PSI - Issue 71

Rakesh Kumar Sahu et al. / Procedia Structural Integrity 71 (2025) 203–209

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2.3. Neural network In this paper, time domain data extracted from Abaqus simulations either single or multiple defects are used to analyze the isotropic beam structure. The data extraction process is followed by the mode purification process to get the specific features of Lamb wave modes as discussed in section 2.1. Whereas, the damage index is calculated by comparing the signal of the damaged state response, and pristine response. These refined data are used as the input to the two-layer feed-forward neural network. This neural network is trained to identify the complex pattern of data and distinguish the different cases considered in this paper for single and multiple defects. In the two-layer feed-forward neural network consists of 3 elements, the input layer, the hidden layer and the output layer. The input layer uses the features extracted from data followed by the hidden layer and provides some weight and biases to the input data and the output layer for predicting the final data. These weights and biases are adjusting then used to generate the relation between the input and output layer using Levenberg-Marquardt algorithm. Levenberg-Marquardt modifies the model parameters that best fit the data which is achieved by minimizing the sum of the squared error of prediction and actual data. Data set preparation starts from detecting damage-sensitive feature extraction from the mode purified symmetric waveform. In this study, damage-sensitive features extracted from pure symmetric waveform are Hilbert envelope peak, Hilbert envelope peak time instance, difference of Hilbert envelope peak time instance and standard deviation. For training and predicting data with the neural network, input data files, target data files and prediction files are fed in the neural network. The input dataset comprises several features, including central frequency, the number of Hilbert peaks, Hilbert peak time instances, the difference in Hilbert peak time instances, and their standard deviation. The data for these features are obtained from various test cases designed as follows: (i) varying the damage width of a single notch while maintaining constant damage location and depth, (ii) varying the damage location while keeping the width and depth constant, and (iii) altering the number of damages. In the first scenario, where the width of single notch-type damage is varied, the width ranges from 1 mm to 20 mm, with an increment of 1 mm. Simulations are performed from 50 kHz to 300 kHz, with a frequency increment of 25 kHz. The location of the damage (750 mm from the reference point) and the depth (0.75 mm) are kept constant. In the second scenario, where the location of notch type damage is varied, simulations are carried out at distances of 4 mm, 8 mm, 12 mm, 16 mm, and 20 mm from the start of the test length. These distances correspond to damage locations at 25%, 50%, and 75% of the test length. The frequency range remains the same (50 kHz to 300 kHz), with an increment of 25 kHz. In the third scenario, varying numbers of damages are introduced. In this case, configurations include one damage of 10 mm width located at 750 mm from the reference point, two damages of 5 mm width located at 675 mm and 825 mm, three damages of 3.33 mm width at 675 mm, 750 mm, and 825 mm, and four damages of 2.5 mm width located at 660 mm, 720 mm, 780 mm, and 840 mm. For all these cases, the depth of the damage is held constant at 0.75 mm. For the target data set features given are the number of damages, damage width in (mm) and damage location in from reference in (mm) for all the test cases mentioned above. For the prediction data set central frequency, number of Hilbert peaks, Hilbert peak time instance and standard deviation are provided. From the training set, it utilizes 70% for training, 15% for validation and 15% for testing 3. Numerical Simulation A 2D finite element numerical model is developed to simulate Lamb wave propagation in an isotropic Al beam using Abaqus Dynamic/Explicit. A schematic representation of the numerical model is shown in Fig. 2. The dimension of the beam is 1500mm*3mm, and the distance between the actuator and sensor is 300mm symmetric about the center of the beam. 70.3 GPa, 2700 Kg/m3, and 0.33 are the elastic modulus, density, and Poisson’s ratio of Al, respectively.

Fig. 2. Actuator-plate-sensor configuration for study of Lamb wave propagation