9.3.4 Response Surface Models After the modal analyses performed for all of the sampling points, initial response surfaces are created by applying Kriging model, a sophisticated meta-modelling algorithm [6]. Following this, the auto-refinement procedure is implemented by ANSYS ® Design Exploration [7]. Since LHS design does not necessarily cover extremes (i.e. corners of the design space), the refinement points are chosen mainly at the extremes. In the refinement procedure, maximum %2 of predicted related error is considered as a convergence criterion. In order to satisfy this error criterion 23 refinement points are automatically inserted into design space. These refinement points can be seen in Table 9.5. In this response surface generation, since Kriging model, an interpolated response surface model, is used, it is ensured that the response surface passes through all of the DOE points. To evaluate response surface accuracy, using of verification points to compare the predicted and observed values of the output parameters of the response surface is a better way. For this aim, eight verification points are placed where the distance from existing DOE points and refinement points are maximum. These verification points can be seen in Table 9.6. The goodness of fit of the response surface for verification points is assessed by five error measures in ANSYS ® Design Explorer as Maximum Relative Residual, Root Mean Square (RMS) Error, Relative Root Mean Square Error, Relative Maximum Absolute Error, and Relative Average Absolute Error [7]. For these error measures, the value of 0 % indicates the best quality of the response surface. Table 9.7 shows the results of goodness of fit of the response surfaces. In this case, it can be seen that the error values are less than 2.5 %. And it can be said that this error is perfectly adequate for this case. In order to observe how the geometric parameters affect the vibration characteristics of the joined-wing configurations, response surfaces are constructed and presented based on the definitions listed in Table 9.7. Natural frequency responses corresponding to Mode 1, Mode 2, Mode 3 and Mode 4 is given in Figs. 9.7, 9.8, 9.9, and 9.10, respectively. Figures 9.7 and 9.8 shows that “Mode 1” and “Mode 2” have similar tendencies and they peak up when joint location is in between 450 mm and 550 mm. If the influence of the aft wing sweep angle is considered, it can be seen that it has almost no effect on the natural frequencies. As it can be seen from Figs. 9.9 and 9.10, Mode 3 and Mode 4 have similar tendencies; however, their characteristics are completely different from Mode 1 and Mode 2. From these figures, it is observed that joint location has highest influence on Mode 3 and Mode 4. The frequency values are at its absolute minimum and maximum value when the joint location is in Fig. 9.6 Corresponding mode shapes of the of joined-wing for Design Point 2 92 B. Alanbay et al.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==