Nonlinear Autoregressive Exogenous modeling of a large anaerobic digester producing biogas from cattle waste

Bioresource Technology 170 (2014) 342–349

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Nonlinear Autoregressive Exogenous modeling of a large anaerobic digester producing biogas from cattle waste Anil K. Dhussa a, Surinder S. Sambi b, Shashi Kumar c, Sandeep Kumar c, Surendra Kumar c,⇑ a

Ministry of New and Renewable Energy, Govt. of India, Block-14, CGO Complex, Lodhi Road, New Delhi 110 003, India University School of Chemical Technology, Guru Gobind Singh Indraprastha University, Sector – 16 C, Dwarka, Delhi 110078, India c Department of Chemical Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India b

h i g h l i g h t s  Anaerobic digester yields dynamic behavior under frequent changes in feed.  An empirical approach utilizing ANN has been used.  NARX network has been used to model the dynamic behavior.  Predictions of biogas produced compare well with plant data within ±8% deviation.

a r t i c l e

i n f o

Article history: Received 24 May 2014 Received in revised form 21 July 2014 Accepted 22 July 2014 Available online 1 August 2014 Keywords: Biogas Artificial Neural Network NARX model Anaerobic digester Cattle waste treatment

a b s t r a c t In waste-to-energy plants, there is every likelihood of variations in the quantity and characteristics of the feed. Although intermediate storage tanks are used, but many times these are of inadequate capacity to dampen the variations. In such situations an anaerobic digester treating waste slurry operates under dynamic conditions. In this work a special type of dynamic Artificial Neural Network model, called Nonlinear Autoregressive Exogenous model, is used to model the dynamics of anaerobic digesters by using about one year data collected on the operating digesters. The developed model consists of two hidden layers each having 10 neurons, and uses 18 days delay. There are five neurons in input layer and one neuron in output layer for a day. Model predictions of biogas production rate are close to plant performance within ±8% deviation. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Anaerobic processes are one of the most attractive methods for the treatment of organic liquid effluents and organic solid wastes. The reason is obvious because it produces biogas which contains methane and carbon dioxide. Biogas is a renewable energy source. It can be used as a fuel and can be converted into electricity using biogas engine. Biogas can also be upgraded or enriched to contain more than 95% methane (also known as bio-methane), which can be used to produce chemicals or fed to natural gas grid to supplement its requirement. Due to these benefits, anaerobic digestion over a period of time has become a well-established technology for the treatment of liquid and solid organic wastes. At Haebowal (in Ludhiana, Punjab, India), Punjab Energy Development Agency (PEDA), Chandigarh established a waste-to-energy

⇑ Corresponding author. Tel.: +91 9897077460; fax: +91 1332273560. E-mail address: [email protected] (S. Kumar). http://dx.doi.org/10.1016/j.biortech.2014.07.078 0960-8524/Ó 2014 Elsevier Ltd. All rights reserved.

plant in October 2004, which utilizes 235 ton/day cattle dung (manure). Location of the plant was rightly chosen as there was a huge dairy complex nearby, producing more than 2000 ton/day of cattle dung/manure. This facility was created as one of the major initiatives of Ministry of New and Renewable Energy, Government of India, to set up waste-to-energy demonstration plants based upon different technologies under United Nations Development Programme – Global Environmental Facility (UNDP-GEF programme). This waste-to-energy (WTE) plant demonstrates BIMA (Biogas Induced Mixing Arrangement) digester technology, which is the patented technology of Entec, Austria. Initially the plant operated successfully, but with the passage of time plant faced shortage of raw material due to one or other reason such as prolonged rainy season, improper management of cattle dung collection from dairies by the contractor due to very early milking of cattle, and higher raw material cost insisted by the farmers. This resulted in short supply of cattle dung/manure varying in wide range between 110 and 235 ton/day. Due to frequent variation in operating conditions namely influent flow rate, dry

