Journal of Food Engineering 62 (2004) 8995 www.elsevier.

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A neural network approach for thermal/pressure food processing

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Department of Chemical Engineering, Universidad Complutense de Madrid, Avda. Complutense, s/n. 28040 Madrid, Spain Department of Applied Mathematics, Universidad Complutense de Madrid, Avda. Complutense, s/n. 28040 Madrid, Spain Department of Engineering, Instituto del Fr o (CSIC), Ciudad Universitaria, C/ Jose  Antonio Novais, 10 E-28040 Madrid, Spain Received in revised form 28 May 2003

Abstract High-pressure processing is an interesting technology for the food industry that oers some important advantages compared to thermal processing. But, the results obtained after a pressure treatment depend as much on the applied pressure as the temperature during the treatment. Modelling the thermal behaviour of foods during high-pressure treatments using physical-based models is a really hard task. The main diculty is the almost complete lack of values for thermophysical properties of foods under pressure. In this work, an articial neural network (ANN) was carried out to evaluate its capability in predicting process parameters involved in thermal/pressure food processing. The ANN was trained with a data le composed of: applied pressure, pressure increase rate, set point temperature, high-pressure vessel temperature, ambient temperature and time needed to re-equilibrate temperature in the sample after pressurisation. When ANN was trained, it was able to predict accurately this last variable. Then, it becomes a useful alternative to physical-based models for process control since thermophysical properties of products implied are not needed in modellisation. 2003 Elsevier Ltd. All rights reserved.
Keywords: Neural network; High pressure; Food processing; Modelling

1. Introduction High-pressure (HP) food processing is an expanding technology that has attracted the industry attention, mainly due to the advantages that oers in comparison to thermal processing (preservation of nutritional value, minimal change of organoleptic properties, . . .). Nowadays, high pressure is principally used in the food industry to control the microbiological and/or enzymatic activity of its products. In both cases, the obtained results depend so much on the applied pressure as the temperature during the treatments. Pressure and temperature are set at the beginning of the processes. Pressure can be considered as a constant during the treatment (pressure losses are usually compensated automatically by the HP machine) whereas temperature is a parameter that varies during the process. Pressurisation always induces a temperature increase in the processed food and the pressure transmitting medium due to the work of compression. After it, heat transfer
Corresponding author. Tel.: +34-91-544-5607; fax: +34-91-5493627. E-mail address: psanz@if.csic.es (P.D. Sanz). 0260-8774/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0260-8774(03)00174-2
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through the wall of the high-pressure vessel causes temperature gradients in the product. Then, it is dicult to know the real temperature at which a high-pressure treatment has been developed if appropriate measure systems are not available in the HP equipment. Depending on the length of the treatment, this can be or not completely developed at a temperature very dierent to the programmed one. Some attempts have been made by dierent authors to model the thermal behaviour of foods during highpressure treatments, but a lot of diculties make the task very hard (Otero & Sanz, 2003). The main problem is the almost total lack of appropriate thermal properties of foods and pressurising uids under pressure. Those for water are known (Otero, Molina-Garc a, Ramos, & Sanz, 2002a), but those corresponding to real foods or, at least, for components relevant to them have not been experimentally obtained under pressure. Moreover, the calculation of the adiabatic temperature increase/decrease after the pressure build up/release is rather dicult since it depends on the referred thermophysical properties (Otero, Molina-Garc a, & Sanz, 2000). Finally, when solid samples are considered, two ways of heat transfer are implied: convective heat

