# An EMD-LSTM Deep Learning Method for Aircraft Hydraulic System Fault Diagnosis under Different Environmental Noises

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## Abstract

**:**

## 1. Introduction

## 2. Aircraft Hydraulic System Model Building and Data Collection

#### 2.1. Aircraft Hydraulic System Definition and AMESIM Model Build

#### 2.2. Normal State and Fault State

#### 2.3. Data Collection

_{p}); the flowrate signal at the hydraulic pump outlet (Q

_{p}); the pressure signal (P

_{f}) and the flowrate signal (Q

_{f}) at the oil filter exit position; the pressure signal (P

_{a}) and the flowrate signal (Q

_{a}) of the actuator inlet; and the velocity signal(V

_{a}) and the displacement signal (D

_{a}) of the actuator. All the signals are shown in Table 3.

## 3. The EMD-LSTM Method

#### 3.1. EMD and PCA Method

_{max}(t) and the minimum envelope curve e

_{min}(t); all data points in signal x(t) are wrapped between these two curves. We calculate the average value of the e

_{max}(t) and e

_{min}(t), and mark it as e(t). Then, we subtract the e(t) from the original signal x(t), and obtain a new signal x

_{1}(t) =x(t)–e(t). At this time, we test whether x

_{1}(t) meets the two conditions of the IMFs: 1. in the decomposed signal, the equivalent points are equal to zero or equal to one, and 2. the signal is about the local symmetry of timeline. If it is satisfied, it is recorded as IMF

_{1}(t) = x

_{1}(t). If it is not satisfied, we use x

_{1}(t) as the original signal and repeat the above operation.

_{1}(t) is separated from x(t), and we obtain a residual signal r

_{1}(t), r

_{1}(t) = x(t) -IMF

_{1}(t). Then, we use r

_{1}(t) as a new original signal to repeat the above operation. After N times, the signal can obtain N components of the IMFs, which can be expressed as follows:

_{a}, P

_{p}, D

_{a}. The horizontal coordinates are the number of sampling time points, and the frequency is 100 Hz. The unit of each point is 0.01 s. The first subfigure is the original signal, the last subfigure is the residual r component, and the other subfigures are the IMFs, as shown in Figure 4.

_{a}obtains 18 IMFs, the EMD of P

_{p}obtains 19 IMFs, and the EMD of D

_{a}obtains 12 IMFs. From Figure 4, different IMFs can reflect the characteristics of the original signal to a certain extent. Each original signal can obtain a set of feature vectors after the EMD, and the EMD results can be marked as F

_{n}= [IMF

_{1}, IMF

_{2}, … IMF

_{K}, r], with k meaning the total number of IMFs after the EMD, and r meaning the residual after the EMD. From the three sets of EMD signals in the figures, the types of information containing and expressing are different, so the total number of IMFs are not consistent. The IMFs after the EMD enriches the input features of the LSTM networks. However, it is inevitable that there are redundancy or repetition of information, and the input dimensions of the LSTM are not the same. Therefore, the PCA method needs to be applied to reduce the dimension of the input IMFs.

_{n}in this simulation is chosen as 5 IMFs. If the IMFs are higher than 5 for PCA reduction, the process is shown in Figure 5.

#### 3.2. Three Inner Structure of LSTM Networks

_{i}pass their internal information to the neuron t

_{i+}

_{1}of the next time point. In this way, the input information and the output information at the neuron of time point t

_{i}can map the effect of all the previous time points, and form a feedback structure similar to a ring. However, in an actual application of a RNN, when the distance between t

_{i+m}and t

_{i}is too large, there may be a problem that t

_{i}cannot map the input and output characteristics of the time point t

_{i+m}. This situation is called the gradient disappearance in the RNN, or long-term dependence. This problem is solved by the LSTM network algorithm proposed by Hochreiter [37]. The LSTM network adopts its unique internal three gate units structure, and through the structure of the three gate units, it can control the transmission rate in the historical information dissemination in the RNN. The information is sent into the three different gate units according to the important degree, so it solves the gradient explosion of the long distance. The mathematical expression of the LSTM model can be written as follows:

**x**

_{t}is the input of the LSTM network, and

**h**

_{t}is the output of the hidden layer in the network.

