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Research Papers

Classification and Fault Detection Methods for Fuel Cell Monitoring and Quality Control

[+] Author and Article Information
Natalie L. H. Lowery

Postgraduate Researcher
Department of Mathematics and Statistics,
University of Reading,
Whiteknights,
P.O. Box 220,
Berkshire RG6 6AX, UK
e-mail: n.l.h.lowery@pgr.reading.ac.uk

Maria M. Vahdati

Doctor, Lecturer in Renewable Energy
Department of Construction Management and Engineering,
University of Reading,
Whiteknights,
P.O. Box 220,
Berkshire RG6 6AY, UK
e-mail: m.m.vahdati@reading.ac.uk

Roland W. E. Potthast

Professor of Applied Mathematics
Department of Mathematics and Statistics,
University of Reading,
Whiteknights,
P.O. Box 220,
Berkshire RG6 6AX, UK
e-mail: r.w.e.potthast@reading.ac.uk

William Holderbaum

Doctor, Senior Lecturer in Mathematical Engineering
School of Systems Engineering,
University of Reading,
Whiteknights,
P.O. Box 220,
Berkshire RG6 6AY, UK
e-mail: w.holderbaum@reading.ac.uk

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY. Manuscript received June 28, 2012; final manuscript received December 10, 2012; published online March 21, 2013. Assoc. Editor: Ken Reifsnider.

J. Fuel Cell Sci. Technol 10(2), 021002 (Mar 21, 2013) (8 pages) Paper No: FC-12-1061; doi: 10.1115/1.4023565 History: Received June 28, 2012; Revised December 10, 2012

In this paper, various types of fault detection methods for fuel cells are compared. For example, those that use a model based approach or a data driven approach or a combination of the two. The potential advantages and drawbacks of each method are discussed and comparisons between methods are made. In particular, classification algorithms are investigated, which separate a data set into classes or clusters based on some prior knowledge or measure of similarity. In particular, the application of classification methods to vectors of reconstructed currents by magnetic tomography or to vectors of magnetic field measurements directly is explored. Bases are simulated using the finite integration technique (FIT) and regularization techniques are employed to overcome ill-posedness. Fisher's linear discriminant is used to illustrate these concepts. Numerical experiments show that the ill-posedness of the magnetic tomography problem is a part of the classification problem on magnetic field measurements as well. This is independent of the particular working mode of the cell but influenced by the type of faulty behavior that is studied. The numerical results demonstrate the ill-posedness by the exponential decay behavior of the singular values for three examples of fault classes.

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Figures

Grahic Jump Location
Fig. 1

Simplified diagram of a fuel cell. The thick blue line in the middle represents the anode, membrane, and cathode. At the anode hydrogen is oxidized and the hydrogen ions cross the membrane to the cathode, where oxygen is reduced to produce water. The membrane is made from some electric insulator and so the electrons produced in the oxidation of hydrogen, cannot cross it. Instead, they are forced to travel through a wire running from the anode to the cathode. This circuit has some external load attached to it, which is powered by the electrons.

Grahic Jump Location
Fig. 2

Here the first image (a) shows a grid used for simulation of currents within a fuel cell. In this case the grid is 5 × 5 × 2 but the size can be varied. The second image (b) shows a close up view of the same grid, with numbered nodes. Currents are calculated using the Kirchoff mesh and knot rules. At each of the nodes the sum of the incoming currents and outgoing currents is zero and the sum of the voltages in a closed loop is zero. This gives a number of simultaneous equations, which can be solved to determine the currents in the grid. The corresponding magnetic fields are found by application of a discretized version of the Biot–Savart operator.

Grahic Jump Location
Fig. 3

A linearly nonseparable problem. The two classes shown cannot be separated by a line.

Grahic Jump Location
Fig. 4

The nonseparable problem shown in Fig. 3 can be broken down into two linearly separable problems

Grahic Jump Location
Fig. 9

Figure to show the estimations for the distances in decreasing order between the magnetic field classes and the origin in the image space as a logarithmic scale. The blue dashed line corresponds to νℓ = eℓ, the red line corresponds to a νℓ with Gaussian kernel and the black dotted line corresponds to νℓ given by a jump function. (See online figure version for color.)

Grahic Jump Location
Fig. 8

Figure to show the estimations for the distances in decreasing order between the magnetic field classes and the origin in the image space. The blue dashed line corresponds to νℓ = eℓ, the red line corresponds to a νℓ with Gaussian kernel and the black dotted line corresponds to νℓ given by a jump function. (See online figure version for color.)

Grahic Jump Location
Fig. 7

Figure to show the selection of the νℓ used in the distance estimations. The first is the standard basis for RL, the second depicts entries with a Gaussian kernel and the third shows a jump function.

Grahic Jump Location
Fig. 6

Fisher's linear discriminant is performed on magnetic field vectors, where the class labels are defined using the second entries of the vectors of basis function coefficients. The projected values are shown as small red spheres for C1 and large blue spheres for C2. The small purple sphere indicates the projection of a test vector. (See online figure version for color.)

Grahic Jump Location
Fig. 5

Fisher's linear discriminant is performed on vectors of basis function coefficients, where the class labels are defined using the second entries of the vectors of basis function coefficients. The projected values are shown as small red spheres for C1 and large blue spheres for C2. The small purple sphere indicates the projection of a test vector. (See online figure version for color.)

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