Neural Model for the Prediction of Volume Losses in the Aging Process of Rums

The rum aging process shows volume losses, called wastage. The numerical operation variables: product, boardwalk, horizontal and vertical positions, date, volume, alcoholic degree, temperature, humidity and aging time, recorded in databases, contain valuable information to study the process. MATLAB 2017 software was used to estimate volume losses. In the modeling of the rum aging process, the multilayer perceptron neuronal network with one and two hidden layers was used, varying the number of neurons in these between 4 and 10. The Levenberg-Marquadt (LM) and Bayesian training algorithms were compared (Bay) The increase in 6 consecutive iterations of the validation error and 1000 as the maximum number of training cycles were the criteria used to stop the training. The input variables to the network were: numerical month, volume, temperature, humidity, initial alcoholic degree and aging time, while the output variable was 1 Instituto Cubano de Investigaciones de los Derivados de la Caña de Azúcar (La Habana, Cuba). beatriz.garcia@icidca.azcuba.cu. ORCID: 0000-0001-8101-0638 2 Ph. D. Universidad Tecnológica de La Habana “José Antonio Echeverría” (La Habana, Cuba). osney@quimica.cujae.edu.cu. ORCID: 0000-0002-0366-0317. 3 Ph. D. Universidad Tecnológica de La Habana “José Antonio Echeverría” (La Habana, Cuba). lourdes@química.cujae.edu.cu. ORCID: 0000-0001-6921-737X. 4 M. Sc. Instituto Cubano de Investigaciones de los Derivados de la Caña de Azúcar (La Habana, Cuba). idania.blanco@icidca.azcuba.cu. ORCID: 0000-0003-1281-3722. 5 Universidad Tecnológica de La Habana “José Antonio Echeverría” (La Habana, Cuba). llopezm@química.cujae.edu.cu. ORCID: 0000-0002-7009-4415. Neural Model for the Prediction of Volume Losses in the Aging Process of Rums Revista Facultad de Ingeniería (Rev. Fac. Ing.) Vol. 29 (54), e10514. 2020. Tunja-Boyacá, Colombia. L-ISSN: 0121-1129, e-ISSN: 2357-5328, DOI: https://doi.org/10.19053/01211129.v29.n54.2020.10514 wastage. 546 pairs of input / output data were processed. The statistical Friedman and Wilcoxon tests were performed to select the best neural architecture according to the mean square error (ECM) criterion. The selected topology has a 6-4-4-1 structure, with an ECM of 2.1∙10 and a correlation factor (R) with experimental data of 0.9898. The neural network obtained was used to simulate thirteen initial aging conditions that were not used for training and validation, detecting a coefficient of determination (R) of 0.9961.


I. INTRODUCTION
In fresh rum, as in most distilled alcoholic beverages, the aroma reminds of the used raw material. Aroma varies when the fresh rum rests in oak containers for a certain time, commonly known as "aging" or aging time. During this time, reactions that cause a transformation of the original organoleptic properties of the distillates occur naturally. [1] The technological production process of the Aged rum that is carried out at the Alcohol and Beverage Reference Center (CERALBE), belonging to the Cuban Research Institute of Sugarcane Byproducts (ICIDCA), comprises several stages.
During the rum aging process, product losses, popularly known as "the Angel portion", occur. The aging of rum does not change or transform the drink but develops and sublimates its latent qualities [2]. That is why, in the context of excellence in which these drinks compete, there is an interest in studying the decrease in the volume of rum during aging concerning the environmental conditions. These losses have not been updated in CERALBE recently, although the volume of losses is known to be high.
The existing technology in the aging cellars allowed the study of the wastages during 13 months; measuring the liquid level of the barrels, alcoholic strength, temperature and humidity. All this stored memory constitutes a valuable source of information that can be useful in understanding the present and predicting the future.
Data mining (DM) is the process of extracting useful and understandable knowledge, previously unknown, from large amounts of data stored in different formats [3]. It allows prediction, classification, association, grouping and correlation tasks based on statistical techniques such as the analysis of principal and computational components such as artificial neural networks [4]. Currently, the DM has become popular due to the increase in the computing capacity of the computers, combined with the increase in the data storage capacity and its quality [5].
Artificial neural networks constitute a computational tool that mimics the functioning of the human brain because it can learn patterns or behaviors from a database [6][7]. Obtaining predictive models from training, which is developed by presenting an input matrix and its corresponding output, has allowed the modeling of different processes.
The predictive models obtained by data mining techniques constitute an alternative to the mathematical models and at the same time, a tool to analyze the information stored in the rum aging processes to predict the percentage of volume losses based on the variables that are registered.

