PSI - Issue 48

Oleh Yasniy et al. / Procedia Structural Integrity 48 (2023) 149–154 Yasniy et al/ Structural Integrity Procedia 00 (2023) 000–000

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relative number of destroyed inclusions under dynamic creep conditions, compared to static creep at this stress level, is maximal. With an increase in creep stress, the difference in the relative number of fractured inclusions under dynamic and static creep conditions will decrease. The calculated data obtained are in satisfactory agreement with the experimental data. The maximum error between the results obtained by the FEM and the experimental data does not exceed 12%. The development of new approaches to the analysis and prediction of fracture mechanics processes provides for the use of machine learning methods. Given the significant amount of experimental data, machine learning methods were used, in particular, the neural network method by Didych et al. (2022). Neural networks are the modern methods of machine learning, which solve tasks of mechanics with high accuracy by Pidaparti et al. (1995), and Mohanty et al. (2009). In particular, like their biological counterparts, neural networks learn from examples. Therefore, they can be trained by applying inputs and, accordingly, target outputs to establish a relationship between them. That is one of the widely used approaches in the area of data prediction is learning with a teacher. Teacher participation means a target output that corresponds to certain input signals. It aims is to minimize the signal error, which is the absolute value of the difference between the output signal and the target signal through the constant adaptation of neurons weights by Goodfellow et al. (2016), Haykin (2006), Alpaydin (2010), Smola et al. (2010). Generally, the neural network is a system of connected simple neurons which interact with each other. Vector x = ( x 1 , ..., x n ) arrives at the artificial neuron. In particular, each signal is multiplied by the weights w 1 , ..., w n , and fed to the adder labeled Σ. Every weight corresponds to the power of one biological synaptic connection. The adder adds weighted inputs, creating the output NET. Each neuron of the network deals only with the signals it receives periodically and with the signals it sends periodically to other neurons. However, such locally simple neurons together can perform quite complex tasks. After that, activation function F transforms the signal NET and allows the neurons to receive the output neural signal Out (Fig.3). 3.1. Method of neural networks

Figure 3. Artificial neuron model by Haykin (2006)

During training, the data, consisting of the strain results at which strain jumps occurred and the corresponding strain jump values were divided into two parts – the training and the test samples. The data set consisted of 89 elements. The first (larger) part was used for the training set. The input data were the creep stress parameters corresponding to the total plastic strain and the value of the jump creep. In contrast, the incremental parameter Δp was chosen as the output. The test sample was left to evaluate the quality of the predictions. In this study, the sum of the squares error function (SOS) was chosen, and the training method was Broyden– Fletcher–Goldfarb–Shanno (BFGS) by Gurney (1997), Richard (1998), Goodfellow et al. (2016). In addition, the hidden activation function is tangential, and the function of output activation is logarithmic. In particular, the stop parameter of the learning network was the number of epochs, which in this study was equal to 1000 by Didych et al. (2022). The prediction error was Mean Absolute Percent Error (MAPE):

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