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transfer that takes place in the pressurising uid between the inner wall of the vessel and the sample and conductive heat transfer in the sample. All these considerations complicate considerably the modelling process. Denys, Van Loey, and Hendrickx (2000) suggested a numerical approach for modelling conductive heat transfer during high-pressure processing, but they only considered the sample and the pressurising uid. Otero, Molina-Garc a, and Sanz (2002b) have shown the enormous signicance of the steel mass of the highpressure vessel in the thermal control of the process. These authors obtained a macroscopic model for liquid water that takes into account all the thermal exchanges in the complete high-pressure system (sample, pressurising uid, steel high-pressure vessel and thermoregulating system). Nevertheless, the use of this model implies knowing the thermophysical properties of the products modelled under pressure and so, nowadays, its employment is limited to water. An articial neural network (ANN) is a mathematical algorithm which has the capability of relating the input and output parameters, learning from examples through iteration, without requiring a prior knowledge of the relationships of the process parameters. Its structure is relatively simple, with connections in parallel and sequence between neurons. This means a short computing time and a high potential of robustness and adaptive n, & Torrecilla, 1998). In performance (Palancar, Arago this study, articial neural network models have been evaluated as potential alternatives to physical-based models for process control in thermal/pressure food processing. Recently, ANNs have been used, successfully, as a modelling tool in several food processing applications like sensory analysis and quality control (colour, texture, human preferences, . . .), classications, microbiology, drying applications, . . .(Edwards & , 2000a, 2000b; Cobb, 1999; Farkas, Rem enyi, & Biro Hussian, Shaur, & Ng, 2002; Ni & Gunasekaran, 1998; Ruan, Almaer, & Zhang, 1995; Xie & Xiong, 1999; . . .). Among them, some papers deal with heat transfer and thermal process predictions. For example, articial neural networks have been developed to predict characteristic parameters of thermal destruction like process time, process lethality or associated quality factors (Afaghi, Ramaswamy, & Prasher, 2001; Sablani, Ramaswamy, & Prasher, 1995). ANN have also determined satisfactorily surface heat transfer coecients (Sablani, Ramaswamy, Sreekanth, & Prasher, 1997; Sreekanth, Ramaswamy, Sablani, & Prasher, 1999) and have been employed to model and control multiple-eect evaporation processes in the cane sugar industry (Benne, Grondin-Perez, Chabriat, & Herv e, 2000). The objective of this study was to evaluate the capability of articial neural networks in modelling the thermal behaviour of foods during high-pressure processing. The main interest in using ANN for modelling is

that thermophysical properties under pressure would not be required.

2. Material and methods 2.1. Sample A physically based simulation model, developed by Otero et al. (2002b), was employed to generate data to feed the ANN. Fig. 1 shows the model realised using Matlab 6 software, Release 12 (The MathWorks, Inc., Natick, MA, USA) and its toolbox Simulink. Thermophysical properties of the sample and the compressing medium under pressure are needed to simulate high-pressure treatments with this model. Since only those for water are known (Otero et al., 2002a), liquid water was employed as sample and pressure medium. The model considered the complete high-pressure system: thermoregulating bath, the refrigeration uid (ow, mass, mechanical properties, . . .), the steel mass of the high-pressure vessel, the temperature at the entrance and exit of the coil surrounding the vessel, the ambient temperature, etc, . . . and is described in depth in Otero et al. (2002b). Also temperature variations with pressure were calculated as described by Otero et al. (2000) and included in the model. This analytical model yielded the evolution of temperature with time in four points of the system (in the liquid water inside the high-pressure cylinder, at the entrance and exit of the surrounding coil and inside the thermoregulating bath). The use of computer simulation to generate data to feed the ANN instead experimental determination is fully justied given the proved accuracy of the model for liquid water (Otero et al., 2002b). Many precedents exist in literature (Afaghi et al., 2001; Farkas et al., 2000a, 2000b; Geeraerd, Herremans, Cenens, & Van Impe, 1998; Sablani et al., 1995) that employ simulation data instead real experimental data since it makes possible to create extensive data sets. A wide range of processing conditions were considered as detailed in Table 1. The dened range of each parameter covered the common range of processing conditions reached in the prototype. Initial temperatures of the sample (liquid water), the thermoregulating bath and the entrance and exit of the surrounding coil were the same as the set point temperature. Initial highpressure vessel temperature could oscillate between set point temperature and ambient temperature depending on the thermoregulation time elapsed. Simulation processes were run for these conditions and the time needed to recover the initial temperature in the sample after pressurisation was collected. Two set of data, totally independent, were obtained: a training set, used to train the neural network model, and a test set

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Fig. 1. Model for the simulation of thermal exchanges in the complete high-pressure equipment (from Otero et al., 2002b).

