A hybrid feedforward neural network model for the cephalosporin C production process

A HYBRID FEEDFORWARD NEURAL NETWORK MODEL FOR THE CEPHALOSPORIN C PRODUCTION PROCESS

R.G.Silva, A.J.G.Cruz, C.O.Hokka, R.L.C. Giordano and R.C.Giordano^*

Departamento de Engenharia Química, Universidade Federal de São Carlos,

Via Washington Luiz, km 235, C.P. 676, 13565-905, São Carlos - SP, Brazil,

Phone: [phone], Fax: [phone]

E-mail: [e-mail]

(Received: November 16, 1999 ; Accepted: April 6, 2000)

Abstract - At present, direct on-line measurements of key bioprocess variables as biomass, substrate and product concentrations is a difficult task. Many of the available hardware sensors are either expensive or lack reliability and robustness. To overcome this problem, indirect estimation techniques have been studied during the last decade. Inference algorithms rely either on phenomenological or on empirical models. Recently, hybrid models that combine these two approaches have received great attention. In this work, a hybrid neural network algorithm was applied to a fermentative process. Mass balance equations were coupled to a feedforward neural network (FNN). The FNN was used to estimate cellular growth and product formation rates, which are inserted into the mass balance equations. On-line data of cephalosporin C fed-batch fermentation were used. The measured variables employed by the inference algorithm were the contents of CO₂ and O₂ in the effluent gas. The fairly good results obtained encourage further studies to use this approach in the development of process control algorithms.

Keywords: neural network, hybrid model, cephalosporin C production, inference of state

INTRODUCTION

Artificial neural networks (ANN) are a generic description for a wide class of computer models, inspired by the structure and behavior of real neurons. They can recognize patterns, reorganize data and, most interestingly, "learn" complex dynamic behaviors of physical systems. In the early 90’s neural networks were one of the fastest growing areas of Artificial Intelligence, Bhat and McAvoy (1990). They are still one of the most promising, because of their ability to represent nonlinear relationships. As a result of their good modeling capabilities, neural networks have been used extensively for a number of chemical engineering applications such as sensor data analysis, fault detection and nonlinear process identification (Hoskins e Himmelblau, 1988; Bhat e McAvoy, 1990; Hernández e Arkun, 1992; Willis et al., 1992). Hussain (1999) presents an extensive review of the various applications utilizing ANNs for chemical process control in recent years.

One of the main barriers to a more widespread use of advanced modeling and control techniques in the chemical and biochemical industry is the cost for model development and validation. Usually modeling costs account for over 75% of the expenditures in the design of an advanced control project (Hussain, 1999).

Specifically in biochemical processes there is a lack of reliable measurements of some key process variables. The difficulty in defining quantitative relationships between microbial growth and production rates turns their inference from other measured variables into a very complex task. Neural networks emerge as a powerful tool in this area (Linko et al., 1999). Such approach has been denominated "software sensoring". The idea is relatively simple. The inference algorithm relates the data moniored on-line, called secondary measurements (mole fractions in the off-gases, pH, dissolved oxygen and so forth) with the key process variables (concentrations of biomass, substrate and product), providing their on-line estimate.

According to van Can et al. (1997; 1999), depending on the amount of knowledge that is used to develop the model, modeling strategies can be classified in white box, black box and gray box. In the white box approach, the model development is mainly driven by the knowledge of the relevant mechanisms and by the so-called first-principles equations (mass balances, thermodynamics, and so on).

In biochemical processes, ANNs have typically been used as black boxes in bioreactor modeling applications (Thibault et al., 1990; Karim and Rivera, 1992; Di Massimo et al., 1992; Syu and Tsao, 1993; Acuña et al., 1998). In a black box strategy the model development is mainly driven by measured input-output data, observations of the system behavior. It is the only possible method when no process knowledge is available. A major advantage of this modeling technique is that, within a reasonable amount of time, one can obtain a highly accurate mathematical model of a system without detailed knowledge of the phenomena occurring during the process. But their great disadvantage is their incapacity for extrapolations.

