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Neural Observer for an Abattoir Wastewater Treatment Process
11th International Symposium on Computer Applications in Biotechnology Leuven, Belgium, July 7-9, 2010
Neural Observer for an Abattoir Wastewater Treatment Process S. Carlos-Hernandez*, E.N. Sanchez** and R. Belmonte-Izquierdo**, L. Diaz-Jimenez* * Cinvestav Saltillo,Km 13, Carr. Saltillo-Mty 25900 Ramos Arizpe, México. (Tel:52-844-4389612; e-mail: [email protected], [email protected]). ** Cinvestav Guadalajara, Apdo Postal 31-438, Plaza La Luna,45090 Guadalajara, Mexico (email:[email protected], [email protected])
Abstract: The paper deals with the development of a Recurrent High Order Neural Observer for an abattoir wastewater treatment by anaerobic digestion. The neural network uses the hyperbolic tangent as activation function and the learning algorithm is based on an extended Kalman filter. This observer is designed to estimate the variables of the methanogenesis stage (biomass and substrate) in a completely stirred tank reactor. A prototype treating real abattoir wastewater is implemented in order to obtain an experimental model, which is used to validate the proposed observer. Keywords: bioprocess, anaerobic digestion, neural observer, wastewater treatment.
1. INTRODUCTION Animal sacrifice in abattoirs produces large quantities of wastes and effluents containing high organic load. In many cases, a lot of them are directly rejected to the ecosystem without an adequate treatment process (Mittal, 2006; Arvanitoyannis and Ladas, 2008). Besides, abattoirs operation requires services as electricity and big quantities of water. Then, it is necessary to implement strategies in order to improve the abattoirs operation and to avoid, or at least to minimize, environmental pollution. Anaerobic digestion is one of the most adequate processes to treat effluents with high contents of organic wastes. The complex molecules are progressively transformed by different bacteria populations; besides to the treated water, a biogas mainly composed of methane and carbon dioxide is obtained. The products of anaerobic digestion have added value, since they can be used to offset treatment costs (Ross, 1991): i.e, reusing and/or recycling treated water and additionally employing biogas for energy generation. However, this bioprocess is sensitive to variations on the operating conditions, such as pH, temperature, overloads, etc. In addition, there exist variables and parameters hard to measure due to economical or technical constraints. Then, estimation and control strategies are required in order to guarantee adequate performances. Anaerobic digestion involves hardly measurable or immeasurable variables which are necessary for supervision and control. Observers and softsensors are an interesting alternative in order to estimate these kinds of variables. In the specialized literature, observers have been already reported; for example, asymptotical observer, proposed by Bastin and Dochain (1990), interval observers (Smith, 1996; Gouze, Rapaport and Hadj-Zadok, 2000, Alcaraz-Gonzalez et al. (2004)), and other approaches (Deza et al., 1993; Lemesle 978-3-902661-70-8/10/$20.00 © 2010 IFAC
and Gouze, 2005; Chachuat and Bernard, 2005). Some of them are developed focusing on diagnosis and fault detection, such as Lardon, Punal and Steyer (2004), Wimberger & Verde (2008). Fuzzy algorithms have been also considered as alternatives to design observers and controllers for bioprocess (Muller et al., 1997; Ascencio, Sbarbaro and Feyo de Azevedo, 2004, Carlos-Hernandez et al, 2009). Complete knowledge of the system model is usually assumed in order to design nonlinear state estimators; nevertheless this is not always possible. Moreover, in some cases special nonlinear transformations are proposed, which are not often robust in presence of uncertainties. An interesting approach for avoiding the associated problem of model-based state observers is the neural network approach. Neural observers require feasible measures and a training algorithm in order to learn the process dynamics; in this case, the model knowledge is not strictly necessary (Pozniak et al., 2001; Ricalde and Sanchez, 2005; Urrego-Patarroyo et al., 2008). Also, different applications of anaerobic digestion to abattoirs have been reported. In example, some researches focus on model development of anaerobic degradation of slaughterhouse effluents (Angelidaki et al., 2000a, b; Lokshina et al., 2003), anaerobic digestion of slaughterhouse byproducts in batch and semi-continuous processes (Hejnfelt and Angelidaki, 2009; Alvarez and Liden, 2008), and other subjects (Salminem and Rintala, 2002). In this paper, a Recurrent High Order Neural Observer (RHONO) is proposed in order to estimate biomass and substrate in an anaerobic process for abattoir effluents treatment. The observer structure is based on hyperbolic tangent as activation function and is trained using an extended Kalman filter. The main advantage of the RHONO is a high performance and independence of the process model. The proposed observer is validated in a model developed from a prototype, which treats real abattoir wastewater. This prototype process is developed in a
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completely stirred tank reactor with biomass fixed in a solid support. 2. COMPONENTS AND METHODS 2.1. Bacterial support The main advantages of the bacteria immobilization are i) high volumetric reaction rates, ii) high bacteria concentration inside the reactor, iii) more possibilities to regenerate the biocatalytic activity of immobilized cell structures, and iv) the ability to conduct continuous operations at high dilution rate without washout phenomena. In this work, a Mexican natural zeolite is used. Previous works were developed in order to characterize this zeolite and to determine its potential as bacterial support. Table 1 shows the main properties of the used natural zeolite.
of 5800 mg L-1 and an initial pH of 7.2. Performances of the wastewater treatment process are evaluated by developing batch tests, with 15 days duration for each one. Different tests are performed with similar operating conditions; the obtained results are used for parametric identification of a methanogenesis stage mathematical model. COD, biogas and pH are measured, to calculate these parameters. The respective identification is done with the model method; thus a comparison between real data and theoretical data is performed using Matlab-Simulink. The obtained model is composed of algebraic equations to represent acid-base equilibria and conservation of materials, and differential equations to model the process dynamics. Biogas (methane and carbon dioxide) is considered as the process output.
