## 5 Analysis of Outage Probability
### The OP (Outage Probability) Under Different Hardware Damage Levels  
In this study, closed-form expressions for the system outage probability (OP) of a vibration-assisted piezoelectric detection system were derived under Rayleigh fading channel conditions, modeling the transmission from the transmitter to the receiver. These formulations were then employed to evaluate system performance under varying levels of signal degradation and hardware impairments.  
Simulation Framework:  
The damage factor is a dimensionless parameter used to quantify the extent of system degradation. It ranges from 0 to 1, where 0 indicates no damage and 1 represents complete failure. For each level of damage, the signal-to-noise ratio (SNR) is recorded to evaluate its effect on signal transmission performance. Due to the limited availability of severely damaged physical samples--making it impractical to evaluate the system at \(\kappa=1\)--MATLAB simulations were conducted to assess the impact of varying damage levels on system performance  
The following are shown in Figure 9:  
1. Outage probability increases with damage level, indicating a positive correlation between system impairment and the likelihood of signal failure.
2. When k \(\leq\) 0.3, the SRP protocol exhibits the lowest outage probability, demonstrating superior robustness under mild damage conditions.
3. As \(\kappa\)\(\geq\) 0.5, the outage probability across all protocols converges to 1. This suggests that enhanced vibrational signals improve the SNR, increasing the ratio of useful signal to noise and thereby reducing the risk of detection failure caused by noise interference.
4. The proposed model focuses solely on the probability distribution of SRP features across different signal classes, which enhances its robustness against outliers and interference from damaging noise.
5. The close agreement between simulated results (Sim) and analytical solutions (Exact) confirms the reliability of the simulation method in accurately predicting protocol performance.  
In Figure 10, it is observed that the outage probability (OP) approaches 1 when the transmission power P = \(-\)5 dB, indicating that transmit power is negatively correlated with outage probability.  
Figure 8: Different seed seeds were tested under field conditions. (**A**) The seismic dispersion of corn seeds. (**B**) The aggregation of corn seeds. (**C**) The experimental object is wheat. (**D**) The experimental object is rapeseed.  
1. The plotted curve demonstrates that outage probability decreases progressively with increasing vibration signal strength. This suggests that stronger vibrational signals enhance signal reliability and provide supportive evidence for the more effective classification of grains and impurities.
2. Improved signal quality yields clearer and more distinguishable signal features, enabling the detection system to more accurately differentiate between seeds and impurities.  
Figure 10: Relationship between vibration signal strength and signal transmission outage probability.  
Figure 9: Relationship between SRP outage probability and damage level.  
Enhanced system stability: Signal enhancement contributes to improved robustness of the detection system, allowing it to handle incoming signals more reliably and reducing interruptions caused by weak or unstable inputs.
4. Optimization of the detection algorithm: Under enhanced signal conditions, the detection algorithm can more effectively extract and utilize signal features for analysis and decision making, thereby improving both the accuracy and reliability of the detection process.