(1) Embedding

Because the oscillation period of the waveform series is 104, the SSA method with a window of 104 was adapted to reduce the noise information of the waveform series. Defining the delay vector **X***k* as **X***k* = *xk*, ··· , *xk*+*M*−1 *T*, 1 ≤ *k* ≤ *N* − *M* + 1, the trajectory matrix **S** of the waveform series can be expressed as:

$$\mathbf{S} = \begin{bmatrix} \mathbf{X}\_1 & \mathbf{X}\_2 & \cdots & \mathbf{X}\_{N-M+1} \end{bmatrix} = \begin{bmatrix} \mathbf{x}\_1 & \cdots & \mathbf{x}\_{N-M+1} \\ \vdots & \ddots & \vdots \\ \mathbf{x}\_M & \cdots & \mathbf{x}\_N \end{bmatrix} \tag{1}$$

where *N* is the waveform series length and *M* is the window ( *M* = 104).

(2) Singular Value Decomposition (SVD)

SVD was performed on the covariance matrix **R** =**SS<sup>T</sup>** of the trajectory matrix **S** to obtain M eigenvalues in descending order λ1 ≥ λ2 ≥ ··· ≥ λ*M* and corresponding eigenvectors **U**1,**U**2, ··· ,**U***M*. Then, the principal components (PC) **V***i* can be expressed as **V***i* = **<sup>S</sup>***T***U***i*/ √ λ*i*, *i* = {1, ··· ,*M*}, and the trajectorymatrix**S**can be expressed as the sum of the elementarymatrices**S***i* (**S***i* = √ <sup>λ</sup>*i***U***i***V***<sup>T</sup> i* , *i* = {1, ··· ,*M*}) obtained by SVD, i.e.,

$$\mathbf{S} = \mathbf{S}\_1 + \mathbf{S}\_2 + \dots + \mathbf{S}\_M \tag{2}$$
