The purpose of the article is to create an effective method to monitor the state of the drill string and the bit without interfering with the drilling process itself in low-time delay mode. For continuous monitoring of the well drilling process, an experimental setup was developed that operates on the basis of the use of the phase-metric method of control. Any movement of the bit causes a change in the electrical characteristics of the probing signal. To obtain a stable signal from a bit immersion depth of up to 250 m, a frequency of probing electrical signals of 166 Hz and an amplitude of up to 500 V were used; sampling rate (analog-to-digital converter) ADC -10101 Hz. To identify the state of the drill string and the bit according to the graphs of dependences of changes in the electrical characteristics of the probing signal on time, the authors of the article investigated a number of deep learning methods, based on the results of the research, a line of capsule neural network (CapsNet) methods was selected. The authors have developed two modifications of 1D-CapsNet and Windowed Fourier Transform (WFT) -2D-CapsNet. To identify the transition between two rock layers with different properties, WFT-2D-CapsNet showed an accuracy of 99%, which is 2-3% higher than the results of modern rock studies based on measurement-while-drilling (MWD) and logging-while-drilling (LWD) methods. The WFT-2D-CapsNet method unambiguously detects selfoscillations in the drill string and detects the good condition of the bit with an accuracy of 99%.