CAPITULO II: PARTE EXPERIMENTAL
2.2.6 Fermentación butírica
Feedforward network Feeback network
utput
Unsupervised Figure 5 . 1 . Neural network models (dotted line i llustrates the training scheme).
Of all the available neural networks, the multilayer feedforward neural network is widely used for the application of chemical and bioprocess engineering. This thesis focuses on the application of the type of the muItilayer feedforward neural network (MFNN) to a TPFBBR. Table 5 . 1 summarises the categorisation of some neural networks used widely in many engineering appl ications.
Chapter 5 . S quential Neural Network Model for a TPFBBR
Table 5 . 1 Categorisation of some neural networks.
classification
Multilayer perceptron supervised feed forward function
approximation classification Radi al basis function supervised or
feed forward function
network unsupervised
approximation
Self-organizing map unsupervised feed fo rward classification
Learning Vector
supervised feedforward classification
Quantization (L VQ)
5.2.2
An Artificial Neural Network as a Process Modelling
Tool
87
In order to properly optimize and control a process, it is necessary to develop a good mathematical model. S ince most of the advanced control approaches are based on a mathematical model of the processes under consideration and the optimal operating strategies can be by simulating using the process model under different conditions. For process modell ing, the best possible model is a mechanistic model which consists of a set of differential equations which define the relationship between input variables and output variables. A mechanistic model, however, i s either too difficult to formulate or too difficult to solve the resulting set of equations in many cases. To be more specific, models i n mathematical modelling of biofilm growth are formulated i nvolving either Monod's kinetics or one of its modified expressions such as Haldane expression reflecting product i nhibition or substrate i nhibition or both. If,
Chapter 5 . Squential Neural Network Model for a TPFBBR 8 8
however, kinetic expressions for on-line i nterpretation and simulation of biological processes are desired, these mechanistic models require too detail information about the process to be applicable. Moreover, it is likely that model parameters should be specifi ed and updated to obtain an agreement between actual and predicted value. Other drawbacks are that the development of good kinetic or process model usually requires very time-and money-consuming tasks because the necessary knowledge to give a mechanistic description for a specifi c (bio)chem ical process is usually limited and are stil l poorly understood (Saxen & Saxen, 1 996).
As an alternative to a mechanistic model, there has been major research interest in artificial neural networks (ANNs), a powerful tool for nonlinear modell ing and process control. The main advantages of using ANN s in process modelling are: ( 1 ) it has the ability to learn complex nonlinear relationship with limited prior knowledge of the process structure and (2) it can perform inferences for an unknown combination of input variables (Hong et aI. , 1 998). So ANNs are prime candidates for use in dynami c process modelling for the representation of nonlinear processes. Due to the advantages of a neural network, a number of researchers have successfully applied a neural network based modelling approach to wastewater treatment processes. Capodaglio et aI. ( 1 99 1 ) identified an ANN model for the simulation and forecasting of the sludge bulking based on sludge volume index (SVI) in full-scale activated sludge process. Coli ins & Elli s ( 1 992) applied a neural network model to the prediction of a required chemical dosage in a wastewater treatment plant. Tyagi & Du ( 1 992) used a neural network to predict the effect of heavy metals in the performance of the activated sludge process. Zhao et al. ( 1 997) demonstrated a hybrid model, which consists of a simplified process model and an ANN, for developing a dynamic model of a sequencing batch reactor. In their hybrid model, the outputs of the trained ANN compensated for the output errors of the simplified process model. Karim and Rivera ( 1 992) reviewed the application of ANN in bioprocess state estimation.
The multilayer feedforward neural network (MFNN) seems to be a very attractive choice when neural networks are used for process modelling and control purposes.
Chapter 5 . S quential Neural Network Model for a TPFBBR 89
This is because it has been theoretically proven that the MFNN can approximate any continuous function arbitrarily well provided that enough neurons are used (Cybenko, 1 989). However, in order to obtain a valid model of the process, neural networks, in general, require a large number of training and test data, even for a moderate number of model parameters (the weight and biases). A more detail ed discussion of this i ssue can be found in Baum & Haussler ( 1 989). Another disadvantage is that neural networks are non-parametric models. In a non-parametric model, the model parameters (the weights and biases in the MFNN) usually have no interpretation in relation to the process to be modelled.
5.2.3
M ultilayer Feedforward Neural Networks (MFNN)
The muItilayer (3-layer) feedforward neural network consists of one input layer, one or more hidden layers, and one output layer. The general structure of multi layer (3- layer) feedforward neural network is given in Fig. 5 .2 . The first layer, the input layer, is strictly a preprocessing layer that simply distributes the i nput to the next layer. It does not perform, as subsequent layers do, a nonlinear transformation of its input data. An output layer delivers the output from the neural network. In between these two layers, there could be several layers called "hidden layers" . Input and out data vectors are scaled from 0 to
1
and scaled data are fed into the neural network at the input layer. Each of these layers consists ofneurons (or processing elements), which
are represented by the circle in Fig. 5 . 2 . All the neurons in one layer are connected to all neurons in the following layer by a set of unidirectional weights (represented by the lines in Fig. 5 .2). In addition to the regular neurons, there are bias neurons which provide a constant input of unity. Bias neurons are connected to all the neurons in the hidden and output layers through a set of bias weight. S ince there is only one forward path for the flow of information, these networks are called feu/forward neuralnetwork.
Chapter 5 . Squential Neural Network Model for a TPFBBR 90 Layer I al 1
Out
Xl�
I Xld
I BiasFigure 5 . 2 . Architecture of the multilayer feedforward neural network (MFNN).
Typical neuron performs two functions: a weighted linear combination of its input component (activity) and a nonlinear transformation of this activity value. A single neuron extracted from the
lh
layer is also depicted in Fig. 5 .2 . The input to this neuron consists of the N-dimensional vector X and a unit bias. Each input is multiplied by a weight which denotes connections b etween neuroni
in the previous layer and neuron j in the layerl.
The products are summed up to give the activationpotential (or activation state) s� :
(5. 1 )
The output of the