The fault diagnosis of analog circuits faces problems, such as inefficient feature extraction and fault identification. To solve the problems, this paper combines the circle model and the extreme learning machine (ELM) into a fault diagnosis method for the linear analog circuit. Firstly, a circle model for the voltage features of fault elements was established in the complex domain, according to the relationship between the circuit response, element position and circuit topology. To eliminate the impacts of tolerances and signal aliasing, the 3D feature was introduced to make the indistinguishable features in fuzzy groups distinguishable. Fault feature separability is very important to improve the fault diagnosis accuracy. In addition, an effective classier can improve the precision and the time taken. With less computational complexity and a simpler process, the ELM algorithm has a fast speed and a good classification performance. The effectiveness of the proposed method is verified by simulation. The simulation results show the ELM-based algorithm classifier with the circle model can enhance precision and reduce time taken by about 80% in comparison with other methods for analog circuit fault diagnosis. To sum up, this proposed method offers a fault diagnosis method that reduces the complexity in generating fault features, improves the isolation probability of faults, speeds up fault classification, and simplifies fault testing.

Biaxial contouring systems are widely used in planar precision motion applications, where the assigned feedrate profile strongly affects motion smoothness, contour-following accuracy, and robustness during servo execution. However, many existing studies mainly focus on either controller-side contour-error regulation or planning-layer time optimality, while the influence of jerk-sensitive feedrate transitions on downstream contouring behavior is still insufficiently examined. To address this issue, this paper proposes a jerk-constrained and execution-aware feedrate scheduling framework for biaxial contouring systems. Starting from the admissible feedrate boundary determined by contour geometry and motion constraints, an acceleration-feasible baseline schedule is first generated through bidirectional reachability propagation. Then, jerk-oriented smoothness refinement and critical-region-preserving correction are introduced to suppress abrupt local transitions while maintaining dynamic admissibility and practical traversal efficiency. The refined path-domain schedule is further reconstructed into time-domain axis-level references for closed-loop contouring evaluation. A planning-to-execution simulation study is conducted on three representative contours, including a rounded triangular contour, an elliptical contour, and a butterfly-cross contour. The proposed method is compared with several baseline scheduling strategies under nominal, low-bandwidth, flexible-resonance, and parameter-mismatch conditions. The simulation results indicate that the proposed scheduler can reduce concentrated jerk responses and resonance-sensitive high-frequency excitation while achieving a more balanced tradeoff among traversal time, contouring accuracy, and robustness. The results also show that the benefit of the proposed method becomes more evident for geometrically complex contours and deteriorated servo conditions. The present study provides simulation-based evidence that execution-aware feedrate scheduling is an effective way to improve biaxial contouring performance without redesigning the low-level servo controller.