ABSTRACTFractures influence the mechanical strength of coal roof and floor, constraining the design of hydraulic fracturing for coalbed methane production. Currently, the predominant approach involves the integration of petrophysical logging with machine learning for fracture prediction. Nevertheless, challenges exist regarding the model's accuracy. In this study, we present a novel approach to predict fracture density. Our method optimises a back‐propagation (BP) neural network and utilises principal component analysis for feature extraction. We employ logging parameters (density, compensated neutron and acoustic time difference) obtained from Shouyang Block well SY‐1 and fracture density data from electrical imaging logging to construct the FVDC model's dataset. The BP neural network model is optimised using the Sparrow Search algorithm and Tent Chaotic Mapping. The results demonstrate a substantial enhancement over the BP neural network model, with reductions of 80.102% in mean absolute error, 94.182% in mean square error, 75.879% in root mean square error and 79.764% in mean absolute percentage error. When considering accuracy, the optimised model (97.098%) surpasses the support vector regression model (96.478%), the random forest model (94.404%) and the BP neural network model (85.657%). Scalability testing for the optimised model was conducted using data from well SY‐2, yielding a remarkable prediction accuracy of 96.775%. This performance exceeds that of the BP neural network (with an accuracy of 85.102%), as well as the random forest and support vector regression models (with accuracies of 91.234% and 90.384%, respectively). These results underscore the potential of well logging and machine learning in FVDC prediction.