Table 1 Range of input variables used in the ANN model Variables Applied pressure (MPa) Pressure increase rate (MPa/s) Set point temperature (C) High-pressure vessel temperature (C) Ambient temperature (C) Range 250 350 450 1 1.5 2 40 50 60 70 80 Between set point temperature and ambient temperature (10 C interval) 10 20 30

used to test the trained model. The training set was made up of 202 sets of input and output data and the test set of 50 sets. 2.2. Description of the ANN The ANN used in this work is a Perceptron model also known as Back-propagation Perceptron. This type of network has been selected because it is a good pattern classier. The ANN selected was a feed-forward network with a prediction horizon and supervised learning. It is characterised by layered architectures and strictly feed-forward connections between neurons or back connections are allowed. This ANN was designed and programmed by QuickBasic software, version 4.5. The ANN model consisted of two layers with connections to the outside world (an input layer where data are presented to the network and an output layer which holds the networks response to given inputs) and one hidden layer. The input layer had ve neurons which

corresponded to ve input variables: applied pressure (MPa), pressure increase rate (MPa/s), set point temperature (C), high-pressure vessel temperature (C) and ambient temperature (C). Factor selection was easy since the process was already modelled for liquid water and the relationships between variables were well known. So, input variables were chosen due to its proved inuence in the thermal evolution of the process (Otero et al., 2000; Otero et al., 2002b). It is important to emphasise the nature of these variables. None of them depends on thermophysical properties of products but they characterise the HP process to perform and its initial conditions. The output layer consisted of one neuron for the time (s) needed to re-equilibrate the temperature in the sample after pressurisation, i. e., the time elapsed until reaching the initial or set point temperature in the sample again. This variable was chosen because it is a very representative parameter of the thermal behaviour of the complete system. Its behaviour depends on the behaviour of all the other variables implied. So, if the neural network is able to predict this variable properly, one can suppose that the network would be useful in modelling any other variable related with the thermal behaviour of the system. After pressurisation, the temperature in the sample can be higher than the initial one (set point temperature) due to the work of compression or lower if the high-pressure vessel temperature is much lower than the set point temperature (heat, then, ows from the sample and the pressurising and thermoregulating uids to the steel mass of the vessel). The time needed to re-equilibrate the sample

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temperature up to the set point was calculated with a threshold of 1 C. In this study a feed-forward neural network model with one hidden layer was used. It has been shown that one hidden layer is sucient to approximate any continuous non-linear function, although more complex networks may be employed in special applications (Xie & Xiong, 1999). More hidden layers may cause overtting, since the network focuses excessively on the idiosyncrasies of individual samples (Ruan et al., 1995). The transfer function employed was the sigmoid function bounded between 0 and 1. The numerical values of the input and output variables used by the ANN were normalized values in the range 01. The normalization was made by dividing each actual variable by its maximum range.

at which connection weights are modied during the training phase.

3.1.1. ANN topology: number of neurons in the hidden layer The optimal number of nodes in the hidden layer was selected by using a trial and error method and keeping the learning coecient constant (chosen as 0.5). Dierent complete learning processes were performed beginning with the simplest topology (5,1,1)unable to model the system (Fig. 2)and studying the evolution of some performance indexes as the number of nodes was increased. The process of selection nished when a topology was reached that gave an optimal value of the performance indexes employed. Several parameters were used as performance indexes: Initial slope: Rate of reduction of initial error in the learning process. Final error: Error at the end of the learning process. Iteration: Number of learning runs needed to end the learning process. The criterion used to select the adequate ANN topology consisted of selecting the number of nodes which gave a minimum nal error in a minimal number of iterations during the training of the ANN with a high initial slope. Moreover, the nal use of the ANN must also be considered to select the adequate ANN topology. It is necessary to take into account that light topologies involves smaller learning data sets than heavy topologies. The learning step is; therefore, easier and faster and the nal ANN calculation time is also shorter. Then, it is preferable to select the lighter topology that solves our problem, although it does not yield the minimum error. Bearing all these considerations in mind, a range of 18 neurons in the hidden layer (light topologies) was tested. Figs. 2 and 3 show the prediction errors versus the number of learning runs for the eight dierent topologies tested. Each point, in Figs. 2 and 3, represents

