Evaluation of drying and degradation kinetics using neurocomputing

EVALUATION OF DRYING AND DEGRADATION KINETICS USING NEUROCOMPUTING

W.Kaminski and E.Tomczak

Technical University of Lodz, Faculty of Process and Environmental Engineering

93-005 Lodz, ul. Wolczanska 215, Poland

Phone: (+48+42) 6313708, Fax: (+48+42) 6365663

E-mail: [e-mail], [e-mail]

(Received: September 30, 1999; Accepted: May 30, 2000)

Abstract - Application of artificial neural network (ANN) in chemical engineering with special reference to drying process is discussed in the paper. Two types of networks: RBF and MLP, which are important for the description of a process dynamics, are presented. As an example drying and degradation of ascorbic acid in agricultural products are considered. The final conclusion supported with experimental data states that the type of ANN should be carefully selected because the real capability of the ANN model for a given dynamic problem is expressed in recurrent working mode.

Keywords: drying, degradation of ascorbic acid, modelling of dynamic processes

INTRODUCTION

The recent development of ANN theories and a possibility of their practical implementation provided a new, efficient and universal tool by means of which tasks and problems occurring in many areas can be solved. A wide applicability of ANNs follows, among the other things, from the following features: a possibility to approximate any non-linear mappings, parallel information processing, an ability to learn and adapt, transformation of signals from many inputs and generating many outputs (multi-dimensional systems), solution of modelling problems and identification of dynamic objects. A growing interest in ANN applications has been observed recently with special attention given to the prediction, classification, data association and analysis, signal filtration and optimization.

Of special interest are ANN applications in chemical and process engineering. A significant number of references have been devoted to this subject (Bulsari, 1995; Thyagarajan et al.,1998). The applications refer, among the others, to process engineering, biochemical engineering and metallurgy. There are also studies on modelling of dynamic processes, identification, monitoring and control carried out by feed-forward networks with a feedback and self-organizing networks (Fujiwara, 1995; Yoda & Furuya, 1995; Karjala & Himmelblau, 1995).

A number of examples of ANN applications in drying are also reported:

1) modelling of the drying process (Huang & Mujumdar, 1993; Jinescu & Lavric, 1995; Heyd et al., 1996; Jay & Oliver, 1996; Kaminski et al., 1996a; Kaminski et al., 1998; Hugget et al.,1999)

2) degradation of products during drying (Kaminski et al., 1996b; Kaminski & Tomczak, 1999)

3) process control (Jay and Oliver, 1996).

Additionally, there is an hybrid approach to modelling, which combines a neural model with a mathematical model (Psichogios & Ungar, 1992; Zbicinski et al., 1996). Models of this type are recommended in the cases when a detailed mathematical description of some aspects of the process is available.

ARTIFICIAL NEURAL NETWORKS

Studies on the operation and possibilities of man's nervous system were the inspiration for research on artificial neural networks.

The artificial neural network (ANN) is a system imitating the operation of a biological neural network. It is composed of the set of basic elements (artificial neurons) that are mutually connected. In general, to describe the ANN operation at least three basic properties should be known namely a neuron model (transition function), the network topology and the method of training.

At present several types of networks specialized in carrying out various tasks are distinguished. They can be divided into the following groups:

(1) single-layer networks, e.g. a single-layer perceptron, Kohenen network, vector quantification network,

(2) multilayer networks of one-way information transfer (feed forward), e.g. multilayer percepton (MLP), networks with radial basis functions (RBF), networks using fuzzy logic elements (FLN),

(3) feedback networks, e.g. Hopfield's, Elman and Jordans networks.

A multilayer system which has a typical structure consisting of an input layer, some hidden layers and an output layer is usually applied. Signals are also given in one direction from the input layer, distributed to the hidden layers and then transferred to the output. Fully connected structures occur most frequently. Examples of the multilayer networks are shown in Fig. 1.

On the left-hand side of Fig. 1 a multilayer perceptron (MLP) is shown. Usually, the activation functions in this network type are the sigmoidal or tangensoidal functions. These functions can be in the form:

(2)

The structures presented above are generally used in practice. Linear transition functions are usually assumed for the input and output layer. On the other hand, for neurons in the hidden layers one of the transition functions presented above is chosen. In order to determine the network topology for a given problem, the following factors should be specified: the number of hidden layers, the number of neurons in particular layers, transition functions and scaling coefficient b, the weights of connections.

