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Neural networks for prediction of ultrafiltration transmembrane pressure – application to drinking water production
Journal of Membrane Science 150 (1998) 111±123
Neural networks for prediction of ultra®ltration transmembrane pressure ± application to drinking water production N. Delgrange1,a, C. Cabassuda,*, M. Cabassudb, L. Durand-Bourlierc, J.M. LaineÂc a
Laboratoire d'IngeÂnierie des ProceÂdeÂs de l'Environnement, Institut National des Sciences AppliqueÂes, Complexe Scienti®que de Rangueil, 31077 Toulouse, Cedex, France b Laboratoire de GeÂnie Chimique, LGC-CNRS UMR5503, ENSIGC 18, Chemin de la loge, 31078 Toulouse, Cedex 4, France c Centre International de Recherche sur l'Eau et l'Environnement, Lyonnaise des Eaux, Avenue du PreÂsident Wilson, 78230 Le Pecq, France Received 1 April 1998; accepted 7 July 1998
Abstract Modelling of ultra®ltration plants for drinking water production appears as a necessary step before plants control and supervisory. It ®rst requires a better knowledge about membrane fouling by natural waters. The phenomena involved are very complex, because of the nature of the ¯uid concerned: water. Thus up to now phenomenological model cannot be applied for resource waters. Because of their properties, new modelling tools called neural networks seem to be a promising way to model complex phenomena and therefore to be applied to water treatment. In the present study a neural network is used to model the time evolution of transmembrane pressures for ultra®ltration membranes applied to drinking water production. Different network structures and architectures have been elaborated and evaluated with the aim of computing the pressure at the end of a ®ltration cycle and after the next backwash. For some of these networks a very good accuracy is obtained for both pressures predictions. The inlets are permeate ¯ow rate, turbidity during the cycle and pressure measurements at the cycle start and at the end of the previous cycle. These networks are able to model the effect of both reversible and irreversible fouling on pressures even if no inlet parameter concerning organic matters is considered. # 1998 Elsevier Science B.V. All rights reserved. Keywords: Ultra®ltration; Fouling; Drinking water production; Neural network; Modelling
1. Introduction Ultra®ltration (UF) by hollow ®bre membranes is in increasing development in the ®eld of drinking water production. It appears as a good way to meet the requirements for water quality, even in the case of *Corresponding author. Tel.: +33-5-61-55-97-73; fax: +33-5-6155-97-60. 1 E-mail: [email protected]
resource degradation [1]. Indeed, one of the main advantages of this process is its total ef®ciency to remove particles, colloidal species and microorganisms from raw water. Nowadays, more than 40 UF plants are in operation in the world to produce drinking water [2]. All these plants allow producing water with a very good and constant quality, with respect to even more stringent regulations. However, the plant productivity could probably be improved using process control and supervisory. But advanced control
0376-7388/98/$ ± see front matter # 1998 Elsevier Science B.V. All rights reserved. PII: S0376-7388(98)00217-8
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strategies require models describing the in¯uence of operating parameters to perform short or long-term predictions of the plant behaviour. The ®rst requirement is a better understanding and control of fouling during UF of raw water. In the case of resource water, fouling is mainly due to both particle deposition on the ®bres and to adsorption of organic matter on the surface and into the membrane pores. The industrial solution used to remove particle fouling is backwash: permeated water is injected from outside to inside the ®bres and dislocates the particle deposit. The part of fouling that is removable in this way is called reversible fouling and is generally a short time mechanism. Some authors are studying processes to limit or prevent particle fouling, like gas sparging into the ®bres [3] or use of Dean vortices [4]. Other fouling phenomena are longer time installing, their effects are not removable by backwashes and thus chemical cleanings are needed. This part of fouling is called irreversible fouling. One part of irreversible fouling is due to adsorption. The main dif®culties in drinking water production are linked to the numerous compounds in the raw water and to the great variations of each compound concentration with time and season. Phenomena involved in fouling are in this case particularly complex and interdependent. Thus, despite the great number of studies focusing on fouling during the last 20 years, the phenomenological models developed for ideal solutions are not applicable to describe membrane fouling by natural waters. Therefore, to obtain a model allowing short time predictions of fouling effects in the case of natural waters statistical methods have revealed to be an interesting way. Among such modelling methods, a new approach based on the use of neural networks appeared recently and is in development in the ®eld of chemical engineering. Neural networks are non-linear modelling tools. They are designed by an auto-organisation of their parameters during a learning phase. These parameters are optimised in order to model the relationship between input and output vectors. Neural networks do not need an explicit formulation of the physical relationship of the problem, but can include available theoretical or empirical knowledge of the process physics. Their structure is realised by learning (or optimisation) from a set of experimental values constituting the learning database. Their properties
make them a promising way to model complex phenomena where numerous and noisy data occur. In chemical engineering, the main application domains are modelling [5], prediction, fault detection and diagnosis, and process control [6,7]. In the ®eld of membrane separation processes, the interest is to predict some parameters of ®ltration from the operating conditions and ¯uid properties. Few examples of neural network applications in this area are described in the literature. First trials have been successfully realised in the ®eld of micro®ltration applied in the food industry. Indeed, Dornier et al. [8] used a neural network to predict the effects of two hydrodynamic parameters on the hydraulic resistance of a micro®ltration membrane ®ltering raw cane sugar syrup. In this case a satisfactory prediction of time evolution of the resistance was obtained. The aim of the present work is to design, for a given pilot on a given site, a neural network in order to predict the transmembrane pressure at the end of a ®ltration cycle and at the beginning of the next one from available data on operating conditions and water quality. The ®nal objective is to further use this model for process control on the dedicated site and pilot. To design the network it is necessary to determine the judicious inlet parameters to be taken into account and the best network structure. The following section introduces an overview of the mathematical basic principles of the chosen network model. Then the experimental data and analysis methods are described. Finally, a comparison between predicted and experimental values is presented and discussed. 2. Neural network approach The objective of a neural network is to compute output values from input values by some internal calculations. Neurones (or cells) are processing elements that carry out simple computations from a vector of input values. A neurone performs a nonlinear transformation of the weighted sum of the incoming neurone inputs to produce the output of the neurone (see Fig. 1). Inputs and outputs of each neurone are normally numeric values scaled between 0 and 1. The non-linear transfer function can be the sigmoid function bounded between 0 and 1:
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expression, for n2 to L and for k1 to Nn (the exponents for y and w are added to assign the layer number): ! Nnÿ1 X n nÿ1 nÿ1 nÿ1 yi wi;k w Nnÿ1 1;k : (2) yk f i1
Fig. 1. Schema of neurone k in layer n.
f x
1 : 1 exp ÿx
(1)
Neural networks are organised in several layers. A parameter wi (called weight) is associated with each connection between two cells or neurones. An example of network structure is presented in Fig. 2. In the network information propagates between the neurones in a forward direction. If L represents the number of layers in the network and Nn the number of neurones in the layer n, the computations carried out by the network can be described by the following
Fig. 2. Architecture of a neural network with three input neurones, one hidden layer with four neurones, and two output neurones.
