# Data-Driven Sliding Bearing Temperature Model for Condition Monitoring in Internal Combustion Engines

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## Abstract

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## 1. Introduction

_{2}and other greenhouse gases, elimination of pollutant emissions and increased service life of ICEs [3,4,6]. Because the development of entirely new ICE concepts requires extensive research and development work, engine manufactures are focusing on increasing the efficiency of existing ICE technology in the short term [7]. One possible solution employs newly developed low viscosity oils that have the potential to reduce friction and thus increase engine efficiency [7]. However, such oils in turn pose new challenges for sliding bearings in ICEs and their lubrication.

- 1.
- Condition detection refers to the acquisition of one or more informative parameters which reflect the current condition of the machinery.
- 2.
- Condition comparison consists of comparing the actual condition with a reference condition of the same parameter.
- 3.
- Diagnosis evaluates the results of the condition comparison and determines the type and location of failure. Based on the diagnosis, compensation measures or maintenance activities can be initiated at an early stage.

## 2. Materials and Methods

#### 2.1. Experimental Investigations

_{3}and is used for heavy-duty applications. During fired engine operation, a VA Tech Elin EBG GmbH Indy 80/4P/5500 dynamometer with a pendulum stator acted as a brake and thus controlled the engine speed level. The engine was operated and monitored with the test bed automation system PUMA Open version 1.5.3 from AVL List GmbH (Graz, Austria). Some engine parameters were directly measured and retrieved via the engine’s electronic control unit (ECU). The additionally applied measurement technology, the experimental setup and the engine operating strategy are summarized below. A more detailed description of the experimental methodology can be found in [7].

#### 2.2. Data Selection and Model Requirements

- Due to the applied conditioning systems, coolant-related parameters such as pressure and temperature at inlet or outlet are constant and therefore irrelevant to modeling. This also applies to ambient air temperature. The coolant mass flow, however, is a measurement result that varies according to the applied engine operating point. Therefore, it is considered as a model input candidate.
- Indication system-based measurements such as in-cylinder pressures and key figures derived from them are not considered because they are usually not available on a production engine.
- Linear transformations of a single measured or calculable parameter are not used for modeling. For example, the break mean effective pressure (BMEP) is a linear transformation of the brake torque, which is considered to be available from the ECU of a production engine. Parameters that are calculated from multiple other parameters (e.g., brake-specific fuel consumption is calculated from fuel mass flow and engine power) are considered as model input candidates.

#### 2.3. Machine Learning Methods

#### 2.3.1. Linear Regression and Regularization

- An LM including all available engine parameters (cf. Table 1) as well as the categorical bearing position
- A naive reference LM that includes only the categorical bearing position (equivalent to taking the average temperature of each bearing from the training data)

#### 2.3.2. Gradient Boosting Regression

#### 2.3.3. Support Vector Regression

#### 2.4. Model Training and Selection

## 3. Results

#### 3.1. Cross-Validation Results and Model Selection

#### 3.2. Model Assessment on Test Data

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AI | artificial intelligence |

BMEP | break mean effective pressure |

CM | condition monitoring |

CV | cross-validation |

ECU | electronic control unit |

FSO | full scale output |

GB | gradient boosting |

ICE | internal combustion engines |

LEC | Large Engines Competence Center |

LM | linear model |

MAE | mean absolute error |

MB | main bearing |

ML | machine learning |

MSE | mean squared error |

MV | measured value |

PdM | predictive maintenance |

RBF | radial basis function |

RMSE | root mean squared error |

SVM | support vector machine |

SVR | support vector regression |

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**Figure 1.**Schematic of the thermocouple position at a crankshaft main bearing (

**left**, adapted with permission from [7]); bearing numbers of the instrumented crankshaft main bearings and thermocouple positions (

**right**, as seen from underneath the engine).

**Figure 4.**Distributions of the engine operation parameters (histogram bin widths calculated using the Freedman–Diaconis rule [66]).

**Figure 5.**Engine operation parameter correlation analysis based on Pearson correlation coefficients and Spearman’s rank correlation coefficients.

**Figure 6.**Hierarchical clustering of the engine operation parameters using Pearson correlation and Hoeffding’s D similarity measures ($30\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\mathrm{D}$ ranges from −0.5 to 1 [69]).

**Figure 7.**Illustration of the nested cross-validation for evaluation and comparison of the modeling procedures.

**Table 1.**Measured and calculated engine operation parameters considered for building the data-driven bearing temperature model.

Name | Description | Unit ^{1} | Type | Measuring Instrument ^{3} |
---|---|---|---|---|

T_MB | Crankshaft main bearing temperature (all bearings included; position identification listed below) | °C | target | Type K thermocouple (Class 1) |

MB1, MB2, …, MB7 | Boolean variables (i.e., true or false) denoting if a temperature value is from a specific bearing position | - | identifier | - |

N | Engine speed | min^{−1} | measurement | Rotary encoder in dynamometer (± 5% of grating period) |

Md | Engine torque | N m | calculation ^{2} | Strain gauge load cell in dynamometer (±0.3 % of MV) |

P | Engine power | kW | calculation | - |

load | Engine load | % | calculation | - |

m_oil_inlet | Oil mass flow at inlet | kg h^{−1} | calculation ^{2} | Emerson F200 Coriolis mass flow meter (±0.2 % of MV) |

p_oil_inlet | Oil pressure at inlet | bar(g) | measurement | AVL EZ 0187 (±0.1 of FSO) |

T_oil_inlet | Oil temperature at inlet | °C | measurement | Type K thermocouple (Class 1) |