**c**

_{t}is called the unit state, and it is a unique structure in the LSTM network.

**c**

_{t}is used to preserve information, forget information, or control the flow of information by passing the information to subsequent neuron cells. The first three formulas are the gate unit structure, namely forgotten gate

**f**

_{t}, input gate

**i**

_{t}, and output gate

**o**

_{t}. These three gate structures assist

**c**

_{t}to delete or add information, and limit the output range between 0 and 1 by the Sigmoid layer. When the output is 0, it means that the information is abandoned. When the output is 1, it means that the information is all recorded. σ is the active function, W is the weighted value of the network, and b is the offset of the network. These two parameters will be optimized during the network training. The symbols “.” and “*” here represent the matrix multiplication and the point multiplication between the same dimension matrix. The structure of the LSTM is shown in Figure 6a.

_{t-1}observation for each unit status at the previous time point. The structure of LSTM with observation is shown in Figure 6b. Compared to the traditional LSTM network structure, this structure is more complicated, and the mathematical expression can be written as follows:

_{t}, and introduces r

_{t}as the reset gate. The structure of the GRU is shown in Figure 6c. Its expression can be written as follows:

#### 3.3. The LSTM Network Structure Design

#### 3.4. EMD-LSTM Method for the Aircraft Hydraulic System

## 4. The Simulation Results of the EMD-LSTM Method

#### 4.1. Data Collection and Feature Extraction

#### 4.2. The Fault Diagnostic Results in the Comparison of Three EMD-LSTM Methods

#### 4.3. EMD-GRU Network Structure and Parameter Optimization

#### 4.4. Noise Addition and EMD-GRU Fault Diagnosis under Different Noise Environments

_{n}is the Gaussian white noise power of m dB and P

_{s}is the power of the original signal. The power calculation of the signal is shown in Formula (6):

_{i}means the number i data point. K times of Gaussian white noise is still Gaussian white noise; in order to generate m dB of Gaussian white noise, it can generate a set of standard normal distribution of Gaussian white noise, and take a multiplier m to generate the Gaussian white noise of m dB. Its calculations can be found through Formulas (7) and (8):

_{i}and P

_{ns}mean the number i data point and the corresponding power of the Gaussian white noise. Then, different SNR noise is added to the eight-channel original signals.

_{1}~IMF

_{10}, and the last one is the residual r. The horizontal axis of the coordinate shaft is the number of time points, the sampling frequency is 100 Hz, and the corresponding time for each sampling point is 0.01 s.

#### 4.5. Comparison between EMD-GRU Method with Various Other Fault Diagnostic Methods

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Number | AME-Element | Key Parameter | Value | Meaning |
---|---|---|---|---|

1 | signal03 | Output | 5000 r·min^{−1} | The shaft speed is 5000 r/min, and the pressure of the pump is 3000 psi. |

3 | Accumulato2 | Gas pressure accumulator volume | 1885 psi 2.62 L | Accumulator reduces pressure, as an emergency source. |

4 | presscontol01 | Relief valve cracking pressure | 3436 psi | Pressure relief value, for system discharge. |

5 | tank01 | Tank pressure | 50 psi | Booster tank, for pre-boost to 50 psi. |

7 | pump13 | Nominal shaft speed | 5000 r·min^{−1} | Left engine drive pump (EDP). |

11~14 | pump13 | nominal shaft speed | 5000 r·min^{−1}4166 r·min ^{−1} | Right EDP, Yellow system EMP, Blue system EMP, and RAT. Rated pressure of RAT is 2500 psi. |

10 | constant_3 | constant value | 34.4738 bar | PTU opens when the pressure difference between green and yellow systems is 34.4738 bar. |

Num | Fault Category and Category Number | Key Parameter | Normal Value | Fault Value |
---|---|---|---|---|

2 | pump leakage-1 | Equivalent orifice diameter (mm) | 0.1~0.3 | 1~2 |

6 | filter blockage-2 | Equivalent orifice diameter (mm) | 5~7 | 3~4 |

7 | relief valve spring failure-3 | Open pressure (psi) | 3400 | 2600–3300 |

11 | Actuator inner leakage-4 | Leakage coefficient (L·min^{−1}·bar^{−1}) | 0~0.01 | 0.03~0.05 |

