Model application manual

This notebook describes how to apply the model on different data as presented in the thesis. It will be explained:

• How to create a data set readable by the model
• How to execute the model itself
• And how to conduct Monte Carlo Simulations with the provided code

How to create a readable data set

Creation of a readable data set

The created model requires an excel file in a specific format. A function was created to create a plain excel file in the right format. The function requires a list entailing the product categories which are treated by the model, a string naming the product category which flows into the reuse part of the model, a list indication the products treated in the reuse part of the model, and the number of considered use cycles in the reuse part. Furthermore, a file name has to be provided. The created file will appear in the "data_model" folder.

from functions import input_file_creator

input_file_creator(
    product_categories=['electronics', 'cars', 'industrial applications'], 
    category_for_reuse='electronics', products=['shaver', 'phone', 'TV'],
    considered_use_cycles=2, file_name = 'example_file_creator')

All sheets of the file are empty and to be filled by the user.

import pandas as pd
pd.read_excel('data_model/example_file_creator.xlsx')

	Product categories	share
0	electronics	NaN
1	cars	NaN
2	industrial applications	NaN

import os
os.remove('data_model/example_file_creator.xlsx')

To showcase how to input data, an example file will be considered.

Things to consider populating the data frame

A few sheets are presented as examples. In general, common-sense mistakes need to be avoided.

Ensuring mass conservation when splitting the material flow

The following output shows the first sheet, the split of the initial inflow.

pd.read_excel('data_model/data_example.xlsx', sheet_name='MaTrace_initial_inflow')

	Product categories	share
0	electronics	0.412
1	mobility batteries	0.012
2	hydroprocessing catalysts coke	0.020
3	hydroprocessing catalysts poisoning	0.000
4	hydroformylation catalysts	0.003
5	pet precursors catalysts	0.017
6	dissipative uses	0.090
7	hard metals	0.230
8	magnets	0.006
9	other metallic uses	0.210

The sum of this column has to equal 1.

pd.read_excel('data_model/data_example.xlsx', 
    sheet_name='MaTrace_initial_inflow')['share'].sum(axis = 0)

1.0

The same holds true for the sheet "Reuse_inflow_split".

pd.read_excel('data_model/data_example.xlsx', sheet_name='MaTrace_initial_inflow')

	Product categories	share
0	electronics	0.412
1	mobility batteries	0.012
2	hydroprocessing catalysts coke	0.020
3	hydroprocessing catalysts poisoning	0.000
4	hydroformylation catalysts	0.003
5	pet precursors catalysts	0.017
6	dissipative uses	0.090
7	hard metals	0.230
8	magnets	0.006
9	other metallic uses	0.210

And as well for the sheet "MaTrace_D_secondary_material". In this case, the last two rows need to be excluded since the indicate the export and to production rate.

pd.read_excel('data_model/data_example.xlsx',
    sheet_name='MaTrace_D_secondary_material')

	Product categories	Co metal or compound	W-Co powder
0	electronics	0.0000	0
1	mobility batteries	0.0210	0
2	hydroprocessing catalysts coke	0.0135	0
3	hydroprocessing catalysts poisoning	0.0135	0
4	hydroformylation catalysts	0.0050	0
5	pet precursors catalysts	0.0240	0
6	dissipative uses	0.1670	0
7	hard metals	0.3130	1
8	magnets	0.0170	0
9	other metallic uses	0.4260	0
10	export rate	0.1330	0
11	to production rate	0.8670	1

print(pd.read_excel('data_model/data_example.xlsx', 
    sheet_name='MaTrace_D_secondary_material').iloc[:-2, :])
print()
print('Sum of columns without export rate and to production rate:')
print(pd.read_excel('data_model/data_example.xlsx', 
    sheet_name='MaTrace_D_secondary_material').iloc[:-2, :].sum(axis=0))

                    Product categories  Co metal or compound  W-Co powder
0                          electronics                0.0000            0
1                   mobility batteries                0.0210            0
2       hydroprocessing catalysts coke                0.0135            0
3  hydroprocessing catalysts poisoning                0.0135            0
4           hydroformylation catalysts                0.0050            0
5             pet precursors catalysts                0.0240            0
6                     dissipative uses                0.1670            0
7                          hard metals                0.3130            1
8                              magnets                0.0170            0
9                  other metallic uses                0.4260            0

Sum of columns without export rate and to production rate:
Product categories      electronicsmobility batterieshydroprocessing c...
Co metal or compound                                                  1.0
W-Co powder                                                             1
dtype: object

Furthermore, some transfer coefficients must sum up to 1. In the model one transfer coefficient is sufficient to define a flow which splits into two. However, for the Monte Carlo simulations both are needed.