The output of the neurone k in the layer n, ynk , depends on all the neurones output in layer nÿ1 and on all the weights associated with the neurone k (wnÿ1 i;k corresponds to the weight for the connection between neurone i of the layer nÿ1 and neurone k of the layer n). Neurones can be given biases by introducing an extra input to each neurone, which always has a value of 1. The weight on this extra input is called the bias. It appears in Eq. (2) as w Nnÿ1 1;k and is equivalent to a threshold of the opposite sign. It can then be treated like the other weights. The interest of using the bias term is that it permits to add to the sum a constant input and allows a representation of phenomena having thresholds. The overall function of such a neural network is to compute an output vector O from an input vector I. The input vector is introduced to the ®rst layer, and the last layer (or output layer) computes the output vector. Cells in the internal (or hidden) layers are used to increase the number of parameters and the non-linear character of the neural network. With the kind of function considered, the use of only one hidden layer has been shown suf®cient to approximate any nonlinear function [9]. As a consequence, in this paper a single hidden layer has been used. A crucial point for the development of a neural network is the learning process. Representative examples, obtained by experimental sets, are presented to the network so that it can integrate this knowledge within its structure. The learning process consists in determining the weights that produce from the inputs the best ®t of the predicted outputs over the entire training data set. The weights are ®rst set to random values. An input vector is then introduced in the input layer and is propagated through the network to the output layer. The difference between the computed output vector (O) and the target vector (T) is used to determine the weights using an optimisation procedure in order to minimise the sum of squares of the errors. The errors between network outputs and targets
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are summed over the entire training data set and the weights are updated after every presentation of the complete data set. The numerous parameters and non-linear character of neural networks make it dif®cult to optimise the weights. Non-linear models generate error surfaces containing many local minima, so the ®nal result depends on the initial estimate of the weights. Several iterative methods have been proposed. The most widely used is the backpropagation algorithm, which is based on steepest-descent. In this work, a quasiNewton learning algorithm has been used [10]. This method requires the numerical value of the objective function F and the vector of the ®rst derivatives evaluated for the current set of weights. This method is better than the steepest descent one because it takes into account an evaluation of the second derivatives. Moreover, the number of iterations required for convergence is signi®cantly smaller and the learning time is then shorter. Two data sets have been considered for the learning phase. The ®rst one is called the training data set. It is used to calculate the error function and to update the weights. The second one is called the test database. It allows to select the number of iterations that minimises the error function applied to the test set in order to control the amount of noise incorporated into the model [11]. Fig. 3 is a typical plot of the evolution of prediction error versus number of training iterations. As the number of iterations increases, the learning error drops whereas the test error begins to drop, then reaches a minimum and ®nally increases. At this time the network starts to learn too much noise. As a consequence, in this study the weights retained correspond to the minimum error on the test data set.
Fig. 3. Example of behaviour of training and test set errors in function of the number of training iteration.
Another data set is used to validate and con®rm the prediction accuracy. 3. Materials and methods 3.1. Apparatus and data acquisition The database was created by experiments realised on a pilot plant schematised in Fig. 4 and described in detail by Anselme and Jacobs [12]. It was treating natural water on an experimental site. The pilot uses one module of cellulose acetate hollow ®bres, inner diameter 0.93 mm. The module ®ltering area is 7.2 m2. Raw water is pre-®ltered to 200 mm, then injected in the circulation loop by the feed pump P1. The pilot produces a constant permeate ¯ow rate (Qp), leading to a pressure increase during the ®ltration time. Sequential backwashes are operated. Time evolution of mean transmembrane pressure (Ptm) is presented in Fig. 5. Backwashes are operated with permeated water at a constant pressure, duration and chlorine concentration. The ®ltration time is constant, ®xed to 30 min. The circulation pump P2 maintains a ®xed circulation mean velocity of 0.9 m/s at the inlet of the ®bres. Some parameters are measured at each cycle, just before and after each backwash. Concerning water quality, turbidity is measured at the pre-®lter outlet and temperature into the circulation loop. Concerning operating conditions, inlet pressure, outlet pressure, permeate outlet pressure, permeate ¯ow rate, circulation ¯ow rate are recorded. Some other parameters are not measured at each cycle, and are not exploitable for developing a neural network model like total organic carbon (TOC) and UV absorbance at 254 nm (UV) which are analysed punctually. The available parameters that are measured on-line at each sampling period constitute the database. These parameters are: permeate flow rate (Qp), varying from 250 to 700 l hÿ1; turbidity, varying from 0 to 100 NTU; mean transmembrane pressure (Ptm), varying from 0 to 2 bar; Temperature, varying from 58C to 158C.
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Fig. 4. The ultrafiltration pilot plant.
Fig. 5. Example of evolution of mean transmembrane pressure with time.