g ( x a , xd ) = 0 x& d = f ( x a , x d , u ) y = h( x d )
Table 1. Properties of the mexican natural zeolite used as bacterial support Property Specific surface area Apparent density Microporosity
Specification 28 m2 g-1 0.818 g mL-1 0.051 cm3 g-1
(1)
with:
[
xa = HS
S−
xd = [X 1
S1
u = [S1in
S 2in
CO2 d X2
B
S2
ICin
IC
Z in
H+
]
Z] D]
y = [Q CH 4 QCO2 ]
2.2 Abattoir effluents The samples for this work are collected from an abattoir situated at Saltillo, Coahuila, Mexico. A characterization, after separation of solid materials is done and the respective results are displayed in Table 2. There are reported results concluding organic nitrogen is included in the COD (Procopio Pontes et al., 2002). The inoculum is obtained from a brewery wastewater treatment plant. Then a preliminary stage is required for the bacteria adaptation to the abattoir substrate. Around two months were required in order to form the biofilm in the natural zeolite and one month to adapt the microorganisms to the abattoir effluents. Table 2. Average composition of the considered abattoir effluents Item Soluble solids pH Total solids Total volatile solids Fats (Soxleth) Alkalinity (as CaCO3) COD
where xa and xd are algebraic and dynamic variables, respectively; u represents the input vector, y the process outputs; g is a set of linear algebraic equations, f a set of nonlinear differential equations and h output functions depending on dynamic variables. The different symbols are defined as follows: HS non ionized acetic acid, S- ionized acetic acid, CO2d dissolved carbon dioxide, B bicarbonate, H+ ionized hydrogen, IC inorganic carbon, Z the total of cations, S1in the fast degradable substrate input, S2in the slow degradable substrate input, ICin the inorganic carbon input, Zin the input cations, D the dilution rate, QCH4 methane flow rate and QCO2 carbon dioxide flow rate. For a more details about this model, the reader is referred to the respective references (Carlos-Hernandez et al., 2009). The effect of pH is included on the model by using Haldane growth rates as a function of HS which is directly influenced by this parameter. Besides, Haldane equation allows saturation and inhibition to be considered by means of constants Ks and Ki, respectively. The growth rate for X2 is calculated as:
Value 33.5 % 8.0-8.5 5166 mg L-1 3387 mg L-1 1057 mg L-1 1791 mg L-1 5945 mg L-1
µ2 =
2.3 Experimental setup The experimental set up is described as follows: 4.5 L of wastewater and 500 mL of zeolite colonized by anaerobic bacteria are filled in a 7 L glass reactor, with an initial COD
µ 2 max HS K s 2 + HS + HS
(2) 2
K i2
The validation of the mathematical model is done from experimental data (obtained from the experimental setup previously described) by using the model method (Richalet et al., 1971). The obtained results are presented in Fig. 1; biogas and substrate are considered for this validation since they are the measured variables in the experiments. The solid lines
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correspond to measured data for biogas production and COD transformation which is named as S2.
bioprocesses (BlueSens, 2009). However, substrate and biomass measures are more restrictive. The existing biomass sensors are quite expensive, and are designed from the biological viewpoint (based on capacitance or turbidity properties); hence, they are not reliable for control purposes. Furthermore, substrate measure is done off-line by chemical analysis, which requires at least two hours. State observers are an interesting alternative in order to deal with this situation. 3.1 Observer for biomass and substrate estimation
Fig. 1. Experimental validation of a model for methanogenesis in an anaerobic digestion process. It can be seen that the simulated graphics are close to the real data. Biogas presents a small error at the final stage of simulation, which can be due to an error on the measure system. COD removal presents a larger error; possible reasons for this situation are the saturation and inhibition coefficient values. Besides, both errors (on biogas and on COD removal) can be induced by the identification method, which could require more experimental data in order to obtain a better approximation for the model parameters. On the other hand, only methanogenesis is selected for the analysis shown in this work because this stage presents interesting challenges: it is the most sensitive to variations on the operating conditions, it determines the global dynamics of the process, the process stability is strongly linked to this stage, and finally, it is the main responsible for methane production. After this first parameter identification, other stages and more complete models such as the ADM1 can be considered. After that, the model experimentally validated can be used as a platform for numerical simulations of the anaerobic wastewater treatment. In the present paper, this model is used to evaluate the performance of the proposed neural observer. 3. NEURAL OBSERVER DEVELOPMENT Methanogenesis is very sensitive to variations on substrate concentration; biomass increase can be stopped by an excessive substrate production in the previous stages. Depending on the amplitude and duration of these variations on substrate concentration, the environment can be acidified and biomass growth could be inhibited; hence, the substrate degradation and the methane production can be blocked. Methane production, biomass growth and substrate degradation are good indicators of the biological activity inside the reactor. These variables can be used for monitoring the process and to design control strategies. Sensors have been developed in order to measure methane production in
An artificial neural network (NN) consists of a finite number of neurons (structural element), which are interconnected to each other; they are inspired from biological neural networks. Recurrent NN have at least one feedback loop, which improves the learning capability and performance of the network (Haykin, 1999). This structure also offers a better suited tool to model and control nonlinear systems (Poznyak et al., 2001). Recurrent high order neural networks (RHONN) are a generalization of the first-order Hopfield networks (Rovithakis and Chistodoulou, 2000). The observer developed in this paper uses a RHONN trained with an extended Kalman filter, it is structured as displayed on Fig. 2 and is based on the one proposed in Sanchez et al., (2008).
Fig. 2. Neural observer scheme. where k is a real number representing a time sample, x ∈ Rn is the state vector, u ∈ Rm the input vector, y ∈ Rp the output vector, d ∈ Rn a disturbance vector, e the output error and F (,) a smooth vector field. The proposed recurrent high order neural observer (RHONO) is intended to estimate: methanogenic biomass (X2), slowly degradable substrate (S2) and inorganic carbon (IC), which are variables of the methanogenesis stage. The neural network is trained with an extended Kalman filter (EKF), which provides an efficient computational solution to estimate the state of a non-linear dynamic system with additive state and output white noises (Song and Grizzle, 1995). For KF-based neural network training, the network weights become the states to be estimated. The error between the neural network output and the measured plant output can be considered as additive white noise. The training goal is to find the optimal weight values, which minimize the prediction error.