The input-output transition function in the MLP network has the form:

(3)

where f(×) corresponds to the neuron transfer function.

The RBF-type network is presented on the right-hand side of Fig. 1. The artificial neural networks with radial basis function – RBF, are the networks in which neurons in the hidden layer perform a function changing in the selected centre. The output neuron performs superposition of hidden neuron signals. This enables mapping of the data space (Chen & Chen, 1995; Gorinievsky, 1995). The input-output transition function in the RBF network has the form (Kaminski and Strumillo, 1997):

(4)

where ck (k=1,..., M) are the centres, a k are the scaling factors, (k = 1,...,M) are the transition functions, and wk are the weights combining neurons of the hidden layer with the network output. The most often used form of the transition function f(x) is Gauss function f(x) = exp(-x²) (Haykin, 1994). In the RBF networks five elements should be determined: the number of basic functions M, position of centres c_k, k = 1,..., M, the scaling factor a_k, k = 1,..., M, and weights w_k, k = 1,..., M.

Recurrent networks are characterized by a higher complexity of calculations as compared to the feed forward networks. Due to feedbacks, such networks allow us to obtain the effect of the previous state memory. They are used in the modelling of dynamic processes.

A significant feature of the ANN is that neurons are able to adapt, while weights are subject to modifications during training, which results in the adjustment of weights so that the network carries out specified tasks. This takes place on the basis of experimental data. Usually, the available set of experimental data is divided into two parts: training-learning, and testing (verifying). Training of the network is a process in which variable network parameters are adjusted through a continuous process of the network stimulation induced by the external enforcement.

DESCRIPTION OF PROCESS KINETICS BY MEANS OF ANN

In this study two examples of the mapping of process dynamics during drying are given: drying kinetics and product degradation kinetics. These processes have been described using ANN. Selection of the network type depended largely on the character of changes which were to be mapped, and on the accuracy in experimental data. The network selection was analyzed taking into account its structure, the direction of signal transfer and transition functions. In the case of mapping of drying kinetics, the RBF-type network was applied. The degradation kinetics was described by the MLP network.

A frequently used approach is the description of the object dynamics by an equation which combines the previous outputs and inputs directly with the future outputs from the object.

(5)

where Q(×) is the mapping function used to predict one step ahead of the object behaviour.

This equation does not require knowledge on the inner mechanisms of the system, because it neglects information on the system state and requires access to the externally measurable states of the object activity, i.e. current inputs x(t) and response y(t + 1). A designer decides how many presentations of the object state in the past to be included to the model, so that the total object dynamics be reflected.

The one-step ahead model is based on the assumption that the input signal contains a sufficiently precise information on the object state. This assumption appears to be true for many models being constructed. In many cases, however, the function mapping the process Q defined by equation (5) is assumed and sometimes difficult to define.

In the ANN approach to modelling it is not necessary to formulate an analytical description of the process, i.e. the presentation of an explicit form of the mapping function Q(×). The network is fit to experimental data which characterize the process. This is accomplished by the procedure known as network training, which seeks for the best approximation of an unknown mapping function describing the dynamic system by selecting the best set of weights in the network.

Figure 2 illustrates a so-called controlled learning paradigm where the network is supervised so as to work in a one-step-ahead method in the model predicting the object. The feedback can come from two sources, depending on the position of switch FFN-RecN. In the FFN position, the artificial neural network is combined into the structure of feed forward network, while in the RecN position, the network structure corresponds to the recurrent network.

Initially, during the network training, the switch is in the FNN position. In this configuration, the inputs x(t) and outputs y(t) come from the process, i.e. the data resulting from the object operation are given at the input to the network. On this basis, the teaching algorithm fits weights in the network so that error e between output from the object y(t+1), and the network response y*(t+1) be the smallest possible. In the moment when the training process is finished, a real ability of the network to predict can be tested. After training the network, the feed forward model can be replaced by the recurrent model (Narenda & Parthasarathy, 1990). This change of network configuration enables modelling of parameters difficult for on-line monitoring in the real time. Examples have been given, among others, by Kaminski et al. (1996a), Kaminski et al. (1998), Lubosny (1998) and Swiercz (1998).

