Radial Basis Artificial Neural Network Models for Predicting Solubility Index of Roller

Radial basis artificial neural network models for predicting solubility index of roller dried goat whole milk powder

Sumit Goyal and Gyanendra Kumar Goyal

National Dairy Research Institute, Karnal, India

Abstract.In this work, Radial Basis (Exact Fit) and Radial Basis (Fewer Neurons) artificial neural network (ANN) models were developed to evaluate its capability in predicting the solubility index of roller dried goat whole milk powder. The ANN models were trained with a data file composed of variables: loose bulk density, packed bulk density, wettability and dispersibility, while solubility index was the output variable. The modeling results showed that there is an agreement between the experimental data and the predicted values, with coefficient of determination and Nash - Sutcliffe coefficient close to 1. Therefore, this method may be effective for rapidestimation of solubility index of roller dried goat whole milk powder.

Keywords:Radial Basis Function, ANN, Solubility Index, Goat Milk Powder, MATLAB

1Introduction

A study was planned for predicting the solubility index of roller dried goat whole milk powder by developingradial basis function (RBF)artificial neural network (ANN) models.In today’s tough competition, a key issue that defines the success of a manufacturing organization is its ability to adapt easily to the changes of its business environment. It is very useful for a modern company to have a good estimate of how key indicators are going to behave in the future, a task that is fulfilled by forecasting. A competent predictive method can improve machine utilization, reduce inventories, achieve greater flexibility to changes and increase profits [1].The contribution of goat milk to the economic and nutritional wellbeing of humanity is undeniable in many developing countries, especially in the Mediterranean, Middle East, Eastern Europe and South American countries. Goat milk has played a very important role in health and nutrition of young and elderly people. It has been known for its beneficial and therapeutic effects on the people who have cow milk allergy. These nutritional, health and therapeutic benefits enlighten the potentials and values of goat milk and its specialty products. The chemical characteristics of goat milk can be used to manufacture a wide variety of products, including fluid beverage products (low fat, fortified, or flavoured) and UHT (ultra high temperature) milk; fermented products such as cheese, buttermilk or yogurt,; frozen products such as ice cream or frozen yogurt; butter, condensed/dried products, sweets and candies. In addition, other specialty products such as hair, skin care and cosmetic products made from goat milk have recently gained further attention. Nevertheless, high quality products can only be produced from good quality goat milk. The quality milk should have the potential to tolerate technological treatment and be transformed into a product that satisfies the expectations of consumers in terms of nutritional, hygienic and sensory attributes. Taste is the main criteria used by consumers to make decisions to purchase and consume goat milk and its products [2].In present era, the consumers are extremely conscious about quality of the foods they buy. Regulatory agencies are also very vigilant about quality and safety issues and insist on the manufacturers adhering to the label claims about quality and shelf life. Such discerning consumers, therefore, pose a far greater challenge in product development and marketing. The development of RBF-ANN models for predicting the solubility index of usefuldairy product namely roller dried goat whole milk powderwould be extremely beneficial to the manufactures, retailers, consumers and regulatory agencies from the quality, health and safety points of view.

2Review of Literature

ANN has proved an efficient tool for predictive modelling concerning food products.

2.1Butter

The seasonal variations of the fatty acids composition of butters over three seasons during a 12-month study in the protected designation of origin Parmigiano-Reggiano cheese area were studied. Fatty acids were analyzed by GC-FID, and then computed by ANN. Compared with spring and winter, butter manufactured from summer milk creams showed an optimal saturated/un-saturated fatty acids ratio (−8.89 and −5.79%), lower levels of saturated fatty acids (−2.63 and −1.68%) and higher levels of mono-unsaturated (+5.50 and +3.45%), poly-unsaturated fatty acids (+0.65 and +0.17%), and rumenic acid (+0.55 and +3.41%), while vaccenic acid had lower levels in spring and higher in winter (−2.94 and +2.91%). ANN models were able to predict the season of production of milk creams, and classify butters obtained from spring and summer milk creams on the basis of the type of feeding regimens [3].

