68 X O Chen,Z M Gong,H Huang.S Z Ge,and L B Zhou The 3D airfoil surface fitting can be performed in two stages.In the first stage,a number of specified 2D sectional airfoil profiles are fitted individually.A multi-step template-based optimal profile fitting method is used in each sectional profile fitting.In the second stage,a 3D airfoil profile is generated from interpolating the 2D sectional profiles.The computations involved in the second stage are relatively easy and the details are therefore omitted in this chapter. Due to the complicated nature of the problem,it is required that the airfoil sectional profile fitting method must have the following capabilities. 1.The fitting method should be able to fit a sectional airfoil profile with distortions not only in the aspects of the position and orientation,but also in the shape of the profile. 2.A complete smooth sectional airfoil profiles should be generated, despite the fact that only certain portion of the profile can be measured and the number of the measurement points is limited. During the profile fitting,each measurement point should be treated differently according to its location.This requirement is due to the fact that most of the airfoil surface is covered by the brazing material to be ground/polished away.There are large variations in both the thickness and the position of the brazing material.The measurement data from those covered areas are more noisy,while those for the uncovered area are much more accurate. For some delicate portions of the airfoil,such as the trailing edge of the turbine vane,the profile must be fitted with a high precision.On the other hand,the repair areas of the airfoil should be loosely fitted.Contrary to the objective of fitting,certain corrections from the distortions are made so that the shape of the fitted profile has less variation from that of the design profile.By examining the above stringent requirements,it is clear that normal regression or interpolation methods cannot be applied for this profile fitting problem.A different fitting strategy must be designed. In search of a new fitting method,we notice the fact that,although the actual airfoil profiles of the turbine vanes are largely distorted,they still retain,at least locally,the major features of their design profiles. Otherwise,they would not be repairable and have to be scrapped.It is desirable to extract the useful information from the design profile and utilise it in the generation of the distorted profile.Based on this68 X Q Chen, Z M Gong, H Huang, S Z Ge, and L B Zhou The 3D airfoil surface fitting can be performed in two stages. In the first stage, a number of specified 2D sectional airfoil profiles are fitted individually. A multi-step template-based optimal profile fitting method is used in each sectional profile fitting. In the second stage, a 3D airfoil profile is generated from interpolating the 2D sectional profiles. The computations involved in the second stage are relatively easy and the details are therefore omitted in this chapter. Due to the complicated nature of the problem, it is required that the airfoil sectional profile fitting method must have the following capabilities. 1. The fitting method should be able to fit a sectional airfoil profile with distortions not only in the aspects of the position and orientation, but also in the shape of the profile. 2. A complete smooth sectional airfoil profiles should be generated, despite the fact that only certain portion of the profile can be measured and the number of the measurement points is limited. During the profile fitting, each measurement point should be treated differently according to its location. This requirement is due to the fact that most of the airfoil surface is covered by the brazing material to be ground/polished away. There are large variations in both the thickness and the position of the brazing material. The measurement data from those covered areas are more noisy, while those for the uncovered area are much more accurate. For some delicate portions of the airfoil, such as the trailing edge of the turbine vane, the profile must be fitted with a high precision. On the other hand, the repair areas of the airfoil should be loosely fitted. Contrary to the objective of fitting, certain corrections from the distortions are made so that the shape of the fitted profile has less variation from that of the design profile. By examining the above stringent requirements, it is clear that normal regression or interpolation methods cannot be applied for this profile fitting problem. A different fitting strategy must be designed. In search of a new fitting method, we notice the fact that, although the actual airfoil profiles of the turbine vanes are largely distorted, they still retain, at least locally, the major features of their design profiles. Otherwise, they would not be repairable and have to be scrapped. It is desirable to extract the useful information from the design profile and utilise it in the generation of the distorted profile. Based on this