical relations available to predict natural frequency changes if damage parameters are known. Using these relations, it is possible to create databases containing a large variety of damage scenarios. Damage can be thus assessed by applying an inverse method. The problem is the complexity of the database, especially for structures with more cracks. In this paper, we propose two machine learning methods, namely the random forest (RF), and the artificial neural network (ANN), as search tools. The databases we developed contain damage scenarios for a prismatic cantilever beam with one crack and ideal and non-ideal boundary conditions. The crack assessment was made in two steps. First, a coarse damage location was found from the networks trained for scenarios comprising the whole beam. Afterwards, the assessment was made involving a particular network trained for the segment of the beam on which the crack was previously found. Using the two machine learning methods, we succeeded in estimating the crack location and severity with high accuracy for both simulation and laboratory experiments. Regarding the location of the crack, which was the main goal of the practitioners, the errors were less than 0.6%. Based on these achievements, we concluded that the damage assessment we propose, in conjunction with the machine learning methods, is robust and reliable.

The paper presents a method to detect, locate and evaluate damage severity of Euler-Bernoulli beams, based on how natural frequencies change due to damages. Previous researches that dealt with this issue focused only on quantitative changes, mainly considering a global stiffness reduction in the damaged area. The authors have contrived a correlation between the strain energy stored in a segment of the beam, which is proportional with the mode shape curvature of a considered vibration mode at that location, and the frequency change for this mode if damage appears on that segment. This reveals that for an element of the beam, the stiffness change of a certain mode for a given damage varies between zero and a maximum, depending solely on the location of that element. Moreover, one has to consider different stiffness changes for a damaged element placed on a certain location, depending on the vibration mode. This rule how frequencies of various modes change due to damage are used to create patterns, based on relative frequency shifts, which characterize damaged beams in respect to defect location and severity. The method was validated by numerous experiments, which proved its accuracy and reliability.

A direct approach for the calculation of the natural frequencies and vibration mode shapes of a perfectly clamped-free beam with additional stepwise eccentric distributed masses is developed, along with its corresponding equations. Firstly there is contrived influence of a mass, located on a given position along the beam, upon the modal energies, via an energy analysis method. Secondly, the mass participation coefficient is defined as a function of the mass location and the bending vibration mode number. The proposed coefficient is employed to deduce the mathematical relation for the frequencies of beams with supplementary eccentric loads, generally available for any boundary conditions. The accuracy of the obtained mathematical relation was examined in comparison with the numerical simulation and experimental results for a cantilever beam. For this aim, several finite element models have been developed, individualized by the disturbance extent and the mass increase or decrease. Also, one real system was tested. The comparisons between the analytically achieved results and those obtained from experiments proved the accuracy of the developed mathematical relation.

The paper presents a method to assess damages in beams, based on how natural frequencies of bending vibration modes change due to damages. The authors have contrived a correlation between the strain energy stored in a segment of the beam, which is proportional with the mode shape curvature of a considered vibration mode at that location, and the frequency change for this mode if damage appears on that segment. For a certain mode, damages placed on inflection points of the mode shape curvature, where the strain energy is null, will not produce changes in frequency, while damages placed on maxima will produce the highest changes in frequency. For other locations of damage, the frequency shift will be proportional with the mode shape curvature of the vibration mode at that location. We worked out a general relation, which gives the frequency shift of all bending modes, with one coefficient depending on the support type. To evaluate damages, we determine analytically the relative frequency shift as ratio between the frequency change and the natural frequency of the undamaged beam, for the first ten vibration modes, considering various damage depths and locations. Comparison of results with that obtained by measurements on the real beam permits detection, location and assessment of damages in beams with high accuracy. The method was validated by experiments.

No abstract

This paper introduces a method to identify damages in beam-like structures by analyzing the natural frequency changes of the first six transversal vibration modes. A correlation between the damage location and frequency change is established for each mode separately, by considering the modal strain energy stored in that location. The mathematical relation describing this correlation is used to characterize the dynamic behavior of a beam with a damage of known position and to derive its Damage Location Indicator (DLI) as a six-term vector. The method consists in comparing the vectors describing the damage at any possible location along the beam with the Damage Signature (DS), which is achieved from the measurements that compare the beam's frequencies in healthy and damaged state. A modified Kullback-Leibler Divergence is used to assess the damage location. In order to permit early damage assessment, an improved frequency evaluation algorithm was developed. It is based on signal truncation and consequent spectral lines rearrangement, in order to accurately find the strongest spectral components. The effectiveness of the proposed method is demonstrated by simulations and experiments.

No abstract