# The Rotating Components Performance Diagnosis of Gas Turbine Based on the Hybrid Filter

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Fault Diagnosis Algorithm of Gas Turbine Based on Hybrid Filter

${T}_{t25}$Total temperature at the outlet of LPC | ${T}_{t3}$Total temperature at the outlet of HPC |

${T}_{t45}$Total temperature at the outlet of LPT | ${T}_{t5}$Total temperature at the outlet of HPT |

${P}_{t25}$Total pressure at the outlet of LPC | ${P}_{t3}$Total pressure at the outlet of HPC |

${P}_{t45}$Total pressure at the outlet of LPT | ${P}_{t5}$Total pressure at the outlet of HPT |

Low Pressure Compressor (LPC) | High Pressure Compressor (HPC) |

Low Pressure Turbine (LPT) | High Pressure Turbine (HPT) |

#### 2.2. Problem in the UKF

#### 2.3. Resolution

- (1)
- Construct a variance vector ${\psi}_{k-1}$ which consist of the diagonal elements of ${C}_{k-1}$. Furthermore, obtain the residual vector ${\zeta}_{k}$ which consist of diagonal elements of ${\epsilon}_{k}{\epsilon}_{k}^{T}$.
- (2)
- Similarity calculation between ${\zeta}_{k}$ and ${\psi}_{k-1}$.$${s}_{k}=\frac{\langle {\zeta}_{k},{\psi}_{k-1}\rangle}{\left(\left|{\zeta}_{k}\right|\ast \left|{\psi}_{k-1}\right|\right)}$$

#### 2.4. Health Parameters Estimation

- (3)
- Particles resampling:$${x}_{i}^{k}~\left\{{x}_{i}^{k},{\omega}_{i}^{k}\right\},i=1,2,3,\dots ,100\begin{array}{cc}& \end{array}{\omega}_{i}^{k}=\frac{1}{100}$$
- (4)
- Optimize the health parameters:$${\overline{x}}_{k}={\displaystyle \sum}_{i=1}^{100}{x}_{i}^{k}\ast {\omega}_{i}^{k}$$

- 1
- Generate the measured parameters from a software named Gasturb13 (Gasturb 13 is a simulation software for gas turbine performance calculation with high accuracy). Add noise w to these measured parameters. $w\in N\left(0,{0.002}^{2}\right)$, N is the normal probability density function.
- 2
- Establish the Component-level Gas Path Model of turbojet. This model is the detailed expression of the Equations (1) and (2).
- 3
- Build the module of strong tracking filter according the method introduced in Section 2.3. The measured parameters including noise are input into the module and output to the particle filter after being processed by the strong tracking filter.
- 4
- Build the module of particle filer with weight optimization according to the method introduced in Section 2.4. This module is used to estimate the health parameters.
- 5
- Input the measured parameters to the particle filter and estimate the health parameters. The way to simulate the failure are listed as follows:$$\begin{array}{c}{F}_{LPC}={F}_{ini}-\Delta F\\ {E}_{LPC}={E}_{ini}-\Delta E\end{array}$$

_{LPC}and ${E}_{LPC}$ are the latest values of low-pressure compressor’s flow coefficient and efficiency coefficient after the failure is simulated. F

_{ini}and ${E}_{ini}$ are the initial values of low-pressure compressor’s flow coefficients and efficiency coefficient before failure are simulated. $\Delta F=\widehat{F}\left(T-{T}_{failure}\right)$. $\Delta F$ named the failure factor is variation volume of F

_{ini}. $\widehat{F}$ denotes the degradation value of flow coefficients during every sampling time if failure happen. The meaning of $\Delta E$ and $\widehat{E}$ are similar to that of $\Delta F$ and $\widehat{F}$. T and T

_{failure}represent current sampling time and failure occurrence time. The design working parameters of engine are as follows:

Efficiency of LPC: E_{LPC} = 0.868 | Pressure ratio of LPC: ${\pi}_{LPC}$ |

Efficiency of HPC: E_{HPC} = 0.878 | Pressure ratio of HPC: ${\pi}_{HPC}$ |

Efficiency of high-pressure rotator: E_{HPR} = 0.98 | Efficiency of low-pressure rotator: E_{LPR} = 0.98 |

Efficiency of burning room: E_{BR} = 0.98 | Air intake coefficient of cabin: E_{AI} = 0.01 |

Cooling coefficient of HPT: C_{HPT} = 0.03 | Efficiency of HPT: E_{HPT} = 0.89 |

Cooling coefficient of LPT: C_{LPT} = 0.01 | Efficiency of LPT: E_{LPT} = 0.91 |

Design rotating speed of Low Pressure Rotator: S_{LPR} = 10^{4}r/m | |

Design rotating speed of High Pressure Rotator: S_{HPR} = 1.6 × 10^{4}r/m | |

Total temperature at the outlet of burning room: T_{t4} = 1600 K | |

Heat value of fuel: FHV = 4.29 × 104 |

^{−6}and 6.4 × 10

^{−6}, as shown in Table 1. There are:

^{−6}and 4.05 × 10

^{−6}respectively, as shown in Table 2.

## 3. Conclusions

- 1
- The strong tracking filter is used to eliminate the noise contained in measurements and the accuracy of measured parameters is enhanced when the turbojet performance changes slowly. Besides, the estimation accuracy remains high when the working state of turbojet changes abruptly by adjust the variance ratio of measurements.
- 2
- An optimization method for strong tracking filter is proposed. By calculating the similarity between covariance vectors at different sampling times of measured parameters, the value of scale factor can be obtained. This calculation method replaces the traditional way of relying on experience.
- 3
- In particle filter, to ensure the diversity of particles, paper proposes a weight optimization method to adjust the weights of different particles. The regulation equation is derived according to the regulator R and the mean of all weights. By above method, the high accuracy of probability density function can be ensured.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 6.**Estimated health parameters of low-pressure compressor by the traditional unscented Kalman filter and particle filter.

**Figure 7.**Estimated health parameters of low-pressure compressor (LPC) by the proposed hybrid filter.

**Table 1.**Error analysis under the condition of slow degradation of performance based on traditional method.

Estimated Parameters | Maximum Error | Mean Value of Error | Variance |
---|---|---|---|

Efficiency coefficient | 0.162% | 0.118% | 5.2 × 10^{−6} |

Flow coefficient | 0.158% | 0.112% | 6.4 × 10^{−6} |

**Table 2.**Error analysis under the condition of slow degradation of performance based on proposed method.

Estimated Parameters | Maximum Error | Mean Value of Error | Variance |
---|---|---|---|

Efficiency coefficient | 0.094% | 0.076% | 2.59 × 10^{−6} |

Flow coefficient | 0.089% | 0.073% | 4.05 × 10^{−6} |

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**MDPI and ACS Style**

Zeng, L.; Dong, S.; Long, W.
The Rotating Components Performance Diagnosis of Gas Turbine Based on the Hybrid Filter. *Processes* **2019**, *7*, 819.
https://doi.org/10.3390/pr7110819

**AMA Style**

Zeng L, Dong S, Long W.
The Rotating Components Performance Diagnosis of Gas Turbine Based on the Hybrid Filter. *Processes*. 2019; 7(11):819.
https://doi.org/10.3390/pr7110819

**Chicago/Turabian Style**

Zeng, Li, Shaojiang Dong, and Wei Long.
2019. "The Rotating Components Performance Diagnosis of Gas Turbine Based on the Hybrid Filter" *Processes* 7, no. 11: 819.
https://doi.org/10.3390/pr7110819