On the Constrained Maximum Entropy Solution of the Population Balance Equation
نویسندگان
چکیده
The population balance equation (PBE) is an integro-partial differential equation, which admits analytical solutions only for a few simple cases. We propose for the first time a novel converging sequence of continuous approximations to the number concentration function as a solution to the PBE. The uniqueness and convergence of such a sequence are assured by being an optimal solution to a constrained NLP, which maximizes the constrained Shannon entropy function. This entropy maximization problem is convex and is solved in a finite dual space by using the standard Leveberg-Marquardt algorithm. The proposed method provides not only the maximum missed information about the distribution, but also its low order moments.
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