The concentration of omega3 compounds obtained for the esterification of squid oil by molecular distillation was carried out in two stages. This operation can process these thermolabile and high molecular weight components at very low temperatures. Given the mathematical complexity of the theoretical model, artificial neural networks (ANN) have provided an alternative to a classical computing analysis. The objective of this study was to create a predictive model using artificial neural network techniques to represent the concentration process of omega3 compounds obtained from squid oil using molecular distillation. Another objective of this study was to analyze the performance of two different alternatives of ANN modeling; one of them is a model that represents all variables in the process and the other is a global model that simulates only the input and output variables of the process. The alternative of the ANN global model showed the best fit to the experimental data.
Molecular distillation is based on the evaporation of components from a mixture, usually in the form of a falling film, produced by contact with a heated surface, followed by subsequent condensation on a cold surface. Thus, molecular distillation or shortpath distillation is a special type of ultrahigh vacuum distillation that takes place in special equipment where the distance between the evaporation and condensation surfaces is shorter than its mean free path. This technology is useful for the separation, purification and concentration of thermo labile substances with low vapor pressure (Pramparo
The main feature of this operation is the operative pressure (100.1 Pa). Under these conditions, the relative volatility of components increases and temperature decreases, allowing for the separation of compounds at lower temperatures. The molecules that leave the evaporation surface suffer no collisions before their condensation (Setyawan
The degree of separation that is achieved by a molecular distillation process is not an exclusive function of the relative volatilities of the compounds, since transport resistances and the interfacial resistance characteristic of the molecular kinetic play an important role in the performance of this operation. When the liquid evaporates, the vaporliquid interface is cooled and, for mixtures, the composition of the most volatile components decreases in the interface. This leads to the formation of driving forces for mass, diffusive, and heat transfers (Vansant,
The detailed mathematical description of the phenomena that occur in this operation generates a complex mathematical resolution, resulting in numerous studies aimed at finding the best model for this process. With regard to the mathematical description of molecular distillation with phenomenological models, many advances have been reported, ranging from the modeling of a conventional falling film evaporator to specific molecular distillators derived from the first ones. Lutisan
Given the mathematical complexity of the phenomenological model that this operation represents, new solution techniques have been studied, including Artificial Neural Networks (ANN) (Bulsari,
Depending on how the elements in the different layers are connected and the direction of sequential information flow among layers, networks are classified as feedforward networks and recurrent networks. In feedforward networks, unidirectional signals flow from the input layer to the output layer, i.e. data are sent to neurons from the transfer layer to the next layer, but they do not send data to neurons in the same layer. In recurrent networks, the signal moves in two directions and the output of some neurons is forwarded to another neuron or neurons that belong to previous layers (Shao
ANN have provided an alternative to classical computing for those problems where traditional methods have not provided convincing results, or solutions for complex problems where all phenomena taking place cannot be incorporated into a mathematical model. ANN may have different applications from image and voice processing, pattern recognition, and planning and adaptive interfaces for human/machine systems to signal filtering, prediction, control, and optimization of phenomena. Shao
Fish oils are a rich source of polyunsaturated fatty acids called omega3. These kinds of fatty acids have an essential role in the human diet since they have the ability to prevent diseases such as cardiovascular, cancer, Alzheimer, and arthritis. Particularly in fish oils, there are two omega3 fatty acids, 5,8,11,14,17eicosapentaenoic acid (EPA, 20:5ω3) and 4,7,10,13,16,19docosahexaenoic acid (DHA, 22:6ω3) that are functional constituents of importance for the physiology of the human body (Swanson,
Rossi
There is no information available in the literature on modeling of the molecular distillation operation through the artificial neural network to obtain a concentration of omega 3 fatty acids from squid oil. The objective of this study was to create a predictive model using artificial neural network techniques to represent the concentration process by molecular distillation of omega3 compounds such as the ester ethylics of EPA and DHA obtained from squid oil. Another objective of this study was to analyze the performance of two different alternatives of ANN modeling; one of them is a model that represents all variables in the process and the other is a global model that simulates only input and output variables of the process.
To construct and validate the ANN predictive model experimental data were used from Rossi
Squid oil is composed primarily of triglycerides whose fatty acids can be separated by a transesterification reaction with ethyl alcohol whose resulting product is the ethyl ester of the fatty acid (EE). Rossi
Rossi
The processing elements of the neural network model used are an input layer, a hidden layer, and an output layer. Interconnections among the different layers can be seen in
Structure of the artificial neural network used in modeling the molecular distillation operation.
The development of networks has two stages, the training phase where experimental data are used to make the network imitate the physical phenomenon, and the test phase where real critical values and network approximation values are compared. The training phase occurs due to the learning ability of the ANN. Network learning is a process for fixing the ANN free parameters through a continuous stimulation in the environment where the system is located. For a given ANN topology, it is possible to work with different forms of learning which increase their applications (Haykin,
In this study, the network used in the simulation of the process was the multilayer perceptron network with the backpropagation supervised learning method (Haykin,
Algorithms are used to model ANN. An algorithm consists of an initial loop where the neuron number of the hidden layer is fixed and looks for the best training adjusted to the experimental data. A second loop contains the first loop and includes the variation in neuron number in the hidden layer. Finally, the results of the algorithm are the optimum number of the hidden layer with the corresponding best training. The flow sheet of the algorithm used to model the process of concentration of omega3 compounds by molecular distillation for obtaining the optimum number of neurons in the hidden layer with its corresponding best training are shown in
Flow sheet of the algorithm used to model the process of the concentration of omega3 compounds by molecular distillation for obtaining the optimum number of neurons in the hidden layer with the best training.
For the process for concentrating omega3, it was necessary to model two stages of molecular distillation. Two alternatives for modeling ANN were tried: Alternative A (global model) that models the overall process of the two stages as a single process without the intervention of internal current values and Alternative B (staged model), which consists of the development of an ANN model for each stage of molecular distillation, which is simulated under sequential structure modeling.
Both alternatives work with a multilayered network. The neurons in the hidden layer allow a nonlinear mapping of the system. The number of neurons in the input layer is equal to the number of independent variables in the input of each ANN model, and the number of neurons in the output layer corresponds to the number of output variables resulting from each ANN model.
The function of the hidden layer is the hyperbolic tangent sigmoid transfer function (1):
The results achieved by the global ANN model were confronted with the experimental data reported by Rossi
Variables and parameters involved in the artificial neural network
Alternative A: Global model  Alternative B: Individual model  

