Intelligent Systems for Penicillin Fermentation Process Modelling

Copyright © IFAC Computer Applications in Biotechnology, Osaka, Japan, 1998

INTELLIGENT SYSTEMS FOR PENICILLIN FERMENTATION PROCESS MODELLING

J. A. Lopes, J. C. Menezes Centre for Biological and Chemical Engineering, 1ST Av.Rovisco Pais P-1096, Portugal tel. (351-1) 8417347, fax. (351-1) 8419062, qmenezes@a/fa.ist.utl.pt

Abstract: 1bree different modelling methodologies were compared using industrial data for penicillin fennentation: artificial neural-network (ANN) models (feedforward and global recurrent), a mechanistic model, and a combination of these (hybrid model). Training and validation data sets were chosen through multivariate statistical techniques to ensure that the available operating conditions range was evenly covered. For comparable correlation/predictive capacities hybrid models outperformed ANN and mechanistic models, requiring fewer training examples than standard ANNs and much less time to be developed than mechanistic models. The NeurOn-Line® environment for the intelligent systems platform G2® from Gensym was used in this work. Copyright © 1998 IFAC Keywords: neural-networks; hybrid modelling; industrial production systems; knowledgebased systems; multivariable systems

to establish at all in many practical situations. Changes, for example, in inoculum quality and variability in raw materials composition are two common problems in industrial fermentation processes that can hardly be included in a workable mechanistic model.

I.INTRODUCTION Artificial neural-networks (ANN) are non-mechanistic models that learn by example (i.e., empirical models). ANN are especially suited to model highly non-linear dynamic systems such as biochemical processes (Baughman and Liu,1995) and have been used extensively in many different biochemical areas, namely in fermentation processes (Chattaway et al.,1993; Stephanopoulos et al.,1993, Montague and Morris, 1994; CAB6,1995)

Thus, there are very few mechanistic models of real fermentation processes and the available ones most often have limited correlation and predictive power due to inadequate modelling of process kinetics (Menezes, 1996).

Mechanistic models, on the contrary, are based on fundamental physical principles such as conservation laws (e.g., mass and energy). These laws translate mathematically in balance equations containing two types of terms: rate equations defining relevant observable phenomena (e.g., reaction or transport) and flow terms for mass or energy in and out of the system (i.e., operating variables such as substrate feeds in fermentation processes). However, rate equations based on first principles are very difficult and time consuming to obtain or simply impossible

Relative to mechanistic models, empirical models do not need a detailed process description. Instead they require a large process database. Thus a robust and accurate model can be built for processes difficult or impossible to model otherwise, in a fraction of the time required for mechanistic models. ANN models are strongly dependent on the quality of available data and their validity is only guaranteed in their training range. Thus, process optimisation should not be performed based only on this type of modelling.

307

1.1 Hybrid modelling

3. MODELLING The penicillin production process is a rare case of a bioprocess for which reasonably accurate mechanistic models are now available - viz., 8 out of the 15 proposed models (see review in Menezes,1996). We compared the relative performances of a published mechanistic model, a standard ANN model and an hybrid model.

Hybrid models combining the benefits of the two modelling strategies above can also be established. Neural-networks can be used to model kinetic terms while the fundamental-principle structure of mechanistic models will provide the overall model with extrapolation capacity. The application of the hybrid modelling concept to bioprocesses is still limited to a few laboratory scale fermentation processes or studies with data generated from existing mechanistic models (psichogios and Ungar, 1992; Thompson and Krarner,1994; Azevedo et al., 1997, Simutis and Lubbert, 1997; Van Can et al, 1996;1997). Here we report on the use of hybrid models and multivariate statistical techniques to penicillin fermentation in an industrial pilot-plant.

3.1 Mechanistic model The mechanistic model used in this work was that of Menezes et al. (1994), defined by equations I to 10 bellow. The model assumes segregation of biomass in two states (live and dead, equations I and 2), consumption of complex substrates (lumped initially together with the main carbon substrate, equation 4), an increasing penalty in growth with biomass concentration (pellet size) to account for internal diffusional limitations (equation 6) and a purely exogenous maintenance metabolism (equation 8)

1.2 Multivariate Statistical Techniques In model development the available data is usually divided in two sets: training and validation. Often in practice this is done randomly, which is inadequate with small databases. An alternative way would be to apply statistical techniques to map the data to enable a rational choice of training and validation sets. When a large number of strongly correlated variables are involved - as in bioprocesses - data mapping and compression can be best achieved with principal component analysis (PCA). With PCA process variables are projected onto a lower dimensional space where the projections (principal components or scores) are orthogonal. Plots of the principal components show relations across experiments, while plots of the model coefficients (loadings) show relations among variables (Albert et al., 1996; Martin and Morris, 1996). In processes where time is also an important variable (e.g. fedbatch), data compression can be performed efficiently by multiway principal components analysis (MPCA) reported by MacGregor et al. (1994).