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matter (DM) and volatile solids (VS), BIMA digesters operate under unsteady state or dynamic conditions. Such a situation is referred to as shock loading conditions. And thus BIMA digester always was remained/operated under shock loading conditions. Every day production of biogas and consequently electricity fluctuated. Under these circumstances it was necessary to make a prior estimate of biogas production based upon past history, if possible. In order to achieve this goal, data were collected for a period of one year. As anaerobic digestion is a complex biochemical process, occurring in several sequential steps, so Artificial Neural Network (ANN) modeling of anaerobic process based upon huge data set has been considered a plausible option. This paper reports analysis, modeling, and result of this study. To the best of our knowledge, Nonlinear Autoregressive Exogenous (NARX) model has not yet been developed for a large size anaerobic digesters (10000 m3 volume). A NARX model consists of exogenous inputs, which means that the model relates the current value of a time series with past values of that series, or with the present and past values of the same series for predictions/forecasting. Artificial Neural Network is a very powerful modeling tool which can represent complex input/output relationships without requiring a detailed flow pattern of anaerobic digester. It can deal with most of simulation and prediction problems. It is a massively parallel network which can learn very complex nonlinear relation from a large data set. Artificial Neural Networks have been used by many researchers for modeling the many chemical and biochemical processes (Çoruh et al., 2014; Guo et al., 2001; Huanga et al., 2011; Gitifar et al., 2013). These networks have also been applied to model anaerobic digestion process. Yetilmezsoy (2013) developed ANN models to predict biogas production rate and methane production rate on the basis of the steady state data from pilot scale mesophilic ‘Up flow Anaerobic Sludge Blanket’ (UASB) reactor of 90 L volume. Qdais (2010) developed an Artificial Neural Network for modeling of biogas production from Russeifah biogas plant belonging to Jordan Biogas Company, which utilized 60 ton/day of organic waste from slaughter house, restaurants, fruits, vegetable and dairy markets. Their study illustrates that the error during simulation process can be minimized using time-series data learning and hence they set output as a time-dependent variable on the preceding three days inputs. However, there was no mention of type of dynamic network used by them for time series prediction and a static network was only depicted in the research paper. Strik (2005) used ‘MATLAB’ neural network toolbox to predict trace gases namely hydrogen sulfide and ammonia in biogas stream. They used two 20 L lab scale anaerobic continuous stirred tank reactors (CSTRs), one for H2S and other for NH3 production. Ozkaya (2007) developed a neural network model to predict methane percentage in landfill gas from field-scale landfill bioreactor (Placement area = 1250 m2; height of test cell = 5 m). Mahanty et al. (2013) developed a Neural Network to produce specific methane yield from industrial sludge of Ulsan industrial complex at laboratory scale. After the exhaustive literature review, it has been observed that most of the researchers have used static neural networks for modeling of anaerobic digesters and the digesters are of small size. Therefore, dynamic neural networks have not yet been used for the modeling of large size anaerobic digesters producing biogas. Dynamic neural networks are generally more powerful than static networks, because dynamic networks possess memory, they can be trained to learn from time varying pattern. In dynamic networks the output depends not only on the current input to the networks but also on the current and/or previous inputs, outputs or states of the network (Beale et al., 2013). So, dynamic networks are more suitable for time series type predictions.

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NARX network is one of the dynamic networks, which have been used by many researchers in different fields for time series prediction. It has been demonstrated that NARX recurrent neural networks have the potential to capture the dynamics of nonlinear complex systems (Diaconescu, 2008). Arbain (2012) have used NARX network for water level forecasting of Dungun River. Su (1992) have shown that NARX network in biological wastewater treatment facility and in catalytic reforming system in a petroleum refinery for multiple-step ahead prediction are more superior to feed forward dynamic networks. The literature review has motivated us to model the behavior of large size anaerobic digesters operating at Haebowal under dynamic conditions to predict the biogas production by NARX network, and thus this is the main theme of present paper. 2. Methodology 2.1. Description of the plant Fig. 1 depicts the process flow diagram of the WTE plant. The fresh cattle manure is collected in the collection tank. It is mixed with fresh water in a homogenization tank to obtain the waste slurry of uniform characteristics (solid concentration <10%). Waste slurry is fed to two BIMA (Biogas-Induced-Mixing-Arrangement) digesters, connected in parallel, working volume of each digester is 5000 m3, and so total digester volume becomes 10,000 m3. The main advantage of BIMA digester is its mixing system (does not require mechanical moving parts), its ability to control scum/sediments, and its capacity to handle reasonable high concentration of solids. A biological desulphurization unit has been created in the separated upper section in the digester to reduce H2S content of biogas below 200 ppm. Biogas produced in the digester passes through upper section before it can be utilized to generate power by biogas engine. Biogas can also be stored, if necessary in a dry type gas holder made of a synthetic polyester membrane, which is suspended in a concrete silo. The digested substrate from the digester is dewatered in a screw press. The BOD/COD concentration of the press water is reduced to acceptable levels in a conventional Effluent treatment plant. The dried manure obtained through screw presses shows much better availability of nutrients for the plants/crops due to its biochemical composition, and thus can be sold to farmers. Presently it is picked up by farmers themselves from the plant site at a nominal cost of Rs. 1100.00 per ton for their use. Electric power generated is sold to the state utility services. 2.2. NARX model Artificial Neural Network (ANN) provides a modeling technique for modeling process systems, which is based upon measurements of input–output variables. It does not require application of conservation laws for mass, momentum and energy, and also constitutive properties and correlations associated with the process system. This approach is capable of developing models for steady state or dynamic behavior of the process. NARX model is one of the neural networks methodologies, which can be used to model the dynamic behavior of the process. A neural network in general consists of highly interconnected layers of neuron like nodes (Chetouami, 2007). There are input and output layers, and hidden layers placed between them. The numbers of nodes in input and output layers correspond to input and output variables of the process respectively. The number of hidden layers and the number of nodes in each of them are decided by the user, and can vary from one to a finite number. In NARX model, values of input variables and output variables of previous times or days are utilized to predict the current value

