# Diesel Engine Fault Prediction Using Artificial Intelligence Regression Methods

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## Abstract

**:**

## 1. Introduction

## 2. Diesel Engine Model

- A zero-dimensional thermodynamic model (0D).
- A lumped mass model for the torsional vibration of the crankshaft.
- A fault simulation model.

#### 2.1. Thermodynamic Model

#### 2.2. Torsional Vibration Model

#### 2.3. Model Validation

#### 2.4. Fault Simulation Model

## 3. Dataset

#### 3.1. Fault Classes

- Normal operation;
- Pressure reduction in the intake manifold;
- Compression ratio reduction in the cylinders;
- Reduction in the amount of fuel injected into the cylinders.

#### 3.1.1. Normal

#### 3.1.2. Pressure Reduction in the Intake Manifold

#### 3.1.3. Compression Ratio Reduction in the Cylinders

#### 3.1.4. Reduction in the Amount of Fuel Injected into the Cylinders

#### 3.2. Additive White Gaussian Noise Process

#### 3.3. Data Normalization

#### 3.4. Partitioning the Dataset

#### 3.5. Dataset Regression

#### 3.5.1. Artificial Neural Networks

#### 3.5.2. Random Forest

#### 3.5.3. Regression Metrics

#### 3.5.4. Pearson Correlation Coefficient

## 4. Feature Extraction

#### 4.1. Feature Subsets

#### 4.1.1. Estimation of Maximum Pressure Inside the Cylinders

#### 4.1.2. Estimation of Mean Pressure Inside the Cylinders

#### 4.1.3. Spectral Analysis

#### 4.2. Feature Vector

## 5. Results and Discussions

#### 5.1. Regressor Hyperparameter Tuning

#### 5.2. Regression Tests

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Validation of the developed thermodynamic model for different rotations: (

**a**) 2100 and (

**b**) 2500 RPM.

**Figure 7.**Process of applying additive noise: (

**a**) $M\left(t\right)$ with 15 dB, (

**b**) $M\left(t\right)$ with 0 dB, (

**c**) $P\left(\theta \right)$ with 15 dB, (

**d**) $P\left(\theta \right)$ with 0 dB, (

**e**) $T\left(\theta \right)$ with 15 dB, and (

**f**) $T\left(\theta \right)$ with 0 dB. Note that the black line represents the original signal without noise. On the other hand, the gray line denotes the signal with noise. The new variable with AWGN ${\stackrel{\u02c7}{V}}_{{s}_{i}}(\xb7)$ is ${\stackrel{\u02c7}{V}}_{{s}_{i}}(\xb7)={V}_{{s}_{i}}(\xb7)+\nu $, where $\nu $ is white Gaussian noise in $L=[15,0]$ dB signal-to-noise ratio (SNR).

**Figure 8.**K-fold blocks. Gray blocks correspond to the test sets, and white blocks, to the training sets.

**Figure 9.**Box plots of 3500-DEFault dataset for feature subsets $F\left(k\right)$, $A\left(k\right)$, $P\left(k\right)$, ${\mu}_{{p}_{i}}$, and ${M}_{{p}_{i}}$, respectively, for different AWGN levels: (

**a**) 60 dB, (

**b**) 30 dB, (

**c**) 15 dB, and (

**d**) 0 dB. The plot shows the median; 25% quartile; 75% quartile; and the lower and upper ranges (whiskers), which are the max. and min. for each distribution, respectively.

**Figure 10.**Error plots of several tuning curves with AWGN SNR level $L=60$ dB in the training step: (

**a**,

**d**) $\Delta {P}_{r}$, and ANN and RF regressors, respectively; (

**b**,

**e**) $\Delta {r}_{1}$, and ANN and RF, respectively; and (

**c**,

**f**) $\Delta {m}_{{c}_{1}}$, and ANN and RF regressors, respectively. In the above graphs, the dotted lines represent ${\mu}_{\mathrm{RMSE}}$, and the whiskers represent ${\sigma}_{\mathrm{RMSE}}$ after 5-fold cross-validation.

**Figure 11.**Plots of several regression tests with AWGN SNR level $L=60$ dB: (

**a**,

**d**) $\Delta {P}_{r}$, and ANN and RF regressors, respectively; (

**b**,

**e**) $\Delta {r}_{1}$, and ANN and RF regressors, respectively; and (

**c**,

**f**) $\Delta {m}_{{c}_{1}}$, and ANN and RF regressors, respectively. In the above graphs, the black lines represent the perfect predictions, and the black dots represent the true (x-axis) vs. predicted (y-axis) elements. All graphs have an interval between zero and fifty (x- and y-axes), that is, with the same amplitudes as the severity values of the dataset.

