^{*}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Combining a simplified on-board turbo-shaft model with sensor fault diagnostic logic, a model-based sensor fault diagnosis method is proposed. The existing fault diagnosis method for turbo-shaft engine key sensors is mainly based on a double redundancies technique, and this can't be satisfied in some occasions as lack of judgment. The simplified on-board model provides the analytical third channel against which the dual channel measurements are compared, while the hardware redundancy will increase the structure complexity and weight. The simplified turbo-shaft model contains the gas generator model and the power turbine model with loads, this is built up via dynamic parameters method. Sensor fault detection, diagnosis (FDD) logic is designed, and two types of sensor failures, such as the step faults and the drift faults, are simulated. When the discrepancy among the triplex channels exceeds a tolerance level, the fault diagnosis logic determines the cause of the difference. Through this approach, the sensor fault diagnosis system achieves the objectives of anomaly detection, sensor fault diagnosis and redundancy recovery. Finally, experiments on this method are carried out on a turbo-shaft engine, and two types of faults under different channel combinations are presented. The experimental results show that the proposed method for sensor fault diagnostics is efficient.

With ever-increasing demands being placed on modern aero-engine control systems, the number of control variables and sensors is increasing [

Wallhagen and Arpasi proposed using analytical redundancy sensor technology to improve the reliability of the engine control system in 1974 [

The sensor fault diagnosis methods are generally divided into three categories: mathematical models-based, knowledge-based and signal processing-based [

The model-based approach needs a pre-established engine model to acquire the analytic third channel, so the model is built up based on aircraft engine component characteristics and pneumatic thermodynamic equations. Compared to the methods of knowledge-based and signal processing-based, it avoids the difficult problems of knowledge base maintenance and high robustness requirements of measurement data, and can be used to diagnose new sensor failures with no need of history experience or

This article aims to apply the simplified on-board model as an analytical third channel for sensor fault diagnosis of turbo-shaft engines. This system is referred to as the sensor FDD system, and its structure is composed of the simplified on-board turbo-shaft engine and fault detection and diagnosis logic. Considering the measurement noises and modeling errors, sensor dual channel threshold and analytic thresholds are designed that are used for the logic. When the difference among the triplex channels violates a tolerance level, the logic determines the cause of the difference. Due to its simplicity, the sensor fault diagnosis system can be executed with the computing power currently available on line.

This paper is organized as follows: in Section 2, the simplified on-board turbo-shaft model for sensor fault diagnosis, which contains gas generator model and power turbine model with loads, is described. In Section 3, the pre-processes for measurements are presented, sensor fault diagnostic thresholds are calculated, and diagnostic logic is designed based on the simplified model. Experiments are carried out in Section 4, and the results show that compared to the SPSO-SVR method, the one proposed in this paper is useful to diagnose sensor faults of turbo-shaft engines. Finally, our work is summarized in the last section.

The engine model accuracy directly determines the validity of the model-based method for sensor fault diagnosis. A dynamic coefficient approach is used to build up a simplified turbo-shaft on-board engine that satisfies the sensor fault diagnosis requirements. Taking into account of the structure and characteristics of turbo-shaft engine, the model is divided into a gas generator model and the power turbine model with loads.

A similar normalized gas generator speed _{gc}_{fc}_{fc}_{fc}

The change of fuel flow Δ_{fc}_{gc}

The dynamic parameter of gas generator speed at the time point _{ng}_{45}_{c}_{ec}_{T}_{45}(_{Ne}_{45}_{cs}_{ecs}_{45}_{c}_{ec}_{gc}_{45c}_{gc}_{ec}

A simplified gas generator model above idle is established via the steady interpolation table and dynamic parameters. The inputs of the model are _{f}_{1}, and atmospheric pressure _{1}, and the outputs are _{g}_{45}. The detailed program to calculate _{g}

Step 1. Give the initialized parameters of gas generator model, such as _{g}_{45}(0), _{3}(0), and similarly normalize the model parameters based on _{1} and _{1}.