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Power Grid

Biogas Flare

BIMA Digester Make-up Fresh Water

Animal Manure

Bio Gas engine Capacity 1 MW

Gas Storage

Biodesulphurization Unit

Digested slurry Cattle Dung Collection Tank

Homogenization Tank

Effluent Buffer Tank

Treated water Heat Exchanger

Digested Slurry Water Evaporated

Clarifier Screw press

Aerated Effluent Treatment Basin

Press water Digested Solids Yard

To Drain Solids

Dewatered Sludge

Biofertilizer

Fig. 1. Process flow sheet of the waste-to-energy plant.

of output variable. Fig. 2 depicts a NARX model of a system. u(tn), u(tn  1), . . .. . .u(tn  d + 1) are input variables on nth, (n  1)th. . .. . . and (n  d + 1)th days, and y(tn), y(tn  1), . . .. . .y(tn  d + 1) are corresponding output variables. z1 represents one time or day lag. There is one hidden layer of neurons. The model predicting the output variable can be written as follows: Input Layer

One

y(tn)

Output Layer

Hidden Layers

Two

yðtnþ1 Þ ¼ /½yðt n Þ;:::::;yðtk Þ;::::;yðtndþ1 Þ;uðt n Þ;:::::;uðt k Þ;::::::;uðt ndþ1 Þ ð1Þ where y(tk) is the Auto-Regressive Variable or predicted process output, u(tk) is the exogenous variable or process input, and / denotes a nonlinear function. d represents days or time delay. Let x be a column vector containing input variables, y(tk) and u(tk), and w(k) be the vector of weights associated with each input variable. Then, input to the jth neuron in input layer can be calculated as

netj ðt k Þ ¼ Z-1

Output

ð2Þ

i¼1

y(tn-1) Z-1 y(tn+1)

where p is the number of input nodes (neurons), i.e. d + d = 2d; different d’s may be assumed for input and output variables; wji is the connection weight between ith input neuron and jth hidden neuron; bj is the bias term for jth hidden neuron. Output from the jth neuron in hidden layer can be determined as follows:

zj ðtk Þ ¼ f j ½netj ðt k Þ

y(tn-d+1)

ð3Þ

where fj is a function, which is generally taken as sigmoid function. z(tk) is the vector of outputs from q neurons in hidden layer. Now, one can compute input from jth neuron in hidden layer to lth neuron in output layer.

u(tn-d+1)

Z-1

Input

p X wji ðt k Þxi ðt k Þ þ bj

netl ðt k Þ ¼

q X wlj ðt k Þzj ðt k Þ

ð4Þ

j¼1

u(tn-1)

wlj is the weight for the connection between jth node in hidden layer and lth node in output layer. Finally the output from lth node in output layer is calculated by using fl linear activation function as follows:

Z-1

u(tn)

Fig. 2. NARX model.

