PSEAsia2013-04

Proceedings of the 6th International Conference on Process Systems Engineering (PSE ASIA)

25 - 27 June 2013, Kuala Lumpur.

Machine Learning Based Modeling for Solid Oxide

Fuel Cells Power Performance Prediction

M. N. Fuad,a M. A. Hussain,b

aChemical Engineering Department, Faculty of Engineering, UCSI University, 56000

Cheras, Kuala Lumpur

Department of Chemical Engineering, Faculty of Engineering, University of Malaya,

50603, Kuala Lumpur

Abstract

This study applies four different types of machine learning methods to model the power

performance behaviour of a tubular solid oxide fuel cells (SOFC) under different

operating conditions. The corresponding machine learning methods are: artificial neural

network (ANN), fuzzy inference system (FIS), support vector machine (SVM), and

genetic programming (GP). By using four types of inputs of the SOFC operation: i.e.

load current, fuel utilization, inlet air temperature, and air molar flow rate, the task of

the corresponding machine learning methods is to predict the stack voltage and outlet

temperature values of the corresponding SOFC operation. 1000 input-output data

pairings that were generated from the simulations of a physical tubular SOFC model

under various operating conditions were used to train the corresponding machine

learning models. It was found out from this study that ANN method has slightly better

performance in modelling the power performance behaviour of the corresponding SOFC

system under various operating conditions.

Keywords: Solid oxide fuel cells; Machine learning methods; Power performance

prediction

1. Introduction

Solid oxide fuel cells (SOFC) are expected to play a significant role in helping to meet

the ever-increasing demands for cleaner supply energy in the near future (Stambouli,

2011). Already, SOFCs have been proposed as a potential power source for distributed

and stationary power plants and also mobile applications. The advantages of SOFCs are

their high efficiency, modularity, low noise and low environmental pollution. However,

certain challenges, including the optimum operation of the SOFC stacks, need to be

resolved before the technology can be adopted for the real-world applications.

Moreover, this issue will also take into considerations the unique nature of the SOFC

operating phenomena. Clearly, the requirement to satisfy all these challenges will

require the development of an effective control strategy that is specifically tailored to

the SOFC operation. Model-based control strategies that rely on the availability of good

modeling descriptions of the SOFC phenomena are expected to play a crucial role in

this regard.

Machine learning has shown its great utility in modeling complex phenomena in

chemical processes. This utility has brought forward its potential for applications in

advanced process control strategies such as real-time optimization and model-based

20 M. N. Fuad et al.

predictive controls. Although first-principle based modeling is very useful for design

purpose and as an aid for the understanding, black-boxed modeling that employs

machine learning principles such as neural network and support vector machine is very

useful for real-time applications that demand faster and robust computations. Moreover,

the developments of the corresponding machine learning models are less demanding as

long as sufficient collections of input-output data samples are available for training

purpose. Once trained, the corresponding models can be used effectively and efficiently

to achieve various objectives such as operation point optimization or model-based

controls. Therefore, driven by these motivations, this paper seeks to study the

application of several machine learning methods to model the power performance

behavior of a solid oxide fuel cells operation. Specifically, four types of machine

learning methods i.e. artificial neural network, fuzzy inference system, support vector

machines and genetic programming are applied in this study in order to observe their

performances in modeling the operating behavior of the corresponding SOFC system.

2. Brief Descriptions of the Corresponding Machine Learning Methods

2.1. Artificial Neural Networks

Artificial neural networks (ANN) are a computational tool modeled on the

interconnection of the neurons in the nervous systems of the human brain and that of

other animals (Bishop, 1995). The structure of a feed-forward multilayer ANN is

displayed in Figure 1. In this structure, the information is passed from the input layer to

the hidden layer via various network connections and finally to the output layer. The

training phase of ANN consists of submitting samples of input-output data (called the

training data) to the network and adjusting the connection weights until the measure of

difference between the target data and ANN output is minimized. Past study has proven

that the standard multilayer feed-forward network with a single hidden layer can be

used to approximate continuous function of arbitrary complexity (i.e. universal

approximation theorem).