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The RHONO structure is composed configuration as described by (3)-(5):
(
)
(
(
)
Xˆ 2 (k + 1) = w11 S Xˆ 2 (k ) + w12 S 2 Xˆ 2 ( k ) + w13 S ICˆ (k )
(
of
a
parallel
In this section, a methodology to tune the RHONO is proposed.
)
)
+ w14 S 2 Xˆ 2 (k ) Din (k ) + L1e(k )
(
)
(
a). The covariance matrices are initialized as diagonals, verifying the next inequality:
)
( ) +w S ( ) ( ) ˆ ˆ ˆ IC (k + 1) = w S ( IC (k ) ) + w S ( IC (k ) ) + w S ( Xˆ ( k ) ) + w S ( ICˆ ( k ) ) D (k ) + w S ( ICˆ ( k ) ) IC ( k ) + L e( k ) Sˆ2 (k + 1) = w21 S Sˆ2 (k ) + w22 S 2 Sˆ2 (k ) + w23 S ICˆ ( k ) 2
24
3.2. Observer tuning methodology
Sˆ2 (k ) Din (k ) + w25 S 2 Sˆ2 (k ) S 2in ( k ) + L2 e(k )
Pi (0) > Ri (0) > Qi (0)
(10)
2
31
32
33
2
2
2
34
in
35
in
3
This condition implies that a priori knowledge is not required to initialize the vector weights (Haykin, 2001). In fact, higher entries in Pi(0) correspond to a higher uncertainty in the a priori knowledge. It is advisable to set Pi(0) inside the range 100-1000, and so on for the other covariance matrices on (7). In this way, the covariance matrices for the Kalman filter are initialized as diagonals, with nonzero elements:
(3)
with the output given as:
YˆCH 4 = R1 R2 µˆ 2 Xˆ 2
(4)
YˆCO 2 = λˆR2 R3 µˆ 2 Xˆ 2
(5)
P1 (0) = P2 (0) = P3 (0) = 1000
It is assumed that pH, methane and carbon dioxide are measured, as well as the inputs. Besides, in order to obtain the neural network weights (w), the EKF training is performed on-line as follows: wi (k + 1) = wi (k ) + η i K i (k )ei (k ) K i (k ) = Pi ( k ) H i (k ) M i (k )
Q1 (0) = Q2 (0) = Q3 (0) = 0.1
b). Since the neural network outputs do not depend directly on the weight vector, the matrix H is initialized as Hi(0)=0.
i = 1,..., n
with:
c). It is assumed that weights values are initialized to small random values with zero mean value and normal distribution.
M i (k ) = [ Ri (k ) + H iT (k ) Pi (k ) H i (k )] −1
(7)
ei (k ) = y (k ) − yˆ (k )
where ei(k)∈Rp is the observation error, Pi(k)∈RLixLi is the prediction error covariance matrix at step k, wi(k)∈RLi is the weight (state) vector, Li is the respective number of neural network weights, y(k)∈Rp is the plant process, yˆ ∈Rp is the NN output, ηi is the learning rate, Ki(k)∈RLixp is Kalman gain matrix, Qi(k)∈RLixLi is the NN estimation noise covariance matrix, Ri(k)∈Rpxp is the error noise covariance, Hi(k)∈RLixp is a matrix computed as:
d). The learning rate determines the magnitude of the correction term applied to each neuron weight; it usually requires small values to achieve good training performance. Then, it is bounded as 0 < η < 1. e). The observer gain (L), which is similar to a Luenberger observer gain, is set by trial and error; unfortunately there is a shortage of clear scientific basis to define it. However, it is bounded as 0 < L < 0.1 for a good performance on the basis of training experience. 4. RESULTS AND DISCUSION
T
(8)
A set of simulations close to real conditions and considering the model experimentally validated are performed in order to evaluate the estimations of the proposed observer. This offline validation of the observer is a first stage; on-line validation is currently in progress.
where i=1,…,n and j=1,…,Li. The hyperbolic tangent is used as the activation function:
S ( x) = α tanh( β x)
(11)
An arbitrary scaling can be applied to Pi(0), Ri(0), and Qi(0) without altering the evolution of the weight vector.
(6)
Pi (k + 1) = Pi ( k ) − K i (k ) H iT (k ) Pi (k ) + Qi (k )
∂yˆ (k ) H ij (k ) = ∂wij (k )
R1 (0) = R2 (0) = R3 (0) = 1
(9)
with α = β = 1 and x the respective state to be estimated (biomass, substrate and inorganic carbon). This function is used because the antisymmetric functions allow the neural network to learn the respective dynamics in a faster way in comparison with other activation functions (Sanchez and Alanis, 2006). In addition, the hyperbolic tangent derivative is easy to obtain.
The figure 3 shows the neural observer performance considering a step on the input substrate S2in, which corresponds to 100% increase from the initial value; the step is incepted at t = 300 h and stopped at t = 600 h. The observer is initialized at random values in order to evaluate the convergence: which is clearly illustrated at the beginning of the simulation; after that, the estimated state variables are very close to the corresponding variables from the process model. Specifically, biomass X2 is estimated adequately by the proposed observer. Besides, S2 is well estimated except at
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10.5
x 10
6.95
11.5
6.8
9.5
x 10
-3
X System 2
X Estimated 2
X2 (AU)
0.15
Din, which amplitudes correspond to 100%, 100% and 20% of their initial value respectively. The step in incepted at t=300h and stopped at t=600h for each input. The observer behaviour is illustrated on Fig 5.
pH
the maximum and minimum values, where a small transitory error is present. This situation could be due to the simple structure of the observer. On the other hand, the disturbance affects severely the estimation of IC; it is possible that the estimation error is due to the complexity of the IC dynamics and to the single structure of the observer, as for the case of S2; however, the estimation is well done in steady state. -3
6.65
7.5
X 2 System 2
0.12
9 X2 (AU)
S2in (mol/L)
X Estimated
0.09
6.5 0
500 1000 Time (Hours)
5.5 0
1500
7.5
0.029
3.6
x 10
IC System IC Estimated 1500
0.024
2.7
500 1000 Time (Hours)
x 10
-3
0.022
0.02
0.018 0
500 1000 Time (Hours)
2
S Estimated
0.021
1.4
2
2.1
0.017 0
0.9 0
1500
500 1000 Time (Hours)
1500
0.3 0
500 1000 Time (Hours)
1500
1.5
500 1000 Time (Hours)
1500
Figure 5. Observer performance considering a step on the inputs S2in, Din and ICin.