Live and dead biomass concentrations were not measured separately. Instead, total dry-weight (X) was measured and Xtive and Xoe.d estimates were obtained from the model. Since there were no actual measurements for these variables, ANNs were trained to predict the total biomass concentration. The mechanistic model parameters are sununarised in appendix.

dX live = "v . -F dt ~"hve 111

X live -K X · V D hve

dX

X death

death -="-= KDX hve -FlI1 - dt V

dP

P

-=7tX l · -F --KhP dt Ive 111 V

dS

S

G

dt = -oX live - Fin V + Sin Vs

(3)

(4)

Fin -FOUl

I!max S I!=--'-"'=---

The industrial production of penicillin-G is a fedbatch process characterised by two distinct operating regimes. In the initial phase large concentrations of substrates are used to produce large amounts of biomass, while in the second phase, the substrate is maintained at a low level to enable penicillin biosynthesis.

(2)

(5)

dV -= dt

2. PENICILLIN FERMENTATION PROCESS

(1)

KXXlive

+S

7tmaxS 1t=-Kp+S S = Smax

(6)

S

(7) (8)

Ks+S

0,=..J:....+~+~

3

Kxs

Data from 11 penicillin batches (240 h) in a I m stainless steel bioreactor, with an high-producing strain of Penicillium chrysogenum, under real industrial operating conditions, were used. Details of all materials and methods can be found in Menezes et al. (1994).

X

=

(see notation at the end)

308

X live

(9)

Yps

+ Xdead

(10)

3.2 Standard ANN model

3.4 Global recurrent ANN model

A static feedforward ANN was constructed with activating node functions (ANF) of sigmoidal type (equation 11). The second order Broyden-FletcherGoldfarb-Shanno (BFGS) backpropagation algorithm was used for training (NeurOn-Line®,1996).

Recurrent neural networks using only operating and state variables as inputs can be very useful for one step ahead predictions. However, errors in fedback predictions generate higher errors for the next prediction, propagating very effectively throughout the fermentation. A recurrent neural network with one time delay was built (figure 2) and the test was performed in two ways: simulation along the entire fermentation and simulation correcting network outputs with real observed variables. While in the first case we can predict an entire batch based only on the operating conditions in the second case predictions can only be made until the end of the sampling time (8 hour spacing).

ANF(x)

(11)

=- -2 -x 1 I +e-

Selection of inputs and network topology were optirnised by trial and error using process knowledge and known rules-of-thumb (Bauglunan and Liu,1995). The best set of inputs was formed by eight variables: time (t), volume (V), total feed rate (Fin), substrate feed rate (Sin *G.), nitrogen feed rate (Nin), precursor feed rate (FAKin), nitrogen concentration (N) and precursor concentration (F AK) (figure 1). The ANN topology chosen was 8: 10: 1. Outputs were the total biomass concentration (X) and penicillin concentration (P) at the next sampling time. All data introduced in the network was linearly compressed between 0.05 and 0.95. Before building the training and validation sets, data was interpolated by means of cubic splines thus obtaining hourly spaced synchronised values of all variables. Irregular spaced sampling of variables tend to degrade ANN performance. ANN training was stopped when a minimum error was reached for the validation data set (Bishop, 1995).

4. TRAIN AND VALIDATION DATA

Multiway principal component analysis was applied to all 11 fermentation data sets. The first three principal components (scores) accounted for 65% of the total process variance which shows that process variables are strongly correlated. The model coefficients or loadings were also useful to inspect variable correlations.

3.3 Hybrid model

Figure 3 is a single plot of the first PC against the second PC. This map contains about 56% of the total process variance. Batches on clusters can then be used as test batches while batches ranging outside the nominal regions (ellipsoids) are considered as outliers and are not suitable to be used for testing.

In the present work, experimental specific growth and production rates were computed from mass balances similar to equations 1 to 3. Differentiation of live into death biomass was not considered explicitly, thus equations I and 2 were added together and the autolysis constant (kD) was set to o. The obtained experimental specific rate profiles were then used to train two separate networks one for each of the specific rates: biomass growth rate (11) and penicillin production rate (n) .

Fig. 2. Recurrent ANN with one time delay

~

-;

[XJ or[PJ

1

...8

~

0

f

-1

11

.~

Cl.

-. -3 -3

·2

_1

Princlpol Component.,

Fig. 1. The two methodologies based on ANN (CD hybrid model
Fig. 3. Score plot showing relations among the 11 batches used to build the models

309

Batches 2 and 3, 1 and 9, 10 and 7 are close together. Batches 4 and 11 are outliers because they are outside the 90% confidence limit region (Hotelling' s T2 statistic). Batches 2, 7 and 9 (representing 28% of the total database) were chosen to be the validation data set since they are close to existing batches and it is expected that the space occupied by those batches is covered by existing ones in the training set.

