Algorithm 1. Offline modeling phase

Step 1: Input multimodal process data $X={\left[x_m\left(1\right),x_m\left(2\right),\dots ,x_m\left(n\right)\right]}^T$;

Step 2: Calculate trend variables $\overline{X}$ by (21) and (22);

Step 3: Divide $\overline{X}$ through a window of length $H,$ obtaining $H^{*}$ through ADF test;

Step 4: Further divide the shorter window $L$ into ${\overline{X}}_{new},$ obtaining $L^{*}$ through ADF test;

Step 5: Obtain $X_{t1},X_{t2},\cdots$ by step 3 and step 4, and model them separately using DLPPCA, saving $T_{\alpha t}{}^2$ and $SP{E}_{\alpha t}$;

Step 6: Similar to Step 5, obtain $X_{s1},X_{s2},\cdots$ by step 3 and step 4, and model them separately using DLPPCA, saving $T_{\alpha s}{}^2$ and $SP{E}_{\alpha s}$.