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1116 © IWA Publishing 2012 Water Science & Technology | 65.6 | 2012

A data-driven model for maximization of methane

production in a wastewater treatment plant

Andrew Kusiak and Xiupeng Wei

ABSTRACT

A data-driven approach for maximization of methane production in a wastewater treatment plant is

presented. Industrial data collected on a daily basis was used to build the model. Temperature, total

solids, volatile solids, detention time and pH value were selected as parameters for the model

construction. First, a prediction model of methane production was built by a multi-layer perceptron

neural network. Then a particle swarm optimization algorithm was used to maximize methane

production based on the model developed in this research. The model resulted in a 5.5% increase in

methane production.

doi: 10.2166/wst.2012.953

Andrew Kusiak (corresponding author)Department of Mechanical and Industrial

Engineering,2139 Seamans Center,The University of Iowa,Iowa City, IA 52242,USAE-mail: andrew-kusiak@uiowa.edu

Xiupeng WeiDepartment of Mechanical and Industrial

Engineering,3131 Seamans Center,The University of Iowa,Iowa City, IA 52242,USA

Key words | data-mining algorithms, methane production maximization, neural networks, particle

swarm optimization, wastewater treatment plant

INTRODUCTION

Anaerobic digestion is widely used to treat sludge in manymunicipal wastewater treatment plants around the world.It involves a process in which microorganisms break

down biodegradable waste in the absence of oxygen(Marchaim ; Lettinga ). As a result of anaerobicdigestion, methane and carbon dioxide rich biogas areproduced. The biogas can then be used to generate electri-

city or heat.Biological, chemical, and physical reactions are

involved in the anaerobic digestion process (Batstone et al.). Owing to the complexity of the anaerobic process,building formal models is a challenge. The models presentedin the literature are usually non-linear and non-stationary

with restrictive assumptions that may not hold in practice(Mailleret et al. ).

Numerical studies on comprehensive anaerobic diges-

tion models for prediction and optimization (Schubertet al. ; Tay & Zhang ; Sotemann et al. )have been reported in the literature. Data-mining algor-ithms such as neural networks have shown success in

building models of the anaerobic digestion process. Anadaptive neuro-fuzzy inference system was applied formodeling anaerobic digestion of primary sludge in a

wastewater treatment plant (Cakmakci ). The model

satisfactorily predicted effluent volatile solid and methaneyield. Holubar et al. () applied several feed-forwardback propagation neural networks to model and sub-

sequently control methane production in anaerobicdigesters. Gas composition, methane production rate,pH, volatile suspended solids and other parameters weremeasured and simulated to determine the best feeding

profile.Data mining is a powerful tool to analyze data in scien-

tific and engineering applications, such as bioinformatics,

manufacturing, and wind energy (Braha ; Frank et al.; Kusiak et al. ; Seckin ). Evolutionarycomputation algorithms are widely used to solve complex,

linear and non-linear optimization problems. Successfulapplications of evolutionary computation algorithms havebeen reported in engineering, marketing and science

(Dasgupta &Michalewicz ; Rud ; Thiele et al. ).In this paper, methane production is maximized with a

data-driven model derived by a multi-layer perceptron(MLP) neural network. To maximize methane production,

particle swarm optimization (PSO) is employed to find opti-mal solutions for control variables and other uncontrollablevariables. The model and the maximization results are then

discussed in detail.

Figure 1 | Flow chart of anaerobic digestion.

Table 1 | Data description

Dataset Description No. of instances

1 Training dataset: building predictionmodel

576 observations

2 Test dataset: testing prediction model 148 observations

Total dataset: 724 data points 724 observations

1117 A. Kusiak & Xiupeng Wei | Data-driven model for optimization of methane production Water Science & Technology | 65.6 | 2012

METHODS

Data and parameter description

The data used in this research was collected at theDes Moines Wastewater Reclamation Facility (WRA),located in Des Moines, Iowa. WRA is designed to recycle

wastewater from 16 municipalities, counties, and sewerdistricts.