A white noise is added to biogas production in order to evaluate the effect of output measurement noise in the variables estimation. The obtained results are shown in Figure 4. x 10
S System 2.5
S 2 Estimated
Fig. 3. Observer performance considering a step on the input substrate S2in.
10
0.025
S System
S 2 (mol/L)
IC (mol/L)
IC System IC Estimated
1500
2
1500
S2 (mol/L)
500 1000 Time (Hours)
6 0
IC (mol/L)
0.06 0
500 1000 Time (Hours) -3
-3
10.5
x 10
The pH variation due to disturbances on the inputs is shown at the top of Figure 5. Here again, methanogenesis variables are adequately estimated. The simple structure of the proposed observer can be the reason for the negligible error in states estimation. Thus, the proposed observer is an interesting approach in order to estimate those important variables of the abattoir wastewater treatment process considered in this paper.
-3
X Estimated
X2 (AU)
QCH4 (mol/h)
2
5. CONCLUSIONS AND PERSPECTIVES
X System 8.8
7.6
6.4 0
500 1000 Time (Hours)
2
9
7.5
6 0
1500
0.0245
2.7
x 10
500 1000 Time (Hours)
1500
-3
S Estimated
S2 (mol/L)
IC (mol/L)
2
0.022
0.0195
2.2
S System 2
1.6
IC Estimated IC System 0.017 0
500 1000 Time (Hours)
1500
1 0
500 1000 Time (Hours)
1500
Figure 4. Observer performance considering noise on the biogas production. As can be seen in Fig. 4, after the observer convergence, the state estimation is well done by the proposed observer for the methanogenesis variables. The biomass X2 is adequately estimated as well as the substrate S2, which presents an evident error at the maximum and minimum values. Inorganic carbon IC is the most affected variable due to the noise on the output; despite this situation, it is well estimated; it could be due to the fast and complex dynamic of inorganic carbon. A last series of simulations is performed in order to verify the variables estimation in face of variations on pH. A variation on pH is obtained through applying a step in S2in, ICin and
A RHONO, using hyperbolic tangent activation functions, and trained with an EFK, is proposed in this paper. The observer is used to estimate the main state variables of the methanogenesis stage in an abattoir wastewater treatment process. Simulation results considering a model experimentally validated illustrate the effectiveness of the observer in face of disturbances. The variables (substrate, biomass) are estimated from methane and dioxide flow rates, which are commonly measured in this process. Estimation of inorganic carbon is more difficult due to this variable complex dynamic behavior, and also due to the simple structure of the proposed observer. However, this does not implies major problems because inorganic carbon could be measured in this kind of processes. Since one of the limiting factors for the implementation of the control strategies is the lack of on-line sensors, the neural observer proposed in this paper presents an interesting alternative to be applied; thus, research efforts are proceeding in order to implement the neural observer in real-time. Other future works are in perspective in order to improve the observer performances as: different kind of structures could be tested to better estimate more complex dynamics of the process; and a dynamic learning rate could enhance the learning capability of the neural net in face of variations in the operating conditions.
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REFERENCES Alcaraz-Gonzalez, V., Harmand J., Rapaport A., Steyer J.P., Gonzalez-Alvarez V., and Pelayo-Ortiz, C. (2004). Software sensors for highly uncertain WWTPs: A new approach based on interval observers. Water Research, 36(10), 2515–2524. Alvarez R., Liden G. (2008). Semi-continuous co-digestion of solid slaughterhouse waste, manure, and fruit and vegetable waste. Renewable Energy, 33 (4), 726-734. Arvanitoyannis, I.S. and D. Ladas (2008). Meat waste treatment methods and potential uses. Int. J. Food Sci. Technol. 43, 543-559. Ascencio, P., Sbarbaro D. and Feyo de Azevedo S. (2004). An adaptive fuzzy hybrid state observer for bioprocesses. IEEE Transactions on Fuzzy Systems, 12(5), 641–651. Bastin, G., and Dochain, D. (1990). On-line estimation and adaptive control of bioreactors. Amsterdam, Elsevier Science Publications. Batstone D.J, Keller J., Newell R.B., Newland M. (2000) Modelling anaerobic degradation of complex wastewater. I: model development. Bioresource Technology, 75 (1), 67-74. Batstone D.J, Keller J., Newell R.B., Newland M. (2000) Modelling anaerobic degradation of complex wastewater. II: parameter estimation and validation using slaughterhouse effluent. Bioresource Technology, 75 (1), 75-85. Blues Sens Company, 2009. Technical information from the web site http://www.bluesens.de, visited on November 22th 2009. Carlos-Hernandez, S., Sanchez, E.N., Beteau, J.F. (2009). Fuzzy observers for anaerobic WWTP: Development and implementation. Control Engineerig Practice, 17, 690– 702. Chachuat, B., and Bernard, O. (2005). Probabilistic observers for a class of uncertain biological processes. International Journal of Robust and Nonlinear Control, 1, 1–16. Deza, F., Bossanne D., Busvelle E., Gauthier J.P., and Rakotopara D. (1993). Exponential observers for nonlinear systems. IEEE Transactions on Automatic Control, 38(3), 482–484. Gouze, J.L., Rapaport A., and Hadj-Sadok Z. (2000). Interval observers for uncertain biological systems. Ecological Modelling, 133(1–2), 45–56. Haykin, S. (1999). Neural Networks: A comprehensive Foundation, 2nd edn. Prentice Hall, New Jersey, USA. Haykin, S. (2001). Kalman Filtering and Neural Networks. John Wiley and Sons, N.Y., USA. Hejnfelt A., Angelidaki I. Anaerobic digestion of slaughterhouse by-products (2009). Biomass and Bioenergy, 33 (8), 1046-1054. Lardon, L., Puñal A. and Steyer J.P. (2004). On-line diagnosis and uncertainty management using evidence theory experimental illustration to anaerobic digestion. Journal of Process Control, 14(7), 747–763. Lemesle, V. and Gouze J.L. (2005). Hybrid bounded error observers for uncertain bioreactor models. Bioprocess Engineering, 27, 311–318.