3.2. Data processing The whole data set is composed of 30 sets of curves, each containing between 30 and 265 cycles. Measured data have been classi®ed cycle by cycle. The evolutions of temperature, Qp, Ptm and turbidity were smoothed by mean values, in order to reduce measurements ¯uctuations without removing peaks. All the input values were normalised between 0.1 and 0.9. The objective of the neural network is to predict the transmembrane pressure during a ®ltration cycle from inlet parameters available for the current cycle. There-
fore, it has to compute the mean transmembrane pressure at the end of current cycle k Ptmÿe k and at the start of next cycle k1 Ptmÿb k 1. So the network outlets are Ptmÿe k and Ptmÿb k 1. The network inputs have been chosen among available parameters that have been identi®ed as signi®cant parameters, on the basis of process knowledge: Turbidity is clearly known to influence reversible fouling. Qp can affect both the suction force on particles in the feed flow and thus reversible fouling, and the flux of adsorbing organic molecules flowing through the pores and thus irreversible fouling. Variations of temperature are very moderate on each curve (1±28C per curve), and do not have enough effect to be taken into account; some tests revealed that putting this parameter in inlet of the network introduced perturbations in predicted results. In this study, since temperature variations and their effects on pressure are negligible, temperature is not introduced as a network inlet. Ptm at the beginning of the cycle represents the membrane condition, taking into account the rate of irreversible fouling remaining after the backwash. It gives the (membraneirreversible fouling) permeability for a given flow rate. As the membrane history and previous water quality can influence membrane performances,
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according to
it could be interesting to take into account some parameters characterising the previous cycle. Turbidity Tur(kÿ1) and Ptm at the end of the previous cycle Ptmÿe k ÿ 1 could be introduced as network inlets. The difference between Ptmÿe k ÿ 1 and Ptmÿb k can characterise the backwash efficiency. As a consequence, the ®ve following inlets can be considered: Qp(k), Tur(k), Tur(kÿ1), Ptmÿb k, Ptmÿe k ÿ 1. To identify the most sensitive parameters, several structures were tested, composed of different combinations of those inlet parameters. The simplest network, called R1, only includes inlets concerning the current cycle. That means three inlets: Qp(k), Tur(k), Ptmÿb k. The most complex network, called R2, includes all the available inlets (®ve inlets): Qp(k), Tur(k), Tur(kÿ1), Ptmÿb k, Ptmÿe k ÿ 1. An other network called R3 was built without Tur(kÿ1) in order to evaluate the in¯uence of this parameter. It includes four inlets: Qp(k), Tur(k), Ptmÿb k, Ptmÿe k ÿ 1. For each neural network structure (R1, R2 and R3), the number of hidden neurones were varied in order to determine the optimal network architecture. In all cases, different weight initialisations were performed and the weights kept are the one for which the error E on the test data set is minimal. By de®nition this error is calculated as following: for each point k on each curve of the test data set, an error E(k) is computed
E k 0:5 Ptmÿe kexperimental ÿ Ptmÿe kcalculated 2 0:5 Ptmÿb k 1experimental ÿ Ptmÿb k 1calculated 2 :
(3)
The global error E is given by the average value of E(k) on the whole test data set (all the points on all the curves). The training data set is composed of seven sets of curves, totalling 565 cycles; the test set contains three sets of curves, totalling 206 cycles. Each set contains time evolution of input parameters (Qp, tubidity, temperature) and outputs (transmembrane pressure at the end of cycle and at the beginning of next cycle). All the available sets of curves (30 sets totalling 1800 cycles) compose the generalisation data set. 4. Results 4.1. Global comparison of the three network structures A ®rst comparison between the different neural network structures and architectures can be realised on the base of the global error previously de®ned. These errors of prediction are presented in Table 1. For the network R1, the lower error is obtained with
Table 1 Errors between calculated and experimental pressures Network
R1 Training Test Generalisation R2 Training Test Generalisation R3 Training Test Generalisation
Number of hidden neurons
Relative error (%)
2
3
4
5
2.4710ÿ5 3.0510ÿ5
2.1310ÿ5 3.2110ÿ5
2.3710ÿ5 2.8510ÿ5 1.1010ÿ4
1.7010ÿ5 3.6610ÿ5
8.9010ÿ6 1.2310ÿ5
4.8010ÿ6 7.8410ÿ6
4.7310ÿ6 7.7510ÿ6
4.6410ÿ6 7.6710ÿ6 1.3310ÿ5
7.3610ÿ6 1.3210ÿ5
5.1510ÿ6 8.0710ÿ6
5.0410ÿ6 7.9210ÿ6 1.2210ÿ5
4.7410ÿ6 8.3910ÿ6
6
3.9 4.4510ÿ6 1.0810ÿ5
1.8
1.7
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Fig. 6. Curve 1: (a), (b) available experimental parameters; (c), (d) experimental and predicted pressures. Crosses: calculated Ptm, end of cycle; upper line: experimental Ptm, end of cycle; dashes: calculated Ptm, next cycle start; lower line: experimental Ptm, next cycle start.
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four neurones in the hidden layer, for R2 with ®ve neurones and for R3 with four neurones. Comparing errors on the test database, the lower one is obtained with the network R2. Nevertheless, the networks R2 and R3 almost lead to the same results. Concerning the network R1, the error on the test data set is more than three times higher. Concerning the generalisation database, which allows a global validation of the model, the networks R2 and R3 are not really distinguishable and lead to the lower error, 1.3310ÿ5 and 1.2210ÿ5, respectively. To give a more phenomenological interpretation on the different models behaviour, let us now compare the performances obtained for typical experimental curves. After an analysis of the experimental set of curves, two typical evolutions have been de®ned. For the ®rst ones, the mean transmembrane pressure at the cycle beginning is nearly stable whatever the evolutions of the recorded water quality parameters are. For the second ones, an evolution of the mean transmembrane pressure at the cycle beginning is observed. 4.2. First type set of curves Fig. 6 is an example set of curves showing a stable mean transmembrane pressure at the cycle beginning.
It represents 270 cycles. Fig. 6(a) shows that temperature in¯uence is not signi®cant, as it varies only from 118C to 128C. Qp is almost constant (Fig. 6(b)). A signi®cant peak of turbidity occurs between cycles 20 and 90 leading to an increase of the experimental Ptm at the end of these cycles. The upper line on Fig. 6(c), representing experimental Ptm at the end of cycles, follows the same evolution as the turbidity curve, which means that particulate fouling occurs. The lower curve, representing transmembrane pressures at cycle beginning, and therefore after backwash, is nearly stable, which means that backwashes are ef®cient to remove fouling. The distance between those two curves thus represents the effect of reversible fouling. The values of Ptm at the end of cycles and of Ptm at the start of cycles computed by the different neural network structures R1, R2 and R3 are plotted and compared to the experimental values. Fig. 6(c) corresponds to networks R2 and R3 and no difference between the two models is observable. Both networks R2 and R3 lead to a good prediction of the pressures. The computed values ®t the experimental curves with a very good accuracy (error less than 5% for each point), as pointed out by Fig. 7 plotting calculated values function of experimental values of Ptm, at the end of previous cycle (Fig. 7(a)) and at the cycle start (Fig. 7(b)).
Fig. 7. Computed Ptm vs. experimental Ptm ± curve 1. Dotted lines: experimental Ptm 5%; crosses: Ptm calculated by R2 or R3; dashes: Ptm calculated by R1. (a) Ptm at the end of cycle, (b) Ptm at next cycle start.
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Fig. 8. Curve 2: (a), (b) available experimental parameters; (c), (d) experimental and predicted pressures. Crosses: calculated Ptm, end of cycle; upper line: experimental Ptm, end of cycle; dashes: calculated Ptm, next cycle start; lower line: experimental Ptm, next cycle start.
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Fig. 9. Calculated Ptm vs. experimental Ptm ± curve 2. Dotted lines: experimental Ptm 5%; crosses: Ptm calculated by R2 or R3; dashes: Ptm calculated by R1. (a) Ptm at the end of cycle, (b) Ptm at next cycle start.
