# Intelligent Fault Diagnosis of Liquid Rocket Engine via Interpretable LSTM with Multisensory Data

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## Abstract

**:**

## 1. Introduction

## 2. Simulation System Construction

#### 2.1. System Simulation of LRE

#### 2.2. Fault Simulation of LRE System

#### 2.2.1. Valve Opening Failure

#### 2.2.2. Hydrogen Turbine Leakage

#### 2.2.3. Cooling Jacket Leakage

#### 2.2.4. Turbine Component Efficiency Decrease

## 3. Methodology

#### 3.1. Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM)

- Forget gate: The forgetting gate decides what information to discard. The input is the calculation result of the previous neuron S
_{t−}_{1}and the current input vector x_{t}. After the two are joined and passed through the forgetting gate ($Sigmoid\left(x\right)=\frac{1}{1+{e}^{-x}}$ will decide what information to keep and what information to discard), a 0–1 vector (the dimension is the same as the output vector C_{t−}_{1}of the previous neuron) is generated (See Equation (5)). When the vector is dotted with C_{t−}_{1}, the information retained by the previous neuron after calculation is obtained, which determines how much C_{t−}_{1}is kept in C_{t}.$${f}_{1}=sigmoid\left({\omega}_{1}\left[\begin{array}{c}{S}_{t-1}\\ {x}_{t}\end{array}\right]+{b}_{1}\right)$$ - Input gate: Represents information to be saved or information to be updated. As shown in the Figure 3b, it is the connection vector between S
_{t−}_{1}and x_{t}. The result obtained after passing through the sigmoid function is the output result of the input gate, which determines how much information from x_{t}can be used to calculate cell state C_{t}.$${f}_{2}=sigmoid\left({\omega}_{2}\left[\begin{array}{c}{S}_{t-1}\\ {x}_{t}\end{array}\right]+{b}_{2}\right)\times \mathrm{tanh}\left({\widehat{\omega}}_{2}\left[\begin{array}{c}{S}_{t-1}\\ {x}_{t}\end{array}\right]+{\widehat{b}}_{2}\right)$$The update status of a new cell is shown in Equation (7).$${C}_{t}={f}_{1}\times {C}_{t-1}+{f}_{2}$$ - Output gate: The output gate determines the hidden vector S
_{t}of the current neurogenic cell output. Different from C_{t}, S_{t}is a little more complicated. It is the multiplication product of the computed $tanh\left(Ct\right)$ with the computed result of the input gate, which is described by the formula as shown in Equation (8).$${S}_{t}=sigmoid\left({S}_{t-1}\right)\xb7\mathrm{tanh}\left({C}_{t}\right)$$

#### 3.2. Bidirectional LSTM

- The forward LSTM reads the input sequence in chronological order and computes the hidden state vector for each time step.
- The backward LSTM reads the input sequence in the reverse order and computes the hidden state vector for each time step.
- The hidden state vectors of the forward and backward LSTMs are added element-wise to obtain the final hidden state vector for each time step.

#### 3.3. Interpertable LSTM Based on Attention Mechanism

- The encoder encodes the input data to generate a set of feature vectors.
- Calculate the similarity between each feature vector and a specific “attention weight” vector to determine the importance of each feature vector.
- Multiply the attention weights with the feature vectors and add the results to obtain a weighted feature vector representation.
- Use the weighted feature vector as input to the next layer and repeat the above steps.
- Finally, add all the weighted feature vectors to obtain a comprehensive representation for the final prediction.

#### 3.4. Spatial Attention Operation

#### 3.5. Temporal Attention Operation

#### 3.6. The Proposed Fault Detection Framework

## 4. Fault Diagnosis

#### 4.1. Overall Model Analysis of Fault Diagnosis

_{s}(=28) time series of each sensor data between 0 and tf (=2 s), constructing a 2D array (N

_{T}× N

_{s}) containing the test data, where N

_{T}(=tf/dts) is the number of sample points during the launch period [41], as illustrated in Figure 10. Due to the different dimensions and orders of magnitude of data, we standardized the data with zero-mean normalization, keeping all dimensions the same weight (because each dimension follows the normal distribution with the mean value of 0 and variance of 1). In the final calculation of distance, the data of each dimension plays the same role. The selection of different dimensions can avoid the great influence on distance calculation.

