70 X O Chen,Z M Gong,H Huang.S Z Ge,and L B Zhou different portions of the profile accordingly.When all the portions of the profile are fitted,the fitting results are appropriately combined together to form a smooth complete profile.The final fitted profile satisfies both the contradictory objectives of profile fitting and distortion correction.Figure 8 shows the schematics of actual 2D profile obtained by OPF.The design data are used as the template,and the sectional profile is derived from the measurement points. 0 Design data --Template of sectional profile created using Cubic Spline Interpolations Measurement points -Actual sectional profile obtained by OPF Figure 8 Actual 2D sectional profile obtained by OPF. 4.3 A Fast Converging Minimisation Algorithm As mentioned in the last section,the optimal profile fitting of a 2D sectional airfoil profiles needs to do unconstrained minimisation in a 3D search space with X-axis shift,Y-axis shift and rotation as the three independent variables.In this section,we present a generic fast converging multi-dimensional minimisation algorithm. There are a number of multi-dimensional minimisation algorithms,such as downhill simplex search method,Hooke-Jeeves pattern search method, Powell conjugate direction method,Cauchy method,Newton method, conjugate gradient methods,and variable metric methods [10,11]. However,for our particular minimisation problem the selection of the methods is limited due to the complication of the index function. The index function in the optimal profile fitting,as given by Equation (4),is the weighted sum distance from the measurement points to the template.The template is represented by a series of points.The three position parameters of the template,i.e.,X-axis shift,Y-axis shift and70 X Q Chen, Z M Gong, H Huang, S Z Ge, and L B Zhou different portions of the profile accordingly. When all the portions of the profile are fitted, the fitting results are appropriately combined together to form a smooth complete profile. The final fitted profile satisfies both the contradictory objectives of profile fitting and distortion correction. Figure 8 shows the schematics of actual 2D profile obtained by OPF. The design data are used as the template, and the sectional profile is derived from the measurement points. Design data Template of sectional profile created using Cubic Spline Interpolations Measurement points Actual sectional profile obtained by OPF Figure 8 Actual 2D sectional profile obtained by OPF. 4.3 A Fast Converging Minimisation Algorithm As mentioned in the last section, the optimal profile fitting of a 2D sectional airfoil profiles needs to do unconstrained minimisation in a 3D search space with X-axis shift, Y-axis shift and rotation as the three independent variables. In this section, we present a generic fast converging multi-dimensional minimisation algorithm. There are a number of multi-dimensional minimisation algorithms, such as downhill simplex search method, Hooke-Jeeves pattern search method, Powell conjugate direction method, Cauchy method, Newton method, conjugate gradient methods, and variable metric methods [10, 11]. However, for our particular minimisation problem the selection of the methods is limited due to the complication of the index function. The index function in the optimal profile fitting, as given by Equation (4), is the weighted sum distance from the measurement points to the template. The template is represented by a series of points. The three position parameters of the template, i.e., X-axis shift, Y-axis shift and