| dc.description.abstract | Numerous data floods research in various fields. Quickly grasping the laws of data and finding out equations are of great significance to the study of system characteristics and control systems. The goal of this thesis is to utilize the sparse identification of non-linear dynamical systems (SINDy method) in order to find the governing equations of a bit rotational velocity system in drilling process.
In this thesis, first several case studies are performed in order to get familiar with the SINDy method and explore the features. It is found out that the results provided by the SINDy have strong dependency on initial conditions.
Then the SINDy method is implemented on three dataset that contain 20 meters, 100 meters and 200 meters behind the bit, respectively. For 20 meters, the governing equation is a first order ODE with a control parameter. For the segments further from the bit(100 meters and 200 meters), a first order ODE that matched the real data could not be found. More complicated SINDy model is needed. Diverse optimizers utilized in the SINDy models can make some difference. However, several optimizers have provided the same results in this study.
The ODE obtained for the segment 20 meters from the bit does not provide the perfect fit for the original data. Therefore, segment division is conducted and ODEs are obtained for each segment. In order to unify the results, curve fitting of the coefficients extracted from the ODEs is done in order to formulate a unified ODE which can represent the entire dataset (20 meters behind the bit). The result shows that the final ODE is a fourth-order ODE with control parameters: top drive speed and the rotational speed of the string at 20 meters behind the bit. The validation work proves that the final ODE is accurate compared to the real data.
In the future, the inputs from the final ODE will be fed into the SINDy model. SINDy should be applied together with these inputs to see if it can successfully discover ODEs for a bit rotational velocity system. What's more, the SINDy method should be employed on longer distances from the bit and the limit of the SINDy is worth exploring. | |