# Applying the Random Forest Method to Improve Burner Efficiency

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Modeling of the Efficiency of Burners

#### 2.1. 3D Model of the Burner

#### 2.2. Mathematical Model of Gas Dynamics

- x-component$$\begin{array}{c}\hfill \frac{\partial}{\partial t}\left(\rho u\right)+u\frac{\partial}{\partial x}\left(\rho u\right)+\upsilon \frac{\partial}{\partial r}\left(\rho u\right)+\frac{w}{r}\frac{\partial}{\partial \theta}\left(\rho u\right)\\ \hfill =-\frac{\partial P}{\partial x}+\mu [\frac{{\partial}^{2}\phantom{\rule{4pt}{0ex}}u}{\partial {x}^{2}}+\frac{1}{r}\frac{\partial}{\partial r}(r\frac{\partial u}{\partial r}+\frac{1}{{r}^{2}}\phantom{\rule{4pt}{0ex}}\frac{{\partial}^{2}\phantom{\rule{4pt}{0ex}}u}{\partial {\theta}^{2}\phantom{\rule{4pt}{0ex}}}]\\ \hfill +\left[-\frac{\partial \left(\overline{\rho {{u}^{\prime}}^{2}}\right)}{\partial x}-\frac{\partial \left(\overline{\rho {u}^{\prime}{\upsilon}^{\prime}}\right)}{\partial r}-\frac{1}{r}\frac{\partial \left(\overline{\rho {u}^{\prime}{w}^{\prime}}\right)}{\partial \theta}\right]\end{array}$$
- r-component$$\begin{array}{c}\hfill \frac{\partial}{\partial t}\left(\rho \upsilon \right)+u\frac{\partial}{\partial x}\left(\rho \upsilon \right)+\upsilon \frac{\partial}{\partial r}\left(\rho \upsilon \right)+\frac{w}{r}\frac{\partial}{\partial \theta}\left(\rho \upsilon \right)-\frac{{w}^{2}}{r}\\ \hfill =-\frac{\partial P}{\partial r}+\mu \left[\frac{{\partial}^{2}\upsilon}{\partial {x}^{2}}+\frac{1}{r}\frac{\partial}{\partial r}\left(r\frac{\partial \upsilon}{\partial r}\right)+\frac{1}{{r}^{2}}\frac{{\partial}^{2}\upsilon}{\partial {\theta}^{2}}-\frac{\upsilon}{{r}^{2}}-\frac{2}{{r}^{2}}\frac{\partial w}{\partial \theta}\right]\\ \hfill +\left[-\frac{\partial \left(\overline{\rho {u}^{\prime}{\upsilon}^{\prime}}\right)}{\partial x}-\frac{\partial \left(\overline{\rho {{\upsilon}^{\prime}}^{2}}\right)}{\partial r}-\frac{1}{r}\frac{\partial \left(\overline{\rho {\upsilon}^{\prime}{w}^{\prime}}\right)}{\partial \theta}\right]\end{array}$$
- $\theta $-component$$\begin{array}{c}\hfill \frac{\partial}{\partial t}\left(\rho w\right)+u\frac{\partial \left(\rho w\right)}{\partial x}+\upsilon \frac{\partial \left(\rho w\right)}{\partial r}+\frac{w}{r}\frac{\partial \left(\rho w\right)}{\partial \theta}+\frac{\upsilon w}{r}\\ \hfill =-\frac{1}{r}\frac{\partial P}{\partial \theta}+\mu \left[\frac{{\partial}^{2}w}{\partial {x}^{2}}+\frac{1}{r}\frac{\partial}{\partial r}\left(r\frac{\partial w}{\partial r}\right)+\frac{1}{{r}^{2}}\frac{{\partial}^{2}w}{\partial {\theta}^{2}}+\frac{2}{{r}^{2}}\frac{\partial \upsilon}{\partial \theta}-\frac{w}{{r}^{2}}\right]\\ \hfill +\left[-\frac{\partial \left(\overline{\rho {u}^{\prime}{w}^{\prime}}\right)}{\partial x}-\frac{\partial \left(\overline{\rho {\upsilon}^{\prime}{w}^{\prime}}\right)}{\partial r}-\frac{1}{r}\frac{\partial \left(\overline{\rho {{w}^{\prime}}^{2}}\right)}{\partial \theta}\right]\end{array}$$