Figure 1. Feed-forward multilayer neural network

2.2. Fuzzy Inference Systems

Fuzzy inference systems (FIS) are simply the applications of fuzzy logic and fuzzy set

theory for data classification, decision analysis, and pattern recognition (Takagi &

Sugeno, 1985). The general architecture of FIS consists of three parts (see Figure 2).

The first part i.e. the fuzzifier, convert the crisp input to linguistic variables by using the

Machine Learning Based Modeling for Solid Oxide Fuel Cells Power Performance

Prediction 21

membership functions stored in the fuzzy knowledge base. In the next part i.e. inference

engine, a collections of IF-THEN type fuzzy rules will convert the fuzzy input to the

fuzzy output. Finally in the defuzzifier part, the fuzzy output of the inference engine will

be converted to crisp output by using the membership function analogous to the ones

employed by the fuzzifier. Currently, two types of fuzzy inference systems are widely

employed, i.e. Mamdani and Takagi-Sugeno. Moreover, the Takagi-Sugeno fuzzy

inference system can be ‘trained’ by an adaptive technique in which the parameters of

the membership functions are optimized with respect to the given samples of input-

output data.

Figure 2. Components of a fuzzy system

2.3. Support Vector Machines

Support vector machines (SVM) are among kernel-based techniques that are very

popular for data classification and regression (Ivanciuc, 2007). More formally, a support

vector machines constructs a hyperplane or set of hyperplanes in a high- or infinite-

dimensional space from several points in training examples (called support vectors)

which can be used for classification or regression. Formerly developed as a linear data

classifier, the extension to nonlinear classification was made possible by using kernel

trick that maps input space into a higher dimensional feature space. The training phase

of SVM amounts to solving an optimization problem that seeks to find the largest

margin hyperplane that represents the best separation of data into its proper categories.

The extension of SVM to nonlinear regression was made possible by using an ε-

insensitive loss function. Generally, the goal of SVM regression (SVMR) is to identify a

function f(x) that for all training patterns x has a maximum deviation ε from the target

values y and has a maximum margin (Ivanciuc, 2007).

2.4. Genetic Programming

Genetic programming (GP) is an evolutionary algorithm-based methodology inspired by

biological evolution to find computer programs that can better perform a user-defined

task (Koza, 1992). It is a specialization of genetic algorithms where each individual is a

computer program (see Figure 3) that will be evolved according to evolutionary

principles that seeks the fittest individuals among the population of the candidate

solutions. The fittest individuals represent computer programs that can perform the user-

defined task optimally. The principle of GP uses various analogs of the naturally

occurring evolutionary operations, including crossover (sexual recombination),

mutation, gene duplication, and gene deletion. Among the numerous applications of GP,

it has been used successfully for symbolic regressions. Specifically, in symbolic

regressions, the task of GP is to find both structure and parameters of a nonlinear model

that minimizes the error criterion between predictions and observed data.


Figure 3. A computer program (e.g. mathematical function) represented as a tree

structure in genetic programming

3. Modeling SOFC Power Performance via Machine Learning Methods

The corresponding machine learning methods (i.e. ANN, FIS, GP and SVM) are used in

this study to model the power performance behavior of a tubular SOFC under various

operating conditions. In this study, each of the corresponding machine learning models

will receive four inputs of the SOFC operation i.e. load current (20-158 A), fuel

utilization (50-90%), inlet air temperature (973-1173 K), and air molar flow rate (0.01-

0.02 mol/s). In turn, the models will predict the stack voltage and outlet temperature

values from the corresponding inputs. The database of the SOFC operation is generated

from the simulations of a physical model of a tubular SOFC for 1000 input dataset.

These input-output data pairings are further partitioned into 800 dataset for

training/validation and 200 dataset for testing. Furthermore, the dataset for the

training/validation are corrupted by ±5% measurement errors while the testing dataset

are left intact. All the input-output dataset in this study are normalized to [-1, 1] in order

to facilitate the training phase. Finally, the training parameters for each of the machine

learning models are tabulated in Table 1.

4. Results and Discussions

Figure 4 shows the parity plots that were generated from the testing data and the

corresponding machine learning model predictions at the conclusion of the trainings.

