## 3 Back Analysis of Slope Mechanical Parameters
### Parameter Research of Inversion Model  
Based on previous research findings, the establishment of the parameter inversion analysis model comprises two parts: the objective function acquisition model and the improved NSGA-II algorithm model. The improved BPGA-NSGA-II model, built upon these two components, enables the acquisition of slope mechanical parameter combinations with relatively small relative errors. However, several key issues still require further research regarding the application of the model. Two key aspects that require further investigation are the topology structure of the BP neural network model and the selection of population size and iteration count for the NSGA-II algorithm. These parameters are closely related to the inversion error and directly affect the accuracy of quantitative analysis of slope dynamic stability. Many scholars have done relevant research on how to determine the topological structure of the BP neural network model [43], which will not be introduced in detail in this article. This paper only studies in detail how to determine the key parameters of the NSGA-II algorithm model. The size of the initial population in the NSGA-II algorithm reflects the diversity of initial solutions. A large initial population can lead to an increase in redundant data and slow down computational speed, while a small initial population may result in a decrease in the accuracy of the Pareto front. Similarly, the number of iterations determines the generations of evolution. If the number of iterations is too high, it can lead to excessively  
Figure 9: Monitoring curve results for JCK17 monitoring hole. long computation times. Conversely, if the number of iterations is too low, it may not be sufficient to evolve the optimal solution that meets the desired accuracy requirements. Thus, configuring the population size and number of iterations is crucial for the algorithm. This study employs the controlled variable method to investigate the individual effects of population size and number of iterations on the Pareto solutions. Given that conducting several trial calculations is necessary, the number of monitoring points does not significantly affect the variation pattern of Pareto solutions. However, it can significantly decrease computational speed. Therefore, in this study, only the error functions of three selected monitoring points were used as objective functions [42]. First, the initial population size was set to 100 and the number of iterations to 50. After each iteration, the mean value of the objective function corresponding to the Pareto frontier was recorded and plotted, as shown in Figure 10.  
As shown in Figure 10, when the number of iterations is less than 15, both objective functions tend to converge rapidly. When the number of iterations is between 15 and 32, the changes in the values of objective functions F1 and F2 tend to be stable. The rate of change for F1 is lower, showing a slight overall increasing trend. On the other hand, F2 exhibits a decreasing trend initially, followed by an increasing trend. When the number of iterations reaches 33, both F1 and F2 experience a minor mutation. However, as the number of iterations increases, F1 stabilizes, with its value remaining between 1.2 and 1.4. Objective function F2 exhibits slight fluctuations, with values fluctuating between 0.038 and 0.048, but the magnitude of these fluctuations is small. Considering all factors, the number of iterations was set to 45. On the basis of determining the number of iterations, further research is required on the initial population size. With 45 iterations, the solving process must be repeated 45 times. A large initial population size ensures the diversity of initial solutions but results in longer computation times. Figure 10 shows that there is a brief plateau period when the number of iterations is between 24 and 27. Therefore, we set the number of iterations to 25 to study the variation patterns of the Pareto front under different initial population sizes.