3. Results and discussion The development of ANN model involves two basic steps, a training/learning phase and a testing/validation phase. 3.1. Learning/training of neural network The learning/training data set (202 input vectors and their corresponding desired responses) was presented to the network and a back propagation algorithm automatically adjusted the weights; so that, the output response to input vector were as close as possible to the desired response (Ni & Gunasekaran, 1998). Each time an estimation was made, the result was compared to the corresponding desired value. Then the estimation error (the dierence between the estimated and desired values) was back distributed across the network in a manner that allowed the interconnection weights to be modied according to the scheme specied by the learning rule. After the weights were modied, the next data set was fed to the network, and a new estimation was made. The estimation error was calculated again and back distributed across the network for the next modication. This process was repeated while the prediction error decreased. The error function was dened as: Ei Yi Di 1

where Ei is the error, Yi is the ANN output for a given input and Di is the desired output for the same input. During this training step, the optimal value of two neural network parameters (number of neurons in the hidden layer and learning coecient) was also determined. The number of neurons in the hidden layer is related to the converging performance of the output error function during the training process of the network and the learning coecient (l) controls the degree

Fig. 2. Error prole for the simplest topology (5,1,1).

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Fig. 3. Error proles in topology optimisation. Learning coecient l 0:5.

the sum of 202 predictions for each iteration obtained from the training set: Sum of errors
202 X Yi Di i1

getting of old patterns. If learning rates are set too high, the neural network will not converge to its true optimum. Fig. 4 shows the error and iteration values versus the learning coecient. The iteration prole shows a relative minimum for l 0:50:85 and the error prole presents a relative minimum for l 0:40:5. The adequate learning coecient value must reach the minimum error in the lower iteration number. Taking all these considerations into account, the adequate learning coecient was chosen as l 0:5. Table 3 shows some statistical properties of the sample data used to learning/training process and the prediction values. From the average, standard deviation and variance values can be deduced that the values and distribution of real and predicted times are similar. 3.2. Validation/testing step

2 In this step, we used the selected topology (5,3,1) and learning coecient (l 0:5) with the previously adjusted weights. Now, no corrections of these weights were made and the ANN was only used to predict. The objective of this step was to evaluate the competence of the trained network. We used 50 test data sets independent of the 202 training sets used previously. 3.2.1. Statistical analysis Fig. 5 shows the predicted and desired output times corresponding to 50 data sets used in the validation step.

The learning process nished when the error increased. Topologies 5,3,1 and 5,7,1 (coarser lines in Fig. 3) reached the minimum error with lower number of iterations than other topologies (Table 2). Finally, the selected topology was 5,3,1 because the number of weights required for the learning/training step was smaller (40% smaller) for similar error values and this topology is more versatile for future applications. 3.1.2. Learning coecient When the optimal conguration of the neural network was found, the learning coecient or learning rate parameter (l) was also optimised throughout a trial and error method. Dierent learning processes were performed for dierent coecients from 0.1 up to 0.99 and the selected topology (5,3,1). The learning coecient is a parameter only used in the learning/training process, so the criteria used to optimise it are based on the learning error and the iteration number mentioned below. The larger the learning rate (close to 1), the larger the weight changes and the faster the learning will proceed. So, a high value of l allows the ANN a quick learning of situations never seen, but it causes also a quick forTable 2 Error and iteration values in the topology optimisation Hidden layer neurons 1 2 3 4 5 6 7 8 Error 12.27 6.83 6.64 6.90 6.57 6.71 6.53 6.82 Iteration 3742 331 211 249 252 296 182 218

Fig. 4. Error and iteration proles in the learning coecient optimisation for the selected topology (5,3,1). Table 3 Statistical variables of desired and predicted values (learning/training step: 5,3,1; l 0:5) Statistical values Average Variance Standard deviation Minimum Maximum Kurtosis Sum Desired values 8135.12 29,211,108 5404.73 656.00 22,821.00 )0.39 398,621.00 Predicted values 8423.27 28,910,267 5376.83 1378.52 19,078.10 )1.28 412,740.26

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J.S. Torrecilla et al. / Journal of Food Engineering 62 (2004) 8995 Table 4 Statistical variables of desired and predicted values (validation step) Statistical values Average Variance Standard deviation Minimum Maximum Kurtosis Skewness Sum Desired values 7184.96 31,754,183 5635.09 610.00 23,000.00 )0.14 1.32 1,436,992.00 Predicted values 7146.51 26,877,727 5184.37 1045.88 18,984.46 )0.81 0.77 1,429,301.55