The WRA includes three complexes to process sludge

and produce methane. Each of the complexes has twoanaerobic digesters that are 115 ft (35.05 m) in diameter,29.5 ft (8.99 m) for side water depth and 15 ft (4.57 m) for

cone depth. The sludge is delivered to the digesters afterbeing mixed in sludge-blending tanks. The temperature inthe digester is kept in a range from 90 WF (32.22 WC) to

105 WF (40.56 WC) and is controlled by a sludge heat exchan-ger. The temperature is generally maintained at 100 WF(37.78 WC). In the absence of oxygen, microorganismsbreak down sludge and produce methane and carbon diox-

ide, which is first stored in a gas sphere with 141,260cubic feet (4,000 m3) of capacity to meet peak usagedemand, and then are delivered to gas generators to produce

electricity. The heat generated in the gas combustion is usedto maintain the temperature of the sludge heat exchangersand also heat plant buildings in the winter season. A flow

chart diagram of the anaerobic digestion at WRA is shownin Figure 1.

The methane production data used in this paper wasfrom daily samples taken over the period from 1/2/2008

to 12/31/2010. As some data points involved errors, e.g.out of range values, the dataset was preprocessed. The pro-cessed dataset included 724 data points and it was divided

into training and test sets. The training set was from 1/2/2008 to 3/31/2010, and it included 576 data points tobuild the prediction model. The test set from 4/1/2010

to 12/31/2010 contained 148 data points and it was usedto test the developed model. The dataset descriptions areprovided in Table 1.

Although the original dataset included 11 parameters,some of them were removed as they did not have obviousinfluence on the methane production. In this research,digester temperature, volatile solids, total solids, detention

time of sludge, pH value and methane production wereselected to build a prediction model. At WRA, digester temp-erature and volatile solids fraction are controllable, and

other parameters are uncontrollable variables. The list ofparameters with their ranges is shown in Table 2.

The methane production model involving the selectedparameters is expressed in Equation (1).

y ¼ f(x1, x2, v1, v2, v3) (1)

Temperature is the most important variable affectingthe rate of digestion and methane production. Eventhough anaerobic microorganism communities can

endure temperature ranging from below freezing to above135 WF (57.22 WC), they thrive best at temperatures from68 WF (20 WC) to 105 WF (40.56 WC) for mesophilic and

113 WF (45 WC) to 135 WF (57.22 WC) for thermophilic diges-ters. To increase methane production, the digester mustbe kept at a consistent temperature, as rapid changes will

disturb bacterial activities. This is also the reason whymost anaerobic digesters require some level of insulationor heating which will generally increase methane pro-

duction in cold seasons.The total solids in wastewater is another variable influ-

encing methane production. The concentration of total

Table 2 | List of parameters

Parameter Description Minimum Maximum

x1 Digester temperature, WF (WC) 90 (32.22) 105 (40.56)

x2 Volatile solids, % 65 85

v1 Total solids, % 2 12

v2 Detention time, day 10 50

v3 pH 6.7 7.8

Methane production, scf/day (m3/day) 72,000 (2,038) 1,032,000 (29,223)

1118 A. Kusiak & Xiupeng Wei | Data-driven model for optimization of methane production Water Science & Technology | 65.6 | 2012

solids has an impact on the effectiveness of the microorgan-isms in the decomposition process during anaerobicdigestion. Igoni et al. () found that methane production

increased when the percentage total solids of wasteincreased. A statistical analysis showed that the formerwas a power function of the latter, and there was a point

where no further increase in the methane productionwould be obtained when the percentage of total solidskept increasing.

