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An Introduction to Modeling and Simulation of Particulate Flows Part 4

Tham khảo tài liệu 'an introduction to modeling and simulation of particulate flows part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Ọ 2007 5 15 page 39 e e Chapter 5 Inverse problems parameter identification An important aspect of any model is the identification of parameters that force the system behavior to match a desired target response. For example in the ideal case one would like to determine the type of near-field interaction that produces certain flow characteristics via numerical simulations in order to guide or minimize time-consuming laboratory tests. As a representative of a class of model problems consider inverse problems where the parameters in the near-field interaction representation are sought the a s and p s that deliver a target particulate flow behavior by minimizing a normalized cost function n .1 A - A 1 dt Ị A dt 5.1 where the total simulation time is T A is a computationally generated quantity of interest and A is the target response. Typically for the class of problems considered in this work formulations n such as in Equation 5.1 depend in a nonconvex and nondifferentiable manner on the a s and p s. This is primarily due to the nonlinear character of the nearfield interaction the physics of sudden interparticle impact and the transient dynamics. Clearly we must have restrictions for physical reasons on the parameters in the near-field interaction a1 or 2 a1 or 2 a or 2 5.2 and p-or 2 P1 or 2 p or 2 5.3 where a-or 2 a or 2 p-or 2 and p or 2 are the lower and upper limits on the coefficients in the interaction forces.24 With respect to the minimization of Equation 5.1 classical gradient-based deterministic optimization techniques are not robust due to difficulties with objective function nonconvexity and nondifferentiability. Classical gradient-based algorithms are likely to converge only toward a local minimum of the objective function unless a sufficiently close initial guess to the global minimum is not provided. Also it is usually 24Additionally we could also vary the other parameters in the system such as the friction particle densities and drag. However we shall .