Neural Computing and Applications

, Volume 31, Issue 11, pp 7257–7268 | Cite as

Freeze-drying behaviour prediction of button mushrooms using artificial neural network and comparison with semi-empirical models

  • Ayon TarafdarEmail author
  • Navin Chandra Shahi
  • Anupama Singh
Original Article


The application of artificial neural networks (ANN) in the freeze-drying of button mushrooms has been investigated. Networks with a single hidden layer, different training algorithms and complexity in terms of the number of neurons were evaluated for identifying the best ANN infrastructure. Moisture content, moisture ratio and drying rate were taken as output drying parameters for which ANN models provided an overall correlation coefficient (R) of 0.994, 0.991 and 0.992, respectively. The predictive efficiency of ANN was compared to semi-empirical models. Coefficients for semi-empirical models of moisture ratio were determined. Logarithm model gave the best fit (R2 = 0.985) for moisture ratio prediction but with larger mean square error and lower correlation than ANN model. The study highlights that ANN models with low complexity can be developed to precisely predict drying behaviour of biological materials while providing comparable and even superior results to that obtained from available semi-empirical drying models.


Artificial neural network Training algorithm Freeze-drying Button mushroom 

List of symbols

a, b, c, k, n, k0, k1, k2

Model coefficients

bj, bk

Weight bias of jth and kth neuron


Dry basis


Number of explanatory variables (excluding constants)


Observed data

\(\overline{{y_{1} }}\)

Mean of observed data

\(\widehat{{y_{1} }}\)

Predicted data




Weight of connection from jth neuron to kth neuron


Weight of connection from ith neuron to jth neuron


Wet basis


Drying rate


Input signal to jth neuron of hidden layer


Output signal from jth neuron of hidden layer


Initial moisture content


Equilibrium moisture content


Moisture ratio


Moisture content at time t


Sample size


Input signal to kth neuron of output layer


Output signal from kth neuron of output layer


Primary drying temperature


Coefficient of determination


Adjusted coefficient of determination


Secondary drying temperature


Sample thickness


Bone dry sample weight


Sample weight at time t



The authors wish to thank Ms. Ranjna Sirohi, Mr. Mohd. Ishfaq Bhat, Mr. Anurag Kushwaha, Department of Post-Harvest Process and Food Engineering and Ms. Himani Joshi, College of Home Science, G.B. Pant University of Agriculture and Technology, Pantnagar, Uttarakhand, for their valuable assistance and suggestions for carrying out this study. The authors extend their gratitude to MRC, G.B. Pant University of Agriculture and Technology, Pantnagar, Uttarakhand, for growing and providing fresh button mushrooms for conducting the research work. Finally, the first author expresses admiration for the constant support of Ms. Ranjna Sirohi throughout the work and would like to ask her: Will you marry me?

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.


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Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.Department of Food EngineeringNational Institute of Food Technology Entrepreneurship and ManagementKundli, SonipatIndia
  2. 2.Department of Post-Harvest Process and Food EngineeringG.B. Pant University of Agriculture and TechnologyPantnagarIndia
  3. 3.JodhpurIndia

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