Crack prediction in beam-like structure using ANN based on frequency analysis

A BSTRACT . The dynamic experimental and numerical analysis of cracked beams has been studied with the aim of quantifying the influence of depth crack on the dynamic response of steel beams. Artificial Neural Method ANN has been used where a numerical simulation was improved in Matlab. A finite element model has also been developed by using the Ansys software, and the obtained results were compared with exact crack length. The study takes into account different hidden layer values in order to determine the sensitivity of the predicted crack depth. The results show that the response of the beam (frequencies) is strongly related to the crack depth, which significantly affects the beam behavior, especially when the crack is very deep where the ANN allows us to identify the crack in lower computational time. Based on the provided results, we can detect that the effect of hidden layer size can affect the results. crack in the pipe and Seguini et al [2 5 ,2 6 ] developed a finite element model of cracked and uncracked pipe by using Ansys software, where different crack depth s have been created in the middle, in the right and the left of the pipe. Experimental analysis has also been done, and the Neural artificial method has been used to identify the crack of different depths. In fact, the obtained results proved the efficiency of the developed model and the used method.


INTRODUCTION
eams have been of great significance in many areas of engineering applications and have generally been used in modeling civil and mechanical engineering problems. In fact, different models and methods have been developed to determine the real response of the beam [1]. However, extensive research on cracked beam behavior based on other improved methods has been done. Yang et al [2] used the energy method to identify the crack in vibrating beams where Galerkin's method has been applied to obtain the vibration modes. The Timoshenko and Euler formulation have been also used to identify the cracks in beam [3] and another approach has been developed for the same concept [4]. Gillich et al [5,6] and Zhou et al. [7,8] examined and detected the damage crack with vibration measurement. The forced vibration of the cracked beam has been also studied [9]. Many other approaches have been used to identify the crack's structures (beam) as the genetic algorithm [10], the efficient hybrid TLBO-PSO-ANN combined to the IGA [11] and the machine learning method [12,13,14]. In fact, recently, the concept of machine learning has been applied for damage detection in different structures where the vectorized data has been used by Tran-Ngoc et al [14]. Moreover, an accurate method based on different approaches has also been proposed by different authors to detect the effect of the cracks on the behavior of a beam-like structure, bridges [15,16,17,18] and composite beams [19,20]. Khatir et al [21,22] proposed a new method considering the XFEM, XIGA and Jaya algorithm in order to identify the crack in the plate. An improved technique (ANN) combined with the Jaya algorithm has been used where an experimental analysis has been done [22]. The sensitivity of the pipe's damage crack has also been studied. In fact, Li et al [23] added a virtual massed to predict the crack's damage. Lee et al [24] used the energy method and committee of neural networks to identify the crack in the pipe and Seguini et al [25,26] developed a finite element model of cracked and uncracked pipe by using Ansys software, where different crack depths have been created in the middle, in the right and the left of the pipe. Experimental analysis has also been done, and the Neural artificial method has been used to identify the crack of different depths. In fact, the obtained results proved the efficiency of the developed model and the used method. This paper investigates by means of numerical and experimental analysis the frequencies and how these later vary depending on the crack depth. However, the results of the study prove the efficiency of the improved machine learning method ANN-PSO which allows us to obtain more accurate results where this later is described in details by Seguini et al [25,26]. The obtained results from the experimental method were compared with an exact numerical method to check the accuracy of the solutions where the frequencies for each depth crack are obtained. Good agreements were found. In fact, a small difference between the numerical and experimental results was also found. A numerical example of the beams with single and double cracks based on the finite element method has been performed, and conclusions based on these results are derived.

NUMERICAL ANALYSIS
he finite element method is one of the most generally used techniques. In order to study and analyze the behavior of the cracked and uncracked 3D steel beams (Fig. 1, 2), the Ansys software (v18.1) has been used. However, two examples of a beam with different properties have been analyzed. The mechanical characteristics of beam I and beam II are respectively presented in Tab. 1 and Tab. 2. Moreover, for each depth crack, the frequencies of different mode shapes have been determined and resumed in the following tables.

Example 1
In the first example of a beam, double notches have been created in the middle of this later with 25 depths (Fig. 3). The cracks are extended from 1mm to 25mm. In fact, a depth crack of 1mm has been created at the top and the bottom, as shown in Fig. 3. Some mode shapes are presented in Figs

EXPERIMENTAL ANALYSIS
n this section, the healthy and damaged free-free beams have been analyzed by using M+P SO Analyzer 4.3, PCB Accelerometers 356A15, and Hammer PCB 086C03. In the first example, the accelerometer has been put on the left side of the beam (Fig. 12c) to determine the frequencies where 19 excisions have been generated by a Hammer, and ten double notches have been created in the middle of the beam I. On the other hand, in the second beam, the accelerometer is located in the right of this later where five crack depths have created in the middle of the beam, and the frequencies of 3 mode shapes have been calculated after the average of 11 positions of hammer impact.

Example 1
In the first example of a beam, a double crack has been created in the middle, as shown in Fig. 13 middle, by extending the crack from 2 mm to 20 mm with 2 mm step on the top and bottom and the obtained frequencies of 3 mode shape have been resumed in Tab. 9.

Example 2
In the second example of a beam, a double crack has been created in the middle as shown in Fig. 14 middle, by extending the crack from 2 mm to 10 mm with 2 mm step and the obtained frequencies of 4 mode shape have been resumed in Tab. 9.

ARTIFICIAL NEURAL NETWORK FOR CRACK PREDICTION
n this section, ANN technique is used for crack prediction based on previous beams. The Artificial Neural Network (ANN) is a computational technique based on biological nervous systems. The ability to learn from experience in order to enhance results is the most important aspect of ANN. As a consequence, ANN can be used in a number of applications, including classification, control systems, detection, image processing, and pattern recognition. As shown in Fig 15, an ANN consists of three major components: an input layer, a hidden layer, and an output layer. where wij is the weights of neuron connection between an input node and neuron in the hidden layers, bj is the bias, wj1 is the weight of neuron connection between neuron in hidden and output layers. 1 b is the bias associated with the single neuron in the output layer. Index i = 1, 2, …, m is the number of collected data and index j = 1, 2, …, n is the number of hidden layer neurons. The total number of parameters (weight and bias) used in the network is n× (m + 2) + 1. Two formulations are used to move from the input to the output layer during the process. First, a summation function related to training parameters and output of previous layers is presented in the following formulation: where w and b denote weight and bias represent training parameters, n presents the number of data textracted into the input layer, and presents the number of neurons selected in the hidden layer. Φ j and i f are input and output data, respectively. Next, Φ j is determined by computing the output of the hidden layer as presented in the following formulation:

CONCLUSION
n this study, numerical and experimental modal analysis of two kinds of beam has been done where a new approach has been adopted in order to identify the cracks. In fact, one of the most important contributions of this work is the clear demonstration that the inherent crack depth can have a significant effect on the response of the beam. From this work, the main conclusions are given below:  The frequencies varied with the crack depth  The experimental and numerical results are in good concordance with a low error percentage for the two considered beams  The effectiveness of Hidden Layer Size produced more accurate results depends on the number of collected data where this analysis confirms the validity.