Parameter identifiablity in the IAWQ Model No. 1 for modelling activated sludge plants for enhanced nitrogen removal

Computers chem. Engng Vol. 20, Suppl., pp. SI455-SI460, 1996

Pergamon

Copyright © 1996 Elsevier Science Lid Printed in Great Britain. All rights reserved 0098-1354•96 $15.00+0.00

S0098-1354(96)00249-9

PARAMETER IDENTIFIABLITY IN THE IAWQ MODEL NO. 1 FOR MODELLING ACTIVATED SLUDGE PLANTS FOR ENHANCED NITROGEN REMOVAL S.R. WEIJERS*, J.J. KOK*, H.A. PREISIG*, A. BUUNEN**, T.W.M. WOUDA*** *Systems & Control Group, Dept. of Applied Physics, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands **Grontmij Advies & Techniek bv, Afdeling Procestechniek & Installaties, P.O. Box 203, NL-3730 AE De Bilt, The Netherlands ***GTD Oost-Brabant, P.O. Box 10 001, NL-5280 DA Boxtel, The Netherlands Abstract - The IAWQ Model No. 1 is well accepted and used for dynamic modelling of activated sludge plants. The model contains many parameters. Some of the model parameters depend on the wastewater and/or plant. In some applications, the model has to describe a real plant quite accurately and some of the parameters have to be determined. As a consequence, model tuning or calibration has become an active area of research during the last few years. This contribution briefly reviews recent literature on calibration strategies and methods for assessing parameter identifiability of the Model. Some identifiability results for full scale plants are presented obtained by a combined analysis of the parametric sensitivity and the Fisher information matrix.

INTRODUCTION In most western countries, more stringent demands are being put on wastewater treatment, especially with respect to nitrogen and phosphorus. Domestic watewater is treated biologically in so-called activated sludge plants. Conventional plants which were designed for removal of organic compounds will have to be upgraded to remove also nitrogen biologically. Nitrogen is removed in two stages, the nitrification stage and the denitrification stage. In the nitrification stage, ammonia is converted to nitrate under aerobic conditions. Also organic compounds (COD) are removed in this stage. In the denitrification stage, organic compounds are removed and nitrate is reduced to nitrogen gas. This process takes place in an anoxic environment, that is without oxygen and with nitrate. Enhanced nitrogen removal plants are more sensitive towards disturbances than conventional plants as a result of interactions between the process stages. Due to disturbances caused by varying load and temperature, process dynamics and process control have to be considered. This motivates application of the IAWQ Model No. I, which is considered to be the state of the art model for dynamic modelling of activated sludge plants with COD and nitrogen removal. As an example for presenting the model, a pre-denitrification plant which is a basic nitrogen removal system is shown in figure 1. After treatment, the wastewater is separated from the sludge in the clarifier. influent m

~

II I

. effluent

aerobic ~ .

1' d r

1' ' ]

[

nnal clarifier

internal recirculation return sludge

~ waste sludge

Figure 1: Scheme of pre-denitrification plant If clarifier dynamics are neglected, the following component balance equations can be written in state space form as

(1)

- D'~b + Di'n "~in,

dt :=

[~r ~r] r =[XT S~[ X'~ $2] r :: state vector: component concentrations in reactors;

X S

:= :=

[XI Xsn XBA Xe Xs XND]T :: suspended components; [Ss SNn SNo SAtkSt SNo So]r :: solute components;

K'tp D

:: ::

D:n

::

stoichiometric matrix times reaction rates as defined in IAWQ Model No. 1; dilution rate matrix, containing all internal flows; influent component concentrations; influent dilution rate matrix.

with:

The IAWQ Model defines the components, processes and the stoichiometry and kinetics K'q~ of the biological processes. In the model, a distinction is made between suspended and solute components. The components, stoichioS1455