Computations obtained with the network R1 are plotted in Fig. 6(d). A small distance between computed and experimental pressures is observable in some parts of the curve. Fig. 7(b) shows that the error of prediction of the transmembrane pressure at cycle beginning is always smaller than 5%. However, concerning the transmembrane pressure at the end of cycle the error is mostly less than 5%, except for about 10 points out of 270 (Fig. 7(a)). To conclude, for the ®rst type of set of curves the three neural network models allow quite a good prediction of both transmembrane pressures at the end of cycles and after backwashes. As previously explained, it means that the in¯uence of reversible fouling on pressure evolution is correctly predicted, as well as the backwash ef®ciency. It has to be pointed out that the only water quality parameter taken into account by the models is turbidity. Then this parameter appears to be suf®cient to correctly represent the effects of reversible fouling on pressure evolution. 4.3. Second type set of curves Fig. 8 is an example set of curves showing an increase of the mean transmembrane pressure at the cycle beginning. It contains 130 points, i.e. 130 cycles. Temperature and permeate ¯ow rate are stable, as shown in Fig. 8(a) and (b). A peak of turbidity reach-
ing 100 NTU occurs between cycles 25 and 90, and quite high values of turbidity (around 20 NTU) are observed until the end of the curve. A signi®cant increase of the Ptm at cycle start is observed showing that backwashes are not ef®cient to restore the ¯ux, probably because of irreversible fouling. This assumption is con®rmed by TOC and UV measurements occasionally carried out during the experiment which show high values of TOC (near 6.6 ppm) and of the UV/TOC ratio (near 5.8) at the middle of the peak of turbidity. Indeed, a statistical analysis of parameter sensibility that was led on data records from ultra®ltration pilot plant runs [13] had shown that the main water quality parameters in¯uencing process performances are not only turbidity, but also TOC and UV/ TOC. Fig. 8(c) shows the Ptm values computed by R3 or R2, as the two computations are identical. Ptm computed by R2 and R3 are in very good agreement with the experimental data. Moreover, the parity plots (Fig. 9(b)) show a very low prediction error. Fig. 8(d) presents the Ptm values computed by R1. A difference between experimental and computed values can be observed all along the curve. Nevertheless, for all the points the prediction error is less than 5% for both pressures (Fig. 9(b)). Compared to R2 or R3, a less satisfying prediction error is obtained with R1. The global mean error is ten times larger for R1 (1.110ÿ4) than for R2
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Fig. 10. Comparison of Ptm calculated by R1 and R3 ± curve 3. Crosses: calculated Ptm, end of cycle; upper line: experimental Ptm, end of cycle; dashes: calculated Ptm, next cycle start; lower line: experimental Ptm, next cycle start.
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Fig. 11. Calculated Ptm vs. experimental Ptm ± curve 3. Dotted lines: experimental Ptm 5%; crosses: Ptm calculated by R2 or R3; dashes: Ptm calculated by R1. (a) Ptm at the end of cycle, (b) Ptm at next cycle start.
(1.3310ÿ5) or R3 (1.2210ÿ5). To give information on the previous cycle is necessary to compute the Ptm during the current cycle with a good accuracy. Ptm at the end of the previous cycle appears as a pertinent information on the previous cycle as its introduction in the inlet decreases prediction errors. It has then to be pointed out that even if there is no information about organic matter (like TOC or UV) in the models inputs, R2 and R3 networks allow a precise estimation of the in¯uence of fouling and of backwashes ef®ciency on pressures. This is probably due to the use of Ptm at the end of the previous cycle, which can provide information on the membrane condition and on backwash ef®ciency. This later parameter is linked to the difference between Ptm at the end of the previous cycle and Ptm after backwash (at the beginning of the cycle) which is also given as inlet to the networks. The difference between performances of networks R1 and R2 or R3 is clearer for the set of curves 3 presented in Fig. 10. In that set of data, a slow increase of Ptm with time occurs that does not correspond to a peak of turbidity and that cannot be explained by the evolution of any available inlet parameter. As for the previous set of curves, networks R2 and R3 predict satisfactorily both Ptm at the end and at the beginning of cycle (Fig. 10(b)), even if there is no inlet concerning organic matter. For all the points the
prediction error is less than 5% for both pressures (Fig. 11(a) and (b)). However, if the network R1 gives a quite good estimation of Ptm at the beginning of cycle (error smaller than 5%), it is not able to predict Ptm at the end of cycle. Indeed, a signi®cant distance is observed between experimental and computed values (Fig. 10(c)), the error is greater than 5% on all points (Fig. 11(a)). The aim of the network was to predict Ptm at the end of the cycle and at the beginning of the next cycle (after the backwash) from information available for the cycle on water quality (turbidity) and on operating parameters (permeate ¯ow rate, Ptm). The last set of curves con®rms previous results: when irreversible fouling occurs, without information on organic matter, it is necessary to take into account information on the previous cycle. Available parameters giving information on the previous cycle are turbidity and Ptm at the end of the cycle. As performances of networks R2 and R3 are almost the same on the whole database (cf. Table 1) introducing turbidity during previous cycle as inlet in the neural network does not induce more accuracy in transmembrane pressure predictions. However, Ptm at the end of previous cycle seems to be a necessary inlet parameter due to the fact that it provides information on the membrane condition at the end of the previous cycle, just before backwash.
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5. Conclusion A neural network was developed to predict the evolution of transmembrane pressure (Ptm) from some operating conditions and water quality parameters, for a pilot producing drinking water by ultra®ltration of natural water. This neural network model ®ts experimental data with a very good accuracy. Only four inlets have been shown to be suf®cient to correctly predict Ptm at the end of current ®ltration period and after next backwash, for this water resource into the given experimental domain. These parameters are turbidity, permeate ¯ow rate, Ptm at the ®ltration start and Ptm before previous backwash. One of the important points is that turbidity has been shown to be a suf®cient parameter to model reversible fouling even in the case of complex natural water, containing also organic matters. Moreover, it has been demonstrated that introducing in inlet the transmembrane pressure before previous backwash allows a good prediction of the pressures in the case of waters containing organic matters even if no information is introduced as model inlet on organic matters. Indirectly, the model is thus able to take into account the in¯uence of irreversible fouling phenomena on pressure evolution. The same methodology could be adapted to some other water resources or plants. Each dedicated model will then open interesting perspectives for controlling and supervising the ultra®ltration process. References [1] C. Cabassud, C. Anselme, J.L. Bersillon, P. Aptel, Ultrafiltration as non-polluting alternative to traditional clarification in water treatment, Filtration and Separation, May/June 1991, pp. 194±198.