DRYING KINETICS

A possibility of material identification on the basis of drying rate curve enables a determination of moisture transport mechanism in the material. The knowledge of drying kinetics is a basis for the determination of other significant parameters or phenomena which characterize the material. Among the others, by an interpretation of the drying curve, in the falling rate period, sorption and desorption curves (Mitura, 1996), moisture diffusion coefficient in the material and its thermal diffusivity can be distinguished (Ketelaars et al., 1995; Michalowski et al., 1982; Mulet, 1994; Ruiz-Cabrera et al., 1996; Yusheng, 1988).

Drying kinetics of any material can be described by the following system of differential equations:

(6)

where Xm – material moisture content, Tm – material temperature, t – time, u(t)=[u₁,...,un] – vector of process parameters, Q₁, Q₂ – mapping functions depending on a drying technique.

This form can be also obtained from mathematical models (Kaminski & Strumillo, 1992). Notation of the drying kinetics can be described by the equations:

(7)

where P₁, P₂ - approximated mapping functions.

An alternative approach to modelling, and particularly to the description of drying kinetics, is the application of artificial neural networks (in this case radial basis type).

DEGRADATION KINETICS

Vitamin C activity in agricultural products is shown by ascorbic acid and dehydroascorbic acid. Products containing vitamin C (vegetables, fruit, seeds, spices, etc.) should be eaten either fresh or immediately after preparation. However, sometimes it is necessary to preserve food products. One of the methods is drying.

Thermal degradation of products containing the vitamin is described by the equation (Karel, 1992; Kajiyama et al., 1998):

(8)

A is the quality index (a relative content of ascorbic acid in a given moment to the initial content). Coefficient k_d is the function of drying kinetics, i.e. changes of moisture content X_m and material temperature T_m in time (Saguay et al., 1978; Mishkin, 1984):

(9)

Equation (8) with reference to eq. (9) can be integrated if the form of eq. (9) is known. No reference is found in the literature to eq. (9) which may be obtained in a theoretical way. Only approximating forms of eq. (9) have been considered (Kaminski et al., 1996).

An alternative approach to eqs. (8) and (9) is to apply multilayer perceptron (MLP) (Kaminski et al., 1996a,b). Kaminski et al. (1998) showed that the description of degradation kinetics with reference to drying kinetics using MLP could be reduced to a one-step-ahead prediction. In a final difference notation the degradation kinetics can be described by the equation:

(10)

The mapping function Q(...) is obtained by means of the network structure of multi-layer perceptron (MLP) type. The inputs to the network are the values of quality index A(t), moisture content in the material X_m(t) and material temperature T_m(t) in moment "t". The output from the network is the quality index A(t+1) in the moment "t+1".

MEASUREMENT AND CALCULATION METHODS

Experiments were carried out in a laboratory vibrofluidized bed dryer of diameter 0.2 m and height 0.9 m, at constant 5 Hz frequency vibrations with amplitude 15 mm. In all measurements the initial height of the static bed was constant and equal to 0.15 m. Drying agent temperature ranged from 60 to 120°C and its flow rate from 30 to 50 m³/h. Experiments were carried out for a model substance (silica gel) containing 3.3 ¸ 3.7 mg/g ascorbic acid (dry matter basis) and agricultural products, namely: fresh green peas, diced potatoes and cut cabbage, containing 0.3 ¸ 0.33 mg/g; 0.47 ¸ 0.56 mg/g; 3.1 ¸ 4.3 mg/g ascorbic acid (dry matter basis), respectively. Concentration of ascorbic acid in the products was evaluated on the basis of the Polish Standard procedure PN -90/A-75101/11 with an accuracy of 3%. More details about experimental set-up can be found elsewhere (Kaminski et al., 1998).

CALCULATIONS

Drying Kinetics

Calculations concerning the prediction of moisture content and temperature of dried material in time for tested products were made using RBF (Fig. 3). Inputs to the network were drying process parameters: air flow rate V_G0 and drying agent temperature at the inlet T_G0 to the apparatus, as well as temperature T_m(i) and material moisture content X_m(i) in the moment before the predicted output from the network. The output from the network included material temperature and moisture content in time "i + 1" as related to the input values. To train and verify the network, the whole set of experimental data was divided into two subsets: a training (8 measurement series) and a testing (1 series). The training set was used to fit weights in the network so as to minimize the error for the predicted values according to the least square method. Depending on the product, the number of weights in the RBF network ranged from 14 to 20 (c.f. Table 1).