The following cell shows the example of the sheet "MaTrace_end_of_life":

pd.read_excel('data_model/data_example.xlsx', sheet_name='MaTrace_end_of_life')

	Product categories	fraction export eol products	fraction collected eol products	collection to recycling rate	postconsumer disposal rate	pre-treatment efficiency
0	electronics	0.2	0.8	0.64	0.36	0.95
1	mobility batteries	0.0	1.0	1.00	0.00	0.85
2	hydroprocessing catalysts coke	0.0	1.0	1.00	0.00	0.85
3	hydroprocessing catalysts poisoning	0.0	1.0	0.00	1.00	0.00
4	hydroformylation catalysts	0.0	1.0	0.90	0.10	0.85
5	pet precursors catalysts	0.0	1.0	0.50	0.50	0.85
6	dissipative uses	0.0	1.0	0.00	1.00	0.00
7	hard metals	0.0	1.0	0.47	0.53	0.77
8	magnets	0.0	1.0	0.99	0.01	0.65
9	other metallic uses	0.0	1.0	0.84	0.16	0.65

The column "fraction export eol products" and "fraction collected eol products" as well as the columns "collection to recycling rate" and "postconsumer disposal" have to sum up to 1 for every product category.

Please also consult the system diagram or the excel file data_example.xlsx to find the respective transfer coefficients.

Defining survival curves

The sheet "MaTrace_in_use_stock" show examples on how to define survival curves in the model implementation:

pd.read_excel('data_model/data_example.xlsx', sheet_name='MaTrace_in_use_stock')

	Product categories	distribution	location	scale	shape
0	electronics	normal	1	4.051716	2.09
1	mobility batteries	weibull	0	10.631501	2.20
2	hydroprocessing catalysts coke	gamma	0	2.894742	2.50
3	hydroprocessing catalysts poisoning	defined_distribution_example_dist	0	0.000000	0.00
4	hydroformylation catalysts	lognormal	1	2.315793	2.50
5	pet precursors catalysts	normal	0	0.578948	2.50
6	dissipative uses	weibull	0	14.435166	3.50
7	hard metals	gamma	0	8.915235	1.16
8	magnets	gompertz	2	13.905022	1.93
9	other metallic uses	lognormal	0	14.628064	1.47

One can select a distribution via the column "distribution". The normal, lognormal, weibull, gamma, and gompertz distribution are preimplemented. The location, scale and shape factors can be set via the corresponding columns. It is also possible to define own distributions.

An example for this is the distribution for the product category "hydroprocessing catalysts poisoning". The string says "defined_distribution_example_dist". This works in the following way. A distribution is defined in the file "defined_distributions.xlsx" (see next cell).

pd.read_excel('data_model/defined_distributions.xlsx').iloc[:10]

	example_dist	example_dist_2
0	1.00	1.00
1	0.60	0.70
2	0.55	0.55
3	0.50	0.50
4	0.45	0.45
5	0.40	0.40
6	0.35	0.35
7	0.30	0.30
8	0.25	0.20
9	0.20	0.20

The file holds survival curves defined by the user. Only the first 10 lines are shown. It is important that the distribution is defined for a sufficient number of years, meaning at least the number of considered years.

To use this distribution in the model, one has to fill the column "distribution" with "defined_distribution_column_name". Hence, when the entry in the column "distribution" says "defined_distribution_example_dist", the defined distribution "example_dist" will be used for this product category. If it says "defined_distribution_exmaple_dist_2" the distribution "example_dist_2" will be used for the product category.

How to execute the model iteself

The first step to execute the model is to load the required data. The model receives a dictionary as input which contains the sheets of the mentioned excel file as pandas data frames. The following code cell creates this dictionary.

file_path = 'data_model/data_example.xlsx'

data_sheets = pd.ExcelFile(file_path).sheet_names



data_dic = {}

for data_sheet in data_sheets:

    try:
        data_dic[data_sheet] = pd.read_excel(file_path, 
            sheet_name=data_sheet).set_index('Product categories')
    except:
        data_dic[data_sheet] = pd.read_excel(file_path, 
            sheet_name=data_sheet).set_index('Products')

Furthermore, the number of years and the start year have to be defined. A pandas dataframe containing the "defined_distributions.xlsx" file has to be passed as well.

number_of_years = 25
start_year = 2022
defined_distributions_pd = pd.read_excel('data_model/defined_distributions.xlsx')

Optionally, one can decide to print the state to have an indication whether the model is stuck or how long it will still run. One can also define whether the simplified model output shall differentiate between use cycles. Lastly, one can select the number of considered use cycles (default is 3).