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[2] M. Roustan, C. Cabassud, Drinking water production: processes and emerging technologies, in: R.K. Jain, Y. Aurelle, C. Cabassud, M. Roustan, S.P. Shelton (Eds.), Environmental Technologies and Trends, Springer, Berlin, 1997. [3] C. Cabassud, S. Laborie, J.M. LaõÃneÂ, How slug flow can improve ultrafiltration flux in organic hollow fibres, J. Membr. Sci. 128 (1997) 93±101. [4] P. Moulin, J.C. Rouch, C. Serra, M.J. Clifton, P. Aptel, Mass transfer improvement in secondary flows: Dean vortices in coiled tubular membranes, J. Membr. Sci. 114 (1996) 235± 244. [5] J.M. Trichard, M. Dornier, M. Decloux, G. Trystram, Potentials of neural networks for dynamic modelling of crossflow filtrations conducted at time-variable operating conditions, Proceedings of Euromembrane '95, pp. 71±74. [6] J.L. Dirion, B. Ettedgui, M. Cabassud, M.V. Le Lann, G. Casamatta, Elaboration of a neural network system for semibatch reactor temperature control: an experimental study, Chem. Eng. Processing 35 (1996) 225±234. [7] K. Fakhr-Eddine, M. Cabassud, P. Duverneuil, M.V. Le Lann, J.P. Couderc, Use of neural networks for LPCVD reactors modelling, Computers Chem. Eng., vol. 20, Suppl., 1996, pp. S521±S526. [8] M. Dornier, M. Decloux, G. Trystram, A. Lebert, Dynamic modelling of crossflow microfiltration using neural networks, J. Membr. Sci. 98 (1995) 263±273. [9] I. Rivals, P. Personnaz, G. Dreyfus, J.L. Ploix, ModeÂlisation, classification et commande par reÂseaux de neurones, ReÂcents ProgreÁs en GeÂnie des proceÂdeÂs, vol. 9, 1995. [10] Dennis, J.E., Jr., Schnabel, R.B., Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983. [11] J.F. Pollard, M.R. Broussard, D.B. Garrison, K.Y. San, Process identification using neural networks, Comput. Chem. Eng. 16(4) (1992) 253±270. [12] C. Anselme, E.P. Jacobs (Eds.), Ultrafiltration in Water Treatment Membrane Processes, McGraw-Hill, New York, 1996. [13] O. Marsigny, Nature et meÂcanismes du colmatage des membranes d'ultrafiltration en production d'eau potable. Application aux techniques de reÂgeÂneÂration, Ph.D. Thesis, Paris VII, France, 1990.
Neural networks for prediction of ultra®ltration transmembrane pressure ± application to drinking water production N. Delgrange1,a, C. Cabassuda,*, M. Cabassudb, L. Durand-Bourlierc, J.M. LaineÂc a
Laboratoire d'IngeÂnierie des ProceÂdeÂs de l'Environnement, Institut National des Sciences AppliqueÂes, Complexe Scienti®que de Rangueil, 31077 Toulouse, Cedex, France b Laboratoire de GeÂnie Chimique, LGC-CNRS UMR5503, ENSIGC 18, Chemin de la loge, 31078 Toulouse, Cedex 4, France c Centre International de Recherche sur l'Eau et l'Environnement, Lyonnaise des Eaux, Avenue du PreÂsident Wilson, 78230 Le Pecq, France Received 1 April 1998; accepted 7 July 1998
Abstract Modelling of ultra®ltration plants for drinking water production appears as a necessary step before plants control and supervisory. It ®rst requires a better knowledge about membrane fouling by natural waters. The phenomena involved are very complex, because of the nature of the ¯uid concerned: water. Thus up to now phenomenological model cannot be applied for resource waters. Because of their properties, new modelling tools called neural networks seem to be a promising way to model complex phenomena and therefore to be applied to water treatment. In the present study a neural network is used to model the time evolution of transmembrane pressures for ultra®ltration membranes applied to drinking water production. Different network structures and architectures have been elaborated and evaluated with the aim of computing the pressure at the end of a ®ltration cycle and after the next backwash. For some of these networks a very good accuracy is obtained for both pressures predictions. The inlets are permeate ¯ow rate, turbidity during the cycle and pressure measurements at the cycle start and at the end of the previous cycle. These networks are able to model the effect of both reversible and irreversible fouling on pressures even if no inlet parameter concerning organic matters is considered. # 1998 Elsevier Science B.V. All rights reserved. Keywords: Ultra®ltration; Fouling; Drinking water production; Neural network; Modelling
1. Introduction Ultra®ltration (UF) by hollow ®bre membranes is in increasing development in the ®eld of drinking water production. It appears as a good way to meet the requirements for water quality, even in the case of *Corresponding author. Tel.: +33-5-61-55-97-73; fax: +33-5-6155-97-60. 1 E-mail: [email protected]
resource degradation [1]. Indeed, one of the main advantages of this process is its total ef®ciency to remove particles, colloidal species and microorganisms from raw water. Nowadays, more than 40 UF plants are in operation in the world to produce drinking water [2]. All these plants allow producing water with a very good and constant quality, with respect to even more stringent regulations. However, the plant productivity could probably be improved using process control and supervisory. But advanced control
0376-7388/98/$ ± see front matter # 1998 Elsevier Science B.V. All rights reserved. PII: S0376-7388(98)00217-8
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strategies require models describing the in¯uence of operating parameters to perform short or long-term predictions of the plant behaviour. The ®rst requirement is a better understanding and control of fouling during UF of raw water. In the case of resource water, fouling is mainly due to both particle deposition on the ®bres and to adsorption of organic matter on the surface and into the membrane pores. The industrial solution used to remove particle fouling is backwash: permeated water is injected from outside to inside the ®bres and dislocates the particle deposit. The part of fouling that is removable in this way is called reversible fouling and is generally a short time mechanism. Some authors are studying processes to limit or prevent particle fouling, like gas sparging into the ®bres [3] or use of Dean vortices [4]. Other fouling phenomena are longer time installing, their effects are not removable by backwashes and thus chemical cleanings are needed. This part of fouling is called irreversible fouling. One part of irreversible fouling is due to adsorption. The main dif®culties in drinking water production are linked to the numerous compounds in the raw water and to the great variations of each compound concentration with time and season. Phenomena involved in fouling are in this case particularly complex and interdependent. Thus, despite the great number of studies focusing on fouling during the last 20 years, the phenomenological models developed for ideal solutions are not applicable to describe membrane fouling by natural waters. Therefore, to obtain a model allowing short time predictions of fouling effects in the case of natural waters statistical methods have revealed to be an interesting way. Among such modelling methods, a new approach based on the use of neural networks appeared recently and is in development in the ®eld of chemical engineering. Neural networks are non-linear modelling tools. They are designed by an auto-organisation of their parameters during a learning phase. These parameters are optimised in order to model the relationship between input and output vectors. Neural networks do not need an explicit formulation of the physical relationship of the problem, but can include available theoretical or empirical knowledge of the process physics. Their structure is realised by learning (or optimisation) from a set of experimental values constituting the learning database. Their properties
make them a promising way to model complex phenomena where numerous and noisy data occur. In chemical engineering, the main application domains are modelling [5], prediction, fault detection and diagnosis, and process control [6,7]. In the ®eld of membrane separation processes, the interest is to predict some parameters of ®ltration from the operating conditions and ¯uid properties. Few examples of neural network applications in this area are described in the literature. First trials have been successfully realised in the ®eld of micro®ltration applied in the food industry. Indeed, Dornier et al. [8] used a neural network to predict the effects of two hydrodynamic parameters on the hydraulic resistance of a micro®ltration membrane ®ltering raw cane sugar syrup. In this case a satisfactory prediction of time evolution of the resistance was obtained. The aim of the present work is to design, for a given pilot on a given site, a neural network in order to predict the transmembrane pressure at the end of a ®ltration cycle and at the beginning of the next one from available data on operating conditions and water quality. The ®nal objective is to further use this model for process control on the dedicated site and pilot. To design the network it is necessary to determine the judicious inlet parameters to be taken into account and the best network structure. The following section introduces an overview of the mathematical basic principles of the chosen network model. Then the experimental data and analysis methods are described. Finally, a comparison between predicted and experimental values is presented and discussed. 2. Neural network approach The objective of a neural network is to compute output values from input values by some internal calculations. Neurones (or cells) are processing elements that carry out simple computations from a vector of input values. A neurone performs a nonlinear transformation of the weighted sum of the incoming neurone inputs to produce the output of the neurone (see Fig. 1). Inputs and outputs of each neurone are normally numeric values scaled between 0 and 1. The non-linear transfer function can be the sigmoid function bounded between 0 and 1:
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expression, for n2 to L and for k1 to Nn (the exponents for y and w are added to assign the layer number): ! Nnÿ1 X n nÿ1 nÿ1 nÿ1 yi wi;k w Nnÿ1 1;k : (2) yk f i1
Fig. 1. Schema of neurone k in layer n.