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metric and kinetic parameters defined are given in the symbol list. For a definition of the stoichiomatric matrix and reaction kinetics is referred to (Henze et al, 1987). The balances in eq. (1) are mass balances for the nitrogen components and for alkalinity. The other components are expressed as COD, so the balances for these components are electron equivalence balances. It should be remarked that final clarification is not regarded in this study, although it is realised that clarification is also important for modelling activated sludge processes. I N T E N D E D USE AND DATA R E Q U I R E M E N T S The IAWQ Model No. 1 has several applications. In each case, parameter values must be fit to the plant and the conditions in the plant. Some of the model parameters are relatively constant for different system configurations and wastewaters and can be assumed. Other parameters show a stronger dependency upon the plant and wastewater. If the intended use is operator training and education, comparison of design alternatives for non-existing plants and design of control systems, then qualitative comparisons are usually sufficient. Default parameter values can then be taken from literature. If the model is to be used for upgrading existing plants, or as an aid in operation, e.g. for process analysis or model-based control, then more accurate models are required. In that case, the following data are needed: • design data, such as reactor volumes and pump capacities; • operational data averaged or as function of time: variations of influent flow and concentrations, other (internal) flows and loads, temperature and aeration; • model components: influent characterisation of the COD and nitrogen fractions distinguished in the model; • model parameters: kinetic and stoichiometric parameters (component fractions can also be viewed as parameters); • with dynamic simulation: initial conditions. This implies that some of the parameters have to be determined, which is referred to as model calibration. Several strategies for model calibration have been reported, They differ in selection of measurements and experiments and parameters to be determined. It is to be investigated if and how the model can be calibrated accurately to existing plants when the model is to be used either for process analysis or for model-based control. In the first case, the model is used off-line and laboratory analyses can be used. For the latter case possible measurements are restricted to on-line sensors. CALIBRATION STRATEGIES Parameters can be determined by fitting modelled outputs to observed plant outputs. Decisions have to be made with regard to experiment duration, sampling frequency, choice of measurements, outputs to be fitted, parameters to be determined and fitting procedure to be used. A first approach to be mentioned is steady state calibration. In steady state calibration, data obtained from the plant are averaged assuming that this average represents a steady state. Two full scale plants were calibrated this way (Lesouef et al., 1992). Some shortcomings of steady state calibration can be indicated. If the input variations are faster than the process dynamics which is ususally the case, then the process does not operate in steady state. When fitting with averaged data one attempts to fit a steady state of the model to an unsteady plant, which may result in biased parameter estimates. Because the system is nonlinear, averaging the output can also introduce bias. Another disadvantage of steady state calibration is that the number of parameters that can be estimated is equal to or smaller than the number of outputs. Better results can be obtained by fitting the dynamic behaviour of the process. Dynamic data contain more information than static data. In principle the number of parameters that can be determined is larger than the number of outputs. For many plants, routinely collected data is available. It is therefore tempting to use historical data for dynamic calibration. The achievable accuracy is limited however, due to low sampling frequency which is typically one per week. Because of the resulting uncertainty in the influent load and the limited number and frequency of outputs to be fitted, calibration was reported to be unsatisfactory (Witteborg et al., 1994, Weijers et al., 1994). For more accurate modelling, special monitoring exercises are therefore required. The experiment duration and sampling frequency have to be chosen in relation to the time constants of the process and the spectrum of influent variations. An important time constant of the process is the hydraulic residence time, which is typically several hours to half a day; experiment duration must therefore be in the order of days. Several calibrations of the IAWQ Model on full scale plants have been reported. The experiment duration and the sampling frequency chosen range from 6 h to 10 days and 0.3 to 3 per hour respectively. In the cases reported, different choices for parameters and outputs were used. For three full scale plants ~a and KNH were determined by trial and error by fitting effluent ammonia and nitrate. S~ was determined from effluent COD. YH and I.tn, kh and Ks were determined from OUR profiles in the reactor (Siegrist and Tschui,1992). For two full scale carrousels the aerated volume and affinity constants for oxygen were determined by trial and error from effluent ammonia and nitrate. COD fractions were derived from influent COD and BOD (Weijers et al., 1994). A full scale plant was calibrated by a combination of steady state and dynamic calibration (Stokes et al.,1993). Here txH, Ks and txa were determined. Measurements on full scale plants are relatively time-consuming and expensive. In continuous plants, excitation may be insufficient to estimate all relevant parameters. As an alternative, special experiments can be used in addition to full scale measurements for determination of parameters. Very valuable in this respect are batch experiments based on respirometry. In respirometry, the oxygen uptake rate (OUR) is measured as a function of time in a sludge-wastewater mixture. Experimental conditions can be chosen such that parts of the IAWQ Model can be