The following code shows the execution of the model:

from combined_reuse_matrace_model import evaluate_cohort_combined_model

matrace_data_dic, reuse_data_dic, graph_data_pd = \
    evaluate_cohort_combined_model(data_dic=data_dic, 
        n_years=number_of_years, start_year=start_year,
        defined_distributions_pd= defined_distributions_pd,
        print_state=True, separate_reuse_graph=True, considered_use_cycles=3)

Year 1 of 25
Year 2 of 25
Year 3 of 25
Year 4 of 25
Year 5 of 25
Year 6 of 25
Year 7 of 25
Year 8 of 25
Year 9 of 25
Year 10 of 25
Year 11 of 25
Year 12 of 25
Year 13 of 25
Year 14 of 25
Year 15 of 25
Year 16 of 25
Year 17 of 25
Year 18 of 25
Year 19 of 25
Year 20 of 25
Year 21 of 25
Year 22 of 25
Year 23 of 25
Year 24 of 25
Year 25 of 25

The returned dictionaries "matrace_data_dic" and "reuse_data_dic" are structured in the same way. The first key takes a string containing the considered year. The second key takes a string indicating a stock or a flow in the year. This will then return a pandas containing the values over product categories or products.

The following code cell shows the second keys of "matrace_data_dic".

matrace_data_dic['0'].keys()

Index(['U.A use stock', 'U.2 use outflow', 'U.3 hoarding inflow',
       'U.4 no hoarding flow', 'U.B hoarding stock', 'U.5 hoarding outflow',
       'U.6 eol products', 'E.2 exported eol products',
       'E.1 to waste treatment', 'E.3 to pretreatment',
       'E.4 E.5 non-selective collection', 'E.6 to recycling',
       'E.7 pretreatment waste', 'E.12 downcycling', 'recycled w-co powder',
       'co metal compound', 'E.8 recycling waste',
       'E.11 exported recycled materials', 'P.1 total recycled products',
       'P.8 export recycled products', 'U.1 product inflow',
       'P.7 processing waste', 'P.5p downcycled scrap', 'P.4p disposed scrap',
       'P.2 manufacturing waste', 'P.5m downcycled scrap',
       'P.4m disposed scrap', 'P.4 disposed scrap', 'P.5 downcycled scrap'],
      dtype='object')

And the following code cell shows the second keys of "reuse_data_dic".

reuse_data_dic['0'].keys()

Index(['total_use_stock', 'total_hoarding_stock', 'to_disposal_flow',
       'use_stock_1', 'storage_stock_1', 'use_1_to_storage_1_flow',
       'use_1_to_disposal_flow', 'storage_1_to_disposal_flow',
       'use_1_to_use_2_flow', 'storage_1_to_use_2_flow', 'use_stock_2',
       'storage_stock_2', 'use_2_to_storage_2_flow', 'use_2_to_disposal_flow',
       'storage_2_to_disposal_flow', 'use_2_to_use_3_flow',
       'storage_2_to_use_3_flow', 'use_stock_3', 'storage_stock_3',
       'use_3_to_storage_3_flow', 'use_3_to_disposal_flow',
       'storage_3_to_disposal_flow'],
      dtype='object')

The following code cell shows the content.

reuse_data_dic['0']['total_use_stock']

Products
computer       0.026567
phone          0.045320
fan            0.082400
dish washer    0.185400
e-bikes        0.024720
power tools    0.019502
Name: total_use_stock, dtype: float64

matrace_data_dic['0']['U.A use stock']

Products
electronics                            0.38391
mobility batteries                       0.012
hydroprocessing catalysts coke            0.02
hydroprocessing catalysts poisoning        0.0
hydroformylation catalysts               0.003
pet precursors catalysts                0.0085
dissipative uses                          0.09
hard metals                               0.23
magnets                                  0.006
other metallic uses                       0.21
Name: U.A use stock, dtype: object

The retuned pandas dataframe "graph_data_pd" contains the stocks and the accumulated outflows.