Another option is the gray box modeling strategy, also called hybrid modeling. It combines a simple first-principles model with an ANN that serves as an estimator of unknown parameters. The ANN can be trained either to predict those parameters (for instance, reaction rate constants of a simple, pseudo-first order reaction) or to substitute complete constitutive equations (i.e., the rate itself, in this case). Researchers are investigating several different design and training techniques to include prior knowledge into ANNs (Thompson and Kramer, 1994; Zorzetto and Wilson, 1996; van Can et al, 1997; Costa et al., 1999; Henriques et al., 1999).

In this paper, the performance of a hybrid ANN model for the inference of state variables of the cephalosporin C production process was studied. The hybrid model consisted of two ANNs, coupled to the mass balance equations. The first network estimated the specific growth rate from selected on-line measurements and initial conditions. The second one was employed to estimate the specific production rate from the specific growth rate predicted by the previous network. The output of both networks was included into the mass balances to estimate biomass, substrate and product concentrations.

THEORETICAL BASIS

Cephalosporin C Production Process

Cephalosporin C is a beta-lactam antibiotic used to produce semi-synthetic cephalosporins, which are widely spread in the pharmaceutical market. Industrial production is still carried out in aerated, stirred tank bioreactors employing submerged cultures of the strictly aerobic fungus Cephalosporium acremonium. As generally occurs in any secondary metabolite production process, there are two distinct phases during the fermentation. In the first phase, the bioreactor is operated in batch mode. Large quantities of biomass are produced but low antibiotic production rates are observed due to a catabolic repression mechanism. At the end of this phase, substrate is added to the reactor at a suitable rate, cell concentration is maintained at a constant level. The synthesis of specific enzymes commences and consequently higher production rates take place.

Many phenomenological models have been proposed to simulate the cephalosporin C production process (Matsumura et al., 1981; Chu and Constantinides, 1988; Araujo et al., 1996; Cruz et al., 1999). Although simplifying assumptions regarding the complex kinetics mechanisms were made in all these models, the problem of a large number of parameters to be estimated still remained. To avoid this problem, the ANN approach can be used.

Neural Network Approach

ANNs consist of connected processing elements called nodes or units. These nodes are organized in layers. One common type of ANN consists of three layers interconnected, with a varied number of nodes. The activity of the input units reflects the raw information that is fed into the network. The activities of the input units and the weights of the connections between the input and hidden units determine the activity of each hidden unit. Similarly, the behavior of the output units depends on the activity of the hidden units and the weights between the hidden and output units. These weights are the internal parameters of the network. The behavior of the ANN depends on them and on the input-output function (typically nonlinear) that is used in the nodes.

Among the variety of ANN architectures that have been proposed, the feedforward neural networks (FNN) are the most frequently applied to model chemical engineering and biochemical process. In FNNs, the information flux described in the previous paragraph is unidirectional (feedforward). Di Massimo et al. (1992) utilized a FNN in a so-called modular approach to model industrial penicillin fermentation. In this approach, the FNNs are arranged in a serial fashion, the previous FNN feeding the next one. The good results obtained by the authors encouraged studies on control strategies using the same FNN (Willis et al., 1992). Cephalosporin C production was modeled by two FNNs, where the first one was used to estimate cell concentration and the second to infer antibiotic concentration (Cruz et al., 1998). These works were based in a black box modeling strategy.

Nevertheless, ANNs may have poor extrapolation characteristics, and their predictions may lack reliability if the data used during the training phase do not cover the whole domain of interest (van Can et al., 1996). Unfortunately, this is a common situation in fermentation technology: changes in strain, small differences in pre-processing, among other factors of difficult assessment, may cause appreciable modifications on the system response. The hybrid approach intends to circumvent this handicap, at least in part.

