tailieunhanh - Design and Optimization of Thermal Systems Episode 3 Part 3

Tham khảo tài liệu 'design and optimization of thermal systems episode 3 part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 522 Design and Optimization of Thermal Systems Therefore the first two numbers in the series are unity and the nth number is the sum of the preceding two numbers. The Fibonacci series may thus be written as n 0123456789 10. Fn 1 1 2 3 5 8 13 21 34 55 89. It can be seen from this series that the numbers increase rapidly as n increases. The fact that for n 2 each number is a sum of the last two numbers is used advantageously to distribute the trial runs or experiments. The method starts by choosing the total number of runs n. This choice is based on the reduction ratio as discussed later. The initial range of values Lo is assumed to be given. Then the Fibonacci search places the first two runs at a distance d1 Fn 2IF from either end of the initial interval. For n 5 this implies placing the runs at d1 F3 F5 3 8 Lo from the two ends of the range. The simulation of the system is carried out at these two values of the design variable and the corresponding objective function determined. The values obtained are used to eliminate regions from further consideration as discussed earlier and shown in Figure . The remaining interval of width L is now considered and runs are carried out at a distance of d2 from each end of this interval where d2 Fn-3 Fn-1 L. The location of one of the runs coincides with that for one of the previous runs due to the nature of the series and only one additional simulation is needed for the second set of points. Again regions are eliminated from further consideration and points for the next iteration are placed at distance d3 from the two ends of the new interval where d3 Fn_4 Fn_2 L L being the width of this interval. Thus the region of uncertainty is reduced. This process is continued until the nth run is reached. This run is placed just to the right of an earlier simulation near the middle of the interval left and thus the region is further halved to yield the final interval of uncertainty Lf. The following simple example illustrates this