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omitted and measured OUR profiles can be fitted to reduced models. Parameter values thus obtained have a direct significance for use in the Model. Three kinds of batch experiments for determination of COD fractions and some of the parameters were proposed by (Kappeler and Gujer, 1992). At present automated respirometers are available (Vanrolleghem, 1994, Spanjers, 1993) which can be used on-line. Batch experiments based on the ammonia uptake rate were used to determine autotrophic growth and decay rate. Besides repiration experiments, also batch experiments based on determinations of filtered and degradable COD fractions by COD balances have been proposed (Lesouef et al., 1992). This kind of test have a less direct relationship with the model, however (Spanjers and Vanrolleghem, 1995). IDENTIFIABILITY A problem encountered in calibration is the identifiability of the IAWQ Model. Identifiability is the ability to obtain a unique combination of parameters describing a system behaviour. A distinction can be made between strucural and practical identifiability. Structural identifiability, also called deterministic, theoretic or a priori identifiability, is a property of the model structure. It relates to the question whether it is at all possible to obtain unique parameter values for a given model structure from selected outputs, in the case of ideal measurements. (/~str6m and Bellman, 1970). Structural idenifiability is a minimum requirement. For obtaining accurate parameter estimates from data practical or a posteriori identifiability is of relevance. Practical identifiability is depending upon experimental conditions, including experimental design as well as quality and quantity of measurements. For determining structural identifiability several methods exist for linear models. For non-linear systems, the situation is more difficult. In principle, Taylor expansion can be used, but the size and complexity of the resulting expressions renders the method suited only for relatively simple models. Linearization is another method, but gives only sufficient conditions; while the non-linear system may be identifiable, the linearised system may be not (Godfrey and DiStefano, 1985). A well known measure for practical identifiability is the Fisher information matrix (Mehra, 1974). Its rank and condition number are tests on identifiability, because it is an approximation of the Hessian of the objective function (S6derstr6m and Stoica, 1989). Let the criterion function be defined as the weighted sum of squared errors between model outputs y(k,O) and measured outputs y~,(k) with weights Rk: N

(2)

J = Z ( y(k,O ) - yl,(k))TRk (y(k,O) - yp(k)). k=l

The output is linearized in the neighbourhood of the optimal parameter vector 0,, as

y(,,0, +a0)=

L a0

Jo,,

a0= y(,,0o)+ YoT(t)80

(3)

with Yo(t) being the output sensitivity functions. Let Q, be the covariance matrix of the measurement noise. Then the Fisher information matrix M can be written as N

M = y . Yo (k)Q; ' Y T "

(4)

k=l

For any unbiased estimator, the inverse of this matrix provides the Cram6r-Rao lower bound on the covariance matrix of the parameter estimates. If M is singular, the experiment is said to be non-informative. If M has full rank the model is locally identifiable. Several functions of M can be defined as a measure of the uncertainty on the estimate of 0 (Walter and Pronzato, 1990). The most important are listed in Table 1 together with an interpretation. Table 1: Experimental design optimality criteria Optimali_[y_....... Objective A min tr(M l) simplified A max tr(M) C min tr(H Ml), H=diag(0i -l, i=l ..... p) D min det(M) -I E max ~ i , (M) modified E

min cond(M) - ~'maxM ~,min M

InterpretationI minimize mean variance minimize mean variance minimize relative (mean) variance minimize volume of ellipsoids minimize largest error (maximal axis) optimize condition number (achieve as spherical shape as possible)