Hybrid Approach

Hybrid (gray box) algorithms attempt to aggregate the main positive characteristics of the phenomenological and neural network approaches. This effect may be pursued either through parallel strategies, where the ANN runs in parallel to a white box model (van Can et al., 1996) or through serial strategies, where the ANN runs in series with a white box model. Psichogios and Ungar (1992) applied the serial strategy to a fermentation process. Their network output was the specific growth rate, which was inserted in the mass balance equations. Thompson and Kramer (1994) used a combination of the serial and parallel strategies to simulate fed-batch penicillin fermentation. Van Can et al. (1997, 1999) used the serial gray box modeling strategy on the modeling of the enzymatic batch conversion of penicillin G.

METHODOLOGY

This work employed a modular design, with two ANNs running in series. The first network estimated the specific growth rate from carbon dioxide and oxygen mole fractions, measured on-line in the exhausted gas. A paramagnetic oxygen analyzer (Rosemount Analytical, model 755) and an infrared carbon dioxide analyzer (Rosemount Analytical, model 880A) were used to monitor the effluent gas. Data were stored in a PC-computer (UNISOFT Supervisory System). Since the bioprocess is inherently transient, the time of the fed-batch run was also used as input to the FNNs.

The forecasting of the lag phase duration is a serious difficulty when modeling a fermentative process. For instance, phenomenological models are not able to take into account effects caused by changes in the process for reactivation of the microorganism. In our training data, two different inoculation procedures were used, resulting in different extensions of the lag phase. Our strategy was to include the growth rate of k previous time intervals as additional inputs to the first ANN.

If we let X denote the input vector to this network, then:

X = [t(p-k), ..., t(p), Y_O2 (p-k), ..., Y_O2 (p), Y_CO2

(p-k), ..., Y_CO2 (p), m_x (p-k), m_x (p-1) ]

where:

p denotes the present time, and k is set to five previous instants Y_O2 oxygen mole fraction in the exhausted gas Y_CO2 carbon dioxide mole fraction in the exhausted gas t time (h) m_x specific growth rate (h)

The output is the specific growth rate in the present time, m_x(p). This architecture was suggested by the work of Hernández and Arkun (1992).

The second network was used to infer the specific production rate at time p, m_p(p). The same topology was used. The inputs to this ANN were: the fed-batch time [t(p-k), ..., t(p)], the specific growth rates [m_x (p-k), m_x (p)] and the specific production rates [m_p (p-k), m_p (p-1)].

For secondary metabolites as cephalosporin, cell growth inhibits the production, as already pointed out by Pirt and Righelato (1967) when studying penicillin production. Therefore the value of m_x must be an input to the second network. The ANN structure is shown in Figure 1 (A and B).

The activation function was sigmoidal (Bhat and McAvoy, 1990).

Database

The database consisted of five experimental runs. The assays were carried on in a conventional bioreactor operated in fed-batch and in repeated fed-batch modes. The on-line measurements used to infer the state of the system are dioxide carbon and oxygen mole fractions in the exhausted gas. The data-sampling interval was 10 s. For training purposes, time intervals encompassed 10 minutes. All the runs were carried out employing the same substrate formulation (Cruz et al., 1999) and operating conditions (T = 26.0 °C, Q_air = 3.00 SLPM, dissolved oxygen concentration controlled at 40% by the stirring speed). During fed-batch operation the feed rates were Run #1, 10.00 mL/h; Run #2, 10.00 mL/h; Run #4,10.75 mL/h; Run #5, 13.25 mL/h and Run #6, 12.00 mL/h.

Different behaviors, concerning substrate consumption, cell growth rate and antibiotic production, were observed for the five assays. For instance, Run#1 had a considerably longer lag phase, due to a shorter inoculation procedure (24 h). Run#2 and Run#4 had a 72 h inoculation period. Runs #5 and 6 were sequential repeated fed-batch of assay # 4; therefore, the microorganism was already adapted to the environment, and the lag phase was not visible in our time scale. The database used to train the two ANNs included four runs. The fifth assay was used to validate the model.

Experimental off-line data were determined using standard methods: dry weight at 105 °C for biomass; enzymatic GOD-PAP method for glucose and High Performance Liquid Chromatography for cephalosporin C. Since specific cellular growth and product formation rates are not directly measurable, they must be calculated from these data. This can be done after differentiating cell and antibiotic concentrations with respect to time.

