Data-Driven Modeling of Nonlinear Delay Differential Equations with Gap Effects using SINDy

An accurate modeling approach to predict the trajectory of a drillstring plays a critical role in drilling operation. Nonlinear Delay Differential Equations (DDEs) have been considered as an effective tool to serve the purpose. This paper introduces a novel data-driven approach to model the borehole propagation dynamics by incorporating nonlinear DDEs with Linear Complementarity Problem (LCP) using the Sparse Identification of Nonlinear Dynamics (SINDy) method. The developed model can predict borehole propagation without relying on physics-based information while retaining the same dynamics as those predicted by physics-based nonlinear DDEs. To assess the resilience of the proposed approach, we introduce noise into the dataset, demonstrating the robustness of the SINDy method. Additionally, a stability analysis of the data-driven DDEs offering insights into its reliability and potential applications.