graph_data_pd

	Electronics 1st use	Electronics 2nd use	Electronics 3rd use	Mobility batteries	Hydroprocessing catalysts coke	Hydroprocessing catalysts poisoning	Hydroformylation catalysts	Pet precursors catalysts	Dissipative uses	Hard metals	Magnets	Other metallic uses	Hoarded	Exported	Downcycled	Non-selective collection	Production losses	Pre-treatment losses	Recycling losses
Year
2022	0.377540	0.005548	0.000821	0.012176	0.020113	0.000113	0.003042	0.008701	0.090867	0.231415	0.006049	0.211641	0.005956	0.008817	0.003840	0.010625	0.000423	0.001204	0.001109
2023	0.281169	0.017890	0.001593	0.012589	0.020090	0.000421	0.003156	0.001363	0.093221	0.219753	0.006182	0.208973	0.045974	0.032574	0.009901	0.034468	0.001577	0.004941	0.004165
2024	0.199773	0.026279	0.002235	0.012901	0.019297	0.000728	0.002181	0.000912	0.095838	0.207615	0.006334	0.202697	0.067202	0.058810	0.014661	0.061596	0.002894	0.010318	0.007728
2025	0.142881	0.031148	0.002443	0.012958	0.017849	0.000909	0.001956	0.000887	0.097935	0.195219	0.005663	0.195900	0.075340	0.081793	0.019619	0.086854	0.004054	0.015708	0.010885
2026	0.106036	0.032665	0.002545	0.012749	0.016026	0.001010	0.001813	0.000769	0.099312	0.182762	0.005026	0.189072	0.075795	0.101039	0.024431	0.109548	0.005039	0.020781	0.013581
2027	0.083086	0.031205	0.002917	0.012286	0.014056	0.001063	0.001694	0.000640	0.099778	0.170409	0.004414	0.182273	0.073877	0.116546	0.028950	0.129684	0.005846	0.025469	0.015808
2028	0.068224	0.028201	0.003453	0.011605	0.012104	0.001080	0.001590	0.000525	0.099193	0.158352	0.003831	0.175593	0.068781	0.128968	0.035074	0.148456	0.006506	0.030823	0.017643
2029	0.057489	0.024919	0.003829	0.010758	0.010275	0.001073	0.001499	0.000435	0.097446	0.146769	0.003287	0.169140	0.062795	0.139154	0.042008	0.166424	0.007057	0.036456	0.019188
2030	0.047519	0.021968	0.003884	0.009806	0.008634	0.001056	0.001422	0.000378	0.094478	0.135845	0.002792	0.163060	0.057904	0.148166	0.048851	0.184186	0.007550	0.041928	0.020573
2031	0.041138	0.019131	0.003691	0.008783	0.007190	0.001019	0.001352	0.000321	0.090127	0.125476	0.002344	0.157197	0.053550	0.155440	0.055173	0.201414	0.007957	0.046971	0.021727
2032	0.034343	0.016645	0.003386	0.007755	0.005957	0.000974	0.001293	0.000288	0.084505	0.115843	0.001952	0.151742	0.050097	0.162294	0.061008	0.219100	0.008339	0.051667	0.022811
2033	0.028269	0.014450	0.003054	0.006757	0.004920	0.000924	0.001240	0.000265	0.077682	0.106887	0.001613	0.146616	0.046845	0.168544	0.066382	0.237046	0.008688	0.056016	0.023804
2034	0.022851	0.012621	0.002727	0.005817	0.004056	0.000861	0.001194	0.000240	0.069864	0.098556	0.001325	0.141769	0.043833	0.174160	0.071330	0.255063	0.009003	0.060031	0.024700
2035	0.018026	0.011123	0.002423	0.004960	0.003344	0.000788	0.001151	0.000217	0.061378	0.090825	0.001083	0.137183	0.040872	0.179258	0.075887	0.272941	0.009289	0.063738	0.025513
2036	0.014967	0.009819	0.002153	0.004191	0.002755	0.000703	0.001110	0.000189	0.052592	0.083600	0.000882	0.132765	0.037721	0.183520	0.080080	0.290082	0.009530	0.067135	0.026206
2037	0.012373	0.008728	0.001925	0.003523	0.002274	0.000615	0.001071	0.000165	0.043978	0.076902	0.000717	0.128559	0.034692	0.187336	0.083949	0.306351	0.009745	0.070268	0.026828
2038	0.010187	0.007783	0.001740	0.002954	0.001882	0.000538	0.001035	0.000147	0.035944	0.070701	0.000585	0.124550	0.031811	0.190751	0.087527	0.321385	0.009938	0.073157	0.027384
2039	0.008353	0.006950	0.001594	0.002477	0.001563	0.000472	0.001001	0.000131	0.028814	0.064961	0.000479	0.120720	0.029177	0.193771	0.090842	0.334887	0.010108	0.075822	0.027878
2040	0.006823	0.006196	0.001475	0.002081	0.001302	0.000416	0.000970	0.000116	0.022792	0.059655	0.000395	0.117060	0.026758	0.196455	0.093922	0.346723	0.010259	0.078284	0.028318
2041	0.005552	0.005507	0.001374	0.001758	0.001089	0.000368	0.000940	0.000103	0.017939	0.054755	0.000329	0.113563	0.024538	0.198844	0.096790	0.356885	0.010393	0.080563	0.028710
2042	0.004501	0.004883	0.001281	0.001493	0.000916	0.000327	0.000912	0.000091	0.014188	0.050235	0.000276	0.110220	0.022505	0.200971	0.099468	0.365487	0.010512	0.082675	0.029060
2043	0.003637	0.004319	0.001191	0.001278	0.000773	0.000291	0.000885	0.000081	0.011382	0.046068	0.000235	0.107022	0.020648	0.202866	0.101973	0.372724	0.010618	0.084636	0.029373
2044	0.002928	0.003814	0.001101	0.001101	0.000656	0.000258	0.000860	0.000072	0.009324	0.042230	0.000202	0.103962	0.018957	0.204554	0.104323	0.378833	0.010713	0.086460	0.029652
2045	0.002350	0.003365	0.001011	0.000955	0.000559	0.000230	0.000836	0.000064	0.007814	0.038698	0.000175	0.101032	0.017419	0.206057	0.106531	0.384045	0.010797	0.088158	0.029901
2046	0.001880	0.002968	0.000923	0.000834	0.000479	0.000204	0.000814	0.000057	0.006685	0.035449	0.000153	0.098227	0.016024	0.207395	0.108610	0.388560	0.010872	0.089743	0.030124

