# Fault-Diagnosis Sensor Selection for Fuel Cell Stack Systems Combining an Analytic Hierarchy Process with the Technique Order Performance Similarity Ideal Solution Method

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

- After all the considerations above, we have found that the AHP and TOPSIS method is the most adaptable for the fault-diagnosis sensor selection. We summarized the following reasons: the fault-diagnosis sensor selection problem is a deterministic MCDM problem and, as compared with other methods, AHP and TOPSIS are optimal for deterministic conditions.
- The weight definition in the fault-diagnosis sensor choosing means subjective judgement steps, and it just maps to the AHP method.
- Compared with other complex process methods, it is easy to apply and use the AHP and TOPSIS methods.
- Among all MCDM techniques, the AHP and TOPSIS techniques require less information.
- Among all MCDM techniques, the TOPSIS technique has good stability in a data variable case.

## 3. Methods

#### 3.1. The AHP Technique

- Depending on how thorough the knowledge about the system is, determine the main target and establish the measures and policies involved in the planning and decision-making.
- Establish a hierarchical framwork, and define the location of all the factors that we use in this framwork according to different goals and different functions.
- Determine the degree of correlation between neighboring layer factors. Establish pairwise comparison matrices, determine the relative weight of a factor on the previous layer and the significance of the corresponding factors on this layer.
- Obtain the composite weight of every level factor to the target. Moreover, the sorting needs to be done, and the importance of the main target of the bottom element at the framwork needs to be defined.
- Establish the weight of each layer element of the system goal, perform the total sorting, and determine the importance of the overall goal of the lowest element in the hierarchical structure.

_{mn}refers to the value appearance of the determination of pairwise comparison values (alternative m, alternative n) for all alternatives (m, n = 1, 2, …, n). Here, m refers to a row of A and n refers to a column of A. In Equation (1), a

_{mn}cannot be equal to 0.

_{max}(Equation (2)):

_{max}refers to the largest eigenvector.

#### 3.2. TOPSIS Technique

- First, establish a decision matrix for alternatives (Equation (4)):$$D=\left[\begin{array}{cccccc}{y}_{11}& {y}_{12}& \cdots & {y}_{1j}& \cdots & {y}_{1J}\\ {y}_{21}& {y}_{22}& \cdots & {y}_{2j}& \cdots & {y}_{2J}\\ \vdots & \vdots & \cdots & \vdots & \cdots & \vdots \\ {y}_{i1}& {y}_{j2}& \cdots & {y}_{ij}& \cdots & {y}_{iJ}\\ \vdots & \vdots & \cdots & \vdots & \cdots & \vdots \\ {y}_{I1}& {y}_{I2}& & {y}_{Ij}& \cdots & {y}_{IJ}\end{array}\right]$$
_{ij}is the jth criterion value related to the ith alternative, I is total number of alternatives, and J is total number of criteria. - Second, obtain the normalized decision matrix Z(=z
_{ij}) (Equation (5)):$${z}_{ij}=\frac{{y}_{ij}}{\sqrt{{{\displaystyle \sum}}_{i=1}^{I}{y}_{ij}{}^{2}}}$$_{ij}is the normalized value for the jth criterion value related to the ith alternative and I is the total number of alternatives. The reason why we use the vector normalization technique is that many researchers have analyzed the effects of different normalizations for TOPSIS, and they have found that the vector normalization method is most suitable for TOPSIS [56,57]. Moreover, in this process, they have computed the consistency of the results of all the alternatives, and analyzed the sensitivity of the weight for different normalization methods applied on TOPSIS. - Third, obtain the weighted normalized decision matrix X(=x
_{ij}) (Equation (6)):$${x}_{ij}={\omega}_{j}\xb7{z}_{ij}$$ - Fourth, calculate the P-I and N-I results (Equations (7) and (8)):$$\mathrm{P}\text{-}\mathrm{I}\mathrm{solution}:{x}_{j}{}^{+}=\{\begin{array}{ll}\underset{i}{\mathrm{max}}{x}_{ij},& i\in {l}^{\prime}\\ \underset{i}{\mathrm{min}}{x}_{ij},& i\in {l}^{\u2033}\end{array}$$$$\mathrm{N}\text{-}\mathrm{I}\mathrm{solution}:{x}_{j}{}^{-}=\{\begin{array}{ll}\underset{i}{\mathrm{min}}{x}_{ij},& i\in {l}^{\prime}\\ \underset{i}{\mathrm{max}}{x}_{ij},& i\in {l}^{\u2033}\end{array}$$
- Fifth, obtain a symmetric n-dimensional Euclidean distance from every result to the P-I result and the N-I result (Equations (9) and (10)):$$\mathrm{Symmetric}\mathrm{distance}\mathrm{to}\mathrm{P}\text{-}\mathrm{I}\mathrm{solution}:{d}_{i}{}^{+}=\sqrt{{{\displaystyle \sum}}_{j=1}^{J}{\left({x}_{ij}-{x}_{j}{}^{+}\right)}^{2}}$$$$\mathrm{Symmetric}\mathrm{distance}\mathrm{to}\mathrm{N}\text{-}\mathrm{I}\mathrm{solution}:{d}_{i}{}^{-}=\sqrt{{{\displaystyle \sum}}_{j=1}^{J}{\left({x}_{ij}-{x}_{j}{}^{-}\right)}^{2}}$$
- Sixth, obtain the closeness to the ideal result (Equation (11)):$${C}_{i}{}^{*}=\frac{{d}_{i}{}^{-}}{\left({d}_{i}{}^{-}+{d}_{i}{}^{+}\right)}$$
- Seventh, determine the order of the C
_{i}* value to define the performance of the alternatives. The larger the C_{i}* value is, the better the performance of the alternatives is.

