Full-field Measurements for Anomaly Detection of Mechanical Systems using Convolutional Neural Networks and LSTM Networks 107 Fig. 2 Flowchart of LSTM cell [9]. it =σ(Wi · [ht−1,xt]+bi) (2) ˜Ct =tanh(WC · [ht−1,xt]+bC) (3) Ct =ft ⊙Ct−1 +it ⊙ ˜Ct (4) ot =σ(Wo · [ht−1,xt]+bo) (5) ht =ot ⊙tanh(Ct) (6) Where W represents the weights and b are the biases of the neural network. σ is the sigmoid function and tahn is the hyperbolic tangent used as activation functions for the gates. Meanwhile, [ht −1,xt] represents a concatenation between the previous time-step output and the current input data. This work proposes a combination of CNN and LSTM layers in order to extract both spatial and temporal information from the system for abnormal behavior classification, by identifying if there is a nonlinearity in the system and a multiclass classification to predict different locations of nonlinearities. Experimental Setup This study examines the classification of normal and abnormal vibrations in a metallic plate subjected to controlled vibrational tests. Both linear (normal) and non-linear (abnormal) states were induced, with data collected at various excitation frequencies. The testing subject for the experiment consists of a metallic plate, with 6 inches of width, 17 inches height and 0.05 inches thickness, and it was tested using a mechanical shaker. A Laser Doppler Vibrometer (LDV) was used to record the vibrational data for 133 points on the plate’s surface. Two states were analyzed: 1. Linear State: The plate vibrated freely, representing normal conditions. 2. Non-Linear State: Rubber bumpers were placed behind the plate, simulating structural damage and altering the vibrational patterns. Different frequencies were employed for excitation including 298 Hz, 548 Hz, 1704 Hz, 2118 Hz, 2435 Hz, 2792 Hz, 3907 Hz, 4960 Hz, and 5300 Hz were used to test the plate’s response, chosen based on modal analysis. In the non-linear state, bumpers were placed as show Figure 3. Vibrational signals were recorded at each frequency, capturing the plate’s oscillations. The data collected from all 133 points was divided into training and testing subsets, with linear and non-linear data used to train the machine learning models, and testing data to evaluate their classification performance. One sample of the data can be seen in Figure 4. To optimize the training of the neural network and improve the efficiency of the simulations, exhaustive data preparation was carried out, which included: • Capturing Plate Movement: Each of the 133 mesh points represents the movement at that specific point on the plate. An interpolation of these points was performed to recreate the continuous movement of the plate.
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