It is easily possible to create a stacked area chart out of it.

import matplotlib.pyplot as plt

plt.rcParams["figure.figsize"] = [10, 7]
graph_data_pd.plot.area()

plt.legend(reversed(plt.legend().legendHandles), reversed(
    graph_data_pd.columns), bbox_to_anchor=(1.05, 1))

plt.ylabel('Stock distribution by product categories and losses in %')
plt.tight_layout()
plt.show()

How to conduct Monte Carlo simulations with the provided code

The code to conduct Monte Carlo simulations consists of three files which need to be executed one after another:

• monte_carlo_simulations.py
• monte_carlo_evaluation.py
• monte_carlo_uncertainty.py

In the following it will be discussed what each file does and how to use it. To do so, files and the data used in the cobalt case study will be used. Each of the files has the variable "proof_of_concept" in the very top. If this is "True", an exemplary Monte Carlo simulation and evaluation considering 10 runs will be conducted. If it is set to "False" the results as presented in the thesis will be reproduced.

# The folder holding the results of the following demonstration
# needs to be deleted in order to be created and populated.
# This is a necessary step but not relevant in the context of 
# the explenation.
import shutil
try:
    shutil.rmtree('monte_carlo_results/proof_of_concept/')
except:
    print('Dictionary does not excist.')

Executing "monte_carlo_simulations.py"

At the start of the file, the user can adjust the settings. Those are the number of runs ("n_runs"), the number of the considered years ("n_years"), the start year ("start_year"), and the number of the considered use cycles ("considered_use_cycles").

Then, the data to be loaded needs to be specified. Firstly, the file entailing the survival curves designed by the user has to be loaded (see above). Secondly, the path to the input data (format as described above) has to be specified. Lastly, the excel file containing the uncertainty rating has to be set.

This file must entail the same sheet names as the input file. Instead of the data, the colums must hold the uncertainty score (0 to 5, as explained in the main body of the thesis).

If an input shall not be varied, the column can be either deleted from the file holding the uncertainty scores, or all values can be set to 0. Only numerical inputs can be considered.

The following cell shows one sheet of the excel holding the input data. The next one shows the uncertainty ratings of those inputs.

pd.read_excel('data_cobalt_case_study/data_input_cobalt_extended_data_set.xlsx', sheet_name='MaTrace_in_use_stock')

	Product categories	distribution	location	scale	shape
0	portable batteries	weibull	0	4.051716	2.09
1	mobility batteries	weibull	0	10.631501	2.20
2	hydroprocessing catalysts coke	weibull	0	2.894742	2.50
3	hydroprocessing catalysts poisoning	weibull	0	1.505266	2.50
4	hydroformylation catalysts	weibull	0	2.315793	2.50
5	pet precursors catalysts	weibull	0	0.578948	2.50
6	dissipative uses	weibull	0	14.435166	3.50
7	hard metals	weibull	0	8.915235	1.16
8	magnets	weibull	0	13.905022	1.93
9	other metallic uses	weibull	0	14.628064	1.47
10	superalloys	weibull	0	17.282543	1.74

pd.read_excel(
    'data_cobalt_case_study/data_uncertainty_rating_cobalt_case_study.xlsx',
    sheet_name='MaTrace_in_use_stock')

	Product categories	shape	scale
0	portable batteries	0	0
1	mobility batteries	1	4
2	hydroprocessing catalysts coke	2	4
3	hydroprocessing catalysts poisoning	2	4
4	hydroformylation catalysts	2	4
5	pet precursors catalysts	1	4
6	dissipative uses	2	3
7	hard metals	1	2
8	magnets	1	2
9	other metallic uses	1	2
10	superalloys	1	2

As it can be seen, only the uncertainty scores for the columns "shape" and "scale" appear. This is intended since only numerical values can be varied by this implementation and the location of the Weibull distribution is a factor which was not considered.

Once the paths and the settings are defined, the script can be run. The next cell executes the script for 10 runs.

%run monte_carlo_simulations.py

Creating dictionary for results. Path: monte_carlo_results/proof_of_concept
Importing data
Creating inputs for Monte Carlo simulations based on uncertainty score
Normalize inputs

c:\Users\rapha\Desktop\master_thesis_hand_in\monte_carlo_simulations.py:154: PerformanceWarning: indexing past lexsort depth may impact performance.
  for column in input_pd.loc[:, ("MaTrace_initial_inflow", "share")].columns:

Starting runs
Run 1 of 10
Mass balance run 0: True
Run 2 of 10
Mass balance run 1: True
Run 3 of 10
Mass balance run 2: True
Run 4 of 10
Mass balance run 3: True
Run 5 of 10
Mass balance run 4: True
Run 6 of 10
Mass balance run 5: True
Run 7 of 10
Mass balance run 6: True
Run 8 of 10
Mass balance run 7: True
Run 9 of 10
Mass balance run 8: True
Run 10 of 10
Mass balance run 9: True
Total time - seconds: 21,  hours: 0.005833333333333334
Time per run: 2.1
Inputs and results are stored.

