# Dimensional Control of Aircraft Transmission Bodies Using CNC Machines and Neuro-Fuzzy Systems
## 4 Solution to the Problem  
### Data Analysis  
The difference between the \(\mathrm{HPD_{CMM}}\) and \(\mathrm{HPD_{CNC}}\) deviations, i.e., the measurement difference \(\mathrm{E=HPD_{CMM}-HPD_{CNC}}\), was calculated for the data from Figure 8 referring to the bearing seat deviations measured on the CMM and CNC machine. Then, these values were compared with data defining the curvatures of the reference surfaces of the covers. The results are shown in Figure 10.  
In the next stage of data analysis, the correlation of hole position deviations determined from measurements made on the CMM and CNC machine was calculated (Figure 11a). The Pearson correlation coefficient value for the \(\mathrm{HPD_{CMM}}\) and \(\mathrm{HPD_{CNC}}\) variables was determined, which is R = -0.43 and corresponds to a moderate correlation. This means that the results of measurements on the CNC machine do not reflect the results of measurements on the CMM well. A correlation was also determined between the curvature of the reference surface of the cover and the difference in deviations determined on the CMM and CNC machine (\(\mathrm{E=HPD_{CMM}-HPD_{CNC}}\)) (Figure 11b). The value of Pearson's correlation coefficient then amounted to R = 0.8, which corresponds to a very high correlation.  
The analysis of the linear correlation shows that the results of measurements on the CNC machine are not very reliable because they are not strongly correlated with the results of measurements on the CMM. There is, however, a very strong relationship between the differences of measurements on CMM and CNC machine (E) and the curvature of the reference surface of the cover. The greater the curvature of the cover, the greater the difference E. This relation is explained by the fact that the measurement in the state mounted on the CNC machine is all the less reliable, the greater the curvature of the cover in an unmounted state during measurement on the CMM. The conclusion is that the results of measurements on the CNC machine together with the results of the surface curvature measurement can be used to determine the actual deviation of the hole position without measuring this parameter on the CMM.  
Figure 11: Correlation of measurement data: (**a**) hole position deviation; (**b**) surface curvature.  
Figure 10: Curvature of the reference surface of the cover in combination with the difference of measurement results on CMM and CNC machine.  
The presented measurement data were selected as a result of preliminary tests. The quality of the neuro-fuzzy systems with two and three inputs was tested. The system with two inputs was based on the surface curvature measured on CMM (SC\({}_{\text{CMM}}\)) with the deviation of the position of the hole measured on the CNC (HPD\({}_{\text{CNC}}\)), i.e., data presented in Table 1. The system with three inputs additionally included the height of the bearing seat face, measured on a CNC machine. It turned out that the introduction of the third input adversely affected the size of the model error. As a result of the data tests, no correlation of the variable determining the height of the bearing seat face with the remaining data was found. This is due to the fact that the face of the bearing seat is made with greater dimensional tolerance than the other analyzed features and there is a greater variance of the measurement data. This resulted in a deterioration of the results generated by the neuro-fuzzy model with three inputs. Thus, finally a model based on two input variables was used.