f x
1 : 1 exp ÿx
(1)
Neural networks are organised in several layers. A parameter wi (called weight) is associated with each connection between two cells or neurones. An example of network structure is presented in Fig. 2. In the network information propagates between the neurones in a forward direction. If L represents the number of layers in the network and Nn the number of neurones in the layer n, the computations carried out by the network can be described by the following
Fig. 2. Architecture of a neural network with three input neurones, one hidden layer with four neurones, and two output neurones.
The output of the neurone k in the layer n, ynk , depends on all the neurones output in layer nÿ1 and on all the weights associated with the neurone k (wnÿ1 i;k corresponds to the weight for the connection between neurone i of the layer nÿ1 and neurone k of the layer n). Neurones can be given biases by introducing an extra input to each neurone, which always has a value of 1. The weight on this extra input is called the bias. It appears in Eq. (2) as w Nnÿ1 1;k and is equivalent to a threshold of the opposite sign. It can then be treated like the other weights. The interest of using the bias term is that it permits to add to the sum a constant input and allows a representation of phenomena having thresholds. The overall function of such a neural network is to compute an output vector O from an input vector I. The input vector is introduced to the ®rst layer, and the last layer (or output layer) computes the output vector. Cells in the internal (or hidden) layers are used to increase the number of parameters and the non-linear character of the neural network. With the kind of function considered, the use of only one hidden layer has been shown suf®cient to approximate any nonlinear function [9]. As a consequence, in this paper a single hidden layer has been used. A crucial point for the development of a neural network is the learning process. Representative examples, obtained by experimental sets, are presented to the network so that it can integrate this knowledge within its structure. The learning process consists in determining the weights that produce from the inputs the best ®t of the predicted outputs over the entire training data set. The weights are ®rst set to random values. An input vector is then introduced in the input layer and is propagated through the network to the output layer. The difference between the computed output vector (O) and the target vector (T) is used to determine the weights using an optimisation procedure in order to minimise the sum of squares of the errors. The errors between network outputs and targets
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are summed over the entire training data set and the weights are updated after every presentation of the complete data set. The numerous parameters and non-linear character of neural networks make it dif®cult to optimise the weights. Non-linear models generate error surfaces containing many local minima, so the ®nal result depends on the initial estimate of the weights. Several iterative methods have been proposed. The most widely used is the backpropagation algorithm, which is based on steepest-descent. In this work, a quasiNewton learning algorithm has been used [10]. This method requires the numerical value of the objective function F and the vector of the ®rst derivatives evaluated for the current set of weights. This method is better than the steepest descent one because it takes into account an evaluation of the second derivatives. Moreover, the number of iterations required for convergence is signi®cantly smaller and the learning time is then shorter. Two data sets have been considered for the learning phase. The ®rst one is called the training data set. It is used to calculate the error function and to update the weights. The second one is called the test database. It allows to select the number of iterations that minimises the error function applied to the test set in order to control the amount of noise incorporated into the model [11]. Fig. 3 is a typical plot of the evolution of prediction error versus number of training iterations. As the number of iterations increases, the learning error drops whereas the test error begins to drop, then reaches a minimum and ®nally increases. At this time the network starts to learn too much noise. As a consequence, in this study the weights retained correspond to the minimum error on the test data set.
Fig. 3. Example of behaviour of training and test set errors in function of the number of training iteration.
Another data set is used to validate and con®rm the prediction accuracy. 3. Materials and methods 3.1. Apparatus and data acquisition The database was created by experiments realised on a pilot plant schematised in Fig. 4 and described in detail by Anselme and Jacobs [12]. It was treating natural water on an experimental site. The pilot uses one module of cellulose acetate hollow ®bres, inner diameter 0.93 mm. The module ®ltering area is 7.2 m2. Raw water is pre-®ltered to 200 mm, then injected in the circulation loop by the feed pump P1. The pilot produces a constant permeate ¯ow rate (Qp), leading to a pressure increase during the ®ltration time. Sequential backwashes are operated. Time evolution of mean transmembrane pressure (Ptm) is presented in Fig. 5. Backwashes are operated with permeated water at a constant pressure, duration and chlorine concentration. The ®ltration time is constant, ®xed to 30 min. The circulation pump P2 maintains a ®xed circulation mean velocity of 0.9 m/s at the inlet of the ®bres. Some parameters are measured at each cycle, just before and after each backwash. Concerning water quality, turbidity is measured at the pre-®lter outlet and temperature into the circulation loop. Concerning operating conditions, inlet pressure, outlet pressure, permeate outlet pressure, permeate ¯ow rate, circulation ¯ow rate are recorded. Some other parameters are not measured at each cycle, and are not exploitable for developing a neural network model like total organic carbon (TOC) and UV absorbance at 254 nm (UV) which are analysed punctually. The available parameters that are measured on-line at each sampling period constitute the database. These parameters are: permeate flow rate (Qp), varying from 250 to 700 l hÿ1; turbidity, varying from 0 to 100 NTU; mean transmembrane pressure (Ptm), varying from 0 to 2 bar; Temperature, varying from 58C to 158C.
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Fig. 4. The ultrafiltration pilot plant.
Fig. 5. Example of evolution of mean transmembrane pressure with time.