## 4. Results

#### 4.1. The Whole Process of Fault-Diagnosis Sensors for FCS

#### 4.2. Criteria for Fault-Diagnosis Sensors Selection for FCS

- Constructional Parameters: Constructional parameters are related to the size and shape of the fault-diagnosis sensors, the installation ease, and expansion ability.
- Efficient Parameters: Efficient parameters are related to the efficiency and performance of fault-diagnosis sensors.
- Economical Parameters: Economic parameters include the cost of all parts of the fault-diagnosis sensor.
- Safety Parameters: Safety parameters include the incidence of sensor breakage or electrical leakage and the safety of the sensor system in an emergency.
- Resilience and tolerance: Resilience and tolerance parameters related to the ability of a fault-diagnosis sensor system to provide the required capability in the face of adversity and the fault-tolerant design of the sensor. In an FCS system, there are different kinds of adversities, such as electromagnetic and light interference, sudden power cuts, and the best detection distance range, and we have to evaluate the capacity, which is related to the ability to deal with all these interferences, and ensure that the error diagnosis process of the fault-diagnosis sensor system continues. Tolerance is related to the capability of the fault-diagnosis system to continue error-free work in the situation of an unexpected failure (complete unworking, fixed deviation, drift deviation, and accuracy degradation).

#### 4.3. Assigning the Weights of the Criteria via AHP

- Compressor motor checking: the main function of this part is to check the angular speed and motor torque of the compressor, and record the size of the compressor current.
- Supply Manifold checking: the main function of this part it to check the exist air mass flow rate and temperature of the of the inlet manifold.
- Air Cooler checking: the main function of this part is to check the air mass flow rate and temperature of the magic cooler. Moreover, it can also check the humidity of the magic cooler.
- Static humidifier checking: the main function of this part is to check the exit air mass humidity, temperature, and pressure of the stack humidifier, and also check the injected vapor mass flow rate.
- Outlet manifold checking: the main function of this part if to check the outlet manifold exit air mass flow rate, pressure, and humidity.
- Stack cathode checking: this main function of this part is to check the cathode and anode exit hydrogen mass flow rate, hydrogen pressure, relative hydrogen humidity, and exit vapor mass flow rate.

_{i}and rv

_{k}) in Table 3, Table 4, Table 5, Table 6, Table 7 and Table 8 are released depending on the Equations (2) and (3) (the rescaled weights for the main right eigenvector for the pairwise comparison are shown in Table 3, Table 4, Table 5, Table 6, Table 7 and Table 8). Here, the calculated weight for the fault-diagnosis sensor sub-criteria (w

_{k}) is obtained by multiplying the criteria of the rescaled weight û

_{i}and the sub-criteria of the rescaled weight rv

_{k}.

