## 3 Processing Method of Vibration Piezoelectric Signal
### Evaluate the Anti-Interference Performance of SRP
 \tag{17}\]  
where \(C_{K}^{k}=\frac{K!}{E!(K-k)! },\theta_{\delta_{s,j}\bar{F}_{k}}=\frac{\lambda_ {\delta_{s,j}\bar{F}_{k}}\bar{F}_{k}N_{0}}{1-\kappa\rho_{s}}\), and \(K\) is the Neumann function reference [21], concluding that  
\[F_{X}(x)=1-\text{exp}\Big{(}-\theta_{B\delta_{s,j}}x\Big{)}-\sum\limits_{k=1}^ {K}C_{K}^{k}(-1)^{k}\text{exp}\left(-\theta_{B\delta_{s,j}\bar{F}_{k}}x-\frac {k\Omega_{\delta_{s,j}\bar{F}_{k}}}{x}\right), \tag{18}\]  
Combining it with \(f_{\gamma_{\delta_{s,j}\bar{s},j+1}}(\omega)=\lambda_{\delta_{s,j}\bar{s},j+1} \text{exp}\Big{(}-\lambda_{\delta_{s,j}\bar{s},j+1}\omega\Big{)}\), we obtain the following:  
\[OP_{j,s}=1-(I_{1}+I_{2}), \tag{19}\]  
where  
\[ \begin{split}& I_{1}=\sqrt{\frac{\lambda_{\delta_{s,j}\delta_{s,j+1} }\theta_{B\delta_{s,j}}\rho_{s}N_{0}}{1-\kappa\rho_{s}}}K_{1}\left(2\sqrt{ \frac{\theta_{B\delta_{s,j}}\rho_{s}N_{0}\lambda_{\delta_{s,j}\bar{s},j+1}}{1 -\kappa\rho_{s}}}\right),\\ & I_{2}=2\sum\limits_{k=1}^{K}C_{K}^{k}(-1)^{k}\lambda_{\delta_{ s,j}\bar{s},j+1}\rho_{s}N_{0}\sqrt{\frac{\theta_{B\delta_{s,j}}}{k\theta_{\delta_{s,j} \bar{F}_{k}}\left(1-\kappa\rho_{s}\right)^{2}+\rho_{s}N_{0}\lambda_{\delta_{s, j}\bar{s},j+1}\left(1-\kappa\rho_{s}\right)}},\end{split}  \tag{20}\]  
where  
\[ \begin{split}\Phi_{1,s,j}=\sqrt{\frac{\lambda_{\delta_{s,j}\bar{ s},j+1}\theta_{\delta_{s,j}\bar{F}_{k}N_{0}}}{\left(1-\kappa\rho_{s}\right)}},\\ \Phi_{2,s,j}=\lambda_{\delta_{s,j}\bar{s},j+1}N_{0}\times\sqrt{ \frac{\theta_{B\delta_{s,j}}}{k\theta_{\delta_{s,j}\bar{F}_{k}}\left(1-\kappa \rho_{s}\right)^{2}+\rho_{s}N_{0}\lambda_{\delta_{s,j}\bar{s},j+1}\left(1- \kappa\rho_{s}\right)}},\\ \sigma_{1,s,j}=K_{1}\left(2\sqrt{\frac{\theta_{B\delta_{s,j}\bar{ F}_{k}N_{0}\lambda_{\delta_{s,j}\bar{s},j+1}}}{1-\kappa\rho_{s}}}\right),\\ \sigma_{2,s,j}=K_{1}\left(2\sqrt{\frac{\theta_{B\delta_{s,j}}}{1 -\kappa\rho_{s}}\left(\frac{\delta\theta_{s,j}\bar{F}_{k}\left(1-\kappa\rho_{s }\right)}{1-\kappa\rho_{s}}\right)}\right),\end{split} \]  
Substituting (20) into (11), we obtain \(OP_{SRP}\) as the following:  
\[OP_{SRP}=\left\{ \begin{array}{l}1;if\kappa\geq 1/\rho_{s}\\ 1-\prod\limits_{j=1}^{T_{1}+1}\left[\begin{array}{c}2\Phi_{1,s,j}\sigma_{1,s, j}+\\ 2\sum\limits_{k=1}^{K}(-1)^{k}C_{K}^{k}\Phi_{2,s,j}\sigma_{2,s,j}\end{array} \right];\end{array} \right. \tag{21}\]  
1. Amplitude represents the magnitude of vibration, which correlates with the impact force of seeds on the vibrating plate. 2. Waveform characterizes the dynamic collision behavior between seeds and the vibrating surface, including impact duration and variations in collision intensity. The applied signal processing and feature extraction algorithms are described below: (1) Time-domain analysis Analysis of the waveform characteristics in the time domain reveals that collision signals typically exhibit sharp rise and fall times, which are indicative of sudden mechanical impacts. In contrast, the intrinsic vibration signal of the tray exhibits smoother, more continuous waveform patterns, reflecting its periodic and stable nature. (2) Frequency-domain analysis The frequency-domain analysis is performed using the Fast Fourier Transform (FFT) algorithm, which converts time-domain signals into their corresponding frequency components. This transformation allows for the identification of dominant frequency characteristics. The inherent vibration of the tray produces a distinct spectral peak near the predefined excitation frequency, whereas collision events introduce additional frequency components, particularly in higher frequency ranges, reflecting the impulsive and non-periodic nature of such interactions.