## 6 Application
The confidence interval is calculated for the coordinates in each of the divided small division intervals and the envelope diagram is drawn according to the endpoints of the confidence interval, as shown in Figure 9. The envelope area is further calculated according to the confidence interval envelope map and the envelope area is divided in parallel, as shown in Figure 10. The area of each small trapezoid is calculated and summed to obtain a total area value of 5.9632 for the confidence interval envelope. Similarly, the same method can be used to draw the confidence region envelope map projected on the planes _xoy_ and _yoz_ and to calculate the corresponding envelope area. Figure 8: Expanded graph of the original sample data. Figure 5:0 Interval division diagram of the \(z\)-axis of the projection plane. According to the above calculation method, the projection envelopes of the three, two-dimensional coordinate planes _xoy_, _yoz_, and _xoz_ of the semi-physical simulation data and the external field data are drawn and the corresponding areas are calculated, as shown in Figure 5:1 The black line is the semi-physical simulation data envelope polyline, the blue line is the external field data envelope polyline, and the corresponding area ratios of the planes _xoy_, _yoz_, and _xoz_ are 71.75%, 56.61%, and 79.68%, respectively. Observing the graph envelope situation shows that the integrity detection is not satisfied. The simulation data that do not satisfy the integrity detection in this example are directly fused with the field test data based on the Bayesian method, and the fusion result is shown in Figure 5:2  
Figure 5:3 Area segmentation chart. Figure 5:4 Statistical envelope of the confidence intervals. Figure 5:5 Envelope completeness judgment diagram of the three 2D coordinate planes. Figure 5:6 Envelope judgment diagram of the landing point coordinates in the external field. Notes: Blue Star: field coordinates; Black Circle: semi-physical simulation coordinates; Black beige: 3 sigma criteria after the coordinates of the envelope point. Considering situations where the above examples do not satisfy the integrity detection conditions, a surrogate model of the semi-physical simulation system based on the BPNN method is considered, and the test conditions are supplemented. The semi-physical simulation test is repeated under the supplementary test conditions to obtain supplementary landing point data, thereby obtaining a complete semi-physical simulation landing point dataset. The envelope of the field datapoints is shown in Figure 5:7  
According to the test conditions corresponding to the landing point data in the calculation example, based on the BPNN method, the test conditions of the nonenveloped field landing point data are predicted. The predicted data results are shown in Figure 5:8  
According to the prediction results of the test conditions that are not enveloped, the originally set test condition range is expanded. After that, the semi-physical simulation test is carried out under the complete test conditions and the corresponding simulation data of the landing point coordinates are obtained to realize the expansion of the semi-physical simulation landing data and obtain a complete semi-physical simulation landing dataset. Based on Bayesian theory, the semi-physical simulation data in the calculation example and the field test data are fused and analyzed, and the empirical distribution function image is drawn as shown in Figure 5:9  
The qualitative analysis in Figure 13 shows that the empirical distribution function fused with the field test data is closer to the cumulative distribution function of the actual flight landing point of a 534A aircraft after supplementing the simulation data, which does not satisfy the completeness test as a whole. Let the CDF of the data population be \(F_{t}^{o}(x)\); the EDF of the fusion after supplementation be \(F_{t}^{s}(x)\); and the EDF of the directly fused data be \(F_{t}^{d}(x)\).