PSI - Issue 72

Oleh Yasniy et al. / Procedia Structural Integrity 72 (2025) 188–194

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layers of neurons: an input layer, hidden layers, and an output layer. This architecture allows MLPs to effectively model complex nonlinear relationships between input and output parameters, which is the key to accurately predicting the behavior of shape memory alloys. To train the MLP neural network, the data from 1000-1020 loading and unloading cycles of SMA material were used. The dataset for the loading period (up direction) contained 3475 elements. The data set was divided into three parts: 80% of the data was randomly selected for model training, 10% of the data was selected for model validation during the training process to control overfitting, and another 10% was selected for testing to evaluate the quality of model predictions on new data. For the unloading period (down direction), 3371 elements were used, which were distributed in the same way. This approach to data distribution allowed us to create balanced samples for different phases of the loading and unloading cycles, which ensured more accurate model training and its ability to predict the hysteresis behavior of the material at different frequencies. In this paper, the following forecasting error metrics were employed to evaluate the model performance: mean absolute error (MAE), mean squared error (MSE), and mean absolute percentage error (MAPE). These metrics allowed us to evaluate not only the accuracy of the model predictions but also how it responds to large errors and how stable its results are when predicting the behavior of the alloy at different loading frequencies. The choice of several metrics allowed us to obtain a comprehensive picture of the model's performance and its ability to accurately predict the hysteresis behavior of the material at different loading and unloading frequencies of the SMA material. 3. Results and discussion The hysteresis behavior of the SMA nickel-titanium alloy at different loading frequencies was modeled using machine learning, namely an MLP neural network. For the loading stage, we used a model with the MLP 3-54-1 architecture, where three input parameters (stress, cycle number, and loading frequency) were processed by 54 neurons in the hidden layer, which provided the model with the ability to reflect complex nonlinear relationships accurately. The MLP 3-39-1 model with 39 neurons in the hidden layer was used for the unloading stage. The hidden layer in each model had a hyperbolic tangential activation function, which allowed for the effective detection of nonlinear material properties. The output layer with a linear activation function provided accurate predictions of strain values. Fig. 1 shows the dependence between the experimentally determined and predicted material strain and . , respectively. a b

Fig. 1. The predicted versus true strain  , obtained using the ANN method for the stages of loading (a) and unloading (b) of the NiTi SMA material.