Comparison of methods for multivariate moment inversion—Introducing the independent component analysis

• A comparison of different methods for multivariate moment inversion was carried out.
• The independent component analysis was firstly used to solve this problem.
• Unimodal, bimodal and multimodal bivariate distribution functions were analyzed.
• Combination of methods with enhanced accuracy and robustness were proposed.
• 3rd and 4th orders 2-D quadratures could be obtained with just 4 and 6 points.

Despite the advantages of the moment based methods in solving multivariate population balances models, these methods still suffer with the so-called multivariate moment inversion problem. Although univariate moment inversion is achieved without major problems this is not true for multivariate cases, for which there is no well established methodology. This work presents a comparative analysis of the existing methods regarding their accuracy and robustness. A new moment inversion method based on the independent component analysis was proposed and analyzed. Improvements in accuracy and robustness were achieved by combination of different moment inversion methods.

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