v l ðtk Þ ¼ f l ½netl ðtk Þ

ð5Þ

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It is mentioned that if felt necessary bias term can also be incorporated in neurons in hidden and output layers, i.e. in Eqs. (4) and (5), as done previously in Eq. (2). 2.3. Collection of data Values of operational variables were collected from the plant for 350 days. The data include flow rate, % DM (dry matter), and % VS (volatile solids) of feed slurry, and pH and temperature in the BIMA (Biogas-Induced-Mixing-Arrangement) digester, and biogas generation per day. The statistical summary of the variables are given in the Table 1. In this study flow rate, % DM, % VS, pH and Temperature were taken as input variables and biogas generation as target or output variable. The data were pre-processed by transforming the data into normalized data using the maximum value of the corresponding variables. Hence normalized data were having a range of [0–1]. This is suitable for the treatment by the sigmoid activation function in the ANN. Fig. 3 shows variation of variables viz., % DM (dry matter), % VS (volatile solids), influent flow rate, and biogas generated for a typical month. During this month pH and the temperature remained constant close to 6.6 and 24 °C respectively. 2.4. Implementation of NARX model In this study, MATLAB R2013a was used for modeling and simulation of anaerobic process. 350 data sets were divided into two parts, one part contained 335 data set and other one contained 15 data set only. 335 data sets were used for the training of Neural Network and rest 15 data set were used for validation of the model by comparing the biogas production obtained in the plant with that predicted by the model. The development of NARX model architecture involves several steps which are to be performed iteratively to arrive at optimum architecture and methods. These are as follows: Fig. 3. Daily variation of operating variables in a particular month.

(a) Assume Network architecture i.e. number of hidden layers, neurons in each hidden layer and number of delays. (b) Divide data set (335 data) into 3 data set viz. training set, validation set and test set. For this step also suitable function is to be chosen. (c) Optimize network architecture by using appropriate criteria. This also includes the selection of appropriate training algorithm. In the following subsections, above details have been described for optimized network only. 2.4.1. Division of data set The data set was divided into three subsets, training set, validation set and test set. Training set is used for computing the gradient and updating the network weights and biases. Validation set is used to get an estimate of out of sample error. Validation error is unbiased estimate of out of sample error provided that out of

sample error is just measured and is not used. In present work this error has been used as the stopping criteria for iteration. During the training process validation error initially decreases, however when the network tends to overfit the data, the validation error begins to increase. The weights and biases are saved at the minimum of validation set error. Hence, validation error is no more an unbiased estimate of out of sample error. To get an unbiased out of sample error a third set called test set has been used (CC BY-NC-ND, 2012). In this work, 70%, 15% and 15% data sets were used as training set, validation set and test set respectively. Three type of functions provided by MATLAB for dividing the data namely, dividerand, divideblock and divideint were tested. dividerand divides the data set randomly into the three subsets i.e. training set, validation set and test set. divideblock divides the data set into three subsets using three contiguous blocks. The first 70% of the data are assigned to the training set, the next 15% to the validation set

Table 1 Statistical summary of operating variables based upon plant data for 350 days. Variables Feed flow rate HRT DM VS pH Temperature Biogas generated

Unit 3

m /day day % % °C m3/day

No. of data

Minimum

Maximum

Average

Median

350 350 350 350 350 350 350

59 22.62 3.24 72 6.1 20 1008

442 169.49 38.31 88.52 6.9 33 7000

228.87 49.29 9.03 82.03 6.58 26.95 3874.89

232 43.1 9.09 82.3 6.6 27 3600

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Table 2 Evaluation of functions used for dividing the data. Mean Squared Error (MSE) Function

Overall

Training set

Validation set

Test set

Correlation coefficient, R

dividerand divideint divideblock

0.0059 0.0048 0.0044

0.0053 0.0039 0.0035

0.0069 0.0069 0.0059

0.0076 0.0072 0.0071

0.9013 0.9195 0.9265

Table 3 Determination of appropriate time lag. Time lag, No. of days

Overall performance

Training

Validation

Test

Correlation coefficient, R

5 10 15 20 25 16 17 18 19

0.0061 0.0059 0.0056 0.0044 0.0055 0.0054 0.0056 0.0044 0.0047

0.0053 0.0050 0.0051 0.0030 0.0038 0.0034 0.0041 0.0035 0.0040

0.0079 0.0087 0.0059 0.0069 0.0087 0.0092 0.0074 0.0059 0.0052

0.0081 0.0075 0.0075 0.0087 0.0101 0.0111 0.0110 0.0071 0.0074

0.8988 0.9004 0.9068 0.9284 0.9097 0.9110 0.9088 0.9265 0.9236

Table 4 Selection of neurons in hidden layer. Mean Square Error (MSE) NARX model

Number of neurons in hidden layers

Overall

Training set

Validation set

Test set

Correlation coefficient, R

With d = 18 days

5–5 10–10 15–15 20–20 25–25 50–50 5–10 10–5 10–8 10–12 12–12 13–13 14–14

0.0047 0.0044 0.0056 0.0045 0.0049 0.0046 0.0053 0.0054 0.0051 0.0050 0.0051 0.0054 0.0050

