Processing and analysis of rotary drilling tool angular velocity signals based on dynamic mode decomposition

Developing a signal processing algorithm for downhole drilling operations based on the dynamic mode decomposition method is essential for suppressing measurement noise from drilling instruments and improving the accuracy of numerical differentiation estimates in low signal-to-noise ratio conditions. When analyzing the twisting of the drill string, it is necessary to calculate angular acceleration through angular velocity measurements. However, numerical differentiation may amplify noise in the data, and filtering noise could potentially suppress critical data features. Therefore, proposing the application of the Dynamic Mode Decomposition (DMD) algorithm for feature extraction from angular velocity measurement signals is crucial. This involves applying DMD to the time-series signals collected by sensors, extracting low-rank components from the signals using a threshold method, and reconstructing denoised signals for improved data quality. In the experimental research of simulated signals, the processed measurement signal matches the theoretical signal curve. Additionally, the processed measurement signal reduces root mean square error, improves signal-to-noise ratio, and decreases numerical differentiation estimation error.