#### 4.4. Determining the Final Result via TOPSIS

_{1}) relative to sub-criteria CT

_{11}is 0.102. The value is obtained by multiplying the calculated weight of sub-criteria C

_{11}(w

_{k}(0.296 in Table 4)) and the normalized decision matrix value for C

_{11}($0.343=\frac{2}{\sqrt{{2}^{2}+{1}^{2}+{3}^{2}+{4}^{2}+{2}^{2}}}$). After that, depending on Table 11 and Equations (7) and (8), the P-I and N-I results can be decided. The P-I and N-I results can be seen in Table 12.

_{i}* value in Table 13, we can find that the fault-diagnosis sensor SE

_{2}has the highest value (0.747). In contrast, sensor SE

_{4}has the smallest value (0.151). Moreover, we also find that companies pay more attention to the Constructional Parameters (C

_{1}) and Economical parameters (C

_{2}) (the rescaled weights (û

_{i}) for these two parts in Table 3 are 0.36 and 0.367, respectively). Moreover, in the Constructional Parameters (C

_{1}), companies pay more attention to the criteria C

_{11}(the rescaled weight (û

_{i}) for C

_{11}is 0.296; the lower the criteria data, the better), and in the Economical parameters (C

_{2}), companies pay more attention to the criteria C

_{21}(the rescaled weight (û

_{i}) for C

_{21}is 0.156; the smaller the criteria value, the better). Therefore, when we use these two criteria (C

_{11,}C

_{21}) to compare all the sensors, we can find that SE

_{2}has the smallest value (1 for C

_{11}and 2 for C

_{21}, see Table 10). Therefore, compared with other sensors, SE

_{2}has the smallest size and shape, while the compressor motor inspection has the lowest cost, and these two parts are also the most important reason why SE

_{2}is optimal. Additionally, companies should pay more attention to these two parts when considering other new sensors. Therefore, given the result above, companies can select fault-diagnosis sensor SE

_{2}to ensure that the FCS fault-diagnosis process is more efficient, economical, and safer compared with other alternatives.

## 5. Discussion

_{i}* value, the better). The main contribution of this paper is to help Fuel Cell Stack Systems companies to select the appropriate fault-diagnosis sensor to ensure that the Fuel Cell Stack Systems fault-diagnosis process is more economical, efficient, and safer.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**The FCS scheme and the corresponding fault-diagnosis sensor system. Note. C = Collecting data. CS = Compressor motor checking part. SM = Supply Manifold checking part AC = Air Cooler checking part. SH = Static humidifier checking part. OM = Outlet manifold checking part. SC = Stack cathode checking part.

**Figure 3.**Multi-level hierarchical structure for the FCS fault-diagnosis sensor criteria weight definition.

The Paired Comparison Reference Rank | ||
---|---|---|

Significance Rank | Relation Type | Interpretation |

1 | Same significance | Two options dedicated to the same degree to the target |

3 | Little significance of an option to the other | Assessment is slightly more inclined to one option over another |

5 | High significance | Assessment is strongly inclined to one option over another |

7 | Higher significance | Very high inclination to one option over another |

9 | Absolute significance | One option is absolutely more significant than another |

2,4,6,8 | Intermediate values between the two ratios | When there is a need to subdivide |

Criteria | Sub-Criteria |
---|---|

Constructional Parameters (C_{1}) | The size and the shape of the fault-diagnosis sensor (C_{11}) |

The installation easiness (C_{12}) | |

The expansion ability (C_{13}) | |

Economical Parameters (C_{2}) | Compressor motor checking sensor cost (C_{21}) |

Supply manifold checking sensor cost (C_{22}) | |

Air cooler checking sensor cost (C_{23}) | |

Static humidifier checking sensor cost (C_{24}) | |

Outlet manifold checking sensor cost (C_{25}) | |

Stack cathode checking sensor cost (C_{26}) | |

Efficient Parameters (C_{3}) | Compressor motor checking (C_{31}) |

Supply manifold checking (C_{32}) | |

Air cooler checking (C_{33}) | |

Static humidifier checking (C_{34}) | |

Outlet manifold checking (C_{35}) | |

Stack cathode and anode checking (C_{36}) | |

Safety Parameters (C_{4}) | Incidence of sensor breakage or electrical leakage (C_{41}) |

Safety of the sensor system in an emergency (C_{42}) | |

Resilience and tolerance parameters (C_{5}) | fault-diagnosis sensor system resilience ability (C_{51}) |

fault-tolerant design of the sensor (C_{52}) |

**Table 3.**Consequence of comparison of four fault-diagnosis criteria and the rescaled weight of the significance of them.