The volatile solids in wastewater are measured as thetotal solids, excluding the ash content, as obtained by com-plete combustion of the feeding waste. They contain the

biodegradable volatile solids and refractory volatile solids.The former is useful in estimation of the biodegradabilityof the waste and the latter is not easily degraded by microor-ganisms, so volatile solids concentration affects both

methane production and the composition quality.Detention time is a critical element in control of the

anaerobic process. As the methane formers are slower to

grow and are sensitive to changes in the operation con-ditions, a short detention time results in sludge beingwashed out of the digester. A longer detention time allows

the creation of a buffering alkalinity to form and stabiliz-ation of the microorganism environment.

Anaerobic microorganisms, especially methanogens, are

sensitive to pH in the digester and their growth can be inhib-ited by acidic conditions. The pH value for anaerobicdigestion usually varies between 5.5 and 8.5. At an earlystage of digestion, acetogenesis can lead to accumulation

of large amounts of organic acids resulting in an acidicenvironment with a low pH value. When digestion reachesthe late methanogenesis stage, the concentration of ammo-

nia rises and the pH value may exceed 8.The prediction accuracy of the model built by the

multi-layer perceptron neural network is measured with

five metrics, the mean absolute percentage error (MAPE),the fractional bias (FB), the root mean square error(RMSE), the normalized mean square error (NMSE), and

the coefficient of determination (R2) shown in Equations(2)–(6).

MAPE ¼ 1N

XNi¼1

jy⌢i � yijyi

(2)

FB ¼ y⌢

m � ym0:2ðy⌢m þ ymÞ

(3)

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

XNi¼1

ðyi � y⌢

iÞ2vuut (4)

NMSE ¼PN

i¼1 (yi � y⌢

i)2

PNi¼1 (y

⌢

i)2

(5)

R2 ¼ 1�PN

i¼1 (yi � y⌢

i)2

PNi¼1 (yi � ym)

2 (6)

where y⌢

i is the predicted value obtained from the model,

and yi is the actual value measured at the WRA. y⌢

m andym are the mean of predicted and observed values respect-ively, and N is the number of test data points.

Development and validation of the prediction model

The multi-layer perceptron (MLP) neural network involves

multiple fully connected layers. Except for the inputnodes, each node is a neuron with a non-linear activationfunction. MLP utilizes a supervised learning mechanism,called back propagation, for training. MLP is a modification

of the standard linear perceptron able to distinguish datathat is not linearly separable (Cybenko ).

Dataset 1 and dataset 2 of Table 1 were used to train and

test the MLP neural network model. In all, 2000 singlehidden-layer neural networks were trained. The number of

Table 3 | MLP neural networks

MLP structure Validation error Training algorithm Error function Hidden activation Output activation

MLP 5-4-1 0.0055 BFGS 44 SSE Tanh Logistic

MLP 5-3-1 0.0057 BFGS 32 SSE Tanh Logistic

MLP 5-10-1 0.0058 BFGS 83 SSE Tanh Identify

MLP 5-11-1 0.0059 BFGS 18 SSE Logistic Logistic

MLP 5-22-1 0.0058 BFGS 44 SSE Tanh Sine

1119 A. Kusiak & Xiupeng Wei | Data-driven model for optimization of methane production Water Science & Technology | 65.6 | 2012

neurons in the hidden layer varied from 3 to 22. Table 3

summarizes the best performing neural networks. Tomeasure the model accuracy, the sum of squared error(SSE) is used in this paper. The SSE is the sum of the

squared difference between the target and actual outputvalues on each output unit (Braha ). The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm (Bonnans

et al. ) was used to minimize SSE while building eachneural network model. The iteration number of the BFGSalgorithm ranged between 18 and 83 as shown in the third

column in Table 3. Multiple non-linear hidden and outputactivation functions, including identity, logistic, tanh, andexponential, were used for the neurons. The activation func-tions used in the models are listed in Table 3. The MLP

neural networks successfully identify the non-linear relation-ship between the process variables as demonstrated with thelow validation errors shown in Table 3.

