## 1 Introduction  
Electric drive transmission systems, as core components of electric vehicles and industrial power equipment, directly impact equipment performance and safety [1, 2]. During long-term operation, the system is inevitably subject to various fault risks. Among these faults, an open-phase fault in the motor severely disturbs the spatial symmetry of the air-gap magnetic field, causing significant electromagnetic torque pulsations and unbalanced magnetic pull forces. These pulsations and pull forces exacerbate mechanical vibration and noise, reducing system reliability and creating serious safety hazards [3, 4]. To address open-phase faults, existing research has proposed fault-tolerant control strategies to maintain electromagnetic torque stability. These strategies effectively reduce electromagnetic torque pulsations and ensure continuous power output. Ref. [5] introduced a fault-tolerant control strategy using decoupled transformation matrices and current constraints, which preserves consistent air-gap magnetomotive force (MMF) through post-fault current redistribution. Ref. [6] developed two objective-oriented fault-tolerant operating modes for a DTP-PMSM: a loss minimization mode optimizing efficiency by reducing copper loss, and an electromagnetic torque maximization mode optimizing power output retention. These provide strategic options for optimal fault-tolerant operation across diverse conditions. Ref. [7] introduced a fault-tolerant strategy with feedforward voltage compensation, effectively reducing current harmonics and stabilizing speed and torque in DTP-PMSM under open-phase faults conditions. Ref. [8] combined virtual voltage vector technology with model predictive current control algorithms, significantly improving steady-state stability and dynamic response under open-phase faults conditions. Ref. [9] enhanced the robustness and operational stability of motor-drive systems under open-phase faults by refining the conventional deadbeat-predictive current fault-tolerant control method. Notably, passive fault-tolerant control and self-fault-tolerant control are increasingly favored for their benefits, such as eliminating the need for additional hardware redundancy, offering rapid response, lowering implementation costs, and reducing system complexity. Ref. [10] proposed a non-phase shift self-fault-tolerant control for DTP-PMSM using a proposed single-inverter parallel drive, enabling seamless transitions between normal operation and phase-fault conditions without precise fault diagnosis, thereby enhancing autonomous system recovery during abrupt faults. The dynamic response of electric drive transmission systems under various fault conditions have been extensively studied, providing a robust theoretical foundation for system condition monitoring and fault diagnosis. Ref. [11] established an electromechanical coupling dynamic model for the multi-motor drive systems, deeply revealing the influence mechanism of open-circuit faults on system dynamic responses, specifically electromagnetic torque pulsations and gear vibrations. Refs. [12; 13; 14] introduced an integrated motor-gear electromechanical model that combines a magnetic network motor model with a dynamic planetary gear system model. This method effectively describes the system's distinct electromagnetic-mechanical oscillation behavior and its evolution process during gear spalling faults and motor stator winding inter-turn short-circuit fault. Ref. [15] established an electromechanical coupling model of a permanent magnet synchronous motor (PMSM) and a gear system, which demonstrated the inherent correlation between the degree of gear crack propagation and the characteristic harmonic components of the motor stator current, thereby providing a quantitative basis for evaluating mechanical faults using electrical signals. [PERSON]. [16] employed the electromechanical coupling effect to effectively identify and extract the characteristic frequencies induced by tooth surface spalling defects in the system response. Meanwhile, [PERSON].