# 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

- Lyon, R.E.; Richard, W. A Microscale Combustion Calorimeter; Federal Aviation Administration Washington DC Office of Aviation Research: Washington, DC, USA, 2002; No. DOT/FAA/AR-01/117. [Google Scholar]
- Hostikka, S.; Matala, A. Pyrolysis Model for Predicting the Heat Release Rate of Birch Wood. Combust. Sci. Technol.
**2017**, 189, 1373–1393. [Google Scholar] [CrossRef] - Lyon, R.E.; Walters, R.N.; Stoliarov, S.I. Screening flame retardants for plastics using microscale combustion calorimetry. Polym. Eng. Sci.
**2007**, 47, 1501–1510. [Google Scholar] [CrossRef] - Schartel, B.K.; Pawlowski, H.; Richard, E.L. Pyrolysis combustion flow calorimeter: A tool to assess flame retarded PC/ABS materials. Thermochim. Acta
**2007**, 462, 1–14. [Google Scholar] [CrossRef] - Xu, Q.; Jin, C.; Majlingova, A.; Restas, A. Discuss the heat release capacity of polymer derived from microscale combustion calorimeter. J. Therm. Anal. Calorim.
**2018**, 133, 649–657. [Google Scholar] [CrossRef] - Standard Test Method for Determining Flammability Characteristics of Plastics and Other Solid Materials Using Microscale Combustion Calorimetry; ASTM D7309; American Society for Testing and Materials: West Conshohocken, PA, USA, 2013.
- Keshavarz, M.H.; Dashtizadeh, A.; Motamedoshariati, H.; Soury, H. A simple model for reliable prediction of the specific heat release capacity of polymers as an important characteristic of their flammability. J. Therm. Anal. Calorim.
**2017**, 128, 417–426. [Google Scholar] [CrossRef] - Yang, C.Q.; He, Q. Textile heat release properties measured by microscale combustion calorimetry: Experimental repeatability. Fire Mater.
**2012**, 36, 127–137. [Google Scholar] [CrossRef] - Lyon, R.E.; Walters, R.N. Heat release capacity. In Proceedings of the Fire and Materials Conference, San Francisco, CA, USA, 22 January 2001; pp. 285–300. [Google Scholar]
- Lyon, R.E.; Walters, R.N. Thermal analysis of polymer flammability. Bridg. Centuries Sampe’s Mater. Process. Technol.
**2000**, 24, 1721–1729. [Google Scholar] - Mensah, R.A.; Xu, Q.; Asante-Okyere, S.; Jin, C.; Bentum-Micah, G. Correlation analysis of cone calorimetry and microscale combustion calorimetry experiments. J. Therm. Anal. Calorim.
**2018**, 136, 589–599. [Google Scholar] [CrossRef] - Yilmaz, I.; Kaynar, O. Multiple regression, ANN (RBF, MLP) and ANFIS models for prediction of swell potential of clayey soils. Expert Syst. Appl.
**2011**, 38, 5958–5966. [Google Scholar] [CrossRef] - Asante-Okyere, S.; Xu, Q.; Mensah, R.A.; Jin, C.; Ziggah, Y.Y. Generalized regression and feed forward back propagation neural networks in modelling flammability characteristics of polymethyl methacrylate (PMMA). Thermochim. Acta
**2018**, 667, 79–92. [Google Scholar] [CrossRef] - Mensah, R.A.; Jiang, L.; Xu, Q.; Asante-Okyere, S.; Jin, C. Comparative evaluation of the predictability of neural network methods on the flammability characteristics of extruded polystyrene from microscale combustion calorimetry. J. Therm. Anal. Calorim.
**2019**, 138, 3055–3064. [Google Scholar] [CrossRef] - Jang, J.S. ANFIS: Adaptive-network-based fuzzy inference system. IEEE Trans. Syst. Man Cybern.
