Modeling a production scale milk drying process: parameter estimation, uncertainty and sensitivity analysis

A. Ferrari, S. Gutierrez, Gürkan Sin

Research output: Contribution to journalJournal articleResearchpeer-review


A steady state model for a production scale milk drying process was built to help process understanding and optimization studies. It involves a spray chamber and also internal/external fluid beds. The model was subjected to a comprehensive statistical analysis for quality assurance using sensitivity analysis of inputs/parameters, and uncertainty analysis to estimate confidence intervals on parameters and model predictions (error propagation). Variance based sensitivity analysis (Sobol's method) was used to quantify the influence of inputs on the final powder moisture as the model output. Bayesian Inference using Markov Chain Monte Carlo sampling was used to quantify the uncertainty on the estimated parameters using available process data. In a full scale process the inputs with major range of variation are: moisture content at concentrate chamber feed (variation around 4%), and humidity at chamber inlet air (variation > 100%). The sensitivity analysis results suggest exploring improvements in the current control (Proportional Integral Derivative) for moisture content at concentrate chamber feed in order to reduce the output variance. It is also confirmed that humidity control at chamber inlet air stream would not be necessary because, despite its wide range of variation (air taken from outside), its impact on output variance is low. The uncertainty analysis results showed that confidence intervals obtained for parameters were reasonable, although some of them were found significantly correlated. For model applications, this means that model simulations should be performed using not only parameter values but also their correlation matrix by means of non-linear error propagation methods such as Monte Carlo techniques. The separate effects on model prediction uncertainties due to parameter estimation and measurement errors were studied. The results indicate that the error in measurements is the main responsible for the uncertainty in output predictions. Therefore using proper filtering of measurements, the comprehensively tested model is ready to support simulation based efforts for further process optimization. (C) 2016 Elsevier Ltd. All rights reserved.
Original languageEnglish
JournalChemical Engineering Science
Pages (from-to)301-310
Publication statusPublished - 2016


  • Sensitivity analysis
  • Uncertainty analysis
  • Bayesian Inference
  • Milk drying process


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