Table 1. RMS test values for two unseen batches for the three models considered RMS mechanistic model standard ANN model hybrid model

5. THE G2 KNOWLEDGE BASE

Penicillin (P2 batch 2 batch 9 100 100

biomass {X) batch 2 batch 9 100 100 95

74

180

166

83

68

157

109

Because ANN predictions are relatively noisy, due to discrete changes in operating variables, outputs from standard ANN were smoothed using cubic splines. Models based on ANN fail predictions for the fmal stages of both fermentations in Figure 5. This can be traced to the training set. In comparison, the mechanistic model appears to be the better in predicting penicillin concentration. The last two data points in batch 9 penicillin profile (Table 1 and Figure 58) produce the difference between RMS values with the two ANN-based models. In general it was found that the non-linearity of biomass concentration profiles was best captured by standard ANN and hybrid models than by the simplistic Contois model in the mechanistic model (equation 6).

G2<1> is an real-time intelligent system from Gensym where processes can be monitored, anallsed, modelled, optimised and supervised on-line.G2 and the neural network module NeurOn-Line (NOL) were the platforms used to build and train the networks and to perform simulations using the models described. An application was built where the three models run in parallel and which can be used in the future to process supervision based on data acquisition from the fermentation tank, on-line sensors and off-line analysers. This is application will send warning messages to process operators, based on model comparisons and a set of rules capturing process knowledge not included in the models.

~ ~-------------------------,

6. RESULTS AND DISCUSSION A comparison of the mechanistic model, standard ANN and hybrid modelling for the prediction of biomass and penicillin is show in figure 5A for batch 2 and figure 5B for batch 9. Table 1 summarises the root mean squares (RMS) for the three models, normalised with the mechanistic model RMS value for each case. The reported RMS values are of the same order of magnitude for each variable and the two batches. This demonstrates that ANN-based models are an alternative to hard to obtain mechanistic models. It also shows that under nominal process conditions (slowly varying and similar from batch to batch) the advantages of hybrid models over standard ANN ones is not fully realised.

120

80

UIO

200

B o o

---

.0

80

120

0

2.0

o

,..,...,.,...- ,

180

200

Fennent.tk»n age [h)

Fig.5. Comparison of the results obtained by each of the three models for batch 2 [A] and batch 9 [E] (points represent experimental data: o biomass, 6. penicillin; lines represent predictions: mechanistic model; - hybrid model; - - standard ANN model)

310

Global recurrent networks were tested to try to solve the above problem (figure 6). When the network is used to predict the entire fermentation without correcting the predictions at the end of each sampling interval, errors on outputs propagate throughout the run. If fedback predictions are corrected with the real measured data that become available during the interval, then more accurate predictions are obtained. Failure of the recurrent type network without input correction is clearly shown for the predicted substrate profile where errors accumulate after 120 hOUTS. This deviation is also seen in biomass and penicillin profiles as the wrong substrate prediction is used in their computation for the next interval.

" ,....------------r Q

o ~~

o

_ _ _-_-_-~-~

"

to

120

180

100

240

Fig.6. Comparison (batch 7) between a global recurrent network with and whithout correction of predictions. (points represent experimental data: Cl biomass, 6. penicillin, o substrate; lines represent predictions: - corrected; uncorrected)

7. CONCLUSION In this work we compared three different methodologies for modelling a fermentative penicillin production process. Mechanistic, standard ANN and hybrid models were compared and tested with data not used in their training. The selection of training and validation batches was made using a statistic multivariate teclmique as an alternative to the common procedure of randomly choosing the data. We have found the statistical procedure superior and more reliable than the random one.

ACKNO~EDGEMENTS

The authors greatly acknowledge Companhia Industrial Produtora de Antibi6ticos SA (CIPAN) in Portugal for providing the data. JPL acknowledges a grant from PRAXIS XXI LOO9-P31B-09/96.

It was shown that for comparable predictive capacities hybrid models outperformed ANN and mechanistic models, requiring fewer training examples than standard ANN and much less time to be developed than mechanistic models.