3.2. Data processing The whole data set is composed of 30 sets of curves, each containing between 30 and 265 cycles. Measured data have been classi®ed cycle by cycle. The evolutions of temperature, Qp, Ptm and turbidity were smoothed by mean values, in order to reduce measurements ¯uctuations without removing peaks. All the input values were normalised between 0.1 and 0.9. The objective of the neural network is to predict the transmembrane pressure during a ®ltration cycle from inlet parameters available for the current cycle. There-
fore, it has to compute the mean transmembrane pressure at the end of current cycle k Ptmÿe k and at the start of next cycle k1 Ptmÿb k 1. So the network outlets are Ptmÿe k and Ptmÿb k 1. The network inputs have been chosen among available parameters that have been identi®ed as signi®cant parameters, on the basis of process knowledge: Turbidity is clearly known to influence reversible fouling. Qp can affect both the suction force on particles in the feed flow and thus reversible fouling, and the flux of adsorbing organic molecules flowing through the pores and thus irreversible fouling. Variations of temperature are very moderate on each curve (1±28C per curve), and do not have enough effect to be taken into account; some tests revealed that putting this parameter in inlet of the network introduced perturbations in predicted results. In this study, since temperature variations and their effects on pressure are negligible, temperature is not introduced as a network inlet. Ptm at the beginning of the cycle represents the membrane condition, taking into account the rate of irreversible fouling remaining after the backwash. It gives the (membraneirreversible fouling) permeability for a given flow rate. As the membrane history and previous water quality can influence membrane performances,
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according to
it could be interesting to take into account some parameters characterising the previous cycle. Turbidity Tur(kÿ1) and Ptm at the end of the previous cycle Ptmÿe k ÿ 1 could be introduced as network inlets. The difference between Ptmÿe k ÿ 1 and Ptmÿb k can characterise the backwash efficiency. As a consequence, the ®ve following inlets can be considered: Qp(k), Tur(k), Tur(kÿ1), Ptmÿb k, Ptmÿe k ÿ 1. To identify the most sensitive parameters, several structures were tested, composed of different combinations of those inlet parameters. The simplest network, called R1, only includes inlets concerning the current cycle. That means three inlets: Qp(k), Tur(k), Ptmÿb k. The most complex network, called R2, includes all the available inlets (®ve inlets): Qp(k), Tur(k), Tur(kÿ1), Ptmÿb k, Ptmÿe k ÿ 1. An other network called R3 was built without Tur(kÿ1) in order to evaluate the in¯uence of this parameter. It includes four inlets: Qp(k), Tur(k), Ptmÿb k, Ptmÿe k ÿ 1. For each neural network structure (R1, R2 and R3), the number of hidden neurones were varied in order to determine the optimal network architecture. In all cases, different weight initialisations were performed and the weights kept are the one for which the error E on the test data set is minimal. By de®nition this error is calculated as following: for each point k on each curve of the test data set, an error E(k) is computed
E k 0:5 Ptmÿe kexperimental ÿ Ptmÿe kcalculated 2 0:5 Ptmÿb k 1experimental ÿ Ptmÿb k 1calculated 2 :
(3)
The global error E is given by the average value of E(k) on the whole test data set (all the points on all the curves). The training data set is composed of seven sets of curves, totalling 565 cycles; the test set contains three sets of curves, totalling 206 cycles. Each set contains time evolution of input parameters (Qp, tubidity, temperature) and outputs (transmembrane pressure at the end of cycle and at the beginning of next cycle). All the available sets of curves (30 sets totalling 1800 cycles) compose the generalisation data set. 4. Results 4.1. Global comparison of the three network structures A ®rst comparison between the different neural network structures and architectures can be realised on the base of the global error previously de®ned. These errors of prediction are presented in Table 1. For the network R1, the lower error is obtained with
Table 1 Errors between calculated and experimental pressures Network
R1 Training Test Generalisation R2 Training Test Generalisation R3 Training Test Generalisation
Number of hidden neurons
Relative error (%)
2
3
4
5
2.4710ÿ5 3.0510ÿ5
2.1310ÿ5 3.2110ÿ5
2.3710ÿ5 2.8510ÿ5 1.1010ÿ4
1.7010ÿ5 3.6610ÿ5
8.9010ÿ6 1.2310ÿ5
4.8010ÿ6 7.8410ÿ6
4.7310ÿ6 7.7510ÿ6
4.6410ÿ6 7.6710ÿ6 1.3310ÿ5
7.3610ÿ6 1.3210ÿ5
5.1510ÿ6 8.0710ÿ6
5.0410ÿ6 7.9210ÿ6 1.2210ÿ5
4.7410ÿ6 8.3910ÿ6
6
3.9 4.4510ÿ6 1.0810ÿ5
1.8
1.7
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Fig. 6. Curve 1: (a), (b) available experimental parameters; (c), (d) experimental and predicted pressures. Crosses: calculated Ptm, end of cycle; upper line: experimental Ptm, end of cycle; dashes: calculated Ptm, next cycle start; lower line: experimental Ptm, next cycle start.
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four neurones in the hidden layer, for R2 with ®ve neurones and for R3 with four neurones. Comparing errors on the test database, the lower one is obtained with the network R2. Nevertheless, the networks R2 and R3 almost lead to the same results. Concerning the network R1, the error on the test data set is more than three times higher. Concerning the generalisation database, which allows a global validation of the model, the networks R2 and R3 are not really distinguishable and lead to the lower error, 1.3310ÿ5 and 1.2210ÿ5, respectively. To give a more phenomenological interpretation on the different models behaviour, let us now compare the performances obtained for typical experimental curves. After an analysis of the experimental set of curves, two typical evolutions have been de®ned. For the ®rst ones, the mean transmembrane pressure at the cycle beginning is nearly stable whatever the evolutions of the recorded water quality parameters are. For the second ones, an evolution of the mean transmembrane pressure at the cycle beginning is observed. 4.2. First type set of curves Fig. 6 is an example set of curves showing a stable mean transmembrane pressure at the cycle beginning.
It represents 270 cycles. Fig. 6(a) shows that temperature in¯uence is not signi®cant, as it varies only from 118C to 128C. Qp is almost constant (Fig. 6(b)). A signi®cant peak of turbidity occurs between cycles 20 and 90 leading to an increase of the experimental Ptm at the end of these cycles. The upper line on Fig. 6(c), representing experimental Ptm at the end of cycles, follows the same evolution as the turbidity curve, which means that particulate fouling occurs. The lower curve, representing transmembrane pressures at cycle beginning, and therefore after backwash, is nearly stable, which means that backwashes are ef®cient to remove fouling. The distance between those two curves thus represents the effect of reversible fouling. The values of Ptm at the end of cycles and of Ptm at the start of cycles computed by the different neural network structures R1, R2 and R3 are plotted and compared to the experimental values. Fig. 6(c) corresponds to networks R2 and R3 and no difference between the two models is observable. Both networks R2 and R3 lead to a good prediction of the pressures. The computed values ®t the experimental curves with a very good accuracy (error less than 5% for each point), as pointed out by Fig. 7 plotting calculated values function of experimental values of Ptm, at the end of previous cycle (Fig. 7(a)) and at the cycle start (Fig. 7(b)).
Fig. 7. Computed Ptm vs. experimental Ptm ± curve 1. Dotted lines: experimental Ptm 5%; crosses: Ptm calculated by R2 or R3; dashes: Ptm calculated by R1. (a) Ptm at the end of cycle, (b) Ptm at next cycle start.
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Fig. 8. Curve 2: (a), (b) available experimental parameters; (c), (d) experimental and predicted pressures. Crosses: calculated Ptm, end of cycle; upper line: experimental Ptm, end of cycle; dashes: calculated Ptm, next cycle start; lower line: experimental Ptm, next cycle start.
