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Sensor fault diagnosis is necessary to ensure the normal operation of a gas turbine system. However, the existing methods require too many resources and this need can’t be satisfied in some occasions. Since the sensor readings are directly affected by sensor state, sensor fault diagnosis can be performed by extracting features of the measured signals. This paper proposes a novel fault diagnosis method for sensors based on wavelet entropy. Based on the wavelet theory, wavelet decomposition is utilized to decompose the signal in different scales. Then the instantaneous wavelet energy entropy (

Gas turbines are one of the most important types of power equipment, widely used in modern aircraft propulsion systems and power systems. In order to achieve their challenging customer-driven performance requirements, gas turbines have to operate at their physical limits, which are set by material and gas properties. However, the normal operations of the gas turbines rely on the fine tuned cooperation of many different components, and any minor problem with these components may adversely affect the gas turbine system. Thus, advanced controls and monitoring technologies to improve the safety and reliability of the gas turbine system are widely studied, and at the same time, to reduce the operating cost.

The control and monitoring of gas turbine systems depend on accurate and reliable sensor readings from a considerable number of sensors. All these sensors must be functional to ensure normal operation of a gas turbine, otherwise, sensor failures may mislead the controller, and lead to the paralysis of the entire system. Therefore, in order to improve the reliable operation of systems, it is necessary to employ sensors fault diagnosis in a timely and accurate fashion.

For the reasons described above, sensor fault diagnosis has received considerable attention and many works on this topic have been reported. Isermann [

With increasing demand on small power systems and small propulsion systems, many micro gas turbines are being developed, and excellent success has been achieved in this area. However, the power to weight ratio of a micro-gas turbine should be high, so its EEC (electronic engine controller) should be light and have low power consumption, thus the microcontroller in the EEC is not powerful enough to adopt nonlinear engine model or neural networks for sensor validation. Consequently, the previous approaches are not suitable for micro-gas turbines. To overcome such problems, a simple and efficient approach should be adopted.

Typically, there are five types of sensor faults: the step fault (including the open and short fault), the pulse fault, the periodic fault, the noise fault and the drift fault. If any type of fault occurs, except for the drift fault, transient readings from the sensor will be affected. Thus, the fault status of the sensor could be extracted by analyzing the sensor readings. A mature and efficient tool for signal analysis is Fourier analysis, which transforms the sensor signal from a time-based domain to a frequency-based one. However, it is hard to determine when a particular fault takes place. To improve this deficiency, Gabor proposed the short-time Fourier transform (STFT) [

This paper proposes a fault diagnosis method for micro-gas turbine sensors operating under nonstationary conditions. The fault types mentioned above are investigated, except for drift faults. Based on wavelet theory, wavelet decomposition is utilized to decompose the signal in different scales. Then the instantaneous wavelet energy entropy (

Wavelets are finite-energy functions with good localization properties in both the frequency and time domain, which can be used very efficiently to represent transient signals. For a given mother wavelet

For a given signal ^{2}(ℝ), the results of the wavelet transform are the correlation between the function _{a,b} for each

By selecting a special mother wavelet function ψ(_{j}^{−j}_{j,k} = 2^{−jk}

The discrete wavelet transform (DWT) of signal

In 1989 Mallat presented a fast wavelet decomposition algorithm for discrete wavelet transform, which utilizes the orthogonal wavelet bases to decompose the signal under different scales [

By using Mallat’s mathod, a certain time serise _{j}_{J}

The frequency band of _{j}_{j}

Since the wavelet bases used to decompose the signal are orthogonal, these decomposed signals could be regarded as a direct estimation of local energies at different scales [

For the purpose of unification, the wavelet engery of approximation components at instant

Consequently, the wavelet engery at each sacle (J + 1 scale means approximation components) could be described as:

The total wavelet engery could be defined as:

The concept of entropy is derived from thermodynamic entropy, which can be roughly seen as a measure of the degree of system chaos. In the information world, Shannon defined the Shannon entropy that can represent the degree of chaos of a system [_{1}, _{2}, …, _{n}_{1}, _{2}, …, _{n}_{i}

The concept of wavelet entropy is inherited from Shannon entropy. Many types of wavelet entropies have been defined to solve different problems, and these methods can achieve good detection and recognition performance. Blanco

