基于解轨迹拟合的非线性电路故障特征提取

本文针对一类斜波激励响应轨迹（解轨迹）存在且唯一的非线性电路，提出一种基于解轨迹拟合的故障特征提取方法。通过多项式拟合估计解轨迹麦克劳林多项式系数，由多项式系数间的迭代关系将非线性电路分解为线性子电路。在电路混合节点方程和解轨迹多项式系数基础上，提取各子电路节点故障电流为故障特征，结合多轨迹多项式系数矩阵奇异值分解实现非线性电路多故障特征提取。最后通过仿真实例说明该方法的有效性。

Characteristic Extraction for Nonlinear Circuit Fault Diagnosis Based on Trajectory Polynomial Fitting

It is important to find out the relationship between fault states and fault characteristics clearly in analog circuit fault diagnosis, especially in both the nonlinear case and soft-fault diagnosis. In this paper, an approach of characteristic extraction for nonlinear circuit diagnosis is presented based on trajectory polynomial fitting. Using polynomial fitting, the trajectory produced by ramping power supply can be extended to Taylor series, and the properties of the polynomial coefficients in aspect of fault diagnosis are discussed based on the iterative relationship of the polynomial coefficients. Based on these properties, the problem of nonlinear diagnosis is transformed into linear diagnosis problems, and the fault characteristics corresponding to the fault currents of the circuit nodes can be extracted with rising order of the polynomial. Next, an approach of multi-fault diagnosis is proposed based on singular-value decomposition (SVD) of the coefficient matrix with multi-trajectory fitting. Finally, two examples are given to illuminate that the proposed approach is effective.