# Application of Adaptive Neuro-Fuzzy Inference System in Flammability Parameter Prediction

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}. This research explored the applicability of ANFIS in the prediction of HRC and THR derived from the experiment. The degree of accuracy was determined by comparing the root mean squared error (RMSE) criterion, the coefficient of correlation and the coefficient of determination. A comparative analysis was carried out with multiple linear regression and the feed-forward back propagation neural network to show the efficacy, accuracy and superiority of ANFIS. The modeling results obtained from this research will help validate the robustness of ANFIS and its continual usage in future flammability assessments.

## 2. Experimental Methods

#### 2.1. Material

#### 2.2. Microscale Combustion Calorimetry (MCC)

^{−1}. The volatile pyrolysis products were removed from the pyrolyzer by nitrogen gas and were oxidized with excess oxygen at 900 °C in a tubular combustion furnace. Oxygen consumption calorimetry was applied for calculating the heat release rate from the volumetric flow rate and the oxygen concentration of the gases that flowed out of the combustor [6,13,14,20]. The samples were tested in three replicates and an average of the measured results was recorded. The samples were labelled as xps_1_0.1 representing the first sample tested under 0.1 K s

^{−1}, and so on. The heat release temperature, time to heat release and heat release rate were measured and recorded. HRC was obtained by dividing the specific heat release rate by the corresponding heating rate. Additionally, THR was calculated from the area under the specific heat release rate against time plots at a given heating rate.

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

#### 2.4. Multiple Linear Regression (MLR)

#### 2.5. Model Implementation

## 3. Results and Discussion

#### 3.1. MCC Experimental Results

#### 3.2. Statistical Analysis

#### 3.3. ANFIS Network Prediction Results

- If (input1 is in1mf1) and (input2 is in2mf1), then (output is out1mf1) (1).
- If (input1 is in1mf1) and (input2 is in2mf2), then (output is out1mf2) (1).
- If (input1 is in1mf1) and (input2 is in2mf3), then (output is out1mf3) (1).
- If (input1 is in1mf2) and (input2 is in2mf1), then (output is out1mf4) (1).
- If (input1 is in1mf2) and (input2 is in2mf2), then (output is out1mf5) (1).
- If (input1 is in1mf2) and (input2 is in2mf3), then (output is out1mf6) (1).
- If (input1 is in1mf3) and (input2 is in2mf1), then (output is out1mf7) (1).
- If (input1 is in1mf3) and (input2 is in2mf2), then (output is out1mf8) (1).
- If (input1 is in1mf3) and (input2 is in2mf3), then (output is out1mf9) (1).

^{2}values obtained, one notable conclusion can be made: the model predicted HRC better than THR since both training and testing of HRC had the best results. This is due to the fact that HRC has a direct and significant statistical relationship with the input parameters, whereas THR is almost constant at any given heating rate and sample mass, thus presenting an uneven statistical distribution. It should also be noted that the test results are an indication of the excellent ability of the developed models to predict data beyond the limits of the training range.

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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Property | Value |
---|---|

