[Objective] To ensure the reliability of electrical connections in cable circuits, this paper proposes a method for diagnosing loose electrical contact faults based on multi-amplitude pulse currents. [Methods] Firstly, the variation of contact resistance with key parameters such as temperature and contact area was analyzed through finite element simulation under both normal and loose contact states. Then, a self-developed electrical connection reliability testing device was used to apply pulse currents of different amplitudes, and the contact resistance and temperature were measured under normal and loose contact states, obtaining the variation curve of contact resistance with pulse current amplitude. Finally, a mathematical model of the relationship between contact resistance and current was established, and a derivative-based fault criterion for loose electrical contact was proposed by analyzing the first and second derivatives. [Results] The simulation and experimental results demonstrated that the proposed diagnostic method effectively identified loose electrical contact faults and improved the reliability of electrical connections. [Conclusion] The proposed derivative-based fault criterion provides a novel approach for diagnosing loose electrical contact faults, demonstrating practical application value.