Figure 2 shows the observed and MLP 5-4-1 predictedvalues of methane production. Most methane productionpatterns and peaks were clearly recognized by the model

with a few exceptions of extreme high and low observedvalues, such as high point 110, and extreme low points 17,

Figure 2 | Observed and MLP neural network predicted methane production.

70, 121 and 147. A reason for the discrepancy may have

been because of noise in the data sampled.Performance of the MLP neural network derived model

has been compared with the adaptive neuro-fuzzy inference

system (ANFIS), multiple linear regression, and multiplenon-linear regression models. The comparative results inTable 4 demonstrate that the prediction model built by the

MLP neural network offers better prediction accuracythan the other models. Specifically, the mean absolute per-centage error of the constructed model is 0.1. This error

expresses the relative accuracy of the model. Fractionalbias at 0.01 indicates a satisfactory agreement between thepredicted and the observed value. The root mean squareerror of the model is 92120, which is a large number, how-

ever, the value of the methane production could be largerthan 1,000,000 scf/day (28,317 m3). A relatively small differ-ence between predicted and observed value causes a large

root mean square error. Normalized mean square errorexpressing the normalized average of the square error is0.01 for the built model. The coefficient of determination

value 0.98 indicates a high correlation between the pre-dicted and observed values.

Table 4 | Prediction accuracy

MAPE FB RMSE NMSE R2

MLP 5-4-1 0.10 0.01 92,120 0.01 0.98

ANFIS 0.11 0.01 93,824 0.02 0.95

Multiple linear regression 0.17 0.13 135,459 0.03 0.83

Multiple non-linearregression

0.15 0.01 130,454 0.03 0.88

Figure 3 | Flow chart diagram of the PSO algorithm.

1120 A. Kusiak & Xiupeng Wei | Data-driven model for optimization of methane production Water Science & Technology | 65.6 | 2012

Maximization of methane production

The MLP neural network model is used to maximizemethane production. Since only temperature and volatile

solid fraction can be controlled at the WRA, they are usedas the decision variables. The digester temperature is con-strained in the range 90 WF (32.22 WC) to 105 WF (40.56 WC),

and the volatile solid fraction varies from 65 to 85%. Thedigester temperature and the volatile solid fraction rangesare decided based on the operating practice at WRA. Thesingle objective model maximizing methane production is

expressed in model (7).

maxx1,x2

f(x1, x2, v1, v2, v3)

subject to:

90 ≤ x1 ≤ 105

65% ≤ x2 ≤ 85% (7)

where f is the objective function represented by the model

built in Section 3. The description of the five input variablesused in model (7) is included in Table 2.

Solving the methane production model is a challenge.Heuristic search algorithms like greedy search (Feo &

Resende ) and evolutionary computation algorithmssuch as genetic algorithms (Deb et al. ) are the availablechoices. Particle swarm optimization (PSO) is a stochastic

optimization algorithm (Kennedy & Eberhart ). Thedevelopment of PSO was inspired by the social behaviorof birds flocking or fish schooling. PSO has been success-

fully applied in many research and application areas. Ithas been demonstrated that PSO produces better results inlower computational time compared with other algorithms.Therefore, PSO algorithm was applied in this paper to solve

model (7).The standard PSO algorithm shown in Figure 3 is pre-

sented next.

Step 1: Randomly initialize n particle positions xi∈Rn

and velocities si∈Rn.Step 2: Evaluate fitness value fi using current particle

positions; fbi is the best fitness value for particle i, and fg is

the global best value for all particles. Parameter pbi is thebest individual particle position, and pg is the global bestposition for all particles.

If fi ≤ fbi , then fbi ¼ fi, pbi ¼ xi

If fi ≤ fg, then fg ¼ fi, pg ¼ xi

Step 3: Update all particle velocities si

si ¼ si þ c1r1(pi � xi)þ c2r2(pg � xi)

Step 4: Update all particle positions xi

xi ¼ xi þ si

Step 5: Update fitness value fbi and fg

Step 6: If the stopping condition is satisfied, then fg is thefinal optimal solution with the particle position pg. Other-wise, return to step 3 to start next iteration.