Stage I  Stage II  
Input  


Output 




–  –  




Number of layers  3  3  3 
Number of neurons in the hidden layer  10  6  10 
Hidden layer function  Tansig  Tansig  Tansig 
Where
Where
The input data corresponding to temperature # 1 and 2 (T^{1} and T^{2}) and the output data corresponding to the distillation flow and feeding compound ratio (D^{1}/F and D^{2}/F) and mass fractions of the ethyl ester of fatty acids (X^{1} and X^{2}) are presented in
Experimental data used during the training of the ANN models
Input data  Output responses  

T^{1}  T^{2}  D^{1}/F  D^{2}/F 








100  120  14.3  43.1  9.3  10.8  35.2  44.7  18.3  21.6  27.1  33.0 
100  130  14.3  50.8  9.3  10.8  35.2  44.7  19.8  23.7  25.6  30.9 
100  140  14.3  51.2  9.3  10.8  35.2  44.7  21.8  26.2  23.6  28.4 
110  120  28.4  26.3  10.5  12.2  34.3  43.0  19.7  23.3  26.0  31.0 
110  130  28.4  37.3  10.5  12.2  34.3  43.0  25.7  30.9  19.9  23.5 
110  140  28.4  42.0  10.5  12.2  34.3  43.0  23.8  28.8  21.8  25.6 
120  120  49.5  12.5  13.4  15.7  31.7  39.2  27.4  32.9  18.7  21.0 
120  130  49.5  18.9  13.4  15.7  31.7  39.2  30.6  37.3  15.2  16.9 
120  140  49.5  21.6  13.4  15.7  31.7  39.2  30.5  37.6  15.0  16.9 
Where
The linear regression between targets and outputs of the global ANN model used to train the network are shown in
Lineal regression between the targets and outputs of the global model.
Abbreviation: Y = T is an ideal fit; Data is the experimental data; Fit is the linear regression between ANN model results and experimental data; Output is the ANN model results (relationship between the flow of the distillated phase of stage 2 and the mass composition of omega3 in the distillated phase of stage 2); Target is the experimental data.
Comparison of flow rate between global model and experimental results
T^{1} [°C]  T^{2} [°C] 
Exp % D^{2}/F 
ANN % D^{2}/F 
Error % 