Sensitivity functions were proposed as an indication for identifiability problems in parameter estimation (Reichert et al.. 1995). Visual inspection of linear dependence of sensitivity functions was used to investigate identifiability for a

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denitrification model. A steady-state sensitivity analysis was used to investigate identifiability in a reduced version of the IAWQ Model for a High Purity Oxygen process. The DO concentrations in two reactors, oxygen purity and sludge concentration were chosen as outputs. It was concluded that heterotrophic yield and growth rate can be estimated from these outputs and nitrogen fractions ixp and ixB cannot (Yuan et al., 1993). Sensitivities and sensitivity functions can provide a first indication of importance of parameters. For models with many parameters and many ouputs, it is difficult however to reveal possible dependencies amongst the parameters. It is exactly that information that is condensed in the information matrix, which makes this matrix preferable above the sensitivities for establishing identifiability. The condition number of the observability matrix was proposed as a measure for state observability and parameter identifiability of a reduced model and was used to compare alternative sensor locations (Ayesa et al., 1994). The approach adopted was to estimate the unknown parameters and initial states with an extended Kalman filter. From the measurement matrices of the system and the state transition matrices, which can be computed by numerical integration, the observability matrix was computed. Structural identifiability in respiration experiments has been investigated, which revealed that certain parameter groups can be estimated but not all individual parameters. Practical identifiability and experimental design of respiration experiments was optimised using the Fisher information matrix, resulting in significant improvement of parameter accuracy (Vanrolleghem, 1994). CASE In a joint research effort, the IAWQ Model is evaluated against field data from full scale wastewater treatment plants. Target of this evaluation is to assess minimal amount of analysis data needed and suitable methods for reliable model calibration. Two similar wastewater treatment plants of the carrousel type the Netherlands, with comparable load and volume (18.750 m 3) have been selected. A lay-out of one of the plants is given in figure 2.a.

II .+ f

4--

ffluen

'rR1 ?

41--

~

T

inOu Eent

~

Figure 2.a: Plant lay-out

~i~ ....

R4

Rs~Seclca°nr'ifd I

1o Figure 2.b: Model flowsheet

A special monitoring excercise was performed on both plants. Dynamic data were collected during 2 days for calibration and two days for validation with grab samples every two hours. The following outputs were measured: - oxidation circuit: DO profile, MLSS, actual OUR (oxygen uptake rate), maximal OUR, sludge production; - effluent: COD, Nkj, NH 4, NO 3, suspended solids. The carrousels have been modelled by alternating aerated and non-aerated compartments. The aerated and aerobic parts in the circuit were modelled as aerated compartments RI, R3 and R5 in figure 2.b. The other compartments R2, R4 and R6 represent the anoxic parts in the circuit. The aerobic volumes were determined by means of the measured DO profiles. The two final clarifiers were modelled as an ideal, static splitter. Although some results on identifiability have been reported in literature, no systematic investigation of all the I A W Q Model parameters has been published so far, except for specially designed pilot experiments with optimistic assumptions about available measurements (Larrea et al., 1992). If the recommendations of the task group are combined with the parameters used in full scale calibration experiments mentioned above, the following set of parameters can be composed: ~,LH, Ks, KOH, ~A, ba, KNHA, KOA, l]g, k h and (Ss+Xs). Jeppsson (1994) reported the following parameters to be important: I.tH, bu, l.ta, ka, Kx, "qh. Between these lists a discrepancy can be observed. This may be due to the fact that for different plants and experiments different parameters may be important. Another possibility is that the model is not (well) identifiable, so that one particular set of parameters may give (almost) the same model bchaviour. Sensitivity and the Fisher information matrix are therefore used to establish which parameters can be estimated from the outputs measured in this case, the first results of which are reported below. First, a static sensitivity analysis of the measured effluent concentrations to all parameters was performed. Also sensitivity to operational parameters was included. This analysis indicated that besides kinetic and stoichiometric parameters, also operational parameters are important. In this case, the internal recirculation rate and the aerated volume fraction appeared to be very important. Also the Koa value, which is reported to be not critical (Henze et al, 1987), was found to be rather important. This is a result of the model flowsheet used. In reality, the process will be less sensitive towards this parameter. Some of the parameters which have been reported to be critical, such as hydrolysis rate kh and saturation constant Kx were found to be rather insensitive. The most important