Although ANN method yield the slightly highest prediction accuracy with correlation

coefficient R = 0.99922, the other machine learning methods also exhibit satisfactory

performance in modeling the operating behavior of the corresponding SOFC system. It

should be noted that the corresponding parity plots were generated from the uncorrupted

testing data that was not used in the training phase of the corresponding machine

learning models. As such, the corresponding testing data (i.e. unseen data) can provide

information to evaluate the performance of the corresponding machine learning methods

in learning the behavior of the training/validation dataset that was corrupted by

measurement errors. Moreover, the prediction capabilities of the trained machine

learning models were also investigated further by reproducing the power performance

curves of the corresponding SOFC system at various fuel utilization and inlet air

temperature conditions as shown in Figure 5. As can be seen from the corresponding

figures, all the machine learning methods can reproduce the power performance curve

including the location of the maximum power point satisfactorily.

Machine Learning Based Modeling for Solid Oxide Fuel Cells Power Performance

Prediction 23

Table 1. Machine learning methods and their associated training parameters

Machine learning Training parameters

Artificial neural network (ANN) Multilayer feed-forward neural network with one hidden

layer and 10 neurons in the hidden layer

Training algorithm: Backpropagation algorithm with early

stopping (as implemented by neural network toolbox in

Matlab® software)

Fuzzy inference system (FIS) The training is based on the adaptive network based fuzzy

inference system (ANFIS) as implemented by fuzzy logic

toolbox in Matlab® software

2 membership functions of generalized bell type are

implemented for the input later and linear type

membership function is implemented for the output layer

Training algorithm: hybrid training method (i.e.

backpropagation algorithm with least-squares estimation

method)

Support vector machine (SVM) SVM type: ν-support vector regression (Chang & Lin,

2002) as implemented by LIBSVM package

Kernel type: radial basis function

Genetic programming (GP) Multi-gene symbolic regression (Searson, Leahy, & Willis,

2010) as implemented by GPTIPS package

Maximum number of genes: 5

Maximum tree depth: 6

Population size: 100

Number of generations: 100

Figure 4. Parity plots for the testing data predictions

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ANN, R = 0.99922

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SVM, R = 0.99841

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ANFIS, R = 0.99825

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GP, R = 0.99850


Figure 5. Comparisons of actual and predicted power performance curves (air molar flowrate =

0.012 mol/s)

5. Conclusions

In this study, we have compared different types of machine learning methods to model

the power performance behavior of a tubular SOFC operation. Among the different

types of machine learning methods that were covered in this study, it was found out that

ANN method has slighlty better performance in predicting the power performance

behavior of the corresponding SOFC system under various operating conditions. The

result from this study opens the possibility for applying the corresponding machine

learning method for SOFC performance maps constructions and operation point

optimization.

References

Bishop, C. M. (1995). Neural Networks for Pattern Recognition. Oxford: Oxford University

Press.

Chang, C. C., & Lin, C. J. (2002). Training nu-support vector regression: theory and algorithms.

Neural Computation, 14(8), 1959-1977.

Ivanciuc, O. (2007). Applications of support vector machines in chemistry. In K. B. Lipkowitz &

T. R. Cundari (Eds.), Reviews in Computational Chemistry (Vol. 23, pp. 291-400). Weinheim:

Wiley-VCH.

Koza, J. (1992). Genetic Programming: On the Programming of Computers by Means of Natural

Selection. Cambridge, MA: MIT Press.

Searson, D. P., Leahy, D. E., & Willis, M. J. (2010). GPTIPS: An open source genetic

programming toolbox for multigene symbolic regression. Paper presented at the International

MultiConference of Engineers and Computer Scientists Hong Kong.

Stambouli, A. B. (2011). Fuel cells: The expectations for an environmental-friendly and

sustainable source of energy. Renewable and Sustainable Energy Reviews, 15, 4507-4520.

Takagi, T., & Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling

and control. IEEE Transactions on Systems, Man and Cybernetics, 15, 116-132.

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Actual (FU = 0.75, Tin = 1073 K)

Predicted (FU = 0.75, Tin = 1073 K)

Actual (FU = 0.85, Tin = 1173 K)


Actual (FU = 0.75, Tin = 1073 K)


Actual (FU = 0.85, Tin = 1173 K)


Actual (FU = 0.75, Tin = 1073 K)


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PSEAsia2013-04