# Research on Model-Based Fault Diagnosis for a Gas Turbine Based on Transient Performance

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## Abstract

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## 1. Introduction

- The accuracy of the algorithm should be increased;
- The diagnostic result based on steady-state data and dynamic data should be compared;
- The diagnostic method based on transient process data should be used to analyze field data.

## 2. Methodology

#### 2.1. Modeling of Gas Turbine

**Compressor and Turbine.**The compressor and two turbines (high pressure turbine and power turbine) are modelled using the characteristic map that describes the correlation between pressure ratio, mass flow rate, rational speed, and efficiency. For example, compressor speed and isentropic efficiency can be determined using the characteristic map. Since the design pressure ratio of the compressor is known, and the mass flow rate of the air is determined from the plant operation requirement, mainly referring to power output, the compressor speed and isentropic efficiency can be read off the characteristic map.

_{in}is the inlet temperature. From steady-state characteristics map generated by the field operating data [21], compressor mass flow G

_{c}and component efficiency η can be calculated by Equation (1), which can be used to calculate the power required and the temperature of the discharge air.

_{p}is the heat capacity and R is the gas constant.

**Combustor.**The combustor model involves the prediction of the dynamic response of pressure and temperature inside the combustor. The pressure is determined by the combustor model, while the flow rate is determined by the compressor and turbine model using the characteristics maps. Therefore, the state equation of pressure can be written as:

_{p,g}is heat capacity, and ρ

_{g}is the gas density in the combustor.

**Rotating Shaft.**A rotor is used to connect the compressor and load to the turbine. The mode is described by the following equation.

_{t}is input power from turbine, n is the rotational speed, and P

_{c}is the output power to drive the compressor.

#### 2.2. Cuckoo Search Algorithm

- A cuckoo lays one egg at a time, and selects a bird’s nest to hatch it randomly;
- In a randomly selected group of bird’s nests, the best bird’s nest will be retained to the next generation.
- The number n of available bird’s nests is fixed and the probability that an owner of a bird’s nest can find an exotic birds’ eggs is Pa ∈ [0, 1]. Based on the three ideal states, the updating formula of path and location is as follows, when the cuckoo finds a nest:$$X{\left(t+1\right)}_{i}=X{\left(t\right)}_{i}+\alpha \times L\left(\lambda \right),\text{}i=1,2,\cdots ,n$$
_{i}is the next location number in the cuckoo generation t, α represents the step control variable and L(λ) represents the Levy random search path. Levy flight is a random movement process, the step of its flight distance obeys Levy distribution. The following formula is used to produce a Levy random number:$$L\left(\lambda \right)=\frac{\varphi \times u}{{\left|v\right|}^{\frac{1}{\lambda}}}\left(1<\lambda <3\right)$$$$\varphi ={\left\{\frac{\left(1+\lambda \right)\times \mathrm{sin}\left(\pi \times \frac{\lambda}{2}\right)}{\left[\left(\frac{1+\lambda}{2}\right)\times \lambda \times {2}^{\frac{\lambda -1}{2}}\right]}\right\}}^{\frac{1}{\lambda}}$$

#### 2.3. Diagnostic System

## 3. Case Study

#### 3.1. Overall Performance Test Rig

#### 3.2. Simulation Model Validation

_{1}, and high-pressure turbine discharge pressure.

_{34}and compressor discharge temperature T

_{2}, standing for the minimum, moderate and maximum simulation error, are cited as three examples. The comparative results are shown in Figure 6, Figure 7 and Figure 8. The mean relative error of rotational speed is 0.5%, and the mean relative error of compressor discharge temperature is 4.6%. In conclusion, this model can predict the trend of measurement parameters, and the simulation error is under 4.6%. It proves that this model can support fault diagnosis with transient data.

#### 3.3. Simulation with Component Degradation

#### 3.4. Comparative Study

- The improvement of the compressor flow rate degradation is 13 times the value of its efficiency degradation based on Method A. It does not meet the theoretical value of three. The result of Method B is 1.96, closer to the theoretical value.
- These ratios for high pressure turbines are 3.86 and 5.33. It seems that Method A is more accurate than Method B for high-pressure turbines. Thus, the health condition of high-pressure turbines can be monitored by both Method A and Method B. However, washing decisions are usually made by compressor degradation. This means that Method B is more suitable for supporting maintenance scheduling.
- There is not any maintenance work being carried out for power turbines in this process. Therefore, the improvement of both its flow rate and efficiency should be zero, theoretically. This proves that Method B is more accurate for power turbine diagnosis.