The wavelet entropy proposed above can represent the degree of order/disorder of the measured signal from sensors, which can provide useful information about the underlying state of the sensors. However, in critical circumstanced, such as gas turbine operation, sensor faults should be detected immediately. Gathering a large number of sensor readings and performing a post-analysis is not practical. Thus, it is necessary to define a type of instantaneous wavelet entropy to solve this problem. Based on the definition in [

To obtain the instantaneous wavelet entropy of _{w}_{W}

As defined in _{W}

Thus, we define the normalized _{j}_{j} = E_{Wj}_{Wtol}, j_{j}p_{j}

As mentioned above, the approximation components and detailed components could be obtained through wavelet decompositions, and the detailed componets contain high frequency information of the original siganl. As we all know, a mutation will occur in the measured sensor signal when the sensor fails, and this mutational signal lies in the detailed components certainly. Thus, the

As described in

The diagonal elements _{i}_{j}_{j}_{l}q_{j}

To illustrate the fault diagnosis ability by the proposed

Sampling

As shown in _{mean}_{mean}

The sensor fault diagnosis method is proposed based on the results of the numerical simulations. In order to explain the method clearly, several parameters are defined in

Step 1. Combine the sensor reading at time

Step 2. Figure out the _{IWEE}_{IWEE}

Step 3. Monitor the value of _{IWEE}_{width}_{mean}_{width}

Step 4. For CASE 1 in Step 3, check if S_{IWSE}_{width}_{Amean}_{mean}(k + Nd) − A_{mean}(k)| > Th_{Amean}

The experiments for the proposed method are carried out on the “Chao Ying” engine, which is a single shaft micro-gas turbine developed at the Nanjing University of Aeronautics and Astronautics. The temperature sensor placed in the nozzle is employed to verify the proposed sensor fault diagnosis method. In our system, the temperature sensor is made from a platinum thermocouple, and the temperature range that can be sensed by it is from 0 to 1,600 °C, and the output of the sensor is adjusted to 0 to 5 V. The environment for experiments is shown in

In this experiment, the main parameters for the method are chosen as listed in

Considering minimum detectable fault magnitude (MDFM) is an important parameter for the proposed method, and it is also a significant index of practicality. Henceforth, the minimum detectable fault magnitude for the proposed method should be determined through the experiment, so in the following experiment, four types of faults with 1%, 5%, 10% and 15% magnitude variations are presented. The detailed analysis is as follows.

The results of a sensor with a pulse fault are described in _{IWEE}_{IWEE}_{mean}

The results of a sensor with step fault are illustrated in _{mean}_{Amean}_{mean}_{Amean}

The results of sensor with noise fault are illustrated in _{IWEE}_{IWEE}_{IWSE}

_{IWEE}_{IWEE}

The status of a sensor can be reflected by its output signal, hence it is feasible to perform sensor fault diagnosis by analysing the measured sensor signals. This paper proposes a method for sensor fault diagnosis via wavelet entropy. Based on the wavelet theory, two types of wavelet entropies,

The proposed sensor fault diagnosis method has some limitations that require improvement. Firstly, the types of sensor faults verified are limited, and more types of sensor faults should be tested via the method. Meanwhile, the values in

This work has been partially supported by the Startup Foundation of Nanjing University of Aeronautics and Astronautics (No. S0956-021).

Results of the numerical simulations. _{mean}

Flowchart of proposed sensors fault diagnosis method.

Test environment for the experiments.

Results for the sensor with pulse faults. _{mean}

Results for the sensor with step faults. _{mean}

Results for the sensor with noise faults. _{mean}

Results for the sensor with pulse faults. _{mean}

Parameters for proposed method.

Discription | |
---|---|

_{IWEE} |
The threshold of |

_{width} |
The threshold to distinguish if the mutation of _{IWEE} |

_{IWSE} |
The threshold of |

_{Amean} |
The threshold of changed value of _{mean} |

Chosen parameters values for the experiments.

100 Hz | |

20 | |

5 | |

‘Haar’ | |

_{IWEE} |
0.01 |

_{width} |
60 |

_{IWSE} |
1.15 |

_{Amean} |
0.3 |