## 3 Processing Method of Vibration Piezoelectric Signal
### Evaluate the Anti-Interference Performance of SRP  
The system's performance is highly sensitive to both the statistical channel state information and the stability of the transmitted vibration signals. By incorporating the proposed protocol, the stability and reliability of the vibratory piezoelectric detection system are significantly enhanced. This reduces the likelihood of false alarms and missed detections caused by equipment faults or environmental interference, thereby improving the overall monitoring accuracy of the crop seed drying process. To assess the effectiveness of the shortest routing protocol (SRP), outage probability (OP) metrics and corresponding refined closed-form expressions were derived. By calculating and optimizing the outage probability, the operational performance of the vibratory piezoelectric detection system can be thoroughly evaluated and enhanced. This ensures stable and accurate signal transmission in complex agricultural environments--characterized by factors such as mechanical vibration and elevated temperatures--thus improving the reliability and quality of the drying process monitoring. The channel capacity of the i-th path in the process from sending to receiving was calculated using the following equation:  
\[C_{i}^{ete}=\underset{j=1,2,\ldots,T_{i}+1}{min}\left(C_{\delta_{i,j},\delta_ {i,j+1}}\right)= \begin{cases}(1-\alpha)\tau_{i}log_{2}\Big{(}1+\underset{j=1,2,\ldots,T_{i}+1}{min}\left(\frac{\Delta_{1,i,j}}{\kappa\Delta_{1,i,j}+N_{0}} \right)\Big{)};&if\kappa\geq 1/\rho_{i}\\ \\ (1-\alpha)\tau_{i}log_{2}\Big{(}1+\underset{j=1,2,\ldots,T_{i}+1}{min}\left( \frac{\Delta_{2,i,j}}{\kappa\Delta_{2,i,j}+N_{0}}\right)\Big{)};&if\kappa<1/ \rho_{i}\end{cases}  \tag{10}\]  
The monitoring model constructed using one-dimensional raw time-domain signals exhibited a markedly higher error rate in assessing the drying status of crop seeds. This can be attributed to the fact that the time-domain signal distributions of the seeds during the transition from unheated to heated states are highly similar, resulting in minimal discriminative feature information. Consequently, classification methods relying on voltage peaks, specific frequencies, or full-band spectral features are prone to misclassification. To address this limitation, this study introduces outage probability as a quantitative performance metric. It is defined as the probability that the instantaneous achievable transmission rate falls below the predetermined target rate, which was formally expressed as \(Pr\big{(}C_{s}^{ete}<C_{th}\big{)}\). \[ \begin{split}& OP_{SRP}=Pr\big{(}C_{s}^{ete}<C_{th}\big{)}\\ &=\left\{\begin{array}{l}Pr\bigg{(}\underset{j=1,2,\ldots,T_{s}+1 }{min}\ \Big{(}\frac{\Delta_{1s,j}}{\kappa\Delta_{1s,j}+N_{0}}\Big{)}<\rho_{s} \bigg{)};if\kappa\geq 1/\rho_{s}\\ Pr\bigg{(}\underset{j=1,2,\ldots,T_{s}+1}{min}\ \Big{(}\frac{\Delta_{2s,j}}{ \kappa\Delta_{2s,j}+N_{0}}\Big{)}<\rho_{s}\bigg{)};if\kappa<1/\rho_{s}\\ \end{array}\right.\\ &=1-\prod\limits_{j=1}^{T_{s}+1}(1-OP_{j,s}),\end{split}  \tag{11}\]  
The outage probability of hop \(j\) in SRP is as follows:  
\[\begin{split} OP_{j,s}=\left\{ \begin{array}{l}Pr\Big{(}\frac{ \Delta_{1s,j}}{\kappa\Delta_{1s,j}+N_{0}}<\rho_{s}\Big{)};if\kappa\geq 1/ \rho_{s}\\ Pr\Big{(}\Delta_{2s,j}<\frac{\rho_{s}N_{0}}{1-\kappa\rho_{s}}\Big{)};if \kappa<1/\rho_{s}\\ \end{array} \right.\end{  
where \(\theta_{B\delta_{s,j}}=\frac{\lambda_{B\delta_{s,j}}}{\chi P}\),  
\[ \begin{split}& F_{\frac{\sigma_{\delta_{s,j}}\text{max}(1-\kappa \rho_{s})}{\rho_{s}N_{0}}}\left(\omega\right)\\ &=Pr\Big{(}\underset{k=1,2,-K}{max}\left(\frac{\gamma_{\delta_{s,j }}\bar{F}_{k}(1-\kappa\rho_{s})}{\rho_{s}N_{0}}\right)<\omega\Big{)}\\ &=\left(\frac{F_{\frac{\gamma_{\delta_{s,j}}\bar{F}_{k}(1-\kappa \rho_{s})}{\rho_{s}N_{0}}}(\omega)}{\rho_{s}N_{0}}\Big{)}^{K}=\Big{(}1-\text{ exp}\Big{(}-\theta_{\delta_{s,j}\bar{F}_{k}}\omega\Big{)}\Big{)}^{K}\\ &=1+\sum\limits_{k=1}^{K}C_{K}^{k}(-1)^{k}\text{exp}\Big{(}-k \theta_{\delta_{s,j}\bar{F}_{k}}\omega\Big{)},\end{split}