Accuracy and optimal sampling in Monte Carlo solution of population balance equations

Xi Yu; Michael J. Hounslow; Gavin K. Reynolds

doi:10.1002/aic.14837

Accuracy and optimal sampling in Monte Carlo solution of population balance equations

Xi Yu^*, Michael J. Hounslow, Gavin K. Reynolds

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Implementation of a Monte Carlo simulation for the solution of population balance equations (PBEs) requires choice of initial sample number (N₀), number of replicates (M), and number of bins for probability distribution reconstruction (n). It is found that Squared Hellinger Distance, H₂, is a useful measurement of the accuracy of Monte Carlo (MC) simulation, and can be related directly to N_₀, M, and n. Asymptotic approximations of H^² are deduced and tested for both one-dimensional (1-D) and 2-D PBEs with coalescence. The central processing unit (CPU) cost, C, is found in a power-law relationship, C= aMN_^{^b}^₀, with the CPU cost index, b, indicating the weighting of N_₀in the total CPU cost. n must be chosen to balance accuracy and resolution. For fixed n, M × N_₀determines the accuracy of MC prediction; if b > 1, then the optimal solution strategy uses multiple replications and small sample size. Conversely, if 0 < b < 1, one replicate and a large initial sample size is preferred.

Original language	English
Pages (from-to)	2394-2402
Number of pages	9
Journal	AIChE Journal
Volume	61
Issue number	8
Early online date	22 Apr 2015
DOIs	https://doi.org/10.1002/aic.14837
Publication status	Published - Aug 2015

Bibliographical note

This is the peer reviewed version of the following article: Yu, X., Hounslow, M. J., & Reynolds, G. K. (2015). Accuracy and optimal sampling in Monte Carlo solution of population balance equations. AIChE Journal, 61(8), 2394-2402, which has been published in final form at http://dx.doi.org/10.1002/aic.14837. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving

Keywords

accuracy
coalescence
hellinger distance
Monte Carlo
optimal sampling
population balance model

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10.1002/aic.14837

Monte Carlo solution of population balance equations
This is the peer reviewed version of the following article: Yu, X., Hounslow, M. J., & Reynolds, G. K. (2015). Accuracy and optimal sampling in Monte Carlo solution of population balance equations. AIChE Journal, 61(8), 2394-2402, which has been published in final form at http://dx.doi.org/10.1002/aic.14837. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving
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http://onlinelibrary.wiley.com/doi/10.1002/aic.14837/abstract

Cite this

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title = "Accuracy and optimal sampling in Monte Carlo solution of population balance equations",

abstract = "Implementation of a Monte Carlo simulation for the solution of population balance equations (PBEs) requires choice of initial sample number (N0), number of replicates (M), and number of bins for probability distribution reconstruction (n). It is found that Squared Hellinger Distance, H2, is a useful measurement of the accuracy of Monte Carlo (MC) simulation, and can be related directly to N0, M, and n. Asymptotic approximations of H2 are deduced and tested for both one-dimensional (1-D) and 2-D PBEs with coalescence. The central processing unit (CPU) cost, C, is found in a power-law relationship, C= aMNb0, with the CPU cost index, b, indicating the weighting of N0 in the total CPU cost. n must be chosen to balance accuracy and resolution. For fixed n, M × N0 determines the accuracy of MC prediction; if b > 1, then the optimal solution strategy uses multiple replications and small sample size. Conversely, if 0 < b < 1, one replicate and a large initial sample size is preferred.",

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note = "This is the peer reviewed version of the following article: Yu, X., Hounslow, M. J., & Reynolds, G. K. (2015). Accuracy and optimal sampling in Monte Carlo solution of population balance equations. AIChE Journal, 61(8), 2394-2402, which has been published in final form at http://dx.doi.org/10.1002/aic.14837. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving",

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N2 - Implementation of a Monte Carlo simulation for the solution of population balance equations (PBEs) requires choice of initial sample number (N0), number of replicates (M), and number of bins for probability distribution reconstruction (n). It is found that Squared Hellinger Distance, H2, is a useful measurement of the accuracy of Monte Carlo (MC) simulation, and can be related directly to N0, M, and n. Asymptotic approximations of H2 are deduced and tested for both one-dimensional (1-D) and 2-D PBEs with coalescence. The central processing unit (CPU) cost, C, is found in a power-law relationship, C= aMNb0, with the CPU cost index, b, indicating the weighting of N0 in the total CPU cost. n must be chosen to balance accuracy and resolution. For fixed n, M × N0 determines the accuracy of MC prediction; if b > 1, then the optimal solution strategy uses multiple replications and small sample size. Conversely, if 0 < b < 1, one replicate and a large initial sample size is preferred.

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Accuracy and optimal sampling in Monte Carlo solution of population balance equations

Abstract

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Keywords

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