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parameters for this case were the heterotrophic yield Y,v,growth rate I.tn and decay rate bn, the autotrophic growth rate I.ta and decay rate ba, which is in accordance with experiences reported in literature. The sensitivities of the measured outputs were computed for the static and for the dynamic case with 15 of the more important parameters selected. The measured outputs chosen for the analysis were COD, Nra, Nm and NO3 in the effuent, MLSS in the circuit and the sludge production. From the output sensitivities scaled by the mean output values, the Fisher information matrix was computed and scaled by the parameter values, similar to scaling in the C optimality ctiterion. In the static case, the rank of the matrix was 6 which was to be expected as the number of outputs is also 6. In the dynamic case, computed for a measured influent variation over 2 days, the rank was 14, which illustrates the fact that dynamic data contain more information and will result in more accurate parameter estimates than static data. For the dynamic case, those parameters combinations were determined which result in the lowest condition number, which corresponds to modified E optimal design. Some results are given in table 2 In the table, also the corresponding traces are listed, which can be seen to be relatively low, compared to the highest traces, shown in table 3. This means that, although the model is identifiable for the parameter combinations in table 2, the parameter accuracy is low. It can also be seen that if more then 8 parameters are estimated form the data, the condition number becomes very high, imposing an upper limit of 8 parameters to be estimated. Table 2: Lowest condition numbers of Fisher information matrix for increasin[~ number of parameters Cond Trace p Parameters 1.24 164 2 kh, $1 1.34 55.68 2 [.t#, ba 3.93 131.5 3 ~H, bA, kh 4.77 190.8 3 kh, $1, bA 16.36 1097 4 KOA, kh, tie, St 73.6 155.2 5 I.tn, ba, Kx, Ss, St 320 231 6 [J.H,ba, kh, gx, Ss, St 736 236 7 I-1,#, bA, kh, gx, rib, Ss, St 2389 . . . . . . . . . . . . . . 2046 . . . . . . . . . . 8 ,~H,, bA, kh, gx, ]]~, Ss~,,,S,, X/ In table 3, the highest achievable traces are listed. The parameters appearing here are quite different from those in table 2, and are the parameters showing the highest sensitivities. Here the condition numbers are very high. This is a known disadvantage of the simplified A and C criteria, which may lead to uninformative designs. In this case, the bad conditioning is partly due to the fact that V,,,r, Qic and KOHhave a similar effect on some of the model outputs. Table 3: Hi[hest traces of Fisher information matrix for p 2 3 4 Trace 1.94 104 2.18 104 2.22 104 Condition 414 507 1.85 104 Parameters Yn, Vaer , ~tA , Qic

increasin[ number of parameters 5 6 7 2.41 104 2.49 104 2.44 104 3.79 104 4.40 104 5.43 104 , Xt