After training which took place in the feed forward system, the networks were switched into the recurrent system (c.f. Fig. 2) the operation both for the training and testing sets were checked.

The experiments were carried out at variable process parameters V_G0 and T_G0. As could be expected, drying was more intensive when the drying agent temperature was higher for the same volumetric air flow rate. For any product both X_m and T_m of the material for selected moment in time were different and depended on process parameters. Figure 4 shows drying and temperature curves for the testing series. Experimental data for these series were not used for the network training. Very good agreement of experimental data and values calculated for each of the four products for the testing series was reported. The estimation of neural calculations (the RBF network) was made by means of the correlation coefficient R and the root mean square error d. For the training series R = 0.974¸ 0.997, for the testing series (cf. Fig. 4) R = 0.971¸ 0.997 the error d did not exceed 2%. Taking into account presented results it was found that ability of the RBF network to predict changes in moisture content X_m and temperature T_m of the material in time was very good.

Degradation Kinetics

For the degradation kinetics it was assumed that the initial values of A(i), X_m(i) and T_m(i) were known and obtained in an experimental way. In the analyzed case the mapping function Q(×) was obtained using the multilayer perceptron (MLP) presented in Fig. 5. The assumed network structure operated according to eq. (10). It consisted of three inputs, one hidden layer with the number of neurons selected depending on the material tested and one output. The number of hidden neurons was n = 3 for silica gel; n = 4 for green peas; n = 3 for potatoes, and n = 3 for cabbage. The task of the input neuron was to sum up the obtained signals.

Similarly to the RBF network, after training which took place in the feed forward system, the networks were switched into the recurrent system of operation both for the training and testing sets.

The degradation degree of material depends on its type. This follows from the fact that in each product being analyzed the ascorbic acid is subject to specific chemical bonding, depending on the vegetable tissue composition. Therefore, its degradation kinetics is different. Depending on the structure and shape of dried material particles, the mechanisms of moisture release are different. As can be seen in Fig. 6, for the same process parameters (T_G0 – 80°C and V_G0 – 30 m³/h) the quality index A differs depending on the product.

Drying kinetics of each product is different. Because the quality index in the presented considerations depends on the drying kinetics, changes of the quality index will also be different. From the point of view of checking the network operation this is advantageous because a given network type (in this case MLP) enables correct calculations for different materials of varying kinetics of drying and degradation. This is confirmed by a statistical estimation, as for the training series R = 0.940¸ 0.983, and for the testing series R = 0.937¸ 0.983, while the error d does not exceed 5%.

CONCLUDING REMARKS

Applicability of ANN's in chemical engineering with special reference to drying is discussed in the paper. Two types of network: RBF and MLP, which are important for the description of process dynamics have been presented. As an example of the ANN application, the kinetics of drying of agricultural material and the kinetics of changes in ascorbic acid content in products being dried, have been presented. The artificial neural networks do not require knowledge on the functional relationships between variables affecting the drying or degradation and results of these processes. Drying kinetics of a material, i.e. time-dependent changes of moisture content and temperature for variable process parameters, can be described by means of the RBF type network. It was proved that the MLP-type network of a relatively simple structure made it possible to predict quality index or its changes on the basis of drying kinetics. The presented methods can be used for materials degradation description of arbitrary product components ( e.g. proteins, antibiotics, etc.).

NOMENCLATURES

A quality index c_k centre of RBF f(^.) transfer function k_d coefficient (reaction constans), [1/s] M number of radial basis functions n number hidden neurones P₁,P₂ approximated mapping functions Q₁,Q₂ mapping functions T_G0 drying agent temperature, [°C] T_m material temperature, [°C] t time, [min] V_G0 air flow rate, [m³/h] w_k weight X_m material moisture content, [kg H₂O/kg dry m.basis] u₁,... u_n vector of process parameters y experimental data y* calculated data a_k scaling factor b coefficient in eq. (1) &(2) d root mean squares error F Gaussian function

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Publication Dates

• Publication in this collection
  16 Mar 2001
• Date of issue
  Dec 2000

History

• Accepted
  30 May 2000
• Received
  30 Sept 1999