Lokshina L.Y., Vavilin V.A., Salminen E., Rintala J. (200). Modeling of anaerobic degradation of solid slaughterhouse waste. Applied Biochemistry and Biotechnology, 109 (1), 15-32. Mittal, G.S. (2006). Treatment of wastewater from abattoirs before land Application – a review. Bioresour. Technol. 97, 1119-1135. Muller, A., Marsilli-Libelli S., Aivasidis A., Lloyd T., Kroner S. and Wandrey, C. (1997). Fuzzy control of disturbances in a wastewater treatment process. Water Research, 31(12) 3157–3167. Poznyak, A.S., Sanchez E.N. and Yu W. (2001) Differential Neural Networks for Robust Nonlinear Control, World Scientific Publishing Co. Singapore. Procópio Pontes P., de Lemos Chernicharo C.A., Rocha Porto, M.T. (2002), Estudo comparativo de metodologias para determinação de proteínas em esgotos brutos e tratados, XXVIII Congreso Interamericano de Ingeniería Sanitaria y Ambiental, Cancún, México. Ricalde, L.J. and Sanchez E.N. (2005). Inverse optimal nonlinear high order recurrent neural observer, International Joint Conference on Neural Networks, Montreal, Canada. Richalet, J., Rault, A., Pouliquen, R., & Naslin, P. (1971). Process identification by the model method. Paris: Gordon and Preach. Roos, K.F., (1991). Profitable Alternatives for Regulatory Impacts on Livestock Waste Management, in National Livestock, Poultry and Aquacultural Waste Management National Workshop, (Kansas, MI, USDA Extension Service). Rovithakis, G.A. and Chistodoulou, M.A. (2000): Adaptive Control with Recurrent High-Order Neural Networks. Springer Verlag, Berlin, Germany. Salminen, E., Rintala, J. (2002). Anaerobic digestion of organic solid poultry slaughterhouse waste – a review. Bioresource Technology, 83 (1), 13-26. Sanchez, E.N., Alanis, A.Y. (2006). Neural Networks: Fundamental Concepts and Applications to Automatic Control, in Spanish. Pearson Education, Madrid, Spain. Sanchez, E.N., Alanis, A.Y., and Chen, G. (2008). Discrete Time High Order Neural Control Trained with Kalman Filtering. Springer-Verlag, Germany. Smith, H.L. (1996). Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. Journal of the American Mathematical Society, 33(2), 203–209. Song, Y. and Grizzle J.W. (1995). The extended Kalman filter as a local asymptotic observer for discrete-time nonlinear systems. Journal of Mathematical Systems, Estimation and Control. 5 (1), 59-78. Urrego-Patarroyo, D., Sanchez E.N., Carlos-Hernandez S. and Beteau J.F. (2008). Recurrent Neural Networks Observer for Anaerobic Processes, XIII Latin-american Congress of Automatic Control, Merida, Venezuela. Wimberger, D. and Verde C. (2008). Fault diagnosticability for anaerobic batch wastewater treatment process. Control Engineering Practice, 16 (11), 1344–1353.
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Neural Observer for an Abattoir Wastewater Treatment Process S. Carlos-Hernandez*, E.N. Sanchez** and R. Belmonte-Izquierdo**, L. Diaz-Jimenez* * Cinvestav Saltillo,Km 13, Carr. Saltillo-Mty 25900 Ramos Arizpe, México. (Tel:52-844-4389612; e-mail: [email protected], [email protected]). ** Cinvestav Guadalajara, Apdo Postal 31-438, Plaza La Luna,45090 Guadalajara, Mexico (email:[email protected], [email protected])
Abstract: The paper deals with the development of a Recurrent High Order Neural Observer for an abattoir wastewater treatment by anaerobic digestion. The neural network uses the hyperbolic tangent as activation function and the learning algorithm is based on an extended Kalman filter. This observer is designed to estimate the variables of the methanogenesis stage (biomass and substrate) in a completely stirred tank reactor. A prototype treating real abattoir wastewater is implemented in order to obtain an experimental model, which is used to validate the proposed observer. Keywords: bioprocess, anaerobic digestion, neural observer, wastewater treatment.
1. INTRODUCTION Animal sacrifice in abattoirs produces large quantities of wastes and effluents containing high organic load. In many cases, a lot of them are directly rejected to the ecosystem without an adequate treatment process (Mittal, 2006; Arvanitoyannis and Ladas, 2008). Besides, abattoirs operation requires services as electricity and big quantities of water. Then, it is necessary to implement strategies in order to improve the abattoirs operation and to avoid, or at least to minimize, environmental pollution. Anaerobic digestion is one of the most adequate processes to treat effluents with high contents of organic wastes. The complex molecules are progressively transformed by different bacteria populations; besides to the treated water, a biogas mainly composed of methane and carbon dioxide is obtained. The products of anaerobic digestion have added value, since they can be used to offset treatment costs (Ross, 1991): i.e, reusing and/or recycling treated water and additionally employing biogas for energy generation. However, this bioprocess is sensitive to variations on the operating conditions, such as pH, temperature, overloads, etc. In addition, there exist variables and parameters hard to measure due to economical or technical constraints. Then, estimation and control strategies are required in order to guarantee adequate performances. Anaerobic digestion involves hardly measurable or immeasurable variables which are necessary for supervision and control. Observers and softsensors are an interesting alternative in order to estimate these kinds of variables. In the specialized literature, observers have been already reported; for example, asymptotical observer, proposed by Bastin and Dochain (1990), interval observers (Smith, 1996; Gouze, Rapaport and Hadj-Zadok, 2000, Alcaraz-Gonzalez et al. (2004)), and other approaches (Deza et al., 1993; Lemesle 978-3-902661-70-8/10/$20.00 © 2010 IFAC