**Figure 12.**Plots of several regression tests with AWGN SNR level $L=0$ dB: (

**a**,

**d**) $\Delta {P}_{r}$, and ANN and RF regressors, respectively; (

**b**,

**e**) $\Delta {r}_{1}$, and ANN and RF regressors, respectively; and (

**c**,

**f**) $\Delta {m}_{{c}_{1}}$, and ANN and RF regressors, respectively. In the above graphs, the black lines represent the perfect predictions, and the black dots represent the true (x-axis) vs. predicted (y-axis) elements. All graphs have an interval between zero and fifty (x- and y-axes), that is, with the same amplitudes as the severity values of the dataset.

Stroke type | 4 strokes |

Cylinders | 6 in line |

Valve control | On the head cylinder |

Cylinder valves | 2 valves |

Diameter of the cylinder | 105 mm |

Piston stroke | 137 mm |

Connecting rod length | 207 mm |

Total displacement | 7118 L |

Compression ratio | 16, 8:1 |

Inlet valve closing angle | 203${}^{\circ}$ |

Exhaust valve opening angle | 507${}^{\circ}$ |

Maximum torque and power | 900 N.m/191 kW |

Rotation (in max. torque) | 1600 RPM |

Ignition order | 1–5–3–6–2–4 |

Direction of rotation | Counterclockwise (viewed from behind the wheel) |

Rail pressure | 350 a 1400 bar |

Cooling water temperature | 80–100 ${}^{\circ}$C |

Regressor | Hyperparameter |
---|---|

ANN | $H=120$ |

RF | $B=100$ |

**Table 3.**Summary of RMSE of each failure parameter (FP) in the regression tests for several AWGN levels and ANN regressors.

FP | Regressor | |||
---|---|---|---|---|

ANN-60 dB | ANN-30 dB | ANN-15 dB | ANN-0 dB | |

$\Delta {P}_{r}$ | 0.84 ± 0.06 | 1.03 ± 0.11 | 1.62 ± 0.22 | 1.58 ± 0.34 |

$\Delta {r}_{1}$ | 0.85 ± 0.07 | 1.04 ± 0.13 | 1.58 ± 0.22 | 2.19 ± 0.31 |

$\Delta {r}_{2}$ | 0.85 ± 0.07 | 1.02 ± 0.14 | 1.56 ± 0.24 | 2.22 ± 0.33 |

$\Delta {r}_{3}$ | 0.84 ± 0.05 | 1.06 ± 0.11 | 1.64 ± 0.30 | 2.08 ± 0.29 |

$\Delta {r}_{4}$ | 0.84 ± 0.06 | 1.07 ± 0.15 | 1.63 ± 0.28 | 1.90 ± 0.33 |

$\Delta {r}_{5}$ | 0.86 ± 0.07 | 1.04 ± 0.16 | 1.69 ± 0.32 | 2.16 ± 0.24 |

$\Delta {r}_{6}$ | 0.84 ± 0.05 | 1.04 ± 0.16 | 1.62 ± 0.36 | 1.86 ± 0.18 |

$\Delta {m}_{{c}_{1}}$ | 0.81 ± 0.05 | 1.05 ± 0.12 | 1.79 ± 0.33 | 3.76 ± 0.21 |

$\Delta {m}_{{c}_{2}}$ | 0.83 ± 0.05 | 1.07 ± 0.14 | 1.83 ± 0.28 | 3.16 ± 0.22 |

$\Delta {m}_{{c}_{3}}$ | 0.84 ± 0.05 | 1.09 ± 0.14 | 1.67 ± 0.23 | 3.21 ± 0.18 |

$\Delta {m}_{{c}_{4}}$ | 0.84 ± 0.04 | 1.12 ± 0.11 | 1.69 ± 0.37 | 3.06 ± 0.26 |

$\Delta {m}_{{c}_{5}}$ | 0.84 ± 0.05 | 1.04 ± 0.15 | 1.71 ± 0.35 | 2.82 ± 0.33 |

$\Delta {m}_{{c}_{6}}$ | 0.83 ± 0.05 | 1.09 ± 0.13 | 1.65 ± 0.31 | 2.62 ± 0.32 |

ToE | 15.36 ± 3.57 | 32.67 ± 5.17 | 34.11 ± 1.77 | 32.71 ± 1.50 |

**Table 4.**Summary of RMSE of each failure parameter (FP) in the regression tests for several AWGN levels and RF regressors.

