Any Progress on inverse pyrolysis modelling

Content

What is pyrolysis?

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.

Pyrolysis

How do we model pyrolysis?

Boundary condition

Heat conduction

Reaction rate:

Parameter overview

How do we get these parameters?

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

Usual experiments:

• Thermogravimetrical analysis
• Cone calorimeter
• Micro combustion calorimeter
• …

Exkurs: Thermogravimetrical analysis (TGA)

Approaches

• Forwad fitting
  • Basic graphical fitting [4, 5, 8]
  • Advanced automated fitting [3]
• Inverse modeling [9]
  • Optimization algorithms [1, 7]
  • Machine learning

Forests of randomized trees

Common Methods:

• Random Forests [2]
• Extremly Randomized Trees [6]

Concept

• Ensemble learning methods

Advantages

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

Method

• 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

Method II

Method III

Process I

1. 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 ,

Exkurs: Sampling I

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

Exkurs: Sampling II

Solution:

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

Exkurs: Sampling III

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

Process II

2. Splitting data set in two independent sets (75 % training data set and 25 % validation data set)
3. Train model with training data set
   • Input:
   • Output: ,
   • Model adopts to transform input to output
4. Validate trained model by feeding of validation data set and check for expected outcome

Process III

5. Recalculate with , , calculate RMSE between and

Process IV

6. Evaluate
7. Repeat with different algorithms and different hyperparameter settings

Results

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

1 Reaction, 3 Heating rates

2 Reactions, 3 Heating rates

2 Reactions, 3 Heating rates II

3 Reactions, 3 Heating rates

Evaluation

Advantages over other methods

• Trained model is fast (instant result)
• Trained model is portabel
• Results are pretty good (by now in 53 % of presented case)
  • better for 1 reaction
  • worse for 3 reactions
• If no perfect fit was found, it is at least a good starting point for other methods

Disadvantages over other methods

• Generating samples is costly
• Training a model is costly
• Results are only good in 53 % of presented case

Performance assesment against evelutionary optimization algorithms

Once an inverse replacement model with ET is set up, it is advantageous over SCEUA, since it gives instant results.

Performance assesment against training data set I

Question:

• Is the training data set itself large enough to contain a good fit for the data that shall be predicted?

Process:

• Split data set in training and testing (75/25)
• Calculate RMSE for each training case with each testing case
• Save best fit value for each testing case and plot
• Drawback: High computational costs, since RMSE calculations have to be conducted for a dataset with experimental sets
• So in this case just 10 % of the testing data set is used and compared to the training data set: only calculations

Performance assesment against training data set II

Performance assesment against training data set III

Discussion I:

Ugh! What happend here?

Possible explanations:

• Some error in the code?
• My solution actually performs that bad?
• Ill posed problem and “wrong” solutions found from database?

Discussion II:

Discussion: Evaluation

• When calculating the fit with , we get some numbers that represent the fit
• Without normalization it's not even comparable to other cases
• Even with normalization, question still is:
  • What is a good fit?
    • either as a numeric value
    • or utilizing other criteria to assess
• Let's discuss!

Next steps I

• Use larger sample data sets
  • implementing a database (HDF5)
• Compare to other machine learning models

Next steps II

• Couple with Heat conduction
• Try with different Pyrolysis models
  • gpyro
• Validate with real data
  • first step: PMMA from MacFP

Progress on PROPTI

PROPTI workflow

PROPTI

New functionalities

Focus: Cost Function

• determines the deviation between target data and a model response, e.g. between experimental data and simulation results.

Several different cost functions are presented for estimating material parameter sets that allow the simulation of pyrolysation of solid polymers.

Cost Function - Single Point

Cost Function - Threshold

Cost Function - RMSE

Cost Function - RMSE BANDS

Cost Function - RMSE RANGE

Cost Function - Combination

Discussion

A cost function that uses an area as a target, provides means to incorporate the uncertainty observed in the experiments.

RMSE requires exact matches of the data points, while slight variations in the other cases could still fall inside the target area. BANDS and RANGE could be useful to account for variance that is encountered when repeating a single experiment multiple times and allow for its representation during the IMP.

The ability to combine cost functions in different ways allows to target multiple values, like heat release rate or surface temperature, and their unique features, like heat release peaks on different experimental setups (e.g. different heat fluxes or gas atmospheres), as these may be of crucial importance for the real-scale applications, especially for flame spread modelling.

References