There are two possible solutions for this problem. The first possibility is to smooth the data, fit an interpolation function (for instance, spline polynomials) and then calculate the derivatives. Another approach relies on a phenomenological model to calculate the "experimental" rates from the empirical concentrations. Both strategies are equivalent, since they are in fact smoothing techniques. The choice between them is a matter of convenience. In this work, the second approach was applied, using the model proposed by Cruz et al. (1999).

Balance Equations of Hybrid Model

The mass balances of the main components in the cephalosporin C fed-batch process are:

(1)

(2)

(3)

where:

C_MS substrate concentration in the feed rate, g/L C_p cephalosporin C concentration, g/L C_s substrate concentration (glucose), g/L C_x cell concentration, g/L k_h1.0x10^-4 decomposition rate of product, h^-1 m 1.2x10^-3 maintenance coefficient, (g of substrate)/(g of cell)/h m_x specific growth rate, h^-1 m_p specific production rate, h^-1 Q_MS substrate feed rate, L/h V volume of bioreactor, L Y_x/s 0.51 yield coefficient, (g of cell)/(g of substrate)

Parameters m, k_h and Y_x/s were taken from independent experiments (Cruz et al., 1999). They are considered "perfect" here, that is, their values are assumed without error, and used as constants throughout the work. Certainly, a more generic topology for our hybrid model could be proposed, with an ANN estimating a rate of substrate consumption and of antibiotic degradation. That possibility will be explored in future works. The pseudo-stoichiometric constant Y_x/s could also be an output of the ANN, but we do not consider necessary to do so, since its value was confirmed by innumerous empirical data. Figure 2 illustrates our hybrid model.

RESULTS

The mean square error (MSE) between the neural output and the learning data was the objective function for the training algorithm. Figure 3 (A and B) shows the MSE as a function of the number of presentations during the training phase, for the first ANN. Two different algorithms of search were tested: backpropagation (Rumelhart and McClelland, 1986) and a combined procedure (Cruz et al., 1996), respectively. The combined approach with 300 presentations was selected as our standard training procedure.

For the second ANN a similar behavior was detected. After 300 presentations, the MSE does not decrease significantly. Figure 4 presents the results obtained for the backpropagation procedure (BP) (Figure 4 A) and combined algorithm (CA) (Figure 4 B).

Figure 5 (A, B, C and D) shows the quality of fit obtained for the four sets of training data. The ANN was able to capture the process dynamics very well.

To validate the model, a set of data not used during the training phase was employed. Figure 6 depicts these results. An excellent fitting to the "experimental" values of specific growth rate can be noted.

The next step consisted in the training of the second ANN using the on-line available data and the information produced by the first ANN. The results are shown in Figure 7 (A, B, C and D).

It can be observed that the FNN results fitted fairly well to the "experimental" specific production rates.

The performance of this FNN was tested against the same data set used to validate the first network. Figure 8 presents the results.

The simulation results derived from the hybrid ANN model are plotted in Figure 9 together with the experimental results for biomass, glucose and cephalosporin C.

As it can be observed, the accuracy of the model is satisfactory. The validation run, shown in Figure 10 gave very promising results.

CONCLUSIONS

The hybrid model was successful in capturing the complex dynamics of this system. One very important feature of this approach is that differences in the lag phase duration could be accommodated without effort. This would be an overwhelming task for a phenomenological model: differences in adaptation times are due to innumerous causes, making it almost impossible to predict the beginning of the exponential growth beforehand. This delay must be informed to the "white box" model, as an extra empirical parameter. The algorithm presented in this work by-passed this difficulty.

ACKNOWLEDGMENTS

The authors acknowledge the financial support from FAPESP and CNPq.

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To whom correspondence should be addressed

Publication Dates

• Publication in this collection
  16 Mar 2001
• Date of issue
  Dec 2000

History

• Received
  16 Nov 1999
• Accepted
  06 Apr 2000