Automated Fitting of 

Thermogravimetric Analysis Data

July 2, 2019

Morgan C. Bruns 

Virginia Military Institute (USA)

Isaac T. Leventon

National Institute of 

Standards and Technology (USA)
Predicting Fire Growth

• To engineer safer:

– Buildings

– Products

– Materials

• Accurate 

predictions require 

condensed phase 

pyrolysis models

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Condensed Phase Challenges

• Physics

– Multiphase

– Mechanical 

deformation

• Numerics

– Gas phase 

coupling

– Multiscale

– Moving boundary

• Materials

– Many parameters

– Many materials

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How Many Parameters?

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At least ~6N

material property 

parameters need to 

be quantified

Neglecting

• Radiation

• Mass transport

• Charring

• Temperature 

dependence
How many materials?

• NFIRS categorizes 38 distinct “types” of solid 

materials “First Ignited” 

• These “types” are extremely broad categories 

such as “Plastic”, “Rubber”, and “Plywood” 

• For example, Lyon and Janssens (2005) contains 

data on 50 common plastics

• Additional diversity due to processing variability, 

additives, blends, ageing, etc.

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On the order of 103 distinct materials relevant to 

fire growth predictions
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(101 Parameters) × (103 Materials) 

= 104 Properties for reliable fire growth predictions

A Material Property Database is needed
Material Property Database

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• Being developed at 

NIST

• Adopting “Hierarchical” 

approach

• Critical components

1. Standard formatting

2. Standard metadata

3. Analysis tools
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Global Approach

Hierarchical Approach

Fire Model
Analysis of TGA Data

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Mass

Temperature

How should we estimate pyrolysis kinetic parameters 

from raw TGA data (Mass vs. Temperature)?
Method Requirements

1. Parameters predict data → Accurate

2. Many different materials → Efficient

3. Many different responses → Robust

4. Parameters do not vary → Consistent

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How to be Consistent

1. No free parameters

2. No random numbers

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“With four parameters I can fit an 

elephant, and with five I can make 

him wiggle his trunk.”

~John von Neumann
Pyrolysis Model: Independent 

Unimolecular Reactions

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Appropriateness to be determined by ability to 

predict fire growth.
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Mass

Mass

Loss

Rate

Temperature

Characteristic temperature 

and mass changes:

Analysis of peak condition 

yields:
Nondimensional Form

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Approximate Solution

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Also applies for multiple, independent reactions.
Estimating Parameters

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TGA Data

Approximate 

Solution
Some Details

1. Smoothed data 

derivatives are found 

using Savitzky-Golay

filter

2. “Small” mass loss rate 

peaks are neglected

3. Complete algorithm 

corrects preceding 

equations for 

overlapping reactions

4. Reaction mass changes 

corrected to conserve 

mass

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Requires 

specification of 

two parameters

Requires 

iteration
Verification

1. Assume kinetic parameters

2. Generate TGA data

3. Use algorithm to find parameters

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Purpose:

1. Check implementation

2. Test validity of approximate solution
Single Reaction Verification

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Single Reaction Verification

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ΔT = 10 K:

ΔT = 20 K:

ΔT = 40 K:

Decreasing ξ

Increasing accuracy
Two Reactions Verification

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Closer fit for more separated reactions
Validation

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Purpose:

1. Test algorithm with real TGA data

Materials:

1. Nylon 6,6

2. Flexible 

polyurethane (PU) 

foam

3. Polyvinyl Chloride 

(PVC)

Procedure:

• In nitrogen

• Samples: 3-5.5 mg

• Isothermal heating 

for 20-30 min

• Dynamic heating at 

10 K/min
Validation: Nylon 6,6

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Validation: Polyurethane Foam

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Validation: PVC

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Summary

• Fire models need material property parameters to predict fire 

growth

• Obtaining material properties requires

– Small-scale tests

– Parameter estimation algorithms

• A parameter estimation algorithm is presented for obtaining 

pyrolysis kinetic models from TGA data

• The algorithm performs well for

– Manufactured solution verification cases

– Multiple reaction materials with well-separated reaction peaks

• More work is needed for

– Multiple reaction materials with overlapping reaction peaks

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The quality of any parameter estimation algorithm is 

ultimately determined in model validation

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Small-scale 

Tests 

Flame Spread 

Experiments

Model 

Parameters

Fire Models Flame Spread 

Predictions

Parameter 

Estimation Model 

Validation
IAFSS Measurement and Computation of 

Fire Phenomenona (MaCFP)—Condensed 

Phase Workshop

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April 26, 2020

Waterloo, Canada

https://iafss.org/macfp/