Step 2. Calculate the increase of fuel flow via

Step 3. Interpolate _{ng}_{gc}

Step 4. Calculate _{gc}_{gc}

Then return to step 1 to iterate.

The calculation method of _{45} is similar to that of _{g}_{T}_{45} and _{45}_{cs}_{45}_{c}

Combining the load characteristics with the rotor dynamics equation, the simplified power turbine model with loads is built up via the steady interpolation table and dynamic parameters. The inputs of the model are _{gc}_{fc}_{1}, _{1}, and load angle _{p}_{45}. The following equations solve for the parameter

The process of calculating _{p}_{p}_{Pt}_{p}_{p}_{p}_{p}

In the second stage, the state of the turbo-shaft engine is determined by the load angle. Power demands of power turbine shaft are changed with

When the power turbine shaft power is not balanced, _{p}

The term _{p}_{1} = 300.5 _{1} = 102.4 kPa. _{g}_{p}

As seen from _{g}_{p}

The objective of on-board diagnosis for sensors is to detect and isolate faults as early as possible.

The data acquired by sensors can't be directly used for engine health management or control, as the sensor measurements involve not only the useful signals but also measurement noise and other interference information, which will result in sensor fault diagnosis failures. Therefore, it is necessary to undertake a pretreatment process involving outlier elimination and smoothing of the original data.

For this we use a statistical method to discriminate and eliminate outliers, the framework of which is as shown in

Step 1. Smooth the sensor measurement by five near points at

Step 2. Calculate the sums of squares of these five sensor measurement, and then acquire smooth value:

Step 3. Define the variance

Step 4. Check out the next sensor measurement, if it does not belong to the range

Step 5. Eliminate the outlier and replace it with the following value:

Gas turbine speed is directly influenced to the power of turbo-shaft engine, hence, the experiment to validate the proposed method is focused on the parameter _{g}_{g}

From the figure we can see that there are two outliers identified, and both of them are replaced with the new values within the rational range. Exponential smoothing is used to reduce the measurement noise in the paper.

The control system should maintain the parameter _{g}_{p}_{I}_{g}_{p}_{I}_{D}

The sensor fault detection and diagnosis logic compares the triplex channels (_{A}_{B}_{m}_{A}_{B}_{m}_{g}_{45}, _{p}_{i}^{th}

The residual in

The sensor fault diagnosis logic can fulfill the following functions: (1) sensed data is detected; (2) sensor fault diagnosis; (3) faulty sensor recovery; or (4) anomaly detection. A flow chart of the sensor fault diagnosis logic is given in

The sensor fault detection, diagnosis, and recovery logic indicates that a sensor fault is detected when one of the dual-channel residuals in

The logic indicates that a sensor fault is isolated when the dual channel residual of a particular sensor exceeds the threshold, and also, this sensor's analytical residual exceeds the threshold in either one or both channels. If the threshold violation of the analytical residual occurs only in one channel, the channel that caused this violation is identified as the faulty one. If the threshold violation occurs in both channels, both channels of this particular sensor are considered faulty. Thus, the identity of a faulty sensor and the identity of its failed channel are determined. When both channels of sensor measurement are faulty, the faulty sensor signal used for control system is replaced by the model output. If the dual-channel residual of a particular sensor doesn't exceed the threshold, and this sensor's analytical residual exceeds the threshold in either one channel, some other type faults might happen, otherwise, turbo-shaft control system works normally.

Sensor fault threshold selection directly affects the results of sensor fault diagnosis. In order to make the system able to detect the sensor fault with little amplitude changes, the threshold range needs to be set more smaller, while it will result in misdiagnosis. Therefore, a rational threshold selection is necessary for improving the accuracy of sensor fault diagnosis. In this paper, the threshold is selected by the statistical characteristics of sensor measurement noise and the model errors.