0.0031 0.0035 0.0051 0.0031 0.0030 0.00084 0.0045 0.0046 0.0040 0.0040 0.0039 0.0040 0.0039

0.0065 0.0059 0.0059 0.0073 0.0078 0.0109 0.0066 0.0070 0.0079 0.0079 0.0067 0.0063 0.0075

0.0109 0.0071 0.0075 0.0082 0.0111 0.0163 0.0081 0.0074 0.0072 0.0072 0.0088 0.0111 0.0079

0.9219 0.9265 0.9068 0.9270 0.9187 0.9251 0.9112 0.9107 0.9152 0.9152 0.9200 0.9099 0.9156

and the last 15% to the test set. divideint divides the data set by an interleaved method i.e. data is to cycle between the training set, validation set and test set according to percentages. Initially we took divideblock for data division as suggested in Matlab Central (2013) for time series prediction. Later when optimum NARX architecture and optimum training algorithm were obtained, then the same was verified by taking all 3 divide functions to determine one, giving the smallest Mean Squared Error (MSE). From the Table 2, it can be seen clearly that divideblock function gives smallest overall MSE, as well as smallest MSE for test set, and highest correlation coefficient, R. Therefore, the divideblock was chosen as the divide function for this study.

2.4.2. Selection of appropriate delay or time lag There are two BIMA digesters in WTE plant, each of 5000 m3 volume. In digesters, sampling ports at various heights have been provided. The analysis of samples withdrawn from various ports clearly indicates that the mixing in the BIMA digester can be approximated as that in an ideal CSTR. From the residence time distribution (RTD) functions of an ideal CSTR, it is known that the effluent at any time comprises of fluid elements of different ages (Levenspiel, 1999; Fogler, 2006). Therefore, the biogas production not only depends on the feed conditions of that day but also depends on feed conditions of several previous days. To get the optimum number of delays that could describe the system

dynamics as closely as possible, different values of delays for NARX network were considered during simulations. Chosen NARX network consists of two hidden layers and ten neurons in each hidden layer. The results with traincgb training algorithm are shown in Table 3. From this table, it can be inferred that the delay line with a maximum delay of 18 days for each input and target or output vectors gives overall best performance .

2.4.3. Optimization of neurons in hidden layers Choosing the right network architecture is an important task of ANN-based studies. This is very important for getting good prediction by the developed network. In this study the simulations were conducted for NARX network by taking various numbers of neurons in the hidden layers with 18 days delay. tangent sigmoid transfer function (tansig) at the hidden layers and linear transfer function (purelin) at the output layers were used. Sigmoid transfer function is the most suitable function to describe non-linear relationship such as the case in biogas production (Kanat and Saral, 2009). The Table 4 shows that the simulations were started from 5 neurons in each layer, which were increased by an interval of 5. It was observed that the best validation and test performances (MSE) should lie between 5 and 15 neurons in each hidden layer. Too many neurons lead to over fitting; for example the case with 50 neurons in each hidden layer gives very low training set error

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A.K. Dhussa et al. / Bioresource Technology 170 (2014) 342–349 Table 5 Comparison of performance of training algorithms. Functions

Algorithms

MSE

Correlation coefficient, R

trainlm trainbfg trainrp trainscg traincgb traincgf traincgp trainoss traingdx traingdm traingd

Levenberg–Marquardt BFGS quasi newton Resilient backpropagation Scaled conjugate gradient Conjugate gradient with Powell/Beale restarts Fletcher–Powell conjugate gradient Polak–Ribiere conjugate gradient One step secant Variable learning rate gradient descent Gradient descent with momentum Gradient descent

0.0065 0.0047 0.0070 0.0049 0.0044 0.0045 0.0048 0.0053 0.0052 0.0099 0.0101

0.9044 0.9225 0.8828 0.9188 0.9265 0.9255 0.9222 0.9108 0.9139 0.8283 0.8272

Fig. 4. (a) Variation of MSE with Epochs and, (b) auto correlation of error.

