## 4 Discussion
### Multi-Parameter Estimation Based on Particle Swarm Optimization
The expression of \(w\) is set to \(w=w_{\text{max}}-(M-1)(w_{\text{max}}-w_{\text{min}})/(M-1)\), where \(M\) is the maximum number of iterations set, and \(w_{\text{max}}=0.9\), \(w_{\text{min}}=0.4.c_{1}\) and \(c_{2}\) are acceleration coefficients representing the relative weights of the historical optimal value of the particle and the historical optimal value of all particles. In the algorithm in this section, after comprehensive consideration of convergence accuracy and convergence speed, \(c_{1}\) and \(c_{2}\) are both taken as 2.05. To ensure the accuracy of the parameters, the system randomly generates six different paths to calculate the target and takes the average of the estimated values of these six paths as the estimated parameters. When coupling is not considered, 100 particles are taken, the dimension is 5, the maximum number of iterations is 200, and the parameter vectors estimated by the six different paths are shown in Figure 9a below. When humidity-current coupling is not considered, 100 particles are taken, the dimension is 7, the maximum number of iterations is 400, and the parameter vectors estimated by the six different pathsare shown in Figure 9 below. When full coupling is taken, 100 particles are taken, the dimension is 9, the maximum number of iterations is 400, and the parameter vectors estimated by the six different paths are shown in Figure 9 below. The parameter estimates of the three different models in Equation (15) are shown in Table 3.  
Finally, the life index under normal stress levels (25 \({}^{\circ}\)C, 40%RH, 10 mA) can be extrapolated through the solved multi-stress coupling model. The life estimation results of the full coupling model, the particle swarm algorithm without considering humidity-current coupling, and the coupling model are given and compared with the historical life in reliability prediction. The results are shown in Figure 10 below. According to the blue line in Figure 10, the average life of LEDs is 20,330 h without considering stress coupling, which meets the manufacturer's standard of 20,000 h for LEDs. However, the actual life is worrying. Without considering the coupling of humidity and current, the life is also very different from the actual situation. It is also problematic to have the life too close to the actual life when considering full coupling because the failure of LEDs includes many aspects, including occasional failure and degradation failure. The historical  
Figure 10: Evaluation results of different models under normal stress. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Model** & **In\(\mathbf{\alpha_{0}}\)** & \(-\mathbf{\alpha_{1}}\) & \(-\mathbf{\alpha_{2}}\) & \(-\mathbf{\alpha_{3}}\) & \(-\mathbf{\alpha_{4}}\) & \(-\mathbf{\alpha_{5}}\) & \(-\mathbf{\alpha_{6}}\) & \(-\mathbf{\alpha_{7}}\) & \(\beta\) \\ \hline Not considered & 9.9199 & 1.8379 & \(-\)0.2545 & 1.9083 & & & & 3.2142 \\ Wet electrical coupling is not considered & 9.7209 & 1.4733 & 2.3526 & 0.4251 & \(-\)4.5543 & 2.5625 & & & 3.2474 \\ Fully coupled & 8.3427 & \(-\)1.909 & \(-\)0.0742 & 1.4999 & 1.2987 & 2.6893 & \(-\)2.5929 & 1.3838 & 3.8845 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Three-stress parameter estimates of Weibull distribution. Figure 9: Parameter estimation for three models. (**a**): 3-stress coupling is not considered; (**b**): wet electrical coupling is not considered; (**c**): fully coupled. life scatter points include more stress combinations, such as the number of switching LEDs, salt spray, alternating hot and cold in the morning and evening, and other external factors, as well as different LED manufacturing processes, differences in material quality, and other internal factors, which will lead to the diversity of LED life. There are also defects in the design of the experiment, such as not considering the impact of high temperature and self-heating on humidity, whether the constant temperature, humidity, and current experiment can replace the degradation of LEDs in the real environment, etc.