#### 2.3. Border Conditions

- -
- On the walls:$$\begin{array}{c}\hfill x\in \left(0,L\right):u\left(x,R,\theta \right)=0;\upsilon \left(x,R,\theta \right)=0;w\left(x,R,\theta \right)=0;T\left(x,R,\theta \right)={T}_{w}.\\ \hfill {R}^{*}\in \left({r}_{B},R\right):u\left({x}_{0},{R}^{*},\theta \right)=0;\upsilon \left({x}_{0},{R}^{*},\theta \right)=0;w\left({x}_{0},{R}^{*},\theta \right)=0;T\left({x}_{0},{R}^{*},\theta \right)={T}_{w}.\end{array}$$
- -
- Inlet:$$\begin{array}{c}\hfill r\in \left(0,{r}_{B}\right):u\left({x}_{0},{r}^{*},\theta \right)={U}_{air}+{U}_{fuel};\upsilon \left({x}_{0},{r}^{*},\theta \right)=0;w\left({x}_{0},{r}^{*},\theta \right)={\omega}_{air};\\ \hfill P\left({x}_{0},{r}^{*},\theta \right)={P}_{air}+{P}_{fuel};T\left({x}_{0},{r}^{*},\theta \right)={T}_{air}+{T}_{fuel}.\end{array}$$
- -
- Outlet:$$\begin{array}{c}\hfill p\left(L,r,\theta \right)=0,\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}r\in \left(0,R\right).\end{array}$$

#### 2.4. Mesh Selection and Mesh Convergence Analysis

#### 2.5. Choice of Combustion Model

#### 2.6. Some of the Obtained Results of Forecasting Emissions of Harmful Substances

## 3. Application of Machine Learning to Improve the Efficiency of Burners

#### 3.1. Machine Learning Problem Statement

#### 3.2. Basic Machine Learning Methods

#### 3.3. Criteria for the Quality of Education

#### 3.4. Burner Performance Indicators Obtained from the Results of a Computational Experiment

## 4. Results and Discussion of a Computational Experiment

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AI | Artificial Intelligence |

CFD | Computational Fluid Dynamics |

FGM | Flamelet Generated Manifold |

FGR | Flue Gas Recirculation |

FIR | Fuel-Induced Recirculation |

GMU-45 | Unified oil and gas burner, installed heat output 52.335 MW (45 Gcal/h) |

E-500-13.8-560GMN | The other name TGME-464,Taganrog oil and gas natural circulation boiler, steam capacity 500 t/h, steam parameters 13.8 MPa, 560 °C |

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**Figure 1.**Three dimensional model of the burner in the STAR-CCM+ environment: (

**a**) gas inlet; (

**b**) primary air inlet; (

**c**) secondary air inlet; (

**d**) combustion area in the combustion chamber.

**Figure 2.**Operating burner device type GMU-45 boiler type E-500-13.8-560GMN: (

**a**) general view; (

**b**) enlarged view of the blades.

**Figure 3.**Calculation grid of the study area of the simulated combustion chamber with one burner device type, GMU-45.

**Figure 4.**Calculation grid of the study area of the simulated burner: (

**a**) burner cut; (

**b**) front view.

**Figure 5.**Comparison of test calculations for the combustion of a methane-air mixture with a “basic” size of cells of the computational grid of 0.4–1.0 m: (

**a**) comparison of temperature; (

**b**) comparison of NOx emissions. With a “basic” size of 0.4 m, the number of cells of the computational grid was 5,192,600; with a “base” size of 0.5 m–2,787,464; with a “base” size of 0.75 m–951,840; with a “base” size of 1.0 m–456,125.

**Figure 6.**Comparison of test calculations of the methane–air mixture for different combustion models of the STAR-CCM+ multidisciplinary platform: (

**a**) temperature comparison; (

**b**) comparison of $N{O}_{X}$ emissions.

**Figure 7.**The study of the release of harmful substances at various steam loads of the E-500-13.8-560GMN type boiler: (

**a**) comparison of temperatures; (

**b**) comparison of $N{O}_{X}$ emissions.

**Figure 8.**Influence of flue gas recirculation on the efficiency of a power boiler E-500-13.8-560GMN.

**Figure 9.**Study of the influence of the degree of recirculation during the combustion of a methane-air mixture of the type of power boiler E-500-13.8-560GMN (steam load of 400 tons per hour): (

**a**) temperature comparison; (

**b**) comparison of $N{O}_{X}$ emissions.

**Figure 10.**Study of the influence of the degree of recirculation during the combustion of a methane–air mixture of the type of power boiler E-500-13.8-560GMN (steam load of 315 tons per hour): (

