tailieunhanh - Design and Optimization of Thermal Systems Episode 3 Part 4

Tham khảo tài liệu 'design and optimization of thermal systems episode 3 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Search Methods 547 CSD method the method of feasible directions the gradient projection method and the generalized reduced gradient GRG method. Many efficient algorithms have been developed to obtain the optimum with the least number of trials or iterations. Some of these are available in the public domain while others are available commercially. The difference between all these methods lies in deciding on the direction of the move and the scheme used to return to the constraint. The major problem remains the calculation of the gradients. Linearization of the nonlinear optimization problem is also carried out in some cases and linear programming techniques can then be used for the solution. For details on these and other methods see Arora 2004 . EXAMPLES OF THERMAL SYSTEMS We have discussed a wide range of search methods and their application to thermal systems in Chapter 7 and in this chapter. A few examples are given here for illustration of the application of these methods to practical thermal systems. Optimization of the optical fiber drawing furnace as shown in Figure c can be carried out based on the numerical simulation of the process. Because of the dominant interest in fiber quality the objective function can be based on the tension defect concentration and velocity difference across the fiber all these being the main contributors to lack of quality. These are then scaled by the maximum values obtained over the design domain to obtain similar ranges of variation. The objective function U is taken as the square root of the sum of the squares of these three quantities and is minimized. The two main process variables are taken as the furnace temperature representing the maximum in a parabolic distribution and the draw speed. The univariate search method is applied using the golden section search for each variable and alternating from one variable to the other. Figure shows typical results from this search strategy for the optimal draw .