FP | Regressor | |||
---|---|---|---|---|

RF-60 dB | RF-30 dB | RF-15 dB | RF-0 dB | |

$\Delta {P}_{r}$ | 0.20 ± 0.11 | 0.35 ± 0.14 | 0.37 ± 0.14 | 0.78 ± 0.25 |

$\Delta {r}_{1}$ | 0.10 ± 0.03 | 0.21 ± 0.11 | 0.36 ± 0.06 | 1.37 ± 0.13 |

$\Delta {r}_{2}$ | 0.16 ± 0.17 | 0.27 ± 0.25 | 0.33 ± 0.11 | 1.18 ± 0.14 |

$\Delta {r}_{3}$ | 0.17 ± 0.12 | 0.24 ± 0.19 | 0.31 ± 0.08 | 1.24 ± 0.09 |

$\Delta {r}_{4}$ | 0.16 ± 0.07 | 0.20 ± 0.14 | 0.38 ± 0.30 | 0.95 ± 0.16 |

$\Delta {r}_{5}$ | 0.27 ± 0.12 | 0.28 ± 0.18 | 0.35 ± 0.08 | 1.12 ± 0.14 |

$\Delta {r}_{6}$ | 0.29 ± 0.19 | 0.26 ± 0.17 | 0.37 ± 0.13 | 0.92 ± 0.10 |

$\Delta {m}_{{c}_{1}}$ | 0.26 ± 0.21 | 0.23 ± 0.06 | 0.61 ± 0.08 | 3.16 ± 0.41 |

$\Delta {m}_{{c}_{2}}$ | 0.23 ± 0.12 | 0.24 ± 0.06 | 0.69 ± 0.14 | 2.83 ± 0.08 |

$\Delta {m}_{{c}_{3}}$ | 0.15 ± 0.06 | 0.19 ± 0.04 | 0.49 ± 0.10 | 2.63 ± 0.36 |

$\Delta {m}_{{c}_{4}}$ | 0.22 ± 0.11 | 0.30 ± 0.11 | 0.52 ± 0.08 | 2.62 ± 0.19 |

$\Delta {m}_{{c}_{5}}$ | 0.13 ± 0.05 | 0.18 ± 0.04 | 0.42 ± 0.02 | 2.25 ± 0.09 |

$\Delta {m}_{{c}_{6}}$ | 0.24 ± 0.13 | 0.25 ± 0.05 | 0.48 ± 0.06 | 2.28 ± 0.23 |

ToE | 17.89 ± 1.08 | 18.94 ± 0.81 | 22.67 ± 1.01 | 31.93 ± 1.74 |

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**MDPI and ACS Style**

Viana, D.P.; de Sá Só Martins, D.H.C.; de Lima, A.A.; Silva, F.; Pinto, M.F.; Gutiérrez, R.H.R.; Monteiro, U.A.; Vaz, L.A.; Prego, T.; Andrade, F.A.A.;
et al. Diesel Engine Fault Prediction Using Artificial Intelligence Regression Methods. *Machines* **2023**, *11*, 530.
https://doi.org/10.3390/machines11050530

**AMA Style**

Viana DP, de Sá Só Martins DHC, de Lima AA, Silva F, Pinto MF, Gutiérrez RHR, Monteiro UA, Vaz LA, Prego T, Andrade FAA,
et al. Diesel Engine Fault Prediction Using Artificial Intelligence Regression Methods. *Machines*. 2023; 11(5):530.
https://doi.org/10.3390/machines11050530

**Chicago/Turabian Style**

Viana, Denys P., Dionísio H. C. de Sá Só Martins, Amaro A. de Lima, Fabrício Silva, Milena F. Pinto, Ricardo H. R. Gutiérrez, Ulisses A. Monteiro, Luiz A. Vaz, Thiago Prego, Fabio A. A. Andrade,
and et al. 2023. "Diesel Engine Fault Prediction Using Artificial Intelligence Regression Methods" *Machines* 11, no. 5: 530.
https://doi.org/10.3390/machines11050530