Criteria | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | u_{i} | û_{i} |
---|---|---|---|---|---|---|---|

Constructional Parameters (C_{1}) | 1 | 1 | 2 | 5 | 3 | 0.323 | 0.36 |

Economical Parameters (C_{2}) | 1 | 1 | 2 | 7 | 2 | 0.329 | 0.367 |

Efficient Parameters (C_{3}) | 1/2 | 1/2 | 1 | 3 | 2 | 0.178 | 0.198 |

Safety Parameters (C_{4}) | 1/5 | 1/7 | 1/3 | 1 | 1 | 0.067 | 0.075 |

Resilience and tolerance parameters (C_{5}) | 1/3 | 1/2 | 1/2 | 1 | 1 | 0.104 | 0.116 |

_{i}= Weight for the fault-diagnosis criteria. û

_{i}= rescaled weight for the fault-diagnosis criteria.

**Table 4.**Pairwise comparison result and weight of the Constructional Parameter (C

_{1}) sub-criteria.

Criteria | û_{i} | Sub-Criteria | C_{11} | C_{12} | C_{13} | v_{k} | rv_{k} | w_{k} (û_{i} × rv_{k}) |
---|---|---|---|---|---|---|---|---|

C_{1} | 0.36 | C_{11} | 1 | 4 | 6 | 0.710 | 0.821 | 0.296 |

C_{12} | 1/4 | 1 | 1 | 0.155 | 0.179 | 0.064 | ||

C_{13} | 1/6 | 1 | 1 | 0.135 | 0.156 | 0.056 |

_{i}= rescaled weight for the fault-diagnosis criteria. v

_{k}= Weight for the fault-diagnosis sensor sub-criteria. rv

_{k}= rescaled weight for the fault-diagnosis sub-criteria. w

_{k}= Calculated weight for the fault-diagnosis sensor sub-criteria.

C | û_{i} | Sub-Criteria | C_{2}_{1} | C_{2}_{2} | C_{2}_{3} | C_{2}_{4} | C_{2}_{5} | C_{26} | v_{k} | rv_{k} | w_{k} (û_{i} × rv_{k}) |
---|---|---|---|---|---|---|---|---|---|---|---|

C_{2} | 0.367 | C_{21} | 1 | 3 | 4 | 7 | 4 | 3 | 0.395 | 0.425 | 0.156 |

C_{22} | 1/3 | 1 | 2 | 3 | 5 | 2 | 0.211 | 0.227 | 0.083 | ||

C_{23} | 1/4 | 1/2 | 1 | 2 | 4 | 1 | 0.135 | 0.145 | 0.053 | ||

C_{24} | 1/7 | 1/3 | 1/2 | 1 | 2 | 3 | 0.096 | 0.103 | 0.038 | ||

C_{25} | 1/5 | 1/5 | 1/4 | 1/2 | 1 | 5 | 0.093 | 0.1 | 0.037 | ||

C_{26} | 1/3 | 1/2 | 1 | 1/3 | 1/5 | 1 | 0.069 | 0.074 | 0.027 |

_{i}= rescaled weight for the fault-diagnosis criteria. v

_{k}= Weight for the fault-diagnosis sensor sub-criteria. rv

_{k}= rescaled weight for the fault-diagnosis sub-criteria. w

_{k}= Calculated weight for the fault-diagnosis sensor sub-criteria.

C | û_{i} | Sub-Criteria | CT_{3}_{1} | C_{3}_{2} | C_{3}_{3} | C_{3}_{4} | C_{3}_{5} | C_{36} | v_{k} | rv_{k} | w_{k} (û_{i} × rv_{k}) |
---|---|---|---|---|---|---|---|---|---|---|---|