, bn

, Tl~

8

2.58 104 4.57 106 , KoH

CONCLUSIONS AND FURTHER RESEARCH Several strategies can be used for calibration of the IAWQ Model No. 1. For a rational choice of measurements on full scale plants, identifiability of the model parameters has to be taken into account. Output sensitivity functions have been put forward in literature for investigating identifiability. In addition, the Fisher information matrix can be used. From analysis of this matrix it was observed that not all parameters can be estimated from full scale plant data for the case studied. Model identifiability will be investigated further in order to find a combination of measurements on the plant and special experiments for accurately calibrating the model to full scale plants, using other design criteria of the information matrix than trace and condition number. LIST O F SYMBOLS Stoichiometric parameters: Heterotrophic yield (-) YH': Ya :: Autotrophic yield (-) Fraction biomass yielding inert products (-) fp :: Fraction N in biomass (kg N/kg COD) ixh :: Fraction N in inert products (kg N/kg COD) ix1,:: Kinetic parameters: Heterotrophic growth rate constant (s t ) I.tH :: Heterotrophic decay rate constant (s -~) bH :: Affinity constant for Ss (kg m "3) Ks:: Kott :: Heterotrophic affinity constant for So (kg m 3) KNHH:7 Heterotrophic affinity constant for SNH (kg m 3)

KALKH :: Heterotrophic affinity constant for SACK Correction factor for anoxic growth (-) rl~ :: i.ta :: Autotrophic growth rate constant (s -t) ba :: Autotrophic decay rate constant (s l ) KoA :: Autotrophic affinity constant for So (kg m -3) KNHa :: Autotrophic affinity constant for SNn (kg m 3) KNo :: Affinity constant for SNO (kg m "3) KALKa :: Autotrophic affinity constant for SALt(Mol m -3) kh :: Hydrolysis rate (sL) Kx :: Hydrolysis affinity constant (kg m -3) k,, :: Ammonification rate (s -~) rlh :: Correction factor for anoxic hydrolysis (-)

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Components: Readily biodegradable COD (kg m -3) as:: Soluble inert COD (kg m -3) St:: Ammonia and ammonium (kg N m -3) SNH :: Nitrite and nitrate (kg N m -3) SNO :: S~D :: Soluble biodegradable organic N (kg N m 3) SA LK : : Alkalinity (Mol m "3) Dissoved oxygen (kg m -3) So:: Active heterotrophic biomass (kg m -3) XBH :: XSA :: Active autotrophic biomass (kg m -3) Readily biodegradable COD (kg m -3) Xs:: Particulate inert COD (kg m -3) )(1:: XND : : Particulate biodegradable org. N (kg N m -r) Particulate COD from decay (kg m '~) Xp:: Other:

DO :: Dissolved Oxygen (kg m -r) COD :: Chemical Oxygen Demand (kg 02 m -3) BOD :: Biological Oxygen Demand (kg 02 m 3) NKj :: Kjeldal nitrogen concentration (kg N m 3) OUR :: oxygen uptake rate (kg Oz m-3 s"l) MLSS :: mixed liquor suspended solids (kg m 3) internal reciculation (m 3 s -l) Qic :: Qk :: measurement error covariance matrix V~r :: aerobic volume (m 3) Rk :: weighting matrix V,,er :: aerobic volume (m 3) V,,er :: aerobic volume (m 3) p :: number of parameters 3' :: output (column vector) 0:: parameter vector