and Gouze, 2005; Chachuat and Bernard, 2005). Some of them are developed focusing on diagnosis and fault detection, such as Lardon, Punal and Steyer (2004), Wimberger & Verde (2008). Fuzzy algorithms have been also considered as alternatives to design observers and controllers for bioprocess (Muller et al., 1997; Ascencio, Sbarbaro and Feyo de Azevedo, 2004, Carlos-Hernandez et al, 2009). Complete knowledge of the system model is usually assumed in order to design nonlinear state estimators; nevertheless this is not always possible. Moreover, in some cases special nonlinear transformations are proposed, which are not often robust in presence of uncertainties. An interesting approach for avoiding the associated problem of model-based state observers is the neural network approach. Neural observers require feasible measures and a training algorithm in order to learn the process dynamics; in this case, the model knowledge is not strictly necessary (Pozniak et al., 2001; Ricalde and Sanchez, 2005; Urrego-Patarroyo et al., 2008). Also, different applications of anaerobic digestion to abattoirs have been reported. In example, some researches focus on model development of anaerobic degradation of slaughterhouse effluents (Angelidaki et al., 2000a, b; Lokshina et al., 2003), anaerobic digestion of slaughterhouse byproducts in batch and semi-continuous processes (Hejnfelt and Angelidaki, 2009; Alvarez and Liden, 2008), and other subjects (Salminem and Rintala, 2002). In this paper, a Recurrent High Order Neural Observer (RHONO) is proposed in order to estimate biomass and substrate in an anaerobic process for abattoir effluents treatment. The observer structure is based on hyperbolic tangent as activation function and is trained using an extended Kalman filter. The main advantage of the RHONO is a high performance and independence of the process model. The proposed observer is validated in a model developed from a prototype, which treats real abattoir wastewater. This prototype process is developed in a
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completely stirred tank reactor with biomass fixed in a solid support. 2. COMPONENTS AND METHODS 2.1. Bacterial support The main advantages of the bacteria immobilization are i) high volumetric reaction rates, ii) high bacteria concentration inside the reactor, iii) more possibilities to regenerate the biocatalytic activity of immobilized cell structures, and iv) the ability to conduct continuous operations at high dilution rate without washout phenomena. In this work, a Mexican natural zeolite is used. Previous works were developed in order to characterize this zeolite and to determine its potential as bacterial support. Table 1 shows the main properties of the used natural zeolite.
of 5800 mg L-1 and an initial pH of 7.2. Performances of the wastewater treatment process are evaluated by developing batch tests, with 15 days duration for each one. Different tests are performed with similar operating conditions; the obtained results are used for parametric identification of a methanogenesis stage mathematical model. COD, biogas and pH are measured, to calculate these parameters. The respective identification is done with the model method; thus a comparison between real data and theoretical data is performed using Matlab-Simulink. The obtained model is composed of algebraic equations to represent acid-base equilibria and conservation of materials, and differential equations to model the process dynamics. Biogas (methane and carbon dioxide) is considered as the process output.
g ( x a , xd ) = 0 x& d = f ( x a , x d , u ) y = h( x d )
Table 1. Properties of the mexican natural zeolite used as bacterial support Property Specific surface area Apparent density Microporosity
Specification 28 m2 g-1 0.818 g mL-1 0.051 cm3 g-1
(1)
with:
[
xa = HS
S−
xd = [X 1
S1
u = [S1in
S 2in
CO2 d X2
B
S2
ICin
IC
Z in
H+
]
Z] D]
y = [Q CH 4 QCO2 ]
2.2 Abattoir effluents The samples for this work are collected from an abattoir situated at Saltillo, Coahuila, Mexico. A characterization, after separation of solid materials is done and the respective results are displayed in Table 2. There are reported results concluding organic nitrogen is included in the COD (Procopio Pontes et al., 2002). The inoculum is obtained from a brewery wastewater treatment plant. Then a preliminary stage is required for the bacteria adaptation to the abattoir substrate. Around two months were required in order to form the biofilm in the natural zeolite and one month to adapt the microorganisms to the abattoir effluents. Table 2. Average composition of the considered abattoir effluents Item Soluble solids pH Total solids Total volatile solids Fats (Soxleth) Alkalinity (as CaCO3) COD
where xa and xd are algebraic and dynamic variables, respectively; u represents the input vector, y the process outputs; g is a set of linear algebraic equations, f a set of nonlinear differential equations and h output functions depending on dynamic variables. The different symbols are defined as follows: HS non ionized acetic acid, S- ionized acetic acid, CO2d dissolved carbon dioxide, B bicarbonate, H+ ionized hydrogen, IC inorganic carbon, Z the total of cations, S1in the fast degradable substrate input, S2in the slow degradable substrate input, ICin the inorganic carbon input, Zin the input cations, D the dilution rate, QCH4 methane flow rate and QCO2 carbon dioxide flow rate. For a more details about this model, the reader is referred to the respective references (Carlos-Hernandez et al., 2009). The effect of pH is included on the model by using Haldane growth rates as a function of HS which is directly influenced by this parameter. Besides, Haldane equation allows saturation and inhibition to be considered by means of constants Ks and Ki, respectively. The growth rate for X2 is calculated as:
Value 33.5 % 8.0-8.5 5166 mg L-1 3387 mg L-1 1057 mg L-1 1791 mg L-1 5945 mg L-1
µ2 =
2.3 Experimental setup The experimental set up is described as follows: 4.5 L of wastewater and 500 mL of zeolite colonized by anaerobic bacteria are filled in a 7 L glass reactor, with an initial COD
µ 2 max HS K s 2 + HS + HS
(2) 2
K i2
The validation of the mathematical model is done from experimental data (obtained from the experimental setup previously described) by using the model method (Richalet et al., 1971). The obtained results are presented in Fig. 1; biogas and substrate are considered for this validation since they are the measured variables in the experiments. The solid lines
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correspond to measured data for biogas production and COD transformation which is named as S2.