2.2Cheese

Ni and Gunasekaran observed that a three-layer ANN model is able to predict more accurately than regression equations for the rheological properties of Swiss type cheeses on the basis of their composition [4]. The results of the experiments conducted by Jimenez-Marquez et al.[5] on prediction of moisture in cheese of commercial production using neural networks models can be used both for research to develop the base of knowledge on production variables and their complex interactions, as well as for the prediction of cheese moisture.

2.3Processed Cheese

Linear Layer (Train) and Generalized Regression ANN models have been developed for predicting the shelf life of processed cheese stored at 7-8º C. The comparison of the two developed models showed that Generalized Regression model with spread constant as 10 got best simulated with less than 1% root mean square error (RMSE). The study revealed that computational intelligence models are quite effective in predicting the shelf life of processed cheese [6]. Several other ANN models have been reported for processed cheese [7-8].

2.4Milk

The accuracy of milk production forecasts on dairy farms using a ffann (feedforward ANN) with polynomial post-processing has been implemented. Historical milk production data was used to derive models that are able to predict milk production from farm inputs using a standard ffann, a ffann with polynomial post-processing and multiple linear regression. Forecasts obtained from the models were then compared with each other. Within the scope of the available data, it was found that the standard ffann did not improve on the multiple regression technique, but the ffann with polynomial post processing did [9].

2.5Burfi

Radial basis (exact fit) model was proposed for estimating the shelf life of an extremely popular milk based sweetmeat namely burfi. The input variables were the experimental data of the product relating to moisture, titratable acidity, free fatty acids, tyrosine, and peroxide value; and the overall acceptability score was the output. Mean square error (MSE), RMSE, coefficient of determination (R2)and Nash - Sutcliffe coefficient (E2) were applied for comparing the prediction ability of the developed models. The observations indicated exceedingly well correlation between the actual data and predicted values, with highR2 and E2values,establishing that the models were able to analyze non-linear multivariate data with very good performance and shorter calculation time. The developed model, which is very convenient, less expensive and fast, can be a good alternative to expensive, time consuming and cumbersome laboratory testing method for estimating the shelf life of the product [10].

2.6ANN Modelling in other Foodstuffs

ANNs have been used as a predictive modelling tool for several other foods, viz.,cherries [11], cakes [12], apple juice [13], chicken nuggets [14], Iranian flat bread [15], potato chips [16] and pistachio nuts [17].

The published literature shows that no work has been reported using ANN modelling for predictive analysis on goat milk powder. The present study would be of great significance to the dairy industry, academicians and researchers.

3Method Material

For developing Radial Basis (Exact Fit) and Radial Basis (Fewer Neurons) models for predicting the solubility index of roller dried goat whole milk powder,several combinations were tried and tested to train the RBF-ANN models with spread constant ranging from 10 to 200. The dataset was randomly divided into two disjoint subsets namely, training set (having 78% of the total observations) and testing set (22% of the total observations). RBF-ANN consists of one layer of input nodes, one hidden radial-basis function layer and one output linear layer. The hidden layer containsn neurons. The hidden layer computes the vector distance (or radius) between the hidden layer weight vectors (which can be interpreted as the centers of the radial-basis functions of each neuron) and the input vectors. The resulting distances are multiplied by the hidden layer biases of each neuron and then a RBF (usually, a Gaussian function) is applied to the result [18].The RBF-ANN topology has a special structure that has certain advantages over the more popular Feedforward ANN architecture, including faster training algorithms and more successful forecasting capabilities [1].The input variables for RBF-ANN models were the data of the product pertaining to loose bulk density, packed bulk density, wettability and dispersibility, while solubility index was the output variable (Fig. 1).

Fig. 1.Input and output variables of ANN model.

In the present investigation, manual selection of spread variables (trial and error) was performed.The size of the deviation (also known as spread) determines how spiky the Gaussian functions are [19].

(1) (2)

(3) (4)

Where, = Observed value; = Predicted value; =Mean predicted value; = Number of observations in dataset.MSE (1); RMSE (2); R2 (3); and E2 (4) were used with the aim to compare the prediction ability of the developed models. Neural Network Toolbox under MALTAB software was used for performing the experiments.Training pattern of ANN models is illustrated in Fig. 2.

Fig. 2.Training pattern for ANN network.

