Rate of Penetration Prediction Study Based on the FA-WOA-ET Algorithm

Abstract Accurate prediction of Rate of Penetration (ROP) is critical for optimizing drilling parameters and mitigating risks. However, the high-dimensional, nonlinear nature of logging data limits the accuracy of traditional models. This study aims to propose a hybrid model, FA-WOA-ET, to overcome the challenges of data redundancy and manual hyperparameter limitations in conventional machine learning, providing a precise, real-time ROP prediction solution for complex formations. The proposed method constructs a prediction model using Factor Analysis (FA) and Extremely Randomized Trees (ET), where the Whale Optimization Algorithm (WOA) functions specifically as a hyperparameter optimizer. First, FA processes raw data to extract three independent principal factors—formation pressure environmental, rock mechanical property, and mechanical rock-breaking parameter—as inputs. Second, the ET model predicts ROP based on these factors via large-scale decision trees and majority voting. To prevent local optima in ET's complex parameter space, WOA mimics humpback whale feeding behavior to adaptively lock in key parameters, such as tree count and splitting thresholds. Experimental validation demonstrates that the FA-WOA-ET model exhibits excellent goodness-of-fit and generalization performance, with its prediction residuals following a zero-mean normal distribution. Comparative analysis against the Whale Optimization Algorithm-optimized Extra Trees (WOA-ET), Extra Trees (ET), and Random Forest (RF) models reveals that the Root Mean Square Error (RMSE) of the proposed model is reduced by 17.53%, 20.13%, and 27.99%, respectively, while its goodness-of-fit is improved by 5.81%, 8.27%, and 12.28%, respectively. These results indicate that the new model can more accurately characterize the evolution mechanisms of the rate of penetration (ROP) under complex operating conditions. By enabling the real-time evaluation of influencing factors, this study provides a robust scientific basis for operational guidance, demonstrating a significant impact on enhancing actual drilling efficiency. This paper presents a novel framework where FA extracts physically interpretable inputs to feed an ET-based predictor, while WOA automates the tuning process to ensure global optimality. Unlike traditional black-box models, this structure effectively resolves multicollinearity and hyperparameter uncertainty. The study adds to the industry's knowledge by demonstrating how integrating statistical dimension reduction with bio-inspired optimization significantly enhances prediction robustness in high-dimensional drilling data.