The engine outputs measured by sensors with dual-channels A and B are expressed as follows:

The parameters _{m}_{1} and _{2} are the zero-mean, normally distributed white noise that corrupts the measurements on dual-channels, and independent each other, denoted as _{1}∼^{2}), _{2}∼^{2}). The probability density function of dual-channel random residual Δ_{1} – _{2} is as:

The function _{1} and _{2}. From the

The function Φ is the distributing function of standard normal distribution function, In order to make sure as less misdiagnosis rate as possible, the following equation
_{DR}

The threshold of the analytic residual is determined not only by the measurement noise but also by the modeling errors. The analytic residual can be expressed in the following form:

Considering the random variables _{1}/_{2}/_{AR}_{BR}

From Section 2, we have obtained the modeling errors under steady state and dynamic state. Then both of dual-channel threshold and analytic threshold can be computed.

The capability of sensor the FDD system based on a simplified on-board model to detect, diagnose and recovery a biased sensor is evaluated. A bias is injected into channel A or B of a single sensor _{g}

Experiments on one channel with a step fault and a drift fault under the steady-state of _{A}_{DR}_{AR}_{B}_{BR}

In _{DR}_{A}_{AR}

Two experiments on dual channel with drift faults under the steady-state of

Sensor fault diagnosis logic for turbo-shaft engines is validated under the steady state from the above experiments. Modeling errors of dynamic operation are much more numerous than those of steady state. In order to evaluate the ability of sensor fault diagnosis logic under dynamic operation, the following experiment is designed. When the gas generator speed increases from 81% to 95%, the step fault is injected into the channel A in

Sensor misdiagnosis will happen under the steady state of _{A}_{DR}_{AR}_{B}_{BR}

The sensor FDD system based on a simplified on-board model described in this paper is proposed and developed to diagnose turbo-shaft engine faults on-line. A simplified on-board model for turbo-shaft is designed, and it contains two segments: gas generator model and power turbine model with loads. The sensor fault diagnosis system utilizes dual-channel sensor measurements and also the output of a simplified on-board engine model as the analytical third channel. Through the comparison of triplex channels, the system diagnoses two types of faults in sensors.

The sensor fault detection, diagnosis, and recovery logic is designed, and the sensor FDD system is evaluated extensively at a cruise operating condition using simulated fault cases. Compared to the SPSO-SVR method, the proposed one exhibited its capability to identify a faulty dual-channel sensor and its failed channel at a reasonable fault level. The sensor FDD system based on a simplified on-board model can be used under the steady state and dynamic operation. The diagnostic capability of the sensor fault diagnosis system establishes a benchmark for on-line diagnostics. Any improvement made through the application of advanced diagnostic techniques can be evaluated against this benchmark.

This work has been partially supported by the Fundamental Research Funds for the Central Universities (No. NZ2012110).

Outputs of _{g}

Outputs of _{p}

Sensor fault detection, diagnosis, and recovery principle.

Framework of outlier discrimination and elimination.

Simulation results of outlier discrimination and elimination.

The response to step input by (

Dual-channel sensor fault detection, diagnosis, and recovery logic.

One channel sensor _{g}

One channel sensor _{g}

Dual channel fault with different drift velocities under the steady state of

Dual channel fault with the same drift velocities under the steady state of

Channel A with the step fault in the dynamic operation. (

Statistical results of sensor _{g}

_{DR} |
_{AR}_{BR} | |||
---|---|---|---|---|

Flight idle | 0.045 | 0.15 | 4.5 | 14 |

85% of _{g} |
0.070 | 0.25 | 4.5 | 10 |

99.6% of _{g} |
0.082 | 0.25 | 4.5 | 9 |

Dynamic operation | 0.069 | 0.23 | 4.5 | 32 |

Statistical results of sensor _{45} for the turbo-shaft engine.

_{DR} |
_{AR}_{BR} | |||
---|---|---|---|---|

Flight idle | 0.085 | 0.27 | 4.5 | 9 |

89.0% of _{g} |
0.113 | 0.32 | 4.5 | 8 |

100.1% of _{g} |
0.095 | 0.33 | 4.5 | 8 |

Dynamic operation | 0.114 | 0.32 | 4.5 | 21 |