Radial basis artificial neural network models for
predicting solubility index of roller dried goat whole milk
powder
Sumit Goyal and Gyanendra Kumar Goyal
thesumitgoyal@gmail.com, gkg5878@yahoo.com
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 rapid estimation of solubility index of
roller dried goat whole milk powder.
Keywords: Radial Basis Function, ANN, Solubility Index, Goat Milk Powder,
MATLAB
1
Introduction
A study was planned for predicting the solubility index of roller dried goat whole
milk powder by developing radial 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 well being 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 speadfa, p. 1, 2011.
© Springer-Verlag Berlin Heidelberg 2011
cialty 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 RBFANN models for predicting the solubility index of useful dairy product namely roller
dried goat whole milk powder would be extremely beneficial to the manufactures,
retailers, consumers and regulatory agencies from the quality, health and safety points
of view.
2
Review of Literature
ANN has proved an efficient tool for predictive modelling concerning food products.
2.1
Butter
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].
2.2
Cheese
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 conduct-
ed 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.
2.3
Processed 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].
2.4
Milk
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].
2.5
Burfi
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 high R2 and E2 values, 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].
2.6
ANN 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.
3
Method 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 radialbasis function layer and one output linear layer. The hidden layer contains n 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).
loose bulk density
packed bulk density
solubility index
wettability
dispersibility
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].
 N Q Q
exp
cal
MSE   

n
1 





 N Q Q
exp
cal
R  1   
2

1
Qexp
 
2
2








2
1  N  Qexp  Qcal 
RMSE 

n  1  Qexp 

(1)

 N  Q Q
exp
cal

E 2  1   


 1 Qexp  Qexp
 
 (3)




2
2




(2)



 (4)
Where, Q exp = Observed value; Qcal = Predicted value; Qexp =Mean predicted value;
n = 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.
Training ANN
models
Selecting minimum error
Calculating
error and making
adjustment to
weights
Fig. 2. Training pattern for ANN network.
4
Results 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
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
MSE
9.09751E-05
6.18519E-05
6.23472E-05
6.9358E-05
7.61927E-05
8.0645E-05
8.30617E-05
8.45E-05
8.52238E-05
8.56595E-05
8.60964E-05
8.63882E-05
8.65343E-05
8.68269E-05
8.69734E-05
8.712E-05
8.74136E-05
8.75606E-05
8.78549E-05
8.80022E-05
RMSE
0.009538085
0.007864599
0.007896026
0.008328147
0.00872884
0.008980256
0.009113821
0.009192388
0.009231672
0.009255242
0.009278812
0.009294526
0.009302383
0.009318096
0.009325953
0.00933381
0.009349523
0.00935738
0.009373093
0.00938095
R2
E2
0.990461915
0.992135401
0.992103974
0.991671853
0.99127116
0.991019744
0.990886179
0.990807612
0.990768328
0.990744758
0.990721188
0.990705474
0.990697617
0.990681904
0.990674047
0.99066619
0.990650477
0.99064262
0.990626907
0.99061905
0.999909025
0.999938148
0.999937653
0.999930642
0.999923807
0.999919355
0.999916938
0.9999155
0.999914776
0.99991434
0.999913904
0.999913612
0.999913466
0.999913173
0.999913027
0.99991288
0.999912586
0.999912439
0.999912145
0.999911998
Table 2. Performance of Radial Basis (Fewer Neurons) Model
Spread
Constant
10
20
30
40
50
60
70
MSE
RMSE
R2
E2
9.09751E-05
6.18519E-05
6.23472E-05
6.9358E-05
7.61927E-05
8.0645E-05
8.30617E-05
0.009538085
0.007864599
0.007896026
0.008328147
0.00872884
0.008980256
0.009113821
0.990461915
0.992135401
0.992103974
0.991671853
0.99127116
0.991019744
0.990886179
0.999909025
0.999938148
0.999937653
0.999930642
0.999923807
0.999919355
0.999916938
80
90
100
110
120
130
140
150
160
170
180
190
200
8.45E-05
8.52238E-05
8.56595E-05
8.60964E-05
8.63882E-05
8.65343E-05
8.68269E-05
8.69734E-05
8.712E-05
8.74136E-05
8.75606E-05
8.78549E-05
8.80022E-05
0.009192388
0.009231672
0.009255242
0.009278812
0.009294526
0.009302383
0.009318096
0.009325953
0.00933381
0.009349523
0.00935738
0.009373093
0.00938095
0.990807612
0.990768328
0.990744758
0.990721188
0.990705474
0.990697617
0.990681904
0.990674047
0.99066619
0.990650477
0.99064262
0.990626907
0.99061905
0.9999155
0.999914776
0.99991434
0.999913904
0.999913612
0.999913466
0.999913173
0.999913027
0.99991288
0.999912586
0.999912439
0.999912145
0.999911998
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 constants ranging
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 predict the solubility
index of roller dried goat whole milk powder.
5
Conclusion
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 predicting the solubility index of roller dried goat whole milk
powder has been successfully explored. The methodology is particularly useful for
dairy industry, since meaningful prediction of milk powder quality using 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 predicting the solubility index of the
product.
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