Thermal conductivity/Wm^{−1} K^{−1} | 0.1316 |

Thermal diffusivity/m^{2} s^{−1} | 0.4201 |

Specific heat capacity/kJ g^{−1} K^{−1} | 1.34 |

LOI % | 19.3 |

Density, $\rho $/kg m^{−3} | 52.6 |

Density of molten material, $\rho $/kg m^{−3} | 828 |

N | Mean | SD | Sum | Min | Max | |
---|---|---|---|---|---|---|

HRC/J g^{−1} K^{−1} | 28 | 966.64571 | 349.69697 | 27,066.08 | 580.4 | 1630 |

THR/kJ g^{−1} | 28 | 32.10357 | 1.29257 | 898.9 | 28.6 | 34.6 |

Heating rate | 28 | 1.56786 | 1.1757 | 43.9 | 0.1 | 3.5 |

Mass | 28 | 1.49607 | 0.41362 | 41.89 | 0.93 | 2.11 |

DF | Sum of Squares | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|

Model | 2 | 2.68 × 10^{6} | 1.34 × 10^{6} | 53.85 | 8.68 × 10^{−10} |

Error | 25 | 622,061.52 | 24,882.46 | ||

Total | 27 | 3.31 × 10^{6} |

DF | Sum of Squares | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|

Model | 2 | 3.20 | 1.60 | 0.95 | 0.39 |

Error | 25 | 41.91 | 1.68 | ||

Total | 27 | 45.11 |

HRC/J g^{−1} K^{−1} | THR/kJ g^{−1} | ||||
---|---|---|---|---|---|

Variable | Value | Std. Error | Variable | Value | Std. Error |

Constant | 1392.82 | 120.32 | Constant | 31.42 | 0.99 |

Heating rate | −267.94 | 25.82 | Heating rate | 0.29 | 0.22 |

Sample mass | −4.07 | 73.4 | Sample mass | 0.16 | 0.61 |

Adjusted R^{2} | 0.8 | Adjusted R^{2} | 0.033 |

Training Set | β/K s^{−1} | Mass/m | THR/kJ g^{−1} | HRC/J g^{−1} K^{−1} |

0.1 | 1.00 | 29.3 ± 0.9 | 1528 ± 23.5 | |

0.1 | 1.98 | 31.6 ± 0.7 | 1585 ± 33.3 | |

0.2 | 2.02 | 30.9 ± 0.3 | 1481.5 ± 28.5 | |

0.5 | 0.93 | 32.9 ± 0.5 | 1224.2 ± 39 | |

0.5 | 1.38 | 34.5 ± 1.8 | 1336.0 ± 18.2 | |

1.0 | 0.99 | 31.1 ± 0.7 | 907.1 ± 40.8 | |

1.0 | 1.52 | 31.9 ± 0.5 | 892.3 ± 67.3 | |

1.0 | 2.03 | 32.7 ± 0.3 | 922.6 ± 59.3 | |

1.5 | 1.02 | 33.2 ± 0.8 | 774.7 ± 27.5 | |

1.5 | 1.99 | 32.1 ± 0.9 | 795.0 ± 33.4 | |

1.5 | 1.45 | 32.2 ± 0.5 | 824.3 ± 65.1 | |

2.0 | 0.99 | 33.3 ± 1.3 | 763.8 ± 49.3 | |

2.0 | 1.48 | 34.6 ± 0.7 | 744.2 ± 57.8 | |

2.0 | 1.99 | 32.1 ± 0.7 | 737.4 ± 37.4 | |

2.5 | 1.07 | 32.7 ± 0.5 | 669.8 ± 28.6 | |

2.5 | 1.53 | 32.5 ± 0.8 | 723.6 ± 21.3 | |

2.5 | 2.11 | 33.0 ± 0.6 | 667.28 ± 53.2 | |

3.0 | 0.97 | 32.6 ± 0.5 | 664.6 ± 55.2 | |

3.0 | 1.49 | 32.6 ± 5.5 | 666.6 ± 30.2 | |

3.0 | 2.08 | 32.8 ± 2.5 | 643.7 ± 47.2 | |

3.5 | 1.02 | 32.3 ± 1.6 | 615.1 ± 35.8 | |

3.5 | 1.41 | 31.1 ± 0.5 | 626.3 ± 50.9 | |

3.5 | 1.94 | 32.5 ± 0.9 | 580.4 ± 26.7 | |

Testing Test | 0.1 | 1.46 | 32.4 ± 0.07 | 1630.0 ± 62.4 |

0.2 | 1.06 | 28.6 ± 3.0 | 1422.0 ± 28.3 | |

0.2 | 1.52 | 31.0 ± 1.5 | 1503.0 ± 33.8 | |

0.5 | 1.96 | 31.5 ± 2.8 | 1188.8 ± 25.7 |

Variable | HRC/J g^{−1} K^{−1} | THR/kJ g^{−1} |
---|---|---|

Value | Value | |

Number of nodes | 53 | 35 |

Number of linear parameters | 24 | 9 |

Number of nonlinear parameters | 32 | 12 |

Total number of parameters | 56 | 21 |

Number of training data pairs | 24 | 24 |

Number of checking data pairs | 0 | 0 |

Number of fuzzy rules | 9 | 9 |

Statistical Indicator | HRC | THR | ||
---|---|---|---|---|

Training | Testing | Training | Testing | |

R^{2} | 0.99994 | 0.99904 | 0.99315 | 0.9148 |

RMSE | 0.0224 | 0.625 | 0.00781 | 0.9395 |

Model | HRC | THR | ||||
---|---|---|---|---|---|---|

Training | Testing | Training Time (s) | Training | Testing | Training Time (s) | |

ANFIS | 0.0224 | 0.625 | 7.8 | 0.00781 | 0.9395 | 7.35 |

FFBPNN | 0.382 | 0.980 | 13.3 | 0.457 | 1.048 | 12.26 |

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**MDPI and ACS Style**

Afriyie Mensah, R.; Xiao, J.; Das, O.; Jiang, L.; Xu, Q.; Okoe Alhassan, M.
Application of Adaptive Neuro-Fuzzy Inference System in Flammability Parameter Prediction. *Polymers* **2020**, *12*, 122.
https://doi.org/10.3390/polym12010122

**AMA Style**

Afriyie Mensah R, Xiao J, Das O, Jiang L, Xu Q, Okoe Alhassan M.
Application of Adaptive Neuro-Fuzzy Inference System in Flammability Parameter Prediction. *Polymers*. 2020; 12(1):122.
https://doi.org/10.3390/polym12010122

**Chicago/Turabian Style**

Afriyie Mensah, Rhoda, Jie Xiao, Oisik Das, Lin Jiang, Qiang Xu, and Mohammed Okoe Alhassan.
2020. "Application of Adaptive Neuro-Fuzzy Inference System in Flammability Parameter Prediction" *Polymers* 12, no. 1: 122.
https://doi.org/10.3390/polym12010122