# Reliability Analysis of Hybrid Laser INS Under Multi-Mode Failure Conditions
## 5 Calculation Results and Analysis  
### Global Sensitivity Analysis Based on Mixed Inertial Navigation Function Failure  
Based on Figure 10 and the Kriging surrogate model, a comparative analysis of the predicted and actual rotation angles of the hybrid inertial navigation system's X, Y, and Z three-axis coordinate systems deviating from the virtual body coordinate system due to elastic displacement of structural components under impact overload conditions was obtained. Figure 13 shows that the error between the predicted and actual values based on the Kriging surrogate model is within the allowable range, verifying the reliability and stability of the prediction model.  
Using the global sensitivity analysis based on Bayesian formulas introduced in Section 4.1, the failure probability of the mixed inertial navigation  
The results of sensitivity analysis usually depend on the sampling process of numerical calculation methods. If the sample size is insufficient, the sensitivity index may deviate or fluctuate. By changing the sample size N, the trend of the global sensitivity index of the design variables with respect to the sample size N can be determined, thereby evaluating whether the sensitivity index values of each design variable converge and further verifying the stability and reliability of the global sensitivity index calculation. The analysis results are shown in Figure 16.  
Figure 16: Variation in sensitivity indicators with sample size. (**a**): Variable X4, X6 (**b**): Variable X1, X2, X3, X5, X7.  
Figure 15: Bar chart of global sensitivity calculation results based on Monte Carlo method.  
According to Table 7 and the global sensitivity indicators calculated in Figures 14 and 15, the importance measures of structural design parameters and material performance parameters on the functional failure probability of the hybrid inertial navigation system are presented. The importance ranking of each parameter obtained from the global sensitivity analysis based on the Bayesian formula is: \(H_{Inner\ Frame}>E_{Inner\ Frame}>H_{Outer\ Frame}>W_{Outer\ Frame}>W_{Inner\ Frame}>E_{Founation\ Support}>E_{Outer\ Frame}\). While the ranking obtained from the Monte Carlo method is the same: \(H_{Inner\ Frame}>E_{Inner\ Frame}>H_{Outer\ Frame}>W_{Outer\ Frame}>W_{Inner\ Frame}>E_{Founation\ Support}>E_{Outer\ Frame}\). The consistency of the importance ranking results from both methods indicates that the global sensitivity analysis method based on the Bayesian formula can effectively identify the relative importance of parameters. Among these, the uncertainties of parameters \(H_{Inner\ Frame}\), \(E_{Inner\ Frame}\), and \(H_{Outer\ Frame}\) have the most significant impact on the functional failure probability of hybrid inertial navigation, followed by \(W_{Outer\ Frame}\) and \(W_{Inner\ Frame}\), which have a relatively minor effect, while the uncertainties of parameters \(E_{Founation\ Support}\) and \(E_{Outer\ Frame}\) have the least impact on the system's functional failure probability.  
However, it should be noted that the global sensitivity analysis method based on the Bayesian formula and the global sensitivity analysis method based on the Monte Carlo method only obtain the consistency of the sensitivity index ranking of the two design variables. Due to the differences in theoretical basis and calculation process between the two methods, this analysis is only preliminary.  
From Figure 16, it can be seen that as the sample size increases, the global sensitivity indicators of design variables on the functional failure of hybrid inertial navigation tend toward a constant value, indicating that the proposed global sensitivity analysis method based on the Bayesian formula is convergent.