Here, the dimension for each particle’s position xi andvelocity si is 2. The first element of xi refers to the decision

1121 A. Kusiak & Xiupeng Wei | Data-driven model for optimization of methane production Water Science & Technology | 65.6 | 2012

variable of the digester temperature and is drawn from uni-

form distribution U (90, 105). The second element of xirefers to the decision variable of volatile solids and isdrawn from uniform distribution U (65%, 85%). At the

beginning, si is initialized as 0; c1 and c2 are cognitive andsocial parameters, they are set as 2 in this paper; r1 and r2are random numbers between 0 and 1.

RESULTS AND DISCUSSION

The dataset 2 in Table 1 was used to solve model (7) with thePSO algorithm. In each iteration, the trained MLP neural

network is used to predict the methane production basedon controllable and uncontrollable variables. Then thePSO algorithm determines the best fitness value (heremethane production) by determining the settings of control-

lable variables (here digester temperature and volatile solidsfraction). The initial parameters of the PSO algorithm are asfollows: the population size is 50 and the maximum number

of iterations is set at 20.To obtain a stable production of methane, unchanged

operational conditions for a period of time are preferable,

e.g. a full season; see Figure 4 for the optimization results.Under the operational conditions in which digester temper-ate is set to 102.5 WF (39.12 WC) and volatile solids fraction is

set to 80%, the methane production can be improved by5.5%. The increased methane production is due to theoptimization of controllable settings based on the predictionmodel in Equation (1). It can be seen that the computed

methane production is usually larger than the observedvalues. Moreover, the production for the test period showsless variability than the actual values, which have very

Figure 4 | Observed and maximized methane production.

large differences on a daily basis. The stable output is ben-

eficial for the anaerobic digestion process and plantoperations.

An increase in the digester temperature results in more

complete destruction and decomposition of sludge, thusincreasing methane production. However, since therequired temperature has to be maintained during cold sea-sons by burning part of the methane produced to heat the

digester, a tradeoff between the energy for heating and thetemperature maintenance of the digester leads to maximiza-tion of the methane production. This multi-objective model

deserves investigation to produce optimal operationalconditions.

The concentration of volatile solids is also a factor

impacting methane production. It has been observed thata higher volatility of solids results in higher methane pro-duction if the temperature remains stable. Since thevolatile solids concentration at WRA is high (up to 85%),

it is expected that such a concentration should increasemethane production. Further studies and experiments arerecommended to investigate if there is an upper limit at

which methane production will not increase even if the vola-tile solids concentration keeps increasing.

CONCLUSION

In this paper, a data-driven approach to maximize methaneproduction in a wastewater treatment plant was presented.Controllable variables, temperature, volatile solids, and

uncontrollable variables, total solids, detention days, andpH value were selected to build a prediction model formethane production with a multi-layer perceptron neural

1122 A. Kusiak & Xiupeng Wei | Data-driven model for optimization of methane production Water Science & Technology | 65.6 | 2012

network approach. To maximize methane production, a

single-objective maximization model was formulatedand solved with a particle swarm optimization algorithm.Optimal operational conditions were obtained in response

to uncontrollable variables. The maximization resultsdemonstrated that methane production increased by 5.5%.with the values of the optimized variables being the digestertemperature of 102.5 WF (39.12 WC) and the volatile solids

fraction of 80%.It is recommended that further study should focus on

optimizing trade-offs between digester temperature and the

energy used to heat it. Examining the upper limit for volatilesolid concentration is another area to be investigated. Theoptimal operational conditions obtained from this research

were recommended for testing and validation in a waste-water treatment plant.

ACKNOWLEDGEMENT

This research was supported by funding from Iowa EnergyCenter Grant No. 10-1.

