# Research on Fault Diagnosis of a Marine Fuel System Based on the SaDE-ELM Algorithm

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## Abstract

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## 1. Introduction

## 2. Research Framework

- (1)
- Extract the feature vectors of the state of the marine fuel system and use Gaussian white noise to expand the data samples;
- (2)
- A differential evolution algorithm is used to adaptively acquire the extreme learning initialization parameters, and the fault diagnosis model for marine fuel system is constructed for different types of data, and the minimum value of the objective function is estimated;
- (3)
- Get the test model with SaDE-ELM training and diagnose the most probable state of the marine fuel system according to the new sample.

## 3. Proposed Algorithm

- (1)
- The convergence of learning efficiency and algorithm is a positive relationship; that is, with the improvement of learning efficiency, the convergence of the algorithm is stronger, but when the learning efficiency is large enough, the stability of the algorithm will be worse, thus affecting the performance of the overall algorithm;
- (2)
- The algorithm is easy to fall into a local minimum, so when the algorithm finishes running, the operation ends at a distance far from the global minimum;
- (3)
- The training process of the algorithm can easily lead to the reduction of the overall generalization ability of the algorithm and thus affect the experimental accuracy of the algorithm;
- (4)
- The learning rules in the network are time-consuming and not conducive to the acquisition of real-time information.

#### 3.1. ELM Algorithm

**Theorem**

**3.**

**Proof.**

- (1)
- Ease of use. The model does not have to set a large number of parameters, and the training speed does not need to intervene and also can obtain better experimental results;
- (2)
- Fast learning. The learning time of the model is quite short, which is more conducive to the user’s real-time information acquisition;
- (3)
- Generalization performance is high, and the ELM algorithm has a better generalization performance for different data types;
- (4)
- Activation function selection is flexible. Alternative types of activation function in ELM algorithms are adequate.

#### 3.2. The Differential Evolution (DE) Algorithm

#### 3.3. SaDE-ELM

- (1)
- The main parameters of SaDE-ELM: Scale factor F and hybrid probability CR. The parameters F and CR have a great influence on the convergence, stability and convergence speed of the DE algorithm. SaDE-ELM is proposed. The adjustment process of parameters F and CR is as follows:$${F}_{i}\left(t+1\right)=\{\begin{array}{c}{F}_{1}+ran{d}_{1}{F}_{u},ifran{d}_{2}{r}_{1}\\ {F}_{i}\left(t\right),Otherwise\end{array}$$$$C{R}_{i}\left(t+1\right)=\{\begin{array}{c}ran{d}_{3},ifran{d}_{4}{r}_{2}\\ C{R}_{i}\left(t\right),Otherwise\end{array}$$${F}_{i}\left(t+1\right)$ is the adaptive acquisition scaling factor. $C{R}_{i}\left(t+1\right)$ is the adaptive acquisition of hybrid probability and is an evenly distributed random number within the interval $\left[01\right]$; $ran{d}_{j},j\in \left\{1,2,3,4\right\}$ are evenly distributed random numbers within the interval $\left[0\text{}1\right]$. ${F}_{1}=0.1;{F}_{u}=0.9,{r}_{1},{r}_{2}$ are adjustment parameters.
- (2)
- Construct groups. Based on adaptive acquisition parameters, construct new groups $x\left(t\right)=\left({x}_{1}\left(t\right),{x}_{2}\left(t\right),\dots ,{x}_{N}\left(t\right)\right)$. Each sample is the state of feature matrix $m\times d$ of the marine fuel system, namely $m\times d=D$.
- (3)
- Individuals of the groups are crossed and selected. The final choice of highly competitive individuals is as follows:$${x}_{i}\left(t\right)=\{\begin{array}{c}{U}_{i}\left(t\right),if{E}_{0}\left({U}_{i}\left(t\right)\right)\le {E}_{0}\left({x}_{i}\left(t\right)\right)\\ {x}_{i}\left(t\right),Otherwise\end{array}$$${E}_{0}\left(\xb7\right)$ represents the minimum value ${E}_{0}$ in the objective function, namely the objective function value of each individual in groups.
- (4)
- Define iteration errors. According to the defined number of iterations to determine whether the iteration is terminated, if you continue to step (2) within the iteration range, otherwise go to the next step.
- (5)
- Output the best iteration result, ${E}_{0}\left(best\right)$ and corresponding hidden layer weight $\widehat{\beta}$.
- (6)
- Output ELM algorithm of fault diagnosis results for a marine system.

## 4. Model Construction and Simulation Experiment Results

#### 4.1. Extraction of Fault Feature for Marine Fuel System

#### 4.2. Model Construction

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Flow chart of the Self-adaptive Different Evolution Optimized Extreme Learning Machine (SaDE-ELM) algorithm.

**Figure 6.**Marine fuel oil system. 1—tank, 2—strainer, 3—circulating pump, 4—delivery valve, 5—fuel system filter, 6—high pressure pump, 7—high-pressure pipe, 8—injector, and 9—return pipe.

Hidden Layer Number | Training Time | Training Error | Test Error | |||
---|---|---|---|---|---|---|

ELM | SaDE-ELM | ELM | SaDE-ELM | ELM | SaDE-ELM | |

1 | 0.121 | 3.791 | 0.875 | 0.8 | 1 | 1 |

5 | 1.342 | 6.522 | 0.275 | 0.125 | 0.275 | 0 |

10 | 2.527 | 11.357 | 0.125 | 0.1 | 0.125 | 0 |

15 | 3.712 | 11.388 | 0.075 | 0.05 | 0.075 | 0 |

20 | 3.855 | 18.767 | 0.065 | 0.05 | 0.065 | 0 |

25 | 4.521 | 19.032 | 0.025 | 0 | 0.025 | 0 |

**Table 2.**Performance comparison of different algorithms for fault diagnosis of the marine fuel system.

Algorithm | Training Time | Training Error | Test Error |
---|---|---|---|

BP neural network | 12.531 | 0.5 | 0.625 |

SVM | 10.012 | 0.25 | 0.25 |

SaDE-ELM | 19.032 | 0 | 0 |

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**MDPI and ACS Style**

Wei, Y.; Yue, Y. Research on Fault Diagnosis of a Marine Fuel System Based on the SaDE-ELM Algorithm. *Algorithms* **2018**, *11*, 82.
https://doi.org/10.3390/a11060082

**AMA Style**

Wei Y, Yue Y. Research on Fault Diagnosis of a Marine Fuel System Based on the SaDE-ELM Algorithm. *Algorithms*. 2018; 11(6):82.
https://doi.org/10.3390/a11060082

**Chicago/Turabian Style**

Wei, Yi, and Yaokun Yue. 2018. "Research on Fault Diagnosis of a Marine Fuel System Based on the SaDE-ELM Algorithm" *Algorithms* 11, no. 6: 82.
https://doi.org/10.3390/a11060082