REFERENCES Ayesa, E., Oyarbide, G. and Fl6rez, J., 1994, Numerical evaluation of model identifiability for reduced order models, Proc. 8th FAB, Med. Fac. Landb. en Toegep. Wet. 59 (4a) pp.2001-2014. Ekama, G.A., Dold, P.L. and Marais, G.V.R, 1986, Procedures for determining COD fractions and the maximum specific growth rate of heterotrophs in activated sludge systems, Wat. Sci. Techn. 18, pp. 91-114. Godfrey, K.R. and DiStefano, J.J., 1985, Indentifiability of model parameters, Identification and System Parameter Estimation, Pergamon, Oxford, pp. 89-114 Henze, M. et a1.,1987, IAWPRC Task group on Mathematical Modelling for Design and Operation of biological Wastewater Treatment, Scientific and Technical Reports No. 1, Activated Sludge Model No. 1, IAWPRC, London. Henze, M., 1992, Characterization of wastewater for modeling of activated sludge processes, Wat. Sci. Tech. 25 (6) pp.l-15. Jeppsson, U. and Olsson, G., 1993, Reduced order models for on-line parameter identification of the activated sludge process, Wat. Sci. Tech. 28 (i 1) pp.173-183. Kappeler, J. and Gujer, W., 1992, Estimation of kinetic parameters of heterotrophic biomass under aerobic conditions and characterization of wastewater for activated sludge modelling, Wat. Sci. Techn. 25, pp. 125-139. Holm Kristensen, G., Elberg J~rgensen, P., and Henze, M., 1992, Characterization of functional microorganism groups and substrate in activated sludge and wastewater by AUR, NUR and OUR, Wat. Sci. Tech. 25 (6) pp.43-57. Larrea, L., Garcia-Heras, J.L., Ayesa, E. and Florez, J.,1992, Designing experiments to determine the coefficients of activated sludge model by identification algorithms, Wat. Sci. Techn. 25 (6) pp. 141-148. Lesouef, A., Payraudeau, M., Rogalla, F. and Kleiber, B., 1992, Optimizing nitrogen removal reactor configurations by on-site calibration of the IAWPRC activated sludge model, Wat. Sci tech. 25 (6) pp. 105-123. Mehra, R.K., 1974, Optimal Input Signals for Parameter Estimation in Dynamic Systems - Survey and New Results, IEEE Transactions on Automatic Control, 19 (6) pp.753-768. Reichert, P., Schultess, R. yon and Wild, D., 1995, The use of Aquasim for estimating parameters of activated sludge models, Wat. Sci. Tech. 31 (2) pp. 135-147. Siegrist, H. and Tschui, M., 1992, Interpretation of experimental data with regard to the activated sludge model No. 1 and calibration of the model for municipal wastewater treatment plants, Wat. Sci. Tech. 25 (6) pp. 167-183. S6derstr6m, T. and Stoica, P, 1989, System Identification, Prentice-Hall. Spanjers, H., 1993, Respirometry in Activated Sludge, Ph.D. Thesis, Wageningen Agricultural University. Spanjers, H., and Vanrolleghem, P., 1995, Respirometry as a tool for rapid characterization of wastewater and activated sludge, War. Sci. Tech. 31 (2) pp.105-114. Stokes, L., Takacs, I., Watson, B. and Watts, J.B., 1993, Dynamic Modelling of an ASP sewage works - A Case Study, Wat. Sci. Tech. 28 (11)pp.151-161. Vanrolleghem, P., 1994, On-line modeling of activated sludge processes: development of an adaptive sensor, Ph.D. Thesis, University of Gent. Walter, E. and Pronzato, L., 1990, Qualitative and Quantitative Experiment Design for Phenomenological models A Survey, Automatica, 26 (2) pp. 195-213. Wanner, O., Kappeler, J. and Gujer, W., 1992, Calibration of Activated Sludge Model Based on Human Expertise and on Mathematical Optimization Technique, a Comparison. Wat Sci.Techn. 25 (6) pp. 149-165. Weijers, S.R., J.J. Kok, A. Buunen, L. van Dijk and T.W.M. Wouda, 1994, Simulation of full-scale carrousels with the IAWQ Model No. 1, Proc. 8th FAB, Med. Fac. Landb. en Toegep. Wet. 59 (4a) pp.2101-2103. Witteborg, A.S.M.. Hamming, R.A. and Wetterauw, M., 1994, Modelling of a full scale watewater treatment plant A case study,, Proc. 8th FAB, Med. Fac. Landb. en Toegep. Wet. 59 (4a) pp.1991-2000. Yuan, W., Okrent, D. and M.K. Stenstrom, M.K., 1993, Model Calibration for the high-purity Oxygen Activated Sludge Process - Algorithm Development and Evaluation, Wat. Sci. Tech. 28 (11) pp. 163-171.