## 4. Conclusions

- A new, non-linear, model-based diagnostic method, using gas turbine transient measurements and a cuckoo search (CS) algorithm, was tested to diagnose a gas turbine before and after a washing process.
- Diagnosis with transient measurements is more relevant than diagnosis with steady-state measurements, when gas turbine faults contribute little to performance deviation in steady-state conditions or gas turbine output fluctuates greatly.
- Gas turbine component fault diagnosis using transient data can be more effective than using steady state data, owing to magnifying fault signatures and extending the tracking time to eliminate variable uncertainties.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

π | component pressure ratio |

η | component efficiency |

T_{1} | compressor inlet air temperature |

P_{1} | compressor inlet air pressure |

n_{1} | rotational speed of high pressure turbine |

Q_{c} | compressor inlet air mass flow |

T_{2} | compressor discharge air temperature |

P_{2} | compressor discharge air pressure |

Q_{f} | fuel gas flow |

T_{3} | high pressure turbine inlet temperature |

P_{3} | high pressure turbine inlet pressure |

T_{34} | high pressure turbine discharge temperature |

P_{34} | high pressure turbine discharge pressure |

Q_{t} | high pressure turbine mass flow |

T_{4} | power turbine discharge temperature |

P_{4} | power turbine discharge pressure |

Q_{p} | power turbine mass flow |

P_{c} | power consumption of compressor |

P_{t} | power generation of high pressure turbine |

P_{p} | power generation of power turbine |

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**Figure 6.**Comparison of simulation results and measuring data for high-pressure turbine rotational speed.

**Figure 7.**Comparison of simulation results and measuring data for high-pressure turbine discharge pressure.

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

Pressure ratio | 24.1 |

Exhaust mass flow | 84.31 kg/s |

Power output | 31.4 MW |

Efficiency of compressor | 85% |

Measurement Parameter | Symbol |
---|---|

Rotational Speed | n_{1} |

Discharge Temperature of Compressor | T_{2} |

Discharge Pressure of Compressor | P_{2} |

Discharge Temperature of High Pressure Turbine | T_{34} |

Discharge pressure of High Pressure Turbine | P_{34} |

Compressor efficiency degradation | D_{EC} |

Compressor flow rate degradation | D_{GC} |

High pressure turbine efficiency degradation | D_{ET} |

High pressure turbine flow rate degradation | D_{GT} |

Power Turbine efficiency degradation | D_{EP} |

Power Turbine flow rate degradation | D_{GP} |

**Table 3.**Comparison result of diagnostic results based on steady-state analysis and transient process analysis (%).

Time | Process | D_{GC} | D_{EC} | D_{GC}/D_{EC} | D_{GT} | D_{ET} | D_{GT}/D_{ET} | D_{GP} | D_{EP} |
---|---|---|---|---|---|---|---|---|---|

Before Washing | Steady-state | 5.79 | 1.70 | - | 4.85 | 2.03 | - | 0.88 | 1.53 |

Transient process | 7.83 | 4.62 | - | 5.71 | 2.10 | - | 3.28 | 1.89 | |

After Washing | Steady-state | 2.02 | 1.48 | - | 2.03 | 1.30 | - | −0.17 | 1.07 |

Transient process | 1.54 | 1.41 | - | 2.56 | 1.42 | - | 2.95 | 1.76 | |

Improvement | Steady-state | 3.77 | 0.29 | 13.0 | 2.82 | 0.73 | 3.86 | 1.05 | 0.44 |

Transient process | 6.29 | 3.21 | 1.96 | 3.15 | 0.57 | 5.53 | 0.33 | 0.13 |

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**MDPI and ACS Style**

Zeng, D.; Zhou, D.; Tan, C.; Jiang, B.
Research on Model-Based Fault Diagnosis for a Gas Turbine Based on Transient Performance. *Appl. Sci.* **2018**, *8*, 148.
https://doi.org/10.3390/app8010148

**AMA Style**

Zeng D, Zhou D, Tan C, Jiang B.
Research on Model-Based Fault Diagnosis for a Gas Turbine Based on Transient Performance. *Applied Sciences*. 2018; 8(1):148.
https://doi.org/10.3390/app8010148

**Chicago/Turabian Style**

Zeng, Detang, Dengji Zhou, Chunqing Tan, and Baoyang Jiang.
2018. "Research on Model-Based Fault Diagnosis for a Gas Turbine Based on Transient Performance" *Applied Sciences* 8, no. 1: 148.
https://doi.org/10.3390/app8010148