**1993**, 23, 665–685. [Google Scholar] [CrossRef] - Sharma, M. Artificial neural network fuzzy inference system (ANFIS) for brain tumor detection. arXiv
**2012**, arXiv:1212.0059. [Google Scholar] - Atuahene, S.; Bao, Y.; Ziggah, Y.; Gyan, P.; Li, F. Short-Term Electric Power Forecasting Using Dual-Stage Hierarchical Wavelet-Particle Swarm Optimization-Adaptive Neuro-Fuzzy Inference System PSO-ANFIS Approach Based on Climate Change. Energies
**2018**, 11, 2822. [Google Scholar] [CrossRef][Green Version] - Sihag, P.; Tiwari, N.K.; Ranjan, S. Prediction of unsaturated hydraulic conductivity using adaptive neuro-fuzzy inference system (ANFIS). ISH J. Hydraul. Eng.
**2019**, 25, 132–142. [Google Scholar] [CrossRef] - Emiroğlu, M.; Beycioğlu, A.; Yildiz, S. ANFIS and statistical based approach to prediction the peak pressure load of concrete pipes including glass fiber. Expert Syst. Appl.
**2012**, 39, 2877–2883. [Google Scholar] [CrossRef][Green Version] - Lyon, R.E.; Walters, R.N. Pyrolysis combustion flow calorimetry. J. Anal. Appl. Pyrolysis
**2004**, 71, 27–46. [Google Scholar] [CrossRef] - Hadi, A.A.; Wang, S. A Novel Approach for Microgrid Protection Based upon Combined ANFIS and Hilbert Space-Based Power Setting. Energies
**2016**, 9, 1042. [Google Scholar] [CrossRef] - Lee, C.C. Fuzzy logic in control systems: Fuzzy logic controller. IEEE Trans. Syst. Man Cybern.
**1990**, 20, 404–418. [Google Scholar] [CrossRef][Green Version] - Kisi, O.; Haktanir, T.; Ardiclioglu, M.; Ozturk, O.; Yalcin, E.; Uludag, S. Adaptive neuro-fuzzy computing technique for suspended sediment estimation. Adv. Eng. Softw.
**2009**, 40, 438–444. [Google Scholar] [CrossRef] - Zarandi, M.H.F.; Türksen, I.B.; Sobhani, J.; Ramezanianpour, A.A. Fuzzy polynomial neural networks for approximation of the compressive strength of concrete. Appl. Soft Comput.
**2008**, 8, 488–498. [Google Scholar] [CrossRef] - Takagi, T.; Sugeno, M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern.
**1985**, 1, 116–132. [Google Scholar] [CrossRef] - Al-Sulaiman, M.A. Applying of an adaptive neuro fuzzy inference system for prediction of unsaturated soil hydraulic conductivity. Biosci. Biotechnol. Res. Asia
**2015**, 12, 2261–2272. [Google Scholar] [CrossRef][Green Version] - Pal, M.; Bharati, P. Introduction to Correlation and Linear Regression Analysis. In Applications of Regression Techniques; Springer: Singapore, 2019; pp. 1–18. [Google Scholar]
- Liu, D.; Xu, Z.; Fan, C. Predictive analysis of fire frequency based on daily temperatures. Nat. Hazards
**2019**, 97, 1175–1189. [Google Scholar] [CrossRef] - Zhang, Y.; Shen, L.; Ren, Y.; Wang, J.; Liu, Z.; Yan, H. How fire safety management attended during the urbanization process in China? J. Clean. Prod.
**2019**, 236, 117686. [Google Scholar] [CrossRef] - An, W.; Jiang, L.; Sun, J.; Liew, K.M. Correlation analysis of sample thickness, heat flux, and cone calorimetry test data of polystyrene foam. J. Therm. Anal. Calorim.
**2015**, 119, 229–238. [Google Scholar] [CrossRef] - Fan, C.L.; Zhang, S.; Jiao, Z.; Yang, M.; Li, M.; Liu, X. Smoke spread characteristics inside a tunnel with natural ventilation under a strong environmental wind. Tunn. Undergr. Space Technol.
**2018**, 82, 99–110. [Google Scholar] [CrossRef] - Gao, X.; Jiang, L.; Xu, Q. Experimental and theoretical study on thermal kinetics and reactive mechanism of nitrocellulose pyrolysis by traditional multi kinetics and modeling reconstruction. J. Hazard. Mater.
**2019**, 121645, in press. [Google Scholar] [CrossRef]

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