The printed output reflects the steps of the code. After the data is imported, random numbers following the defined distributions are created. Since some split vectors and transfer coefficients will not sum up to 1 anymore (see above) they have to be normalized. Afterwards, the experiments are run. The data is collected in a dictionary. If several thousand runs are executed, the dictionary is dumped in splits to decrease the runtime.

The results and a file containing the used model inputs can be found in the folder "monte_carlo_results/proof_of_concept".

The following cell shows part of the saved inputs. The rows represent runs.

import pickle
with open('monte_carlo_results/proof_of_concept/inputs.pkl', 'rb') as f:
    input_pd = pickle.load(f)
input_pd

sheet	MaTrace_initial_inflow										...	Reuse_storage_time_3
column	share										...	scale			shape
item	portable batteries	mobility batteries	hydroprocessing catalysts coke	hydroprocessing catalysts poisoning	hydroformylation catalysts	pet precursors catalysts	dissipative uses	hard metals	magnets	other metallic uses	...	e-bikes	power tools	others	smartphones	mobile phones	tablets	laptops	e-bikes	power tools	others
0	0.195626	0.069050	0.049883	0.023999	0.059167	0.004703	0.059462	0.111802	0.152205	0.103031	...	2.360890	1.291785	3.787781	1.432013	1.664109	1.575216	1.521198	1.797884	1.552458	1.790137
1	0.221689	0.031145	0.057574	0.063652	0.049747	0.142862	0.095038	0.195235	0.006055	0.000673	...	2.125174	2.125348	4.687217	1.619985	1.358189	1.447141	1.486905	1.621413	1.769031	1.507384
2	0.203971	0.067055	0.028344	0.034823	0.238051	0.132933	0.013254	0.094126	0.013634	0.018468	...	1.950079	2.244345	4.647316	1.565251	1.402054	1.377444	2.026306	1.699196	1.397294	1.565706
3	0.411710	0.092229	0.039897	0.041033	0.107387	0.019387	0.066506	0.077042	0.014983	0.001555	...	1.975120	2.126083	4.158380	1.663245	1.301536	1.298786	1.530208	1.430551	1.514807	1.453668
4	0.279781	0.026076	0.036750	0.036071	0.015810	0.016235	0.012234	0.252920	0.066690	0.065006	...	2.485666	1.718379	2.079817	1.317759	1.575214	1.413565	1.546306	1.562307	1.452043	1.174145
5	0.282791	0.069646	0.045512	0.080305	0.017813	0.049054	0.052628	0.199520	0.080029	0.001548	...	2.255336	1.821774	3.588646	1.733470	1.747479	1.478725	1.723377	1.577003	1.513890	1.475730
6	0.321172	0.040106	0.077813	0.053932	0.036862	0.058657	0.062004	0.152609	0.024801	0.059288	...	1.975133	3.343770	3.361317	1.345725	1.570218	1.414150	1.409801	1.476518	1.607588	1.452492
7	0.252250	0.032541	0.046556	0.083294	0.096109	0.016466	0.031111	0.144579	0.031795	0.022306	...	1.730407	1.167725	4.327077	1.679690	1.238038	1.600540	1.522313	1.524402	1.467380	1.247346
8	0.267555	0.034854	0.015555	0.001666	0.069714	0.074432	0.065195	0.219638	0.015209	0.033571	...	1.065056	3.033024	3.515732	1.788227	1.506585	1.421502	1.489797	1.832488	1.288020	1.568852
9	0.326831	0.035760	0.133187	0.041984	0.067035	0.004005	0.014350	0.163488	0.058476	0.040129	...	1.811120	3.231110	4.266448	1.281956	1.798759	1.401711	1.200397	1.545702	1.573716	1.740299

10 rows × 541 columns

The results are saved in the form of nested dictionaries:

with open('monte_carlo_results/proof_of_concept/results.pkl', 'rb') as f:
    results_dic = pickle.load(f)

The fist key represents runs:

results_dic.keys()

dict_keys(['0', '1', '2', '3', '4', '5', '6', '7', '8', '9'])

The second part specifies from which part of the model the data is coming from:

results_dic['0'].keys()

dict_keys(['matrace_data_dic', 'reuse_data_dic'])

Since this data structure is hard to handle, the script "monte_carlo_evaluation.py" serves the purpose to transfer the data into multidimensional pandas data frames.

Executing "monte_carlo_evaluation.py"

In order to execute this script, one has to adjust the settings in the beginning of the file so they are the same as the used ones in "mone_carlo_simulations.py". The path to the results has to be defined. Then the file is ready to be executed.

