In the power system, research is being conducted in diagnosing and monitoring the condition of power equipment in a precise way. The Partial Discharges (PD) estimations under high voltage is recognized to be the most renowned and useful approach for accessing the electrical behaviour of the insulation material. The PD is good at localizing the dielectric failures even in the smaller regions before the occurrence of the dielectric breakdown. Therefore, the PD condition monitoring with accurate feature specification will be the appropriate model for enhancing the life span of the electrical apparatus. In this research work, a novel data-driven approach is introduced to detect the PD pulses in power cables using optimization based machine learning models. The proposed model will encompass two major phases: feature extraction and recognition. The first phase of the proposed method concentrates on extracting the wavelet scattering transform-based features. In the second phase, these features are fed as the input to optimized Deep Belief Network (DBN), whose count of the hidden neuron is optimized via a Self Adaptive Border Collie Optimization algorithm (SA-BCO). Finally, the performance evaluation is done in terms of diverse performance measures.