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Fig. 9. Calculated Ptm vs. experimental Ptm ± curve 2. Dotted lines: experimental Ptm 5%; crosses: Ptm calculated by R2 or R3; dashes: Ptm calculated by R1. (a) Ptm at the end of cycle, (b) Ptm at next cycle start.
Computations obtained with the network R1 are plotted in Fig. 6(d). A small distance between computed and experimental pressures is observable in some parts of the curve. Fig. 7(b) shows that the error of prediction of the transmembrane pressure at cycle beginning is always smaller than 5%. However, concerning the transmembrane pressure at the end of cycle the error is mostly less than 5%, except for about 10 points out of 270 (Fig. 7(a)). To conclude, for the ®rst type of set of curves the three neural network models allow quite a good prediction of both transmembrane pressures at the end of cycles and after backwashes. As previously explained, it means that the in¯uence of reversible fouling on pressure evolution is correctly predicted, as well as the backwash ef®ciency. It has to be pointed out that the only water quality parameter taken into account by the models is turbidity. Then this parameter appears to be suf®cient to correctly represent the effects of reversible fouling on pressure evolution. 4.3. Second type set of curves Fig. 8 is an example set of curves showing an increase of the mean transmembrane pressure at the cycle beginning. It contains 130 points, i.e. 130 cycles. Temperature and permeate ¯ow rate are stable, as shown in Fig. 8(a) and (b). A peak of turbidity reach-
ing 100 NTU occurs between cycles 25 and 90, and quite high values of turbidity (around 20 NTU) are observed until the end of the curve. A signi®cant increase of the Ptm at cycle start is observed showing that backwashes are not ef®cient to restore the ¯ux, probably because of irreversible fouling. This assumption is con®rmed by TOC and UV measurements occasionally carried out during the experiment which show high values of TOC (near 6.6 ppm) and of the UV/TOC ratio (near 5.8) at the middle of the peak of turbidity. Indeed, a statistical analysis of parameter sensibility that was led on data records from ultra®ltration pilot plant runs [13] had shown that the main water quality parameters in¯uencing process performances are not only turbidity, but also TOC and UV/ TOC. Fig. 8(c) shows the Ptm values computed by R3 or R2, as the two computations are identical. Ptm computed by R2 and R3 are in very good agreement with the experimental data. Moreover, the parity plots (Fig. 9(b)) show a very low prediction error. Fig. 8(d) presents the Ptm values computed by R1. A difference between experimental and computed values can be observed all along the curve. Nevertheless, for all the points the prediction error is less than 5% for both pressures (Fig. 9(b)). Compared to R2 or R3, a less satisfying prediction error is obtained with R1. The global mean error is ten times larger for R1 (1.110ÿ4) than for R2
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Fig. 10. Comparison of Ptm calculated by R1 and R3 ± curve 3. Crosses: calculated Ptm, end of cycle; upper line: experimental Ptm, end of cycle; dashes: calculated Ptm, next cycle start; lower line: experimental Ptm, next cycle start.
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Fig. 11. Calculated Ptm vs. experimental Ptm ± curve 3. Dotted lines: experimental Ptm 5%; crosses: Ptm calculated by R2 or R3; dashes: Ptm calculated by R1. (a) Ptm at the end of cycle, (b) Ptm at next cycle start.
(1.3310ÿ5) or R3 (1.2210ÿ5). To give information on the previous cycle is necessary to compute the Ptm during the current cycle with a good accuracy. Ptm at the end of the previous cycle appears as a pertinent information on the previous cycle as its introduction in the inlet decreases prediction errors. It has then to be pointed out that even if there is no information about organic matter (like TOC or UV) in the models inputs, R2 and R3 networks allow a precise estimation of the in¯uence of fouling and of backwashes ef®ciency on pressures. This is probably due to the use of Ptm at the end of the previous cycle, which can provide information on the membrane condition and on backwash ef®ciency. This later parameter is linked to the difference between Ptm at the end of the previous cycle and Ptm after backwash (at the beginning of the cycle) which is also given as inlet to the networks. The difference between performances of networks R1 and R2 or R3 is clearer for the set of curves 3 presented in Fig. 10. In that set of data, a slow increase of Ptm with time occurs that does not correspond to a peak of turbidity and that cannot be explained by the evolution of any available inlet parameter. As for the previous set of curves, networks R2 and R3 predict satisfactorily both Ptm at the end and at the beginning of cycle (Fig. 10(b)), even if there is no inlet concerning organic matter. For all the points the
prediction error is less than 5% for both pressures (Fig. 11(a) and (b)). However, if the network R1 gives a quite good estimation of Ptm at the beginning of cycle (error smaller than 5%), it is not able to predict Ptm at the end of cycle. Indeed, a signi®cant distance is observed between experimental and computed values (Fig. 10(c)), the error is greater than 5% on all points (Fig. 11(a)). The aim of the network was to predict Ptm at the end of the cycle and at the beginning of the next cycle (after the backwash) from information available for the cycle on water quality (turbidity) and on operating parameters (permeate ¯ow rate, Ptm). The last set of curves con®rms previous results: when irreversible fouling occurs, without information on organic matter, it is necessary to take into account information on the previous cycle. Available parameters giving information on the previous cycle are turbidity and Ptm at the end of the cycle. As performances of networks R2 and R3 are almost the same on the whole database (cf. Table 1) introducing turbidity during previous cycle as inlet in the neural network does not induce more accuracy in transmembrane pressure predictions. However, Ptm at the end of previous cycle seems to be a necessary inlet parameter due to the fact that it provides information on the membrane condition at the end of the previous cycle, just before backwash.
N. Delgrange et al. / Journal of Membrane Science 150 (1998) 111±123
5. Conclusion A neural network was developed to predict the evolution of transmembrane pressure (Ptm) from some operating conditions and water quality parameters, for a pilot producing drinking water by ultra®ltration of natural water. This neural network model ®ts experimental data with a very good accuracy. Only four inlets have been shown to be suf®cient to correctly predict Ptm at the end of current ®ltration period and after next backwash, for this water resource into the given experimental domain. These parameters are turbidity, permeate ¯ow rate, Ptm at the ®ltration start and Ptm before previous backwash. One of the important points is that turbidity has been shown to be a suf®cient parameter to model reversible fouling even in the case of complex natural water, containing also organic matters. Moreover, it has been demonstrated that introducing in inlet the transmembrane pressure before previous backwash allows a good prediction of the pressures in the case of waters containing organic matters even if no information is introduced as model inlet on organic matters. Indirectly, the model is thus able to take into account the in¯uence of irreversible fouling phenomena on pressure evolution. The same methodology could be adapted to some other water resources or plants. Each dedicated model will then open interesting perspectives for controlling and supervising the ultra®ltration process. References [1] C. Cabassud, C. Anselme, J.L. Bersillon, P. Aptel, Ultrafiltration as non-polluting alternative to traditional clarification in water treatment, Filtration and Separation, May/June 1991, pp. 194±198.
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