PSI - Issue 43

V.I. Golubev et al. / Procedia Structural Integrity 43 (2023) 29–34 V.I. Golubev et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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The fractured inclusion has fixed width (400 meters) and fixed height (100 meters). The location of the inclusion and its parameters are varied: parameter q changes from 0.03 to 0.3, angle changes from -20 to 20 degrees, depth of the inclusion changes up to 2000 meters, horizontal locations of the inclusion cover the whole area. Multiple numbers of direct calculations are performed with different parameters of the inclusion. The result of each direct simulation is the pair made of (a) of inclusion parameters and (b) the corresponding seismogram. The seismogram represents the total response from the background media together with the fractured inclusion, this response is measured on the top surface of the computational domain. The inverse problem is to localize the spatial position of the fractured inclusion and estimate its parameters based on the seismogram. In this work we investigate the applicability of machine-learning algorithms for this problem. Deep convolutional neural network with UNet architecture (Ronneberger et al., 2015) is used to provide a fast solution for the inverse problem of restoring the parameters of the fractured inclusion based on the surface measurements. The dataset of 3990 pairs is created based on direct calculations. The ground truth data contains the encoded parameters of the inclusion - non-fractured areas are marked with zeros and fractured area is marked with the values from 0.5 to 1.0. The mark 0.5 corresponds to the minimal value of fractured region parameter in question, the mark 1.0 - to its maximal value. This dataset is split into train and test sets with the 70:30 ratio. The train set is presented to the neural network during the training phase. The testing of the network is performed using the test set, that was not available for the network during the training. The network was trained for a maximum of 100 epochs using Adam optimization algorithm (Kingma et al., 2014) with constant learning rate 1e-4, using mini-batches of size 10. The training was performed using the MSE loss function. The neural network predicts the location of the inclusion well for all the samples from the train set. An example of this prediction is presented on Fig. 2a. This result is expected to some extent, since the network uses the architecture designed for the segmentation problems. However, the quality of the prediction is surprisingly good, since the response from the fractured region cannot be distinguished from the background with a naked eye. The result of three inclusions localization is presented on Fig. 2b.

a) b) Fig. 2. The fractured inclusion localization result. Top image shows the seismic response recorded. Middle image depicts the real location of the fractured region. Bottom image presents the predicted fractured zones identified by the ML model from the seismic response. For the single inclusion (a) and multiple inclusions (b). The predicted vertical and horizontal positions of the inclusion center are presented at Fig. 3 (a, b). The network architecture targets primarily a spatial localization of the fractured inclusion, so the predictions of the quantitative values of the mechanical parameters of the inclusion are significantly worse. The network fails to identify the angle in a reliable manner. The situation is a little bit better with the parameter q estimation using a single run of the same network. The parameter q is the used mathematical abstraction for the real geological crack description. There are a lot of different micromechanical models of the crack fillers. For example, the Navier-Stokes equations describing the motion of viscous fluid substances can be considered. However, it requires the usage of the tiny mesh elements and drastically increases the computational time. So, the problems having the practical importance can’t be carried out in a reasonable time. The usage of the macroscopic contact Coulomb friction conditions is the compromise between the numerical complexity of the problem and the detail of the physical process description. If the q coefficient is high, then the sliding mode is not occurred. If the q coefficient is close to zero, then the dynamic problem is close to the