A. Creation and Training of the Neural Network
The multilayer perceptron neuronal network with one and two hidden layers, feedforward network, backpropagation training algorithm was used for the modeling of the rum aging process. This type of neural network is easy to use and allows the modeling of complex functions [7][8].
The number of neurons in the hidden layers was varied from 4 to 10 with each of the training algorithms used: Levenberg-Marquadt (L-M) and Bayesian (Bay). The input variables to the network were: numerical month, volume, temperature, humidity, initial alcoholic grade and aging time, while the output variable was volume losses. Table 1 shows the minimum and maximum values for each variable. 546 pairs of input / output data were processed. The original data were normalized between 0.0 and 1.0, given the differences between their magnitudes. For the partition of training data, the "dividerandʺ function was used, with the default division of 70% for training, 15% for testing and 15%, for validation. The increase in 6 consecutive iterations of the validation error and 1,000 as the maximum number of training cycles were the criteria used to stop the training. Both the creation of the neural network and its training were carried out in Matlab 2017.   (null hypothesis), which remarks the equality between two medians, and h1 (alternative hypothesis), which mentions the non-equality between two medians. The selection of the neural architecture is based on the P-value; if it is less than 0.05 then the null hypothesis is rejected [10].

A. Determination of Noise, Cleaning and Selection of the Data to be Used
A data with 900 instances and ten variables were obtained, five of them qualitative:

1) Topology of the neural network. The number of neurons in the hidden layer was
varied from 4 to 10 with each of the training algorithms used (Levenberg-Marquadt and Bayesian) and the behavior of all topologies were compared. The coefficient of determination (R 2 ) of the losses for each of the topologies, as well as the mean square error (MSE) and the mean absolute error (MAE, are shown in Table 2. Table 2. Topology comparison with a hidden layer for each algorithm.  Tables 3 and 4 for each algorithm.  Table 4. Topology comparison with two hidden layers for the Bay algorithm. The topologies shown in Tables 3 and 4 were tested for Friedman to determine if there were statistically significant differences with respect to each configuration. In the first case (L-M algorithm) the result of the P-value for the Friedman test was 0.6959, greater than 0.05, so there are no significant differences between the behaviors of the different topologies. In the second case (Bayesian algorithm), there was a difference between the medians of the topologies, presenting a P-value for the Friedman test of 0.0005, so the Wilcoxon test was performed to define the best neuronal topology according to the criterion of the mean square error. This test was performed between the best topology of this group (6-4-4-1) and the remaining ones;
The four selected correspond to the Bayesian training algorithm, two of them have a hidden layer and the other two. These were subjected to the Friedman test to determine if there were statistically significant differences. The P-value obtained was 0.0153, less than 0.05, showing that there were differences with the topology (6-7-1). The Wilcoxon test was performed to define if there were differences between the best topology (6-4-4-1) with the (6-4-1) since it had been determined, previously, that there was no difference with (6-4-10-1). The P-value obtained was 0.0513, so there are no differences. From these last four selected topologies, anyone expect (6-7-1) can be chosen.
Based on the results of the best model according to the topology of the neural network, according to the criteria of the mean square error and the correlation coefficient separately, it was decided that the neuronal model that best predicts the losses in the rum aging process is (6-4-4-1). The higher correlation coefficient among all topologies, a moderate structural complexity that allows savings in Matlab software calculations and low mean square error values, are reasons that justify the previous decision.

2) Simulation.
In order to verify the predictive capacity of the neural network, already trained and validated, the topology (6-4-4-1) was used to simulate 13 initial aging conditions. These values were determined as the average of the thirteen months of research for each variable analyzed, to ensure the interpolator character of the network. The quality of the model can be seen in Figure 1, where the actual values and those estimated by the neuronal model for the different initial conditions are shown. The average error in the estimate is 3.03%, the maximum error being 7.4%.

IV. CONCLUSIONS
The