Inverse modelling pyrolization kinetics with ensemble learning methods - scripts

These scripts can be used to reproduce the study described in the article "Inverse modelling pyrolization kinetics with ensemble learning methods" [1]. The scripts here are intended to be used with default configuration, if not noted otherwise. To apply this model to your own data, you can adopt the scripts shown in ./test_model/.

./generate_db/

The scripts generate_1c.py, generate_2c.py and generate_3c.py are used to generate the training data for the model. There is an individual script for 1, 2 and 3 components. The reaction kinetic parameters and component fractions are sampled randomly and then the mass loss rate for TGA experiments with four different constant heating rates are calculated. The scripts are intended to be used on multiple CPUs. Example data sets are available for download [2].

In the following table, there are paramaters listed that can easily set by the user. Further parameters, as heating rates and sampling rates can also be modified in the scripts but may need more caution.

Parameter	Description	Default value
i	number of elements that will be generated	6400000
cores	number of CPU cores used for generation	128
rrlimlow	lower boundary of peak reaction rate sampling (in /s)	0.001
rrlimup	upper boundary of peak reaction rate sampling (in /s)	0.01
rtlimlow	lower boundary of peak reaction rate sampling (in °C)	100
rtlimup	upper boundary of peak reaction rate sampling (in °C)	500
Tstart	Start temperature of experiment (in °C)	20
Tend	End temperature of experiment (in °C)	550

Standard output will be the mass loss rate for four TGA experiments with following configuration:

Heating rate	Heating rate value	Time step $\Delta t$	Temperature step $\Delta T$
$\beta_1$	5 K/min	24 s	2 K
$\beta_2$	10 K/min	12 s	2 K
$\beta_3$	30 K/min	4 s	2 K
$\beta_4$	40 K/min	3 s	2 K

The scripts will generate numbered files named features* and labels* individually for each used CPU core. In addition there is a labels* file that holds all generated labels. The naming convention can be seen in the table below and a description of the data structure in the files can be found under Data structure below.

Filename	Description
labels{$N_u$/1000}k_{$\beta_1$}{$\beta_2$}{$\beta_3$}{$\beta_4$}{$n$}_{$\Delta T$/s}.csv	generated labels
features{$N_u$/1000}k_{$\beta_1$}{$\beta_2$}{$\beta_3$}{$\beta_4$}{$n$}{$\Delta T$/s}{$i_{core}$}.csv	generated labels, output per core
labels{$N_u$/1000}k_{$\beta_1$}{$\beta_2$}{$\beta_3$}{$\beta_4$}{$n$}{$\Delta T$/s}{$i_{core}$}.csv	generated labels, output per core

./build_models/

These scripts generate the individual sub models as described in the following table.

Filename	Output	Description
sm1.py	sm1.pickle	Sub model 1 (Classifier for estimation of number of components)
sm3_1c.py	sm3_1c.pickle	Sub model 3 for materials with 1 component (Regressor for estimation of reaction kinetic parameters)
sm3_2c.py	sm3_2c.pickle	Sub model 3 for materials with 2 components (Regressor for estimation of reaction kinetic parameters)
sm3_3c.py	sm3_3c.pickle	Sub model 3 for materials with 3 components (Regressor for estimation of reaction kinetic parameters)

Default parameters are the ones used in the corresponding publication. A contemporary high performance system (128 CPU cores, 1 TB RAM) will be needed for this. However, the following hyper parameter values shall be taken as lower limits to produce models with slightly less accurate predictions but much less computational demand. Pre built models are available for download [3].

Parameter	Sub model 1 (sm1.py)	Sub model 3, 1 Component (sm3_1c.py)	Sub model 3, 2 components (sm3_2c.py)	Sub model 3, 3 components (sm3_3c.py)
Number of estimators	500	1	50	50
Maximum tree depth	100	50	50	50

./test_model/

Scripts to test the complete model

calculate.py in default configuration will calculate predictions from data not used during the training process for 150000 elements and output the prediction of the reaction kinetic parameters to prediction.csv

evaluate.py then evaluates the true (prescribed) and predicted reaction kinetic parameters and initial fractions by calculating R^2 scores. It also calculates mass loss rates from the predictions and compares them to the initial mass loss rates used as input features. For comparison, the normalised RMSE is calculated and the distribution is plotted.

Data structure

labels*.csv

The mass loss rates are calculated from the reaction kinetic parameters can be found at the same row number of the corresponding features* file. The files do not have any header.

Columns description:

Column	Symbol	Description	Unit
1	$r_{1,p}$	Peak reaction rate for component 1	s^-1
2	$r_{2,p}$	Peak reaction rate for component 2	s^-1
3	$r_{3,p}$	Peak reaction rate for component 3	s^-1
4	$T_{1,p}$	Peak reaction temperature for component 1	°C
4	$T_{2,p}$	Peak reaction temperature for component 2	°C
6	$T_{3,p}$	Peak reaction temperature for component 3	°C
7	$Y_1$	Fraction of component 1	1
8	$Y_2$	Fraction of component 2	1
9	$Y_3$	Fraction of component 3	1
10	$A_1$	Pre-exponential factor for component 1	s^-1
11	$A_2$	Pre-exponential factor for component 2	s^-1
12	$A_3$	Pre-exponential factor for component 3	s^-1
13	$E_1$	Activation energy for component 1	J/mol
14	$E_2$	Activation energy for component 2	J/mol
15	$E_3$	Activation energy for component 3	J/mol
16	$Y_1$	Fraction of component 1	1
17	$Y_2$	Fraction of component 2	1
18	$Y_3$	Fraction of component 3	1

features*.csv

The files do not have any header. There is a set of mass loss records for four TGA experiments with identical reaction kinetic parameters and four different heating rates per row. One row can be separated into the four experiments as shown in the following tabel. The mass loss rates are calculated from the reaction kinetic parameters in the same row number of the corresponding labels* file.