REFERENCES Albert, S., Martin, E., Montague, G. and Morris, A (1996), Multivariate statistical process control in batch process monitoring, Preprints of the IFAC Conference, San Francisco Azevedo, S., Dalun, B. and Oliveira, F. (1997), Hybrid modelling of biochemical processes: a comparison with the conventional approach, Comp. Chem. Eng, 21, 751-756 Baughman, D.R. and Liu, Y.A,1995, "neural networks in bioprocessing and chemical engineering", academic press. Bishop, C. (1995), Training with noise is equivalent Neural to Tikhonov regularisation, Computation, 7, 108-116 CAB6 (1995), Preprints of the f!' Conference on Computer Applications in Biotechnology. Chattaway, T., Montague, G.A., and Morris, AJ. (1993), Fermentation Monitoring and Control., in Bioprocessing., vol. 3, pg. 319-354, 2nd ed., Ed. G. Stephanopoulos in "Biotechnology", Eds. H.J. Rebm, G. Reed, VCH, Germany. NeurOn-Line (1996), Reference Manual Version 3.0, Gensym Co. Cambridge ,Massachusetts Martin, E. and Morris, A (1996), An overview of multivariate statistical process control in continuous and batch process perfomance monitoring, Trans. Inst. MC, 18, 51-60

Hybrid models should be especially advantageous in process optimisation because they can be used to For one reason, ANN are better extrapolate. estimators of highly non-linear microbial kinetics than simple rate equations such as Monod or Contois laws. In addition, because hybrid models retain the mechanistic model structure in which operating variables are separated form kinetic terms, they are less dependent on the training operating conditions than standard ANN models. Recurrent networks with correction of fedback predictions are effective models and can be used as one step ahead predictors. They require, however, an optimisation of the prediction window length to avoid error propagation. Future work is being directed to combine hybrid models with process knowledge - such as process engineers knowledge and heuristic rules - into a realtime intelligent system for process control, supervision and optimisation.

311

MacGregor, 1., Nomikos, P. and Kourti, T. (1994), Multivariate statistical process control of batch processes using PCA and PLS, Preprints of the IFAC ADCHEM'94 Conference on Advanced Control of Chemical Processes, Kyoto, Japan Menezes, 1., Alves, S., Lemos, 1. and Azevedo, S. (1994), Mathematical modelling of industrial pilot-plant penicillin-G fed-batch fermentations, J. Chem. Tech. Biotechnol., 61, 123-138 Menezes, 1. (1996), Analysis and modelling of penicillin-G production at industrial pilot-plant scale, PhD thesis, Technical University of Lisbon Montague, G. and Morris, A. (1994), Neural network contributions in biotechnology, TIBTECH, 12, 312-323 Psichogios, C. and Ungar, L. (1992), A hybrid neural network first principles approach to process modeling, AIChE.1. , 38,1499-1511 Simutis, R. and Lubbert, A. (1997), Exploratory analysis of bioprocesses using artificial neural network-based methods, Biotechnol. Prog., 13, 479-487 Stephanopoulos, G., Konstantinov, K., Saner, u., Yoshida, T. (1993), Fermentation Data in Analysis for Diagnosis and Control, Bioprocessing., vol. 3, pg. 355-400, 2nd ed., Ed. G. Stephanopoulos in "Biotechnology", Eds. H.J. Rebm, G. Reed, VCH, Germany. Thompson, M. and Kramer, M. (1994), Modelling chemical processes using prior knowledge and neural networks, AIChE J., 40, 1328-1340 van Can, H., Hellinga, C., Luyben, K. and Heijnen, 1. (1996), Strategy for dynamic process modelling based on neural networks in macroscopic balances, AIChE.1., 42, 3403-3418 van Can, H., Braake, H., Hellinga, C., Luyben, K. and Heijnen, 1. (1997), An efficient model development strategy for bioprocesses based on neural networks in macroscopic balances, Biotechnol. Bioeng., 54, 549-566

APPENDIX

NOTATION AND NOMINAL PARAMETERS Fin Fout KD Kh Kp Ks Kx N P S Sin V

X Yps Y xs ~

(dml.h· l ) (dml.h· l ) (h· l ) (h.I) (g.dm· l ) (g. dm· l ) (g.g-DW.l) (g.dm·l ) (g.dm·l ) (g.dm·l ) (g.dm·l ) (dml ) (g_DW.dm·l ) (g-DW.g·I) (g-DW.g· I) (g.g-DW·I.h· l )

j..l

Specific substrate consumption rate for maintenance Specific biomass growth rate

1t

Specific penicillin production rate

(h0l)

cr

Specific substrate consumption rate Maximum substrate consumption rate for maintenance (0.02) Maximum specific biomass growth rate (0.130) Maximum specific penicillin production rate (0.011)

(g.g-DW·I.h· l )

~max

Ilmax 1tmax

31 2

Combined inlet flow rate Outlet flow rate of evapored water Autolysis rate constant (0.0) Penicillin hydrolysis constant (0.002) Product saturation constant (0.0001) Substrate saturation constant (0.0001) Growth saturation constant (0.131) Soluble organic nitrogen concentration Penicillin-G concentration Substrate concentration Glucose concentration in the syrup Culture broth volume Biomass concentration Substrate to penicillin yeld (1.0) Substrate to biomass yeld (0.52)

(h.I)

(g.g_Dwol.hOI) (h.I) (h· l )