The main dierences appear in the relative maximums and minima. That is probably due to the fact that so extreme values were not well represented in the learning/ training data set (only one or two points). Nevertheless, the ANN model predicted the re-equilibrium times with only 2.5% of relative error and so, it can be considered as enough accurate. Fig. 6 shows the desired times versus the predicted ones, the y x representation and its correlation coecient (r2 0:98). Table 4 shows some statistical properties of the desired times (verication data set) and the corresponding predicted values. There is a signicant dierence in standard deviation and variance values between desired and predicted data (15% and 8% respectively) in contrast to those shown in Table 3 (1% and 0.5% respectively). This fact can be justied if it is taken into account that these data are completely new for the ANN. On the other hand, the Kurtosis, sum and average values are similar, and it can be deduced that both series are similar. The predicted values were very close to desired values and were evenly distributed throughout the entire range. 3.2.2. Statistical comparisons From a statistical point of view, both data series (desired and predicted verication data) have been analysed to determine whether there are statistically

Table 5 Statistical comparisons of desired and predicted verication data Analysis types Comparisons of means Comparisons of standard deviation Comparisons of medians KolmogorovSmirnov test P value 0.79 0.97 0.75 0.86

Fig. 5. Predicted and desired re-equilibration time.

signicant dierences between them. The null hypothesis assumes that statistical parameters (means, standard deviation, medians) of both series are equal. Otherwise an alternative hypothesis is dened. p value was used to check each hypothesis. Its threshold value was 0.05. If p value is greater than the threshold the null hypothesis is fullled. To check the dierences between the data series, dierent tests were carried out. The p value was calculated in each case. Results are shown in Table 5. The t-test was used to compare the means of both series. It was assumed that the variance of both samples could be considered equal. The obtained p value was 0.79 (not less than the threshold) and so, the null hypothesis cannot be rejected. The standard deviation was analysed using the F -test. Here, a normal distribution of samples was assumed. The kurtosis and skewness values (Table 4) verify this assumption. Again, the p value conrms the null hypothesis. The analysis of medians by MannWhitney W test also veries that there is not a statistically dierence between medians at 95% condence level. Finally, KolmogorovSmirnov test also proves the null hypothesis. Then, from a statistical point of view, both samples (desired and predicted verication data) have a similar distribution.

4. Conclusions The possibility of the use of an articial neural network model as an alternative to physical-based models in the prediction of characteristic parameters of thermal/

Fig. 6. Predicted and desired times tting.

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pressure food processing is analysed. Physical-based models are not useful in pressure food processing since they require knowing the thermophysical properties under pressure of the products implied and these are only determined for water. In this work, a network has been built able to predict the thermal behaviour of liquid water under pressure. The input parameters were initial temperatures of the components of the HP equipment and ambient, applied pressure and rate of application. None of these variables were related with thermophysical properties (density, specic heat, . . .) of the products implied. The network predicted the time needed to reequilibrate the temperature in a liquid water sample after its pressurisation with reasonable accuracy. This parameter is very representative of the global thermal behaviour of the complete system, so it is reasonable to suppose that any other related variable would also be properly predicted. For liquid water, considered in this paper, the only important advantage of using this ANN model is the shorter computing time needed for prediction, bearing in mind that a proper analytical model was already developed. But the ANN modelling can be really advantageous for problems in which thermophysical properties under pressure are not available for the samples implied (i.e., most of foods) and so, physicalbased models cannot be employed. Then, experimental observations should be made and the ANN should be trained for each product tested. After an appropriate training, the ANN would be able to predict the thermal behaviour of the products during the HP treatment as we has shown for water. Then, articial neural networks become a promising tool in control of thermal/pressure processes.

Acknowledgements This paper was carried out with the support of the Spanish Plan Nacional de I D I (20002003). MCYT through the AGL2000-1440-C02-01 project. L. Otero is granted (postdoctoral grant) by Consen de la Comunidad de Madrid and jer a de Educacio Fondo Social Europeo. References
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