T_oil_sump | Oil temperature at oil sump | °C | measurement | MAN ECU parameter |

m_coolant | Coolant mass flow | kg h^{−1} | calculation^{2} | Emerson F200 Coriolis mass flow meter (±0.2 % of MV) |

m_air_inlet | Air inlet mass flow | kg h^{−1} | measurement | ABB Sensyflow FMT700-P hot-film anemometer (±0.8 % of MV) |

p_air_intake | Air pressure on intake manifold | bar(g) | measurement | MAN ECU parameter |

T_air_intake | Air temperature on intake manifold | °C | measurement | MAN ECU parameter |

T_air_TC2 | Air temperature upstream of second turbocharger | °C | measurement | MAN ECU parameter |

p_air_EGR | Air inlet pressure upstream of EGR admixing | hPa(g) | measurement | MAN ECU parameter |

T_air_EGR | Air temperature upstream of EGR admixing | °C | measurement | MAN ECU parameter |

EAR | Excess air ratio | - | calculation | - |

m_fuel | Fuel mass flow | kg h^{−1} | calculation^{2} | Coriolis mass flow meter in AVL FuelExact 740 (±0.1 % of MV) |

BSFC | Brake-specific fuel consumption | gkW^{−1} h^{−1} | calculation | - |

visc_oil_inlet | Kinematic oil viscosity based on T_oil_inlet and oil type-related viscosity curves shown in Figure 2 | cSt | calculation | - |

^{1}For modeling, all temperature values are internally converted to Kelvin.

^{2}This parameter was measured during engine tests but is considered calculable or at least available from lookup tables at an ECU.

^{3}The accuracy of the measuring instrument is provided in from of a tolerance classification or as relative value (MV stands for measured value; FSO stands for full scale output).

**Table 2.**XGBoost hyperparameters of the scikit-learn API for gradient boosting regression used for tuning [79].

Hyperparameter | Description |
---|---|

n_estimators | Number of trees used for boosting (corresponds to B) |

eta | Learning rate of boosting updates (cf. gradient descent) |

max_depth | Maximum depth of a single tree |

min_child_weight | Minimum number of data instances/weight for a child node in a tree |

gamma | Minimum loss reduction required for further partitioning on a leaf node |

lambda | Ridge regression-analogous L2 regularization on tree weights |

alpha | Lasso regression-analogous L1 regularization on tree weights |

**Table 3.**Hyperparameters of the scikit-learn implementation for support vector regression used for tuning [73].

Hyperparameter | Description |
---|---|

epsilon | Margin tolerance of $\epsilon $-SVR |

C | Trade-off (regularization) parameter |

kernel | Kernel function to be used (“linear” or “rbf”) |

gamma | Coefficient for RBF kernel |

**Table 4.**Summary of nested cross-validation repeated 25 times (mean, median, standard deviation, minimum, and maximum of repetitions).

RMSE [°C] | MAE [°C] | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

ML Method | Mean | Median | SD | Min. | Max. | Mean | Median | SD | Min. | Max. |

LM_all | 1.0508 | 1.0479 | 0.0323 | 0.9954 | 1.1160 | 0.7908 | 0.7883 | 0.0247 | 0.7546 | 0.8434 |

LM_bearing | 5.4586 | 5.4583 | 0.0044 | 5.4512 | 5.4674 | 4.3627 | 4.3616 | 0.0039 | 4.3574 | 4.3715 |

LM_lasso | 1.0105 | 1.0096 | 0.0198 | 0.9832 | 1.0605 | 0.7644 | 0.7631 | 0.0137 | 0.7420 | 0.7954 |

XGBoost | 1.6080 | 1.5686 | 0.1603 | 1.3567 | 2.0172 | 1.1204 | 1.1228 | 0.0614 | 1.0130 | 1.2477 |

SVR | 0.5514 | 0.5460 | 0.0311 | 0.5016 | 0.6267 | 0.3611 | 0.3611 | 0.0192 | 0.3313 | 0.4032 |

Hyperparameter | Value |
---|---|

epsilon | 2^{−2} |

C | 2^{11} |

kernel | “rbf” |

gamma | 2^{−10} |

Test Data | 5-Fold CV | |||
---|---|---|---|---|

RMSE [°C] | MAE [°C] | Mean RMSE [°C] | Mean MAE [°C] | |

MB1 | 0.2351 | 0.1779 | 0.3472 | 0.2506 |

MB3 | 0.3622 | 0.3247 | 0.4915 | 0.3393 |

MB4 | 0.2746 | 0.2346 | 0.3344 | 0.2461 |

MB5 | 0.7151 | 0.5289 | 1.0296 | 0.7715 |

MB6 | 0.3616 | 0.2745 | 0.4140 | 0.3088 |

MB7 | 0.2311 | 0.1724 | 0.3369 | 0.2502 |

Overall | 0.3995 | 0.2855 | 0.5514 | 0.3611 |

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**MDPI and ACS Style**

Laubichler, C.; Kiesling, C.; Marques da Silva, M.; Wimmer, A.; Hager, G.
Data-Driven Sliding Bearing Temperature Model for Condition Monitoring in Internal Combustion Engines. *Lubricants* **2022**, *10*, 103.
https://doi.org/10.3390/lubricants10050103

**AMA Style**

Laubichler C, Kiesling C, Marques da Silva M, Wimmer A, Hager G.
Data-Driven Sliding Bearing Temperature Model for Condition Monitoring in Internal Combustion Engines. *Lubricants*. 2022; 10(5):103.
https://doi.org/10.3390/lubricants10050103

**Chicago/Turabian Style**

Laubichler, Christian, Constantin Kiesling, Matheus Marques da Silva, Andreas Wimmer, and Gunther Hager.
2022. "Data-Driven Sliding Bearing Temperature Model for Condition Monitoring in Internal Combustion Engines" *Lubricants* 10, no. 5: 103.
https://doi.org/10.3390/lubricants10050103