# Fault Diagnosis for PEMFC Water Management Subsystem Based on Learning Vector Quantization Neural Network and Kernel Principal Component Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proton Exchange Membrane Fuel Cell (PEMFC) Power System and Water Management Failures

#### 2.1. PEMFC Test System

#### 2.2. Types of Water Management Failure

#### 2.2.1. Water Flooding Failure

#### 2.2.2. Dry Membrane Failure

## 3. Diagnostic Methods

#### 3.1. Kernel Principal Component Analysis (KPCA)

_{1}, x

_{2}, …, x

_{n}}, assuming the mapping function is φ(x), when mapped to higher dimensions, the data become a linearly independent variable: φ(x

_{1}), φ(x

_{2}), …, φ(x

_{n}) and choose the appropriate kernel function [20] for D:

_{n}is an n × n matrix, where all the elements are 1/n. Note that the eigenvalues are corresponding to the kernel matrix K and then arrange them in order from the largest to the smallest.

_{1}, a

_{2}, …, a

_{L}) can be calculated and present a new direction to reduce the dimensionality of high-dimensional data [21], as shown below:

_{l}is the first element of the projection vector (l ∈ 1, 2, … L), and a

_{ln}is the corresponding value in the eigenvector calculated above.

_{i}is the i-th principal component, n is the number of total principal components, L is the choice number of principal components, and T is the threshold (according to previous studies, 0.95 is selected in this case).

#### 3.2. Learning Vector Quantization Neural Network (LVQNN)

#### 3.3. KPCA-LVQNN

- Collect the original data. By setting the operating parameters at the rated value, reducing the temperature of PEMFC and reducing the humidity of reaction gas, the PEMFC stack can be in a normal state, water flooding fault state and membrane dry fault state, respectively. The original experimental data of PEMFC system can then be collected in real time with the help of temperature, pressure, flow and voltage sensors.
- Pre-process data. In order to reduce the dimensional differences between different parameters in the original experimental data, the original experimental data are standardized.
- Reduce data dimension. In the original experimental data standardization, the dimension of the data is still very high and has strong coupling, and there are characteristic parameters not related to the diagnosis results. KPCA is used to determine the variance contribution rate and the number of principal components, reduce the dimension of the input feature quantity, and change it into a group of linearly unrelated variables, and finally complete the extraction of fault feature vector.
- Divide the dimensionality-reduced feature data of health status into training and test samples with an ratio of 60% and 40%, respectively.
- Train the neural network. The training set is introduced into LVQNN model to get the trained LVQNN diagnosis model.
- Test the diagnostic results. The test set is input into the trained KPCA-LVQNN and the fault detection results are output.
- Analyze diagnostic results. The performance and feasibility of KPCA-LVQNN are evaluated by calculating the correct rate, false alarm rate and rejection rate, drawing the diagnosis result graph and establishing the confusion matrix. The feasibility of the method is evaluated by comparing with back propagation neural network (BPNN).

## 4. Results and Discussion

#### 4.1. Experimental Data Acquisition

#### 4.2. Fault Feature Vector Extraction

#### 4.3. Fault Diagnosis Results

#### 4.4. Comparative Analysis

## 5. Conclusions

- The KPCA algorithm can reduce the dimension of high-dimensional data, which can extract the essential characteristics of data, and reduce the calculation time. The cumulative contribution rate reaches 95% in the experiment, indicating that the first five principal components can characterize 14-dimensional sample data.
- LVQNN is a self-organizing competitive network with supervised learning, which has a good performance in recognition effect. The analysis results of samples show that the proposed method can accurately diagnose the PEMFC system with three health states: normal state, membrane dry fault and water flooding fault. The recognition accuracy of training set samples and test set samples are 97.6% and 96.9%, respectively, and the operation time is 2.5333 s. The FAR of training set is 1.28% and the FRR is 2.80%. The FAR of the test set is 2.05% and the FRR is 3.42%.
- The proposed method is particularly suitable for processing health status data with high dimensions and abundant samples. Compared with the BPNN method, it is found that the proposed method has higher fault diagnosis accuracy and less computation time, with the testing accuracy improved by 21.22% and the time is shortened by 6.2743 s.
- The proposed KPCA-LVQNN method can not only solve the problem of PEMFC water management subsystem fault diagnosis, but also can be applied in a broader range of engineering fields. Given insufficient experimental conditions, only three health states were detected in this work. Future studies will include more types of health state for detection by collecting more original feature data of failure types.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Voltage and current diagram of PEMFC water flooding and membrane dry experiment: (

**a**) water flooding; (

**b**) dry membrane.

**Figure 4.**Fault diagnosis process of PEMFC water management based on kernel principal component analysis (KPCA)-LVQNN.