**a**) temperature comparison; (

**b**) comparison of $N{O}_{X}$ emissions.

Symbol | Name | Unit of Measure | Minimum | Maximum |
---|---|---|---|---|

${X}_{1}$ | Steam load | tons/h | 170 | 500 |

${X}_{2}$ | Air consumption | m${}^{3}$/h | 4847 | 61,152 |

${X}_{3}$ | Methane consumption | m${}^{3}$/h | 0 | 5375 |

${X}_{4}$ | Biogas consumption | m${}^{3}$/h | 0 | 5000 |

${X}_{5}$ | $C{H}_{4}$ | % | 30.41 | 98 |

${X}_{6}$ | ${C}_{2}{H}_{6}$ | % | 0 | 14.58 |

${X}_{7}$ | ${C}_{3}{H}_{8}$ | % | 0 | 9.09 |

${X}_{8}$ | $C{O}_{2}$ | % | 0 | 31.75 |

${X}_{9}$ | ${N}_{2}$ | % | 0 | 1.05 |

${X}_{10}$ | ${H}_{2}S$ | % | 0 | 0.11 |

${X}_{11}$ | ${H}_{2}$, | % | 0 | 50.1 |

${X}_{12}$ | ${O}_{2}$ | % | 0.179 | 0.232 |

${X}_{13}$ | ${N}_{2}$ | % | 0.750 | 0.768 |

${X}_{14}$ | $C{O}_{2}$ | % | 0 | 0.023 |

${X}_{15}$ | ${H}_{2}O$ | % | 0 | 0.048 |

${X}_{16}$ | Inlet air temperature | K | 446 | 533 |

${X}_{17}$ | Fuel temperature | K | 10 | 25 |

${X}_{18}$ | Swirler blade angle | degrees | 0 | 50 |

${X}_{19}$ | Grid size | m | 0.1 | 1 |

${X}_{20}$ | Excess air ratio | 0.88 | 1.5 |

Method | Percentage of Correct Answers, % |
---|---|

Logistic regression | 73.33% |

Discriminant Function Analysis | 71.67% |

K-Nearest Neighbors Algorithm | 80.00% |

Support vector machine | 56.67% |

Naive Bayes classifier | 21.67% |

Decision tree | 90.00% |

Random forest | 91.67% |

AdaBoost | 70.00% |

Method | F-Measure |
---|---|

Logistic regression | 0.713 |

Discriminant Function Analysis | 0.700 |

K-Nearest Neighbors Algorithm | 0.802 |

Support vector machine | 0.490 |

Naive Bayes classifier | 0.206 |

Decision tree | 0.898 |

Random forest | 0.916 |

AdaBoost | 0.691 |

Method | F-Measure |
---|---|

Random forest + Support vector machine | 0.898 |

Random forest + K-Nearest Neighbors Algorithm | 0.882 |

Random forest + AdaBoost | 0.882 |

Random forest + Logistic regression | 0.866 |

Support vector machine + K-Nearest Neighbors Algorithm | 0.830 |

Support vector machine + AdaBoost | 0.844 |

Support vector machine + Logistic regression | 0.640 |

Support vector machine + Discriminant Function Analysis | 0.710 |

K-Nearest Neighbors Algorithm + AdaBoost | 0.867 |

K-Nearest Neighbors Algorithm + Logistic regression | 0.799 |

K-Nearest Neighbors Algorithm + Discriminant Function Analysis | 0.758 |

AdaBoost + Logistic regression | 0.867 |

AdaBoost + Discriminant Function Analysis | 0.805 |

Logistic regression + Discriminant Function Analysis | 0.713 |

Share of the Test Sample | 10% | 15% | 20% | 25% | 30% |
---|---|---|---|---|---|

F-measure value | 0.901 | 0.910 | 0.917 | 0.881 | 0.900 |

Number of Blocks | 4 | 5 | 6 | 10 |
---|---|---|---|---|

F-measure value | 0.915 | 0.899 | 0.878 | 0.883 |

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## Share and Cite

**MDPI and ACS Style**

Kovalnogov, V.; Fedorov, R.; Klyachkin, V.; Generalov, D.; Kuvayskova, Y.; Busygin, S.
Applying the Random Forest Method to Improve Burner Efficiency. *Mathematics* **2022**, *10*, 2143.
https://doi.org/10.3390/math10122143

**AMA Style**

Kovalnogov V, Fedorov R, Klyachkin V, Generalov D, Kuvayskova Y, Busygin S.
Applying the Random Forest Method to Improve Burner Efficiency. *Mathematics*. 2022; 10(12):2143.
https://doi.org/10.3390/math10122143

**Chicago/Turabian Style**

Kovalnogov, Vladislav, Ruslan Fedorov, Vladimir Klyachkin, Dmitry Generalov, Yulia Kuvayskova, and Sergey Busygin.
2022. "Applying the Random Forest Method to Improve Burner Efficiency" *Mathematics* 10, no. 12: 2143.
https://doi.org/10.3390/math10122143