bioprocesses (BlueSens, 2009). However, substrate and biomass measures are more restrictive. The existing biomass sensors are quite expensive, and are designed from the biological viewpoint (based on capacitance or turbidity properties); hence, they are not reliable for control purposes. Furthermore, substrate measure is done off-line by chemical analysis, which requires at least two hours. State observers are an interesting alternative in order to deal with this situation. 3.1 Observer for biomass and substrate estimation
Fig. 1. Experimental validation of a model for methanogenesis in an anaerobic digestion process. It can be seen that the simulated graphics are close to the real data. Biogas presents a small error at the final stage of simulation, which can be due to an error on the measure system. COD removal presents a larger error; possible reasons for this situation are the saturation and inhibition coefficient values. Besides, both errors (on biogas and on COD removal) can be induced by the identification method, which could require more experimental data in order to obtain a better approximation for the model parameters. On the other hand, only methanogenesis is selected for the analysis shown in this work because this stage presents interesting challenges: it is the most sensitive to variations on the operating conditions, it determines the global dynamics of the process, the process stability is strongly linked to this stage, and finally, it is the main responsible for methane production. After this first parameter identification, other stages and more complete models such as the ADM1 can be considered. After that, the model experimentally validated can be used as a platform for numerical simulations of the anaerobic wastewater treatment. In the present paper, this model is used to evaluate the performance of the proposed neural observer. 3. NEURAL OBSERVER DEVELOPMENT Methanogenesis is very sensitive to variations on substrate concentration; biomass increase can be stopped by an excessive substrate production in the previous stages. Depending on the amplitude and duration of these variations on substrate concentration, the environment can be acidified and biomass growth could be inhibited; hence, the substrate degradation and the methane production can be blocked. Methane production, biomass growth and substrate degradation are good indicators of the biological activity inside the reactor. These variables can be used for monitoring the process and to design control strategies. Sensors have been developed in order to measure methane production in
An artificial neural network (NN) consists of a finite number of neurons (structural element), which are interconnected to each other; they are inspired from biological neural networks. Recurrent NN have at least one feedback loop, which improves the learning capability and performance of the network (Haykin, 1999). This structure also offers a better suited tool to model and control nonlinear systems (Poznyak et al., 2001). Recurrent high order neural networks (RHONN) are a generalization of the first-order Hopfield networks (Rovithakis and Chistodoulou, 2000). The observer developed in this paper uses a RHONN trained with an extended Kalman filter, it is structured as displayed on Fig. 2 and is based on the one proposed in Sanchez et al., (2008).
Fig. 2. Neural observer scheme. where k is a real number representing a time sample, x ∈ Rn is the state vector, u ∈ Rm the input vector, y ∈ Rp the output vector, d ∈ Rn a disturbance vector, e the output error and F (,) a smooth vector field. The proposed recurrent high order neural observer (RHONO) is intended to estimate: methanogenic biomass (X2), slowly degradable substrate (S2) and inorganic carbon (IC), which are variables of the methanogenesis stage. The neural network is trained with an extended Kalman filter (EKF), which provides an efficient computational solution to estimate the state of a non-linear dynamic system with additive state and output white noises (Song and Grizzle, 1995). For KF-based neural network training, the network weights become the states to be estimated. The error between the neural network output and the measured plant output can be considered as additive white noise. The training goal is to find the optimal weight values, which minimize the prediction error.
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The RHONO structure is composed configuration as described by (3)-(5):
(
)
(
(
)
Xˆ 2 (k + 1) = w11 S Xˆ 2 (k ) + w12 S 2 Xˆ 2 ( k ) + w13 S ICˆ (k )
(
of
a
parallel
In this section, a methodology to tune the RHONO is proposed.
)
)
+ w14 S 2 Xˆ 2 (k ) Din (k ) + L1e(k )
(
)
(
a). The covariance matrices are initialized as diagonals, verifying the next inequality:
)
( ) +w S ( ) ( ) ˆ ˆ ˆ IC (k + 1) = w S ( IC (k ) ) + w S ( IC (k ) ) + w S ( Xˆ ( k ) ) + w S ( ICˆ ( k ) ) D (k ) + w S ( ICˆ ( k ) ) IC ( k ) + L e( k ) Sˆ2 (k + 1) = w21 S Sˆ2 (k ) + w22 S 2 Sˆ2 (k ) + w23 S ICˆ ( k ) 2
24
3.2. Observer tuning methodology
Sˆ2 (k ) Din (k ) + w25 S 2 Sˆ2 (k ) S 2in ( k ) + L2 e(k )
Pi (0) > Ri (0) > Qi (0)
(10)
2
31
32
33
2
2
2
34
in
35
in
3
This condition implies that a priori knowledge is not required to initialize the vector weights (Haykin, 2001). In fact, higher entries in Pi(0) correspond to a higher uncertainty in the a priori knowledge. It is advisable to set Pi(0) inside the range 100-1000, and so on for the other covariance matrices on (7). In this way, the covariance matrices for the Kalman filter are initialized as diagonals, with nonzero elements:
(3)
with the output given as:
YˆCH 4 = R1 R2 µˆ 2 Xˆ 2
(4)
YˆCO 2 = λˆR2 R3 µˆ 2 Xˆ 2
(5)
P1 (0) = P2 (0) = P3 (0) = 1000
It is assumed that pH, methane and carbon dioxide are measured, as well as the inputs. Besides, in order to obtain the neural network weights (w), the EKF training is performed on-line as follows: wi (k + 1) = wi (k ) + η i K i (k )ei (k ) K i (k ) = Pi ( k ) H i (k ) M i (k )
Q1 (0) = Q2 (0) = Q3 (0) = 0.1
b). Since the neural network outputs do not depend directly on the weight vector, the matrix H is initialized as Hi(0)=0.
i = 1,..., n
with:
c). It is assumed that weights values are initialized to small random values with zero mean value and normal distribution.
M i (k ) = [ Ri (k ) + H iT (k ) Pi (k ) H i (k )] −1
(7)
ei (k ) = y (k ) − yˆ (k )
where ei(k)∈Rp is the observation error, Pi(k)∈RLixLi is the prediction error covariance matrix at step k, wi(k)∈RLi is the weight (state) vector, Li is the respective number of neural network weights, y(k)∈Rp is the plant process, yˆ ∈Rp is the NN output, ηi is the learning rate, Ki(k)∈RLixp is Kalman gain matrix, Qi(k)∈RLixLi is the NN estimation noise covariance matrix, Ri(k)∈Rpxp is the error noise covariance, Hi(k)∈RLixp is a matrix computed as:
d). The learning rate determines the magnitude of the correction term applied to each neuron weight; it usually requires small values to achieve good training performance. Then, it is bounded as 0 < η < 1. e). The observer gain (L), which is similar to a Luenberger observer gain, is set by trial and error; unfortunately there is a shortage of clear scientific basis to define it. However, it is bounded as 0 < L < 0.1 for a good performance on the basis of training experience. 4. RESULTS AND DISCUSION
T
(8)
A set of simulations close to real conditions and considering the model experimentally validated are performed in order to evaluate the estimations of the proposed observer. This offline validation of the observer is a first stage; on-line validation is currently in progress.
where i=1,…,n and j=1,…,Li. The hyperbolic tangent is used as the activation function:
S ( x) = α tanh( β x)
(11)
An arbitrary scaling can be applied to Pi(0), Ri(0), and Qi(0) without altering the evolution of the weight vector.