Column	Description	Unit
1...266	Mass loss rate at $\beta_1$	s^-1
267...532	Mass loss rate at $\beta_2$	s^-1
533...798	Mass loss rate at $\beta_3$	s^-1
799...1064	Mass loss rate at $\beta_4$	s^-1

Corresponding $T$ is 20...550 °C with $\Delta T=2K$. Then, $t$ is $\frac{T}{\beta}$.

sm1.pickle

The file holds a single python element of class sklearn.ensemble.ExtraTreesClassifier [4]. It is pre trained to estimate the number of components with single reactions represented by input mass loss rate data. It can be loaded via pickle[5] into Python.

Using sm1.predict(X) expects 1064 features as input with following properties:

Feature	Description	Unit
1...266	Mass loss rate at $\beta_1$	s^-1
267...532	Mass loss rate at $\beta_2$	s^-1
533...798	Mass loss rate at $\beta_3$	s^-1
799...1064	Mass loss rate at $\beta_4$	s^-1
799...1064	Mass loss rate at $\beta_4$	s^-1

Corresponding $T$ is 20...550 °C with $\Delta T=2K$. Then, $t$ is $\frac{T}{\beta}$.

Output is a single integer of 1,2 or 3 as the number of components in the material represented by the TGA mass loss rate profile.

sm3_1r.pickle

The file holds a single python element of class sklearn.ensemble.ExtraTreesRegressor [6]. It is pre trained to estimate the reaction kinetic parameters of materials consisting of one component represented by input mass loss rate data. It can be loaded via pickle[5] into Python.

Using sm3_1r.predict(X) expects 1067 features as input with following properties:

Feature	Description	Unit
1...266	Mass loss rate at $\beta_1$	s^-1
267...532	Mass loss rate at $\beta_2$	s^-1
533...798	Mass loss rate at $\beta_3$	s^-1
799...1064	Mass loss rate at $\beta_4$	s^-1
1065	Initial fraction of component 1 ($Y_1=1$)
1066	Initial fraction of component 2 ($Y_2=0$)
1067	Initial fraction of component 3 ($Y_3=0$)

Corresponding $T$ is 20...550 °C with $\Delta T=2K$. Then, $t$ is $\frac{T}{\beta}$.

Output is $log(A_1)$ and $E_1$.

sm3_2r.pickle

The file holds a single python element of class sklearn.ensemble.ExtraTreesRegressor [6]. It is pre trained to estimate the reaction kinetic parameters of materials consisting of two components represented by input mass loss rate data. It can be loaded via pickle[5] into Python.

Using sm3_2r.predict(X) expects 1067 features as input with following properties:

Feature	Description	Unit
1...266	Mass loss rate at $\beta_1$	s^-1
267...532	Mass loss rate at $\beta_2$	s^-1
533...798	Mass loss rate at $\beta_3$	s^-1
799...1064	Mass loss rate at $\beta_4$	s^-1
1065	Initial fraction of component 1 ($Y_1$)
1066	Initial fraction of component 2 ($Y_2$)
1067	Initial fraction of component 3 ($Y_3$)

Corresponding $T$ is 20...550 °C with $\Delta T=2K$. Then, $t$ is $\frac{T}{\beta}$.

Output is $log(A_1)$, $log(A_2)$, $E_1$ and $E_2$.

sm3_3r.pickle

The file holds a single python element of class sklearn.ensemble.ExtraTreesRegressor [6]. It is pre trained to estimate the reaction kinetic parameters of materials consisting of three components represented by input mass loss rate data. It can be loaded via pickle[5] into Python.

Using sm3_3r.predict(X) expects 1067 features as input with following properties:

Feature	Description	Unit
1...266	Mass loss rate at $\beta_1$	s^-1
267...532	Mass loss rate at $\beta_2$	s^-1
533...798	Mass loss rate at $\beta_3$	s^-1
799...1064	Mass loss rate at $\beta_4$	s^-1
1065	Initial fraction of component 1 ($Y_1$)
1066	Initial fraction of component 2 ($Y_2$)
1067	Initial fraction of component 3 ($Y_3$)

Corresponding $T$ is 20...550 °C with $\Delta T=2K$. Then, $t$ is $\frac{T}{\beta}$.

Output is $log(A_1)$, $log(A_2)$, $log(A_3)$, $E_1$, $E_2$ and $E_3$.

prediction.csv

This is the columns description of the output from calculate.py. The file has no header.

Column	Symbol	Description	Unit
1	$log(A_1)$	Pre-exponential factor for component 1	s^-1
2	$log(A_2)$	Pre-exponential factor for component 2	s^-1
3	$log(A_3)$	Pre-exponential factor for component 3	s^-1
4	$E_1$	Activation energy for component 1	J/mol
5	$E_2$	Activation energy for component 2	J/mol
6	$E_3$	Activation energy for component 3	J/mol
7	$Y_1$	Fraction of component 1	1
8	$Y_2$	Fraction of component 2	1
9	$Y_3$	Fraction of component 3	1