100  120  43.1  42.0  2.6 
100  130  50.8  50.1  1.4 
100  140  51.2  51.2  0 
110  120  26.3  28.8  8.7 
110  130  37.3  38.7  3.6 
110  140  42.0  41.2  1.9 
120  120  12.5  10.9  14.7 
120  130  18.9  19.8  4.5 
120  140  21.6  21.0  2.9 
Where T^{1} is the temperature (°C) of stage 1, T^{2} is the temperature (°C) of stage 2, Exp D^{2}/F is the percentage of distillated flow of stage 2 and feeding flow ratio obtained experimentally. ANN D^{2}/F is the ANN model result.
Exp D^{2}/F (Rossi
Comparison of mass composition of omega3 between the global model and experimental results
T^{1} [°C]  T^{2} [°C] 
Exp X^{D2}ω3 [g g^{−1}%] 
ANN X^{D2}ω3 [g g^{−1}%] 
Error 

100  120  39.9  37.8  5.3 
100  130  43.5  45.6  4.8 
100  140  48.0  46.8  2.5 
110  120  43.0  46.6  8.4 
110  130  56.6  53.9  4.8 
110  140  52.6  53.9  2.5 
120  120  60.3  58.9  2.3 
120  130  67.9  67.6  0.4 
120  140  68.1  68.8  1.0 
Where: T^{1} is the temperature (°C) of stage 1, T^{2} is the temperature (°C) of stage 2, Exp X^{D2}ω3 is the percentage of omega3 mass faction in the distillated phase of stage 2 obtained experimentally. ANN X^{D2}ω3 is the ANN model result.
Exp X^{D2}ω3 (Rossi
The relation of % D^{2}/F obtained by the global ANN model, with respect to the temperature of step 2 (T^{2}) when the stage 1 (T^{1}) temperature is parametric is shown in
Relation between the distilled flow of stage 2 and the feeding flow at different temperatures (T2) in stage 2.
T^{1} is the temperature (°C) of stage 1, T^{2} is the temperature of stage 2, ANN is the data obtained by the ANN model, and Exp is the experimental data.
The behavior of
Mass fraction of omega3 in the distilled of stage 2 at different temperatures (T2) in the stage 2.
T^{1} is the temperature (°C) of the stage 1, T^{2} is the temperature of the stage 2, ANN is the data obtained by ANN model, and Exp is the experimental data.
Theoretical concepts based on phenomenological laws were very important for the construction of the ANN structure. Numerous studies (Pramparo
Rigorous phenomenological models can predict the influence that each of the operative variables has and describe the phenomenon that takes place on the inside of the equipment or how the variables affect the performance of the process (Liñan
There are other alternatives to phenomenological models like surface response, fuzzy logic, and genetic algorism, among others, that have a great adaptation capability to the phenomena even for those that are nonlinear, do not require previous knowledge of the phenomena; and do not need great mathematical complexity. ANN also has these advantages (Shao
Modeling with artificial neural networks allows for the prediction of the behavior of a molecular distillation process in two stages to concentrate the ethyl esters of omega3 fatty acids. In addition, the knowledge about the phenomenological concept obtained from the modeling with artificial neural networks were useful for selecting different parameters necessary for building the ANN model.
The authors wish to thank CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas) for supporting this research and the Secretaría de Ciencia, Tecnología e Innovación, Gobierno de la Provincia de Chubut, for their contribution and interest in this subject.