16 | oil pollution-5 | Air content (%) | 0.1~0.3 | 5~15 |

Position | Signal | Mark | Position | Signal | Mark |
---|---|---|---|---|---|

Pump | Pressure | P_{p} | Actuator | Pressure | P_{a} |

Flowrate | Q_{p} | Flowrate | Q_{a} | ||

Oil filter | Pressure | P_{f} | Displacement | D_{a} | |

Flowrate | Q_{f} | Velocity | V_{a} |

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

Lr | 0.001 |

Lr decaying | lr = lr × 0.9/epoch |

Batch size | 800 |

Dropout rate | 0.4 |

Training epochs | 200 |

Activation function | ReLU |

Optimizer | Adam |

Class Number | States | Fault Value | Training Data | Testing Data | Sample Length | Feature |
---|---|---|---|---|---|---|

0 | Normal state | - | 800 | 200 | 5000 | 40 |

1 | Pump leakage | 1~2 | 800 | 200 | 5000 | 40 |

2 | Filter blockage | 3~4 | 800 | 200 | 5000 | 40 |

3 | Relief valve spring failure | 2600–3300 | 800 | 200 | 5000 | 40 |

4 | Oil pollution | 5~15 | 800 | 200 | 5000 | 40 |

5 | Actuator inner leakage | 0.03~0.05 | 800 | 200 | 5000 | 40 |

Class | Algorithm | Accuracy/% | Test Time/s | Software/Mb |
---|---|---|---|---|

1 | LSTM | 97.33 | 1.68 | 5.9 |

2 | LSTM with observation | 97.08 | 1.77 | 7.5 |

3 | GRU | 98.25 | 1.61 | 3.2 |

Class | Fault Diagnostic Model Structure | Accuracy | Test Time | Mode Size |
---|---|---|---|---|

1 | GRU without EMD | 93.16% | 1.31 s | 2.6 mb |

2 | GRU without PCA | 96.33% | 3.99 s | 7.3 mb |

3 | EMD-8-GRU | 95.71% | 1.43 s | 10.3 mb |

4 | EMD-GRU | 98.25% | 1.61 s | 3.2 mb |

Learning rate | 0.1 | 0.01 | 0.001 | 0.0001 | 0.00001 | 0.000001 |

Accuracy/% | 25.5 | 60.4 | 91.2 | 98.1 | 93.2 | 79.2 |

Training time/s | 22 | 47 | 85 | 116 | 456 | 695 |

Batch size | 100 | 200 | 400 | 800 | 1200 | 1600 |

Accuracy/% | 63.5 | 85.2 | 96.8 | 98.4 | 94.5 | 88.2 |

Training time/s | 283 | 209 | 135 | 105 | 99 | 92 |

Algorithm | Accuracy/% | ||
---|---|---|---|

Without Noise | SNR = 70 dB | SNR = 40 dB | |

BP | 73.88 | 59.53 | 35.91 |

SVM | 65.26 | 55.25 | 36.53 |

RF | 75.52 | 66.95 | 44.77 |

CNN | 82.98 | 79.41 | 50.66 |

LSTM | 92.56 | 90.44 | 54.47 |

EMD-GRU (this article) | 98.25 | 95.29 | 89.29 |

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## Share and Cite

**MDPI and ACS Style**

Shen, K.; Zhao, D.
An EMD-LSTM Deep Learning Method for Aircraft Hydraulic System Fault Diagnosis under Different Environmental Noises. *Aerospace* **2023**, *10*, 55.
https://doi.org/10.3390/aerospace10010055

**AMA Style**

Shen K, Zhao D.
An EMD-LSTM Deep Learning Method for Aircraft Hydraulic System Fault Diagnosis under Different Environmental Noises. *Aerospace*. 2023; 10(1):55.
https://doi.org/10.3390/aerospace10010055

**Chicago/Turabian Style**

Shen, Kenan, and Dongbiao Zhao.
2023. "An EMD-LSTM Deep Learning Method for Aircraft Hydraulic System Fault Diagnosis under Different Environmental Noises" *Aerospace* 10, no. 1: 55.
https://doi.org/10.3390/aerospace10010055