Patrick Lauer
University of Wuppertal
lauer@uni-wuppertal.de |

Burning of solids can be separated in two phases:

- Thermochemical decomposition of solid material and phase change from solid to gas phase (Pyrolysis)
- Chemical reaction in the gas phase (Combustion)

To predict fire spread, we need to model burning of solids, hence pyrolysis.

Boundary condition

(1)

Heat conduction

(2)

Reaction rate:

(3)

Parameter | |
---|---|

Activation energie | |

Pre-exponential factor | |

Reaction order | |

Density | |

Conduction coefficient | |

Heat capacity | |

Emissivity | |

Heat of reaction | |

Find parameters with small scale experiments and mathematical fitting, scale up to parts and devices

Usual experiments:

- Thermogravimetrical analysis
- Cone calorimeter
- Micro combustion calorimeter
- …

A small specimen (mg scale) gets heated in a furnace with a constant or transient heating rate. Mass loss of the specimen is captured. It allows to estimate reaction kinetics of this sample. |

Common Methods:

Concept

- Ensemble learning methods

Advantages

- Efficient for big data sets
- Fast to train
- Easy to parallelize

- Train a model to predict reaction kinetic parameters with given reaction rate
- Case study: mockup TGA experiment with constant heating rate
- All data used is randomly generated with the pyrolysis model

- Generating sample data set with the regarding model
- Samples for 1, 2 and 3 reactions, with 3 heating rates applied each
- Up to 1M samples generated, with and ,

Problem:

- Arrhenius equation is an exponential function
- might be
- might be
- Hence we can't sample from a uniform distribution

Challenge:

- Find a distribution to sample from

Solution:

- Introducing (reference temperature), (reference range) and (reference rate), characterizing a triangle of temperature at maximum mass loss rate and width of the peak

- and are sampled from a uniform distribution and then mapped to and
- Mapping between , and , , is done with these equations:

(4)

(5)

(6)

- Splitting data set in two independent sets (75 % training data set and 25 % validation data set)
- Train model with training data set
- Input:
- Output: ,
- Model adopts to transform input to output

- Validate trained model by feeding of validation data set and check for expected outcome

- Recalculate with , , calculate RMSE between and

- Evaluate
- Repeat with different algorithms and different hyperparameter settings

for inverse replacement models with

- 1 reaction, 3 heating rates,
- 2 reactions, 3 heating rates and
- 3 reactions, 3 heating rates

built with Extremly Randomized Trees algorithm