(6)
Pi (k + 1) = Pi ( k ) − K i (k ) H iT (k ) Pi (k ) + Qi (k )
∂yˆ (k ) H ij (k ) = ∂wij (k )
R1 (0) = R2 (0) = R3 (0) = 1
(9)
with α = β = 1 and x the respective state to be estimated (biomass, substrate and inorganic carbon). This function is used because the antisymmetric functions allow the neural network to learn the respective dynamics in a faster way in comparison with other activation functions (Sanchez and Alanis, 2006). In addition, the hyperbolic tangent derivative is easy to obtain.
The figure 3 shows the neural observer performance considering a step on the input substrate S2in, which corresponds to 100% increase from the initial value; the step is incepted at t = 300 h and stopped at t = 600 h. The observer is initialized at random values in order to evaluate the convergence: which is clearly illustrated at the beginning of the simulation; after that, the estimated state variables are very close to the corresponding variables from the process model. Specifically, biomass X2 is estimated adequately by the proposed observer. Besides, S2 is well estimated except at
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10.5
x 10
6.95
11.5
6.8
9.5
x 10
-3
X System 2
X Estimated 2
X2 (AU)
0.15
Din, which amplitudes correspond to 100%, 100% and 20% of their initial value respectively. The step in incepted at t=300h and stopped at t=600h for each input. The observer behaviour is illustrated on Fig 5.
pH
the maximum and minimum values, where a small transitory error is present. This situation could be due to the simple structure of the observer. On the other hand, the disturbance affects severely the estimation of IC; it is possible that the estimation error is due to the complexity of the IC dynamics and to the single structure of the observer, as for the case of S2; however, the estimation is well done in steady state. -3
6.65
7.5
X 2 System 2
0.12
9 X2 (AU)
S2in (mol/L)
X Estimated
0.09
6.5 0
500 1000 Time (Hours)
5.5 0
1500
7.5
0.029
3.6
x 10
IC System IC Estimated 1500
0.024
2.7
500 1000 Time (Hours)
x 10
-3
0.022
0.02
0.018 0
500 1000 Time (Hours)
2
S Estimated
0.021
1.4
2
2.1
0.017 0
0.9 0
1500
500 1000 Time (Hours)
1500
0.3 0
500 1000 Time (Hours)
1500
1.5
500 1000 Time (Hours)
1500
Figure 5. Observer performance considering a step on the inputs S2in, Din and ICin.
A white noise is added to biogas production in order to evaluate the effect of output measurement noise in the variables estimation. The obtained results are shown in Figure 4. x 10
S System 2.5
S 2 Estimated
Fig. 3. Observer performance considering a step on the input substrate S2in.
10
0.025
S System
S 2 (mol/L)
IC (mol/L)
IC System IC Estimated
1500
2
1500
S2 (mol/L)
500 1000 Time (Hours)
6 0
IC (mol/L)
0.06 0
500 1000 Time (Hours) -3
-3
10.5
x 10
The pH variation due to disturbances on the inputs is shown at the top of Figure 5. Here again, methanogenesis variables are adequately estimated. The simple structure of the proposed observer can be the reason for the negligible error in states estimation. Thus, the proposed observer is an interesting approach in order to estimate those important variables of the abattoir wastewater treatment process considered in this paper.
-3
X Estimated
X2 (AU)
QCH4 (mol/h)
2
5. CONCLUSIONS AND PERSPECTIVES
X System 8.8
7.6
6.4 0
500 1000 Time (Hours)
2
9
7.5
6 0
1500
0.0245
2.7
x 10
500 1000 Time (Hours)
1500
-3
S Estimated
S2 (mol/L)
IC (mol/L)
2
0.022
0.0195
2.2
S System 2
1.6
IC Estimated IC System 0.017 0
500 1000 Time (Hours)
1500
1 0
500 1000 Time (Hours)
1500
Figure 4. Observer performance considering noise on the biogas production. As can be seen in Fig. 4, after the observer convergence, the state estimation is well done by the proposed observer for the methanogenesis variables. The biomass X2 is adequately estimated as well as the substrate S2, which presents an evident error at the maximum and minimum values. Inorganic carbon IC is the most affected variable due to the noise on the output; despite this situation, it is well estimated; it could be due to the fast and complex dynamic of inorganic carbon. A last series of simulations is performed in order to verify the variables estimation in face of variations on pH. A variation on pH is obtained through applying a step in S2in, ICin and
A RHONO, using hyperbolic tangent activation functions, and trained with an EFK, is proposed in this paper. The observer is used to estimate the main state variables of the methanogenesis stage in an abattoir wastewater treatment process. Simulation results considering a model experimentally validated illustrate the effectiveness of the observer in face of disturbances. The variables (substrate, biomass) are estimated from methane and dioxide flow rates, which are commonly measured in this process. Estimation of inorganic carbon is more difficult due to this variable complex dynamic behavior, and also due to the simple structure of the proposed observer. However, this does not implies major problems because inorganic carbon could be measured in this kind of processes. Since one of the limiting factors for the implementation of the control strategies is the lack of on-line sensors, the neural observer proposed in this paper presents an interesting alternative to be applied; thus, research efforts are proceeding in order to implement the neural observer in real-time. Other future works are in perspective in order to improve the observer performances as: different kind of structures could be tested to better estimate more complex dynamics of the process; and a dynamic learning rate could enhance the learning capability of the neural net in face of variations in the operating conditions.
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