%run monte_carlo_evaluation.py

Loading file:
Create dictionary:
Start treating data
run 1 of 10
run 2 of 10
run 3 of 10
run 4 of 10
run 5 of 10
run 6 of 10
run 7 of 10
run 8 of 10
run 9 of 10
run 10 of 10
Compact results are stored.

This script creates the multidimensional pandas data frame 'compact_results'. The first key entails the runs, the second the stock or flow, and the third one the product or the product category.

with open('monte_carlo_results/proof_of_concept/compact_results.pkl', 
    'rb') as f:
    compact_results = pickle.load(f)
compact_results

run	0										...	9
stock_flow	total_use_stock								total_hoarding_stock		...	P.5 downcycled scrap
item	sum	smartphones	mobile phones	tablets	laptops	e-bikes	power tools	others	sum	smartphones	...	mobility batteries	hydroprocessing catalysts coke	hydroprocessing catalysts poisoning	hydroformylation catalysts	pet precursors catalysts	dissipative uses	hard metals	magnets	other metallic uses	superalloys
2015	0.195626	0.057242	0.047268	0.02614	0.048304	0.001794	0.006937	0.007942	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
2016	0.177952	0.053884	0.036155	0.02468	0.047307	0.001774	0.006729	0.007423	0.010898	0.001788	...	0.000142	0.000282	0.000015	0.000009	0.000275	0.0001	0.000076	0.000011	0.000022	0.000043
2017	0.1475	0.046705	0.021888	0.020836	0.044188	0.001634	0.006348	0.005901	0.027659	0.004951	...	0.000313	0.000585	0.000032	0.000018	0.000541	0.000227	0.000158	0.000022	0.000044	0.000096
2018	0.116835	0.037369	0.012804	0.015898	0.039273	0.001304	0.005903	0.004284	0.040423	0.008003	...	0.000238	0.000434	0.000024	0.000013	0.000392	0.000175	0.000117	0.000016	0.000033	0.000074
2019	0.090162	0.027998	0.008145	0.011246	0.033273	0.000864	0.005448	0.003187	0.046628	0.009983	...	0.000129	0.000245	0.000013	0.000008	0.000231	0.000092	0.000066	0.000009	0.000019	0.000039
2020	0.069089	0.020143	0.006213	0.007728	0.027022	0.000502	0.005007	0.002473	0.046801	0.010628	...	0.000098	0.000195	0.00001	0.000006	0.000189	0.000069	0.000052	0.000007	0.000015	0.00003
2021	0.053197	0.01421	0.00547	0.005481	0.021222	0.000322	0.00459	0.001902	0.042964	0.010219	...	0.000096	0.000189	0.00001	0.000006	0.000183	0.000068	0.000051	0.000007	0.000015	0.000029
2022	0.041158	0.009933	0.004847	0.004179	0.016291	0.000263	0.004195	0.00145	0.037263	0.009191	...	0.000092	0.000181	0.00001	0.000006	0.000175	0.000065	0.000049	0.000007	0.000014	0.000028
2023	0.031819	0.006883	0.003998	0.003389	0.012354	0.000232	0.003823	0.001141	0.031138	0.007893	...	0.000086	0.000168	0.000009	0.000005	0.000162	0.000061	0.000045	0.000006	0.000013	0.000026
2024	0.024471	0.004703	0.003038	0.002799	0.009323	0.000194	0.003472	0.000942	0.025294	0.006544	...	0.000078	0.000152	0.000008	0.000005	0.000147	0.000055	0.000041	0.000006	0.000012	0.000024
2025	0.01869	0.003151	0.002168	0.002264	0.007016	0.00015	0.003139	0.000802	0.020025	0.005262	...	0.000069	0.000135	0.000007	0.000004	0.000131	0.000048	0.000036	0.000005	0.00001	0.000021
2026	0.014169	0.002059	0.001487	0.001757	0.005248	0.000108	0.002824	0.000686	0.015459	0.004107	...	0.00006	0.000118	0.000006	0.000004	0.000115	0.000042	0.000032	0.000005	0.000009	0.000018
2027	0.010659	0.00131	0.000997	0.001299	0.003875	0.000073	0.002528	0.000577	0.011653	0.003112	...	0.000051	0.000103	0.000005	0.000003	0.0001	0.000036	0.000028	0.000004	0.000008	0.000015
2028	0.007954	0.000811	0.000655	0.000915	0.002804	0.000046	0.00225	0.000472	0.008603	0.002289	...	0.000044	0.000089	0.000005	0.000003	0.000087	0.000031	0.000024	0.000003	0.000007	0.000013