_{Tk}× N

_{s}, and the number of windows to be prepared is N

_{f}= (N

_{T}− N

_{Tk})/N

_{d}+ 1 [42]. By adjusting the size of the sliding window and the stride length, we can control the number of subsequences generated, allowing us to balance the model’s accuracy and complexity.

_{f}CNNS to extract the features of each slice window separately, get N

_{f}feature sequences at different time points, and then splice these sequences together. BiLSTM layer learns the temporal dependencies provided by multiple feature maps extracted in parallel by CNNs. The Softmax layer after the fully connected layer retrieves the probability distribution of failure modes.

#### 4.2. Result Analysis

_{Tk}from 0.8 s to 1.4 s, after multiple tests, it was found that the CNN-LSTM network performs best in terms of fault classification response time when N

_{Tk}is set to 1.2 s. In addition, the shorter the duration of the stride window N

_{d}, the higher the prediction accuracy, but the training cost increases with the number of windows (N

_{f}), so we choose N

_{d}as 0.2 s.

_{Tk}of 0.6 s and a stride window duration N

_{d}of 0.1 s, greatly reducing the amount of data used for training and significantly reducing the training time while maintaining the classification accuracy.

#### 4.3. Comparative Analysis

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 8.**Comparison of partial data between normal mode and failure mode of LRE: (

**a**) Comparison of different parameters (

**b**) Single instance comparison chart.

Components | Classification | Fault Mode | Fault Performance |
---|---|---|---|

Turbopump | Centrifugal Pump | (1) Impeller damage (2) Bearing wear or damage (3) Pump cavitation | Pump efficiency decrease |

Turbine | (1) Blade detachment (2) Bearing wear or damage (3) Turbine blade erosion (4) Gas flow obstruction (5) Turbine inlet flow leakage | Turbine efficiency decrease | |

Downstream flow rate decrease | |||

Pipeline | Gas pipeline | (1) Pipeline blockage (2) Pipeline leakage | Increased flow resistance |

Liquid pipeline | Downstream flow rate decrease | ||

Thrust chamber | Combustion chamber | Combustion deterioration | Combustion efficiency decrease |

Gas generator | Combustion deterioration | ||

Cooling jacket | Cooling jacket blockage | Increased flow resistance | |

Cooling jacket leakage | Downstream flow rate decrease | ||

Nozzle | (1) Nozzle deformation (2) Large nozzle detachment | Nozzle efficiency decrease | |

Others | Regulating valve | Stuck during switching | Reduced flow area |

Cavitation tube | Cavitation tube blockage | Increased flow resistance | |

Sonic nozzle | Sonic nozzle blockage |

Diagnosis Method | CNN | 1DCNN-SVM | CNN-LSTM | 1DCNN-A-BiLSTM |
---|---|---|---|---|

Ten times average classification accuracy/% | 86.99 | 93.83 | 94.76 | 97.39 |

Standard deviation/% | 2.3236 | 1.3798 | 0.6271 | 0.5832 |

Time/s (Using CPU) | 6.8 | 9.4 | 11.3 | 8.7 |

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**MDPI and ACS Style**

Zhang, X.; Hua, X.; Zhu, J.; Ma, M.
Intelligent Fault Diagnosis of Liquid Rocket Engine via Interpretable LSTM with Multisensory Data. *Sensors* **2023**, *23*, 5636.
https://doi.org/10.3390/s23125636

**AMA Style**

Zhang X, Hua X, Zhu J, Ma M.
Intelligent Fault Diagnosis of Liquid Rocket Engine via Interpretable LSTM with Multisensory Data. *Sensors*. 2023; 23(12):5636.
https://doi.org/10.3390/s23125636

**Chicago/Turabian Style**

Zhang, Xiaoguang, Xuanhao Hua, Junjie Zhu, and Meng Ma.
2023. "Intelligent Fault Diagnosis of Liquid Rocket Engine via Interpretable LSTM with Multisensory Data" *Sensors* 23, no. 12: 5636.
https://doi.org/10.3390/s23125636