C_{3} | 0.198 | C_{31} | 1 | 2 | 5 | 3 | 4 | 1 | 0.329 | 0.361 | 0.071 |

C_{32} | 1/2 | 1 | 2 | 4 | 6 | 3 | 0.247 | 0.271 | 0.054 | ||

C_{33} | 1/5 | 1/2 | 1 | 2 | 4 | 1 | 0.132 | 0.145 | 0.029 | ||

C_{34} | 1/3 | 1/4 | 1/2 | 1 | 2 | 3 | 0.105 | 0.115 | 0.023 | ||

C_{35} | 1/5 | 1/6 | 1/4 | 1/2 | 1 | 5 | 0.098 | 0.108 | 0.021 | ||

C_{36} | 1 | 1/3 | 1 | 1/3 | 1/5 | 1 | 0.089 | 0.098 | 0.019 |

_{i}= rescaled weight for the fault-diagnosis criteria. v

_{k}= Weight for the fault-diagnosis sensor sub-criteria. rv

_{k}= rescaled weight for the fault-diagnosis sub-criteria. w

_{k}= Calculated weight for the fault-diagnosis sensor sub-criteria.

Criteria | û_{i} | Sub-Criteria | C_{4}_{1} | C_{4}_{2} | v_{k} | rv_{k} | w_{k} (û_{i} × rv_{k}) |
---|---|---|---|---|---|---|---|

C_{4} | 0.075 | C_{41} | 1 | 3 | 0.75 | 1 | 0.075 |

C_{42} | 1/3 | 1 | 0.25 | 0.333 | 0.025 |

_{i}= rescaled weight for the fault-diagnosis criteria. v

_{k}= Weight for the fault-diagnosis sensor sub-criteria. rv

_{k}= rescaled weight for the fault-diagnosis sub-criteria. w

_{k}= Calculated weight for the fault-diagnosis sensor sub-criteria.

Criteria | û_{i} | Sub-Criteria | C_{4}_{1} | C_{4}_{2} | v_{k} | rv_{k} | w_{k} (û_{i} × rv_{k}) |
---|---|---|---|---|---|---|---|

C_{5} | 0.116 | C_{51} | 1 | 4 | 0.8 | 1 | 0.116 |

C_{52} | 1/4 | 1 | 0.2 | 0.25 | 0.029 |

_{i}= rescaled weight for the fault-diagnosis criteria. v

_{k}= Weight for the fault-diagnosis sensor sub-criteria. rv

_{k}= rescaled weight for the fault-diagnosis sub-criteria. w

_{k}= Calculated weight for the fault-diagnosis sensor sub-criteria.

Value | Meaning |
---|---|

5 | Excellent |

4 | Good |

3 | Normal |

2 | Bad |

1 | Terrible |

A | CT_{1} | CT_{2} | CT_{3} | CT_{4} | CT_{5} | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

CT_{11} | CT_{12} | CT_{13} | CT_{21} | CT_{22} | CT_{23} | CT_{24} | CT_{25} | CT_{26} | CT_{31} | CT_{32} | CT_{33} | CT_{34} | CT_{35} | CT_{36} | CT_{41} | CT_{42} | CT_{51} | CT_{52} | |

SE_{1} | 2 | 4 | 4 | 1 | 3 | 4 | 4 | 5 | 5 | 4 | 4 | 4 | 1 | 5 | 3 | 5 | 2 | 3 | 3 |

SE_{2} | 1 | 1 | 2 | 2 | 4 | 4 | 1 | 2 | 1 | 2 | 2 | 2 | 1 | 2 | 5 | 2 | 1 | 5 | 2 |

SE_{3} | 3 | 3 | 3 | 3 | 5 | 2 | 3 | 1 | 2 | 1 | 4 | 2 | 5 | 3 | 4 | 4 | 4 | 3 | 2 |

SE_{4} | 4 | 2 | 1 | 5 | 2 | 1 | 2 | 3 | 1 | 4 | 2 | 1 | 1 | 5 | 2 | 2 | 2 | 2 | 1 |

SE_{5} | 2 | 4 | 2 | 5 | 2 | 4 | 2 | 3 | 1 | 2 | 1 | 5 | 4 | 3 | 1 | 1 | 2 | 2 | 3 |

A | CT_{1} | CT_{2} | CT_{3} | CT_{4} | CT_{5} | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

CT_{11}MI | CT_{12}MA | CT_{13}MA | CT_{21}MI | CT_{22}MI | CT_{23}MI | CT_{24}MI | CT_{25}MI | CT_{26}MI | CT_{31}MA | CT_{32}MA | CT_{33}MA | CT_{34}MA | CT_{35}MA | CT_{36}MA | CT_{41}MA | CT_{42}MA | CT_{51}MA | CT_{52}MA | |