**Figure 8.**Diagnostic results of KPCA-LVQNN. (

**a**) Training diagnostic results; (

**b**) test diagnostic results.

**Figure 9.**The confusion matrix of KPCA-LVQNN. (

**a**) Training confusion matrix; (

**b**) test confusion matrix.

**Figure 10.**The receiver operating characteristic (ROC) curve of the KPCA-LVQNN for training and test samples. (

**a**) Training samples; (

**b**) test samples.

Parameter | Value |
---|---|

Active area (cm^{2}) | 100 |

rated power (W) | 80 |

film thickness (μm) | 25 |

Platinum loading(mg/cm^{2}) | 0.2 |

Thickness of gas diffusion layer (μm) | 415 |

Number | Variable | Unit |
---|---|---|

1 | Single stack voltage | V |

2 | Single stack current | A |

3 | Single stack power | W |

4 | Stack inlet air flow rate | SPLM |

5 | Stack inlet hydrogen flow rate | SPLM |

6 | Stack inlet air pressure | Bar |

7 | Stack inlet hydrogen pressure | Bar |

8 | Stack outlet air pressure | Bar |

9 | Stack outlet hydrogen pressure | Bar |

10 | Stack inlet air temperature | °C |

11 | Stack inlet hydrogen temperature | °C |

12 | Stack outlet temperature | °C |

13 | Heater temperature | °C |

14 | Heater power | W |

Type | Number | Principal Component | ||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | ||

Normal state | 1 | −0.2393 | 0.7391 | −0.2429 | 0.1793 | 0.0036 |

2 | −0.2393 | 0.7391 | −0.2429 | 0.1793 | 0.0036 | |

3 | −0.2391 | 0.7372 | −0.2401 | 0.1744 | 0.0116 | |

Water flooding failure | 4 | −0.5418 | −0.4562 | −0.4788 | −0.0598 | 0.1566 |

5 | −0.5418 | −0.4562 | −0.4787 | −0.0598 | 0.1566 | |

6 | −0.5414 | −0.4558 | −0.4785 | −0.0597 | 0.1565 | |

Membrane dry failure | 7 | 0.6790 | −0.1276 | 0.0063 | 0.0980 | 0.0342 |

8 | 0.6790 | −0.1276 | 0.0063 | 0.0980 | 0.0342 | |

9 | 0.6796 | −0.1278 | 0.0063 | 0.0984 | 0.0344 |

Health Condition | Normal State | Water Flooding Fault | Membrane Dry Fault | Total Correct Rate | |
---|---|---|---|---|---|

Detection Method | |||||

KPCA and LVQNN | 98.95% | 92.34% | 100% | 96.93% | |

Unpretreated LVQNN | 96.51% | 82.31% | 100% | 93.23% | |

KPCA and BPNN | 96.51% | 84.37% | 71.14% | 82.04% | |

Unpretreated BPNN | 66.07% | 74.87% | 82.41% | 75.71% |

Detection Method | LVQNN | BPNN | ||
---|---|---|---|---|

Using KPCA Dimension Reduction | Without Dimension Reduction | Using KPCA Dimension Reduction | Without Dimension Reduction | |

Computation time (s) | 2.5333 | 3.9743 | 6.9250 | 8.8076 |

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**MDPI and ACS Style**

Jiang, S.; Li, Q.; Gan, R.; Chen, W.
Fault Diagnosis for PEMFC Water Management Subsystem Based on Learning Vector Quantization Neural Network and Kernel Principal Component Analysis. *World Electr. Veh. J.* **2021**, *12*, 255.
https://doi.org/10.3390/wevj12040255

**AMA Style**

Jiang S, Li Q, Gan R, Chen W.
Fault Diagnosis for PEMFC Water Management Subsystem Based on Learning Vector Quantization Neural Network and Kernel Principal Component Analysis. *World Electric Vehicle Journal*. 2021; 12(4):255.
https://doi.org/10.3390/wevj12040255

**Chicago/Turabian Style**

Jiang, Shuna, Qi Li, Rui Gan, and Weirong Chen.
2021. "Fault Diagnosis for PEMFC Water Management Subsystem Based on Learning Vector Quantization Neural Network and Kernel Principal Component Analysis" *World Electric Vehicle Journal* 12, no. 4: 255.
https://doi.org/10.3390/wevj12040255