REFERENCES

Batstone, D. J., Keller, J., Angelidaki, I., Kalyuzhnyi, S. V.,Pavlostathis, S. G., Rozzi, A., Sanders, W. T., Siegrist, H. &Vavilin, V. A. The IWA anaerobic digestion model No1(ADM1). Water Science and Technology 45 (10), 65–73.

Bonnans, J. F., Gilbert, J. C., Lemarechal, C. & Sagastizábal, C. A. Numerical Optimization: Theoretical and PracticalAspects. Springer, New York.

Braha, D. Data Mining for Design and Manufacturing:Methods and Applications. Kluwer Academic Publishers,The Netherlands.

Cakmakci, M. Adaptive neuro-fuzzy modeling of anaerobicdigestion of primary sedimentation sludge. Bioprocess andBiosystems Engineering 30 (5), 349–357.

Cybenko, G. Approximation by superpositions of a sigmoidalfunction. Mathematics of Control, Signals, and Systems 2 (4),303–314.

Dasgupta, D. & Michalewicz, Z. Evolutionary Algorithms inEngineering Applications. Springer, New York.

Deb, K., Pratap, A., Agarwal, S. & Meyarivan, T. A fast andelitist multiobjective genetic algorithm: NSGA-II. IEEETransactions on Evolutionary Computation 6 (2), 182–197.

Feo, T. A. & Resende, M. G. C. Greedy randomized adaptivesearch procedures. Journal of Global Optimization 6 (2),109–133.

Frank, E., Hall, M., Trigg, L., Holmes, G. & Witten, I. H. Data mining in bioinformatics using Weka. Bioinformatics20 (15), 2479–2481.

Holubar, P., Zani, L., Hagar, M., Froschl, W., Radak, Z. & Braun,R. Advanced controlling of anaerobic digestion bymeans of hierarchical neural networks. Water Research 36(10), 2582–2588.

Igoni, A. H., Abowei, M. F. N., Ayotamuno, J. M. & Eze, C. L. Effect of total solids concentration of municipal solid wastein anaerobic batch digestion on the biogas produced.International Journal of Food, Agriculture and Environment5 (2), 333–337.

Kennedy, J. & Eberhart, R. C. Particle swarm optimization.Proceedings of IEEE International Conference on NeuralNetworks 4, 1942–1948.

Kusiak, A., Zheng, H. Y. & Song, Z. Wind farm powerprediction: a data-mining approach. Wind Energy 12 (3),275–293.

Lettinga, G. Anaerobic digestion and wastewater treatmentsystems. Biomedical and Life Sciences 67 (1), 3–28.

Mailleret, L., Bernard, O. & Steyer, J. P. Robust regulation ofanaerobic digestion processes.Water Science and Technology48 (6), 87–94.

Marchaim,U. BiogasProcess forSustainableDevelopment. Foodand Agriculture Organization of the United Nations, Rome.

Rud, O. C. Data Mining Cookbook: Modeling Data forMarketing, Risk and Customer Relationship Management.John Wiley & Sons, New York.

Schubert, J., Simutis, R., Dors, M., Havlik, I. & Lubbert, A. Bioprocess optimization and control: application of hybridmodeling. Journal of Biotechnology 35 (1), 51–68.

Seckin, N. Modeling flood discharge at ungauged sites acrossTurkey using neuro-fuzzy and neural networks. Journal ofHydroinformatics 13 (4), 842–849.

Sotemann, S. W., Ristow, N. E., Wentzel, M. C. & Ekama, G. A. A steady state model for anaerobic digestion of sewagesludge. Water SA 31 (4), 511–527.

Tay, J. H. & Zhang, X. Neural fuzzy modeling of anaerobicbiological wastewater treatment systems. ASCE Journal ofEnvironmental Engineering 125 (12), 149–1159.

Thiele, L., Miettine, K., Korhonen, P. J. & Molina, J. Apreference-based evolutionary algorithm for multi-objectiveoptimization. Evolutionary Computation 17 (3), 411–436.

First received 2 September 2011; accepted in revised form 7 November 2011