SE_{1} | 0.102 | 0.038 | 0.038 | 0.02 | 0.033 | 0.029 | 0.026 | 0.027 | 0.024 | 0.044 | 0.034 | 0.016 | 0.003 | 0.012 | 0.008 | 0.053 | 0.009 | 0.049 | 0.017 |

SE_{2} | 0.051 | 0.009 | 0.019 | 0.039 | 0.044 | 0.029 | 0.007 | 0.011 | 0.005 | 0.022 | 0.017 | 0.008 | 0.003 | 0.005 | 0.013 | 0.021 | 0.005 | 0.081 | 0.011 |

SE_{3} | 0.152 | 0.028 | 0.029 | 0.059 | 0.054 | 0.015 | 0.02 | 0.005 | 0.01 | 0.011 | 0.034 | 0.008 | 0.017 | 0.007 | 0.01 | 0.042 | 0.019 | 0.049 | 0.011 |

SE_{4} | 0.203 | 0.019 | 0.010 | 0.098 | 0.022 | 0.007 | 0.013 | 0.016 | 0.005 | 0.044 | 0.017 | 0.004 | 0.003 | 0.012 | 0.005 | 0.021 | 0.009 | 0.032 | 0.006 |

SE_{5} | 0.102 | 0.038 | 0.019 | 0.098 | 0.022 | 0.029 | 0.013 | 0.016 | 0.005 | 0.022 | 0.008 | 0.021 | 0.014 | 0.007 | 0.003 | 0.011 | 0.009 | 0.032 | 0.017 |

A | CT_{1} | CT_{2} | CT_{3} | CT_{4} | CT_{5} | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

CT_{11}MI | CT_{12}MA | CT_{13}MA | CT_{21}MI | CT_{22}MI | CT_{23}MI | CT_{24}MI | CT_{25}MI | CT_{26}MI | CT_{31}MA | CT_{32}MA | CT_{33}MA | CT_{34}MA | CT_{35}MA | CT_{36}MA | CT_{41}MA | CT_{42}MA | CT_{51}MA | CT_{52}MA | |

SE^{+} | 0.051 | 0.038 | 0.038 | 0.02 | 0.022 | 0.007 | 0.007 | 0.005 | 0.005 | 0.044 | 0.034 | 0.021 | 0.017 | 0.012 | 0.013 | 0.011 | 0.019 | 0.081 | 0.017 |

SE^{−} | 0.203 | 0.009 | 00.01 | 0.098 | 0.054 | 0.029 | 0.026 | 0.027 | 0.024 | 0.011 | 0.008 | 0.004 | 0.003 | 0.005 | 0.003 | 0.053 | 0.005 | 0.032 | 0.006 |

Alternative | d_{i}^{+} | d_{i}^{−} | C_{i}* |
---|---|---|---|

SE_{1} | 0.087 | 0.144 | 0.624 |

SE_{2} | 0.059 | 0.174 | 0.747 |

SE_{3} | 0.128 | 0.079 | 0.381 |

SE_{4} | 0.185 | 0.033 | 0.151 |

SE_{5} | 0.116 | 0.106 | 0.476 |

_{i}* = The relative closeness to the ith ideal solution.

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## Share and Cite

**MDPI and ACS Style**

Jin, G.; Jin, G.
Fault-Diagnosis Sensor Selection for Fuel Cell Stack Systems Combining an Analytic Hierarchy Process with the Technique Order Performance Similarity Ideal Solution Method. *Symmetry* **2021**, *13*, 2366.
https://doi.org/10.3390/sym13122366

**AMA Style**

Jin G, Jin G.
Fault-Diagnosis Sensor Selection for Fuel Cell Stack Systems Combining an Analytic Hierarchy Process with the Technique Order Performance Similarity Ideal Solution Method. *Symmetry*. 2021; 13(12):2366.
https://doi.org/10.3390/sym13122366

**Chicago/Turabian Style**

Jin, Guangying, and Guangzhe Jin.
2021. "Fault-Diagnosis Sensor Selection for Fuel Cell Stack Systems Combining an Analytic Hierarchy Process with the Technique Order Performance Similarity Ideal Solution Method" *Symmetry* 13, no. 12: 2366.
https://doi.org/10.3390/sym13122366