(0.00084) but errors in validation and test sets are very high i.e. 0.0109 and 0.0163 respectively. Thereafter, simulations were performed by using the model having neurons in hidden layers between 5 and 15. It can be seen clearly from the Table 4 that the model with 10 neurons in each hidden layer gives best validation and test set performance (smallest MSEs). Thus, final neural network architecture for NARX model consists of 2 hidden layers each containing 10 neurons, and tapped delay lines with delay of 18 days for each input and output vectors. 2.4.4. Selection of training algorithm In MATLAB, several training algorithms are available to train a network. These algorithms use the gradient of the performance function (MSE) to determine the adjustment of weights to minimize the performance criteria (MSE). The gradient is determined using a technique called back propagation (Beale et al., 2013). In single layer perceptron the desired output is known and synaptic weights can be directly modified to minimize the error. But in

Fig. 5. Daily variation of operating variables during 15 days for which predictions of biogas production rate have been made.

multi-layer perceptron synaptic weights can be modified only for the output layer; synaptic weights of the preceding hidden layer cannot be modified as its desired output is not known. Back propagation technique propagates the output error backward to the immediate preceding hidden layer, and so on. In this way it distributes the error in order to arrive at a best fit or minimum error. There are many variations of the back propagation algorithm. It is very difficult to know which algorithm is best for a particular network and data set. Generally the Levenberg–Marquardt algorithm is the fastest training algorithm and is commonly used. However, in this study all training algorithms given in MATLAB were used one by one to train the network, consisting of 10 neurons in each hidden layer of NARX network with 18 days delay for every input and target or output variables. divideblock for dividing data, tangent sigmoid transfer function (tansig) in hidden layer and

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linear transfer function (purelin) in output layer were used to perform respective tasks. Results in respect of MSE and R with different functions and algorithms are given in the Table 5. It is obvious (Table 5) that traincgb is the best suited training algorithm for NARX model of present anaerobic digester as it gives minimum MSE 0.0044 and maximum value of R = 0.9265. Fig. 4(a) provides plots of MSE versus number of Epochs obtained during training, validation and testing of optimized network with associated algorithms for anaerobic digesters. During the validation, MSE reaches to the minimum value in 21 iterations, but training continues for 6 more iterations before it is stopped. Autocorrelation is the cross-correlation of a time series data with itself. In fact, it is the similarity between observations as a function of time lag between them. For a perfect prediction model, there should only be one nonzero value of the autocorrelation function and it should occur at zero lag. This would mean that prediction errors were completely uncorrelated with each other. As shown in the Fig. 4(b), the autocorrelation of errors in present study falls approximately within the 95% confidence limits around zero except for the one at zero lag. Thus the model appears to be adequate to represent the dynamic behavior of anaerobic digesters (M.D.C., 2014).

3. Results and discussion After ascertaining the prediction capabilities of developed NARX neural network model, the model was used to predict biogas production day by day for the next 15 days. This was done by using one day ahead prediction method. As the 335 data sets were used to train the network, so prediction of biogas were made on 336th day by using that day input data set and the model. Then for the 337th day, actual production of bio-gas of 336th day was also used as input in the trained network, and so on. In order to show the daily variations in influent flow rate, % DM, and % VS during these fifteen days, Fig. 5(a) and (b) have been prepared. It is obvious that there are considerable variations in these three variables. However, the pH is constant, and there are very small variations in operating temperature. The predictions of biogas production rate made by the model are shown in the Fig. 6(a) where both the actual and predicted biogas production rates are plotted as a function of time. Besides, the accuracy of measurement of biogas production rate is ±1%. So the dotted lines corresponding to +1% and 1% deviations with respect to measured values (actual values) have also been shown in the figure. It can be seen from Fig. 6(b) that the developed NARX model is capable of predicting the quantity of biogas produced in the anaerobic digesters of a WTE plant within ±8% deviation inspite of significant variations in operating conditions during these days. 4. Conclusion Anaerobic digesters of a considered WTE plant treat cattle manure to produce biogas, and subsequently electricity. Being microbial process, it is desired to have minimum possible variation in operating conditions. However it is difficult to achieve this goal in practice and the digester shows the dynamic behavior. This work demonstrates the use of NARX network to model the dynamics of a large size anaerobic digester. Developed NARX model predicts daily biogas production rate within ±8% deviation. It is our view that NARX model may be used to estimate daily biogas production rate accurately and also to develop appropriate control strategies for the process. Acknowledgements Authors acknowledge the support provided by Punjab Energy Development Agency (PEDA), Chandigarh, and the Ministry of New and Renewable Energy (MNRE), Government of India, New Delhi, during the course of this research work. References

Fig. 6. (a) Comparison of NARX model prediction with actual biogas production, and (b) comparison of actual and predicted values (biogas production rate).

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