4Results and Discussion

The results of Radial Basis (Exact Fit) and Radial Basis (Fewer Neurons) models developed for predicting solubility index of roller dried goat whole milk powder are displayed in the table 1 and 2, respectively.

Table 1.Performance of Radial Basis (Exact Fit) Model

Spread
Constant / MSE / RMSE / R2 / E2
10 / 9.09751E-05 / 0.009538085 / 0.990461915 / 0.999909025
20 / 6.18519E-05 / 0.007864599 / 0.992135401 / 0.999938148
30 / 6.23472E-05 / 0.007896026 / 0.992103974 / 0.999937653
40 / 6.9358E-05 / 0.008328147 / 0.991671853 / 0.999930642
50 / 7.61927E-05 / 0.00872884 / 0.99127116 / 0.999923807
60 / 8.0645E-05 / 0.008980256 / 0.991019744 / 0.999919355
70 / 8.30617E-05 / 0.009113821 / 0.990886179 / 0.999916938
80 / 8.45E-05 / 0.009192388 / 0.990807612 / 0.9999155
90 / 8.52238E-05 / 0.009231672 / 0.990768328 / 0.999914776
100 / 8.56595E-05 / 0.009255242 / 0.990744758 / 0.99991434
110 / 8.60964E-05 / 0.009278812 / 0.990721188 / 0.999913904
120 / 8.63882E-05 / 0.009294526 / 0.990705474 / 0.999913612
130 / 8.65343E-05 / 0.009302383 / 0.990697617 / 0.999913466
140 / 8.68269E-05 / 0.009318096 / 0.990681904 / 0.999913173
150 / 8.69734E-05 / 0.009325953 / 0.990674047 / 0.999913027
160 / 8.712E-05 / 0.00933381 / 0.99066619 / 0.99991288
170 / 8.74136E-05 / 0.009349523 / 0.990650477 / 0.999912586
180 / 8.75606E-05 / 0.00935738 / 0.99064262 / 0.999912439
190 / 8.78549E-05 / 0.009373093 / 0.990626907 / 0.999912145
200 / 8.80022E-05 / 0.00938095 / 0.99061905 / 0.999911998

Table 2.Performance of Radial Basis (Fewer Neurons) Model

The Radial Basis (Exact Fit) and Radial Basis (Fewer Neurons) models got simulated very well, and gave high R2 and E2 values(table 1 and 2).The best results for radial basis model were with the spread constant 20MSE 6.18519E-05; RMSE: 0.007864599; R2: 0.992135401; E2: 0.999938148.However, no difference was found between the results of the Radial Basis (Exact Fit) and Radial Basis (Fewer Neurons) models as both the models gave similar results with the same spread constantsranging from 10 to 200. Our observations are similar to the earlier findings of Sutrisno et al.[20], who developed ANN models with backpropagation algorithm to predict mangosteen quality during storage at the most appropriate pre-storage conditions which performed the longest storage period. In their experiments R2 was found close to 1 (more than 0.99) for each parameter, indicating that the model was good to memorize data.Fernandez et al.[21] studied the weekly milk production in goat flocks and clustering of goat flocks by using self organizing maps for prediction, establishing the effectiveness of ANN modelling in animal science applications. Another study showed that ANN modelling is a successful alternative to statistical regression analysis for predicting amino acid levels in feed ingredients [22].The experimental results indicate that RBF-ANN modelling could potentially be used to predictthe solubility index of roller dried goat whole milk powder.

5Conclusion

The possibility of using radial basis function artificial neural network (RBF-ANN) model as an alternative to expensive, time consuming and cumbersome laboratory testing method for predictingthe solubility index of roller dried goat whole milk powderhas been successfully explored. The methodology is particularly useful for dairy industry, since meaningful prediction of milk powder qualityusing RBF-ANN modelling reduces costs and time of experimentation; thereby increasing income of the dairy industry. The RBF-ANN models predicted the solubility index of roller dried goat whole milk powder with reasonable accuracy with coefficient of determination and Nash - Sutcliffe coefficient close to 1.From the study, it is concluded that RBF-ANN models are a promising tool for predictingthe solubility index of the product.

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