TAILIEUCHUNG - New Trends and Developments in Automotive Industry Part 7

Công nghệ cơ khí thường tạo ra các giả lập mô phỏng hoạt động của các đối tượng, như quy trình chế tạo thực tế theo trình tự tối ưu hóa sự thực hiện, hiệu quả kinh tế và chi phí năng lượng trước khi quyết định lựa chọn một thiết kế cụ thể. | 200 New Trends and Developments in Automotive Industry Solving the above equations by simple mathematical operations we obtain that p WD f f WT - 1s 27 f p -1 Dff D f f WT WDf W t -1 s 28 The equation 24 is not in a convenient form for computation since the desired vector f is implicitly in the right side of the equationf . However it suggests that an iterative algorithm for estimation of the optimal vector f is given as f k 1 Df k W T WDftk WT -1 s 29 where fk diag f1 k i2-p f2 k 2-p fn k 2-p 30 The above algorithm called the generalized FOCUSS algorithm can be expressed in a more compact form f k 1 Df k WD f k s 31 where the superscript . denotes the Moore-Penrose pseudo-inverse and D f k Dpk diag f1 1-p 2 k f2 1-p 2 k fn 1-p 2 k 32 It s should be noted that the matrix Df exists for all f and even for a negative p. For p 2 the matrix Df J and the FOCUSS algorithm simplifies to the standard LS or the minimum 2-norm solution f WT WWT -1 s 33 3. Results The system of equations describing the tomographic flowmeter was solved with the aid of Linear Least Squares method for overdetermined algebraic set of equations. With the method called FOCUSS FOCal Underdetermined System Solver I have solved a system of underdetermined algebraic set of equations. Condition number of the resulting rectangular matrix was high enough so that the classical Kaczmarz s algorithm was not able to produce correct results. That s why I have to take into account pseudo rank deficiency of the matrix coefficients. I have considered all possible candidate solutions when k was changing from 1 till the full pseudo - rank equal to 1000 Polakowski at al. 2008 a . The images and their relief plots constructed on the basis of the candidate solutions are presented in Figure 4b 6b and 7b. The images and their relief plots constructed on the basis of FOCUSS are presented in Figure 4c 5b c d 6c and 7c. Tomography Visualization Methods for Monitoring Gases in the Automotive Systems 201 Fig. 3. Diagram II r

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