NEURO-FUZZY MODELLING IN ANAEROBIC WASTEWATER TREATMENT FOR PREDICTION AND CONTROL

The aim of the present paper is to develop neuro-fuzzy prediction models in MATLAB environment of the anaerobic organic digestion process in wastewater treatment from laboratory and simulated experiments accounting for the variable organic load, ambient influence and microorganisms state. The main contributions are determination of significant model parameters via graphical sensitivity analysis, simulation experimentation, design and study of two “black-box” models for the biogas production rate, based on classical feedforward backpropagation and Sugeno fuzzy logic neural networks respectively. The models application is demonstrated in process predictive control.


INTRODUCTION
The anaerobic digestion (methane fermentation) of organic waste is the last stage of water depollution, in which organic matter (animal litters, plant sludge, industrial and domestic waste) is mineralised by microorgamisms in the absence of oxygen to safely disposable in the environment substances. A complementary product is biogas consisting mainly of methane, considered as one of the cleanest non-polluting fuels [1]- [8]. The anaerobic digestion is preferred for the higher organic loads treated, the smaller amount of sludge produced, the energy recovery via utilization of the biogas, the reduced operating costs -no need of oxygen supply and control.
The anaerobic wastewater treatment application is still not very popular because of the process complexity and hence its difficult mathematical description. The models used are nonlinear both in terms of parameters and variables, and nonstationary.
The parameter identification encounters various problems [2]- [6] due to the specific features of the microorganisms, low reproducibility of the experiments, limited number of time-consuming and expensive measurements and complex laboratory analyses, noisy experimental data, great number of model parameters, etc.
There arises the need for new types of models of the processes, which describe the nonlinear timevarying behaviour combining knowledge of plant experts, measurements and operational experience. Therefore for the purposes of control, prediction and optimisation fuzzy and neural "black box" models are welcome. The fuzzy sets theory offers a methodology for representing heuristic expert knowledge in a computable way by linguistic labels implemented in linguistic rules thus dealing with uncertainties and avoiding complex mathematical relationships [9], [10]. The fuzzy inference process involves membership functions, fuzzy logic operators and knowledge rules. The membership functions (MFs) allow representation of a degree of membership to a fuzzy set, associated to a linguistic label, for a given input numerical value. The rules ifthen introduce the expert knowledge in a computable way by means mainly of the operators "and" and "or". The fuzzy set and fuzzy logic theory have been successfully applied to different complex process modelling, prediction and control [9] - [12]. The subjectiveness in the choice of the number and the type of MFs as well as their allocation, and in the rule base development can be avoided when inputoutput experimental data is available and an artificial neural network (ANN) trained [11], [12], making use of the basic advantages of multilayer ANNs with nonlinear activation functions to learn from experimental data, to cluster it, to adapt and generalize in mapping nonlinear relationships.
The aim of the recent investigation is to build neuro-fuzzy prediction models of the anaerobic organic digestion process in wastewater treatment on

PROBLEM FORMULATION
The anaerobic digestion is commonly viewed upon as a three-stage process: hydrolysis and liquefaction of the large insoluble organic molecules; acidogenesis, and methanogenesis [1]- [4]. The process takes place under prescribed temperature and pH since the acidogenic bacteria are sensitive to temperature changes while the methanogenic bacteria cannot tolerate pH fluctuations. In recent years more and more complex mathematical models have been introduced in order to better present the biodegradable processes [1]- [3].
Here the fifth order Hill and Barth-nonlinear model [1] with Monod type specific growth rates 1 µ and 2 µ of the acidogenic and the methanogenic bacteria respectively is accepted as an average model to fit the data from a number of laboratory experiments in a continuously stirred tank bioreactor with highly concentrated organic pollutants (cattle wastes) at mesophilic temperature [1], [7], [8]. The model describes the multistage process and the diverse groups of involved microorganisms as follows: The plant nonlinearity is studied by simulation of model (1). The step responses of the biogas production rate Q to equal incremental step changes of ∆0.05 of the input D within the range 0-0.3 when 50 = oi S , g/l are shown in Fig.1 is given in Fig.2. The problem is to develop neuro-fuzzy prediction process models using MATLAB accounting for the plant uncertainties due to the change of the operation point along the nonlinear characteristic as a result of variations in the inputs D and oi S , in the initial states X T (0) and in the nominal plant parameters q oT . These variations reflect the ambient influences, the state of the microorganisms, etc.
The solution of the problem requires the accomplishment of the following tasks: graphical sensitivity analysis for determination of the significant sources (initial states X T (0) and parameters q oT ) of dominating influences on the biogas production rate; -design and carrying out of simulation experiments for collection of realistic inputoutput data accounting for the variations in

SENSITIVITY ANALYSIS AND SIMULATION EXPERIMENTATION
The sensitivity analysis allows excluding correlated and insignificant parameters thus simplifying the plant model. Here it is based on the dimensionless sensitivity functions [3], [4]: The significant simulated sensitivity functions are shown in Fig.3. The sensitivity functions are local properties [4], so the conclusions deduced below by graphical sensitivity analysis depend on the nominal plant parameters and the initial conditions accepted: 1. The significant parameter and initial conditions set is determined for sensitivity functions greater than 1 (in the range of Q).
2. Parameters and initial conditions with similar influences on Q can be equivalently represented by one of them.
Significant parameters and initial conditions p

DESIGN OF NEURAL AND NEURO-FUZZY MODELS
First, a two-layer feedforward neural network (NN) model for prediction in one time-step ahead is  The final weighting matrices W l and the bias vectors B l of the two layers, l=1,2, are:

Biogas flowrate
The tuned rule base is: The simulated responses of the NN model Q nn and of the neuro-fuzzy model Q f as well as the relative modelling errors E nn and E f are shown in Fig.4. The Sugeno FL NN model is both more simple and accurate as seen from Fig.4.

SAMPLE NEURO-FUZZY MODEL APPLICATION FOR CONTROL
The organic waste degradation process is difficult to control not only because it is highly nonlinear and non-stationary but also because it is rather slow and unpredictable. The precise control is of crucial importance because the two types of bacteria that perform the digestion are quite sensitive to the environment media. The already trained Sugeno neuro-fuzzy model can be used to predict the next moment plant output knowing the plant input and output in the current moment. It can be embedded in the feedback to supply the controller with advancing information and thus to improve the performance of the modified control system.
A control system configuration with a Sugeno NF controller (NFC), designed in [11], and a Sugeno FL NN plant predictor in the feedback is depicted in Fig.7. The control system error is formed as the difference between the reference for the biogas production rate Q r and the predicted plant output Q p = Q i+1 -e = Q r -Q p . The Sugeno FL NN plant predictor predicts the biogas production rate in the The enclosure of the Sugeno neuro-fuzzy prediction plant model ensures faster transient responses at different operating points, reduces the maximal dynamic deviation and leads to a more smooth, economic and effective control action [11].

CONCLUSIONS
The main contributions of the paper are the development and comparative study of two "blackbox" prediction models of the biogas production rate in the anaerobic digestion of organic waste in waters, based respectively on classical feedforward backpropagation NN and Sugeno FL NN using MATLAB. The models tackle plant uncertainty related to variable organic loading, ambient influence and microorganisms' state. The FL NN model application in process predictive controller improves the closed-loop system performance.