High-resistance ground faults are difficult to detect with existing ultrahigh voltage direct current (UHVDC) transmission fault detection systems because of their low sensitivity. To address this challenge, a straightforward mathematical method has been proposed for fault detection in UHVDC system based on the downsampling factor (DF) and approximation derivatives (AD). The signals at multiple sampling frequencies were analysed using the DF, and the AD approach was used to generate various levels of detail and approximation coefficients. Initially, the signals were processed with different DF values. The first, second, and third order derivatives of the generated signals were calculated by the AD method. Next, the entropy features of these signals were computed, and the Random Forest-Recursive feature elimination with cross-validation (RF-RFECV) algorithm was used to select a high-quality feature subset. Finally, an ensemble classifier consisting of Light Gradient Boosting Machine (LightGBM), K Nearest Neighbor (KNN), and Naive Bayes (NB) classifiers was utilized to identify UHVDC faults. The MATLAB/Simulink simulation software was used to develop a ±800 kV UHVDC transmission line model and perform simulation experiments with various fault locations and types. Based on the experiments, it has been established that the suggested approach is highly precise in detecting several faults on UHVDC transmission lines. The method is capable of accurately identifying low or high resistance faults, irrespective of their incidence, and is remarkably resistant to transitional resistance. Furthermore, it exhibits excellent performance in identifying faults using a small sample size and is highly reliable.