# Energy Modeling of a Refiner in Thermo-Mechanical Pulping Process Using ANFIS Method

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## Abstract

**:**

## 1. Introduction

## 2. Thermo-Mechanical Pulping Process

## 3. Intelligent Method

#### 3.1. Adaptive Neuro-Fuzzy Inference System (ANFIS)

#### 3.2. Biogeography-Based Optimization Algorithm (BBO)

#### 3.3. Teaching Learning-Based Optimization Algorithm (TLBO)

#### 3.4. Particle Swarm Optimization (PSO)

#### 3.5. Genetic Algorithm (GA)

#### 3.6. Ant Colony Optimization Algorithm (ACO)

#### 3.7. Differential Evolution (DE)

#### 3.8. The Proposed Hybrid Methods for the Refiner Simulation

## 4. Results and Discussion

#### 4.1. Data Validation

#### 4.2. Models Comparison

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

TMP | Thermo-mechanical pulping | Variables | |

BBO | Biogeography-based optimization algorithm | MSE | Mean-square-error |

GA | Genetic algorithm | RMSE | Root-mean-square error |

PSO | Particle swarm optimization algorithm | MAPE | Mean-absolute percentage error |

DE | Differential evolution | $R$ | Correlation coefficient |

ACO | Ant colony optimization algorithm | ${R}^{2}$ | Determination coefficient |

TLBO | Teaching learning-based optimization algorithm | $ML\left(\mathrm{MW}\right)$ | Refining motor load |

ANFIS | Adaptive neuro-fuzzy inference system | $DW\left(\mathrm{L}/\mathrm{min}\right)$ | Refining dilution water flow rate |

RBF | Radial basis function | $PG\left(\mathrm{mm}\right)$ | Refining plate gap |

LC | Low consistency | $Pr$ | Refining production rate |

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**Figure 2.**The structure of the adaptive neuro-fuzzy inference system (ANFIS) method consisting of two rules, two model inputs, one model output.

**Figure 4.**The main steps for implementing biogeography-based optimization algorithm (BBO) [39].

**Figure 5.**A schematic diagram of the teaching learning-based optimization algorithm (TLBO) algorithm [41].

**Figure 8.**Structure of ant colony (ACO) optimization algorithm [46].

**Figure 9.**Differential evolution algorithm flowchart [50].

**Figure 11.**(

**a**) creating an initial fuzzy inference system, (

**b**) the function of the particle swarm optimization algorithm (PSO) algorithm for training the ANFIS, and (

**c**) PSO structure.

**Figure 13.**Testing dataset of BBO for predicting motor load (

**a**), and produced steam during the pulp refining process (

**b**).

**Figure 14.**Test samples of TLBO to estimate motor load (

**a**), and generated steam during the pulp refining process (

**b**).

**Figure 15.**Test samples of PSO to estimate refining motor load (

**a**), and refining steam generation (

**b**).

**Figure 16.**Test samples of genetic algorithm (GA) to estimate refining motor load (

**a**), and refining steam generation (

**b**).

**Figure 17.**Test samples of ACO to estimate refining motor load (

**a**), and refining steam generation (

**b**).

**Figure 18.**Test samples of differential evolution (DE) to estimate refining motor load (

**a**), and refining steam generation (

**b**).

**Figure 19.**Comparison of the statistical indicators for six evolutionary algorithms to predict the motor load, (

**a**) RMSE, (

**b**) MSE, and (

**c**) R.

**Figure 20.**Comparison of the statistical indicators for six evolutionary algorithms to predict the steam generation, (

**a**) RMSE, (

**b**) MSE, and (

**c**) R.

Refining Plate Gap | Refining Dilution Water | Site Ambient Temperature | Feeder Screw Speed | Refining Motor Load | Refining Generated Steam | |
---|---|---|---|---|---|---|

predictor variables | ✓ | ✓ | ✓ | ✓ | ||

Target variable | ✓ | ✓ |

Parameter | Measure |
---|---|

$MAPE$ | $0.0460$ |

${R}^{2}$ | $0.72$ |

$R$ | 0.84 |

$RMSE\left(\mathrm{MW}\right)$ | $0.35$ |

$a$ | $-8.655$ |

$b$ | $1.719$ |

$km$ | $-1.240$ |

**Table 3.**Model evaluation criteria for six evolutionary algorithms contributing to ANFIS for refining motor load prediction.

Optimization Algorithm | MSE-Train | MSE-Test | RMSE-Train | RMSE-Test | R-Train | R-Test |
---|---|---|---|---|---|---|

TLBO | 0.1256 | 0.1216 | 0.3544 | 0.3488 | 0.8392 | 0.8472 |

BBO | 0.1046 | 0.1118 | 0.3235 | 0.3344 | 0.859 | 0.8511 |

DE | 0.1103 | 0.1155 | 0.3321 | 0.3398 | 0.8524 | 0.840 |

AC | 0.1155 | 0.1167 | 0.3399 | 0.3416 | 0.8424 | 0.843 |

GA | 0.08954 | 0.09494 | 0.29924 | 0.30813 | 0.8835 | 0.8677 |

PSO | 0.0705 | 0.0735 | 0.2655 | 0.2712 | 0.9068 | 0.9052 |

**Table 4.**Model evaluation criteria for six evolutionary algorithms contributing to ANFIS to predict the refining steam generation.

Optimization Algorithm | MSE-Train | MSE-Test | RMSE-Train | RMSE-Test | R-Train | R-Test |
---|---|---|---|---|---|---|

TLBO | 0.0221 | 0.0211 | 0.1487 | 0.1452 | 0.8496 | 0.8607 |

BBO | 0.0174 | 0.01757 | 0.13194 | 0.13256 | 0.8689 | 0.8682 |

DE | 0.01789 | 0.01697 | 0.1337 | 0.1303 | 0.8672 | 0.871 |

AC | 0.01925 | 0.01856 | 0.1387 | 0.1362 | 0.8524 | 0.8624 |

GA | 0.01556 | 0.01611 | 0.12476 | 0.12694 | 0.8836 | 0.8804 |

PSO | 0.0105 | 0.0128 | 0.1025 | 0.1131 | 0.924 | 0.9032 |

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## Share and Cite

**MDPI and ACS Style**

Talebjedi, B.; Khosravi, A.; Laukkanen, T.; Holmberg, H.; Vakkilainen, E.; Syri, S.
Energy Modeling of a Refiner in Thermo-Mechanical Pulping Process Using ANFIS Method. *Energies* **2020**, *13*, 5113.
https://doi.org/10.3390/en13195113

**AMA Style**

Talebjedi B, Khosravi A, Laukkanen T, Holmberg H, Vakkilainen E, Syri S.
Energy Modeling of a Refiner in Thermo-Mechanical Pulping Process Using ANFIS Method. *Energies*. 2020; 13(19):5113.
https://doi.org/10.3390/en13195113

**Chicago/Turabian Style**

Talebjedi, Behnam, Ali Khosravi, Timo Laukkanen, Henrik Holmberg, Esa Vakkilainen, and Sanna Syri.
2020. "Energy Modeling of a Refiner in Thermo-Mechanical Pulping Process Using ANFIS Method" *Energies* 13, no. 19: 5113.
https://doi.org/10.3390/en13195113