2029	0.005892	0.000489	0.00042	0.000614	0.001976	0.000027	0.001991	0.000375	0.006242	0.001634	...	0.000038	0.000076	0.000004	0.000003	0.000076	0.000026	0.000021	0.000003	0.000006	0.000011
2030	0.004344	0.000287	0.00026	0.000393	0.001349	0.000015	0.001752	0.000288	0.004468	0.001133	...	0.000032	0.000066	0.000003	0.000002	0.000066	0.000023	0.000018	0.000003	0.000005	0.00001
2031	0.003204	0.000165	0.000153	0.00024	0.000891	0.000008	0.001532	0.000213	0.003166	0.000764	...	0.000028	0.000057	0.000003	0.000002	0.000057	0.000019	0.000015	0.000002	0.000004	0.000008
2032	0.002377	0.000092	0.000086	0.00014	0.000569	0.000004	0.001332	0.000153	0.002227	0.000501	...	0.000024	0.00005	0.000003	0.000002	0.00005	0.000017	0.000013	0.000002	0.000004	0.000007
2033	0.001785	0.00005	0.000046	0.000078	0.000351	0.000002	0.001152	0.000106	0.001561	0.00032	...	0.000021	0.000043	0.000002	0.000002	0.000043	0.000015	0.000012	0.000002	0.000003	0.000006
2034	0.001363	0.000027	0.000023	0.000042	0.00021	0.000001	0.00099	0.000071	0.001095	0.0002	...	0.000018	0.000038	0.000002	0.000001	0.000038	0.000013	0.00001	0.000001	0.000003	0.000005
2035	0.001061	0.000014	0.000011	0.000021	0.000121	0.0	0.000847	0.000046	0.000772	0.000121	...	0.000016	0.000033	0.000002	0.000001	0.000033	0.000011	0.000009	0.000001	0.000003	0.000005
2036	0.00084	0.000007	0.000005	0.00001	0.000068	0.0	0.000721	0.000029	0.000551	0.000072	...	0.000014	0.000029	0.000002	0.000001	0.000029	0.00001	0.000008	0.000001	0.000002	0.000004
2037	0.000675	0.000004	0.000002	0.000005	0.000037	0.0	0.00061	0.000018	0.000399	0.000042	...	0.000012	0.000025	0.000001	0.000001	0.000025	0.000009	0.000007	0.000001	0.000002	0.000004
2038	0.000549	0.000002	0.000001	0.000002	0.000019	0.0	0.000515	0.00001	0.000295	0.000024	...	0.000011	0.000022	0.000001	0.000001	0.000022	0.000008	0.000006	0.000001	0.000002	0.000003
2039	0.00045	0.000001	0.0	0.000001	0.00001	0.0	0.000432	0.000006	0.000223	0.000013	...	0.00001	0.000019	0.000001	0.000001	0.000019	0.000007	0.000005	0.000001	0.000001	0.000003
2040	0.000371	0.0	0.0	0.0	0.000005	0.0	0.000361	0.000003	0.000172	0.000007	...	0.000009	0.000017	0.000001	0.000001	0.000017	0.000006	0.000005	0.000001	0.000001	0.000003
2041	0.000306	0.0	0.0	0.0	0.000002	0.0	0.000301	0.000002	0.000135	0.000004	...	0.000008	0.000015	0.000001	0.0	0.000014	0.000005	0.000004	0.000001	0.000001	0.000002
2042	0.000252	0.0	0.0	0.0	0.000001	0.0	0.00025	0.000001	0.000108	0.000002	...	0.000007	0.000013	0.000001	0.0	0.000012	0.000005	0.000003	0.0	0.000001	0.000002
2043	0.000208	0.0	0.0	0.0	0.000001	0.0	0.000207	0.000001	0.000087	0.000001	...	0.000006	0.000011	0.000001	0.0	0.000011	0.000004	0.000003	0.0	0.000001	0.000002
2044	0.000171	0.0	0.0	0.0	0.0	0.0	0.000171	0.0	0.000071	0.000001	...	0.000005	0.00001	0.000001	0.0	0.000009	0.000004	0.000003	0.0	0.000001	0.000002
2045	0.000141	0.0	0.0	0.0	0.0	0.0	0.00014	0.0	0.000058	0.0	...	0.000005	0.000009	0.0	0.0	0.000008	0.000003	0.000002	0.0	0.000001	0.000001
2046	0.000115	0.0	0.0	0.0	0.0	0.0	0.000115	0.0	0.000047	0.0	...	0.000004	0.000008	0.0	0.0	0.000007	0.000003	0.000002	0.0	0.000001	0.000001
2047	0.000094	0.0	0.0	0.0	0.0	0.0	0.000094	0.0	0.000039	0.0	...	0.000004	0.000007	0.0	0.0	0.000006	0.000003	0.000002	0.0	0.000001	0.000001
2048	0.000077	0.0	0.0	0.0	0.0	0.0	0.000077	0.0	0.000032	0.0	...	0.000003	0.000006	0.0	0.0	0.000005	0.000002	0.000002	0.0	0.0	0.000001
2049	0.000063	0.0	0.0	0.0	0.0	0.0	0.000063	0.0	0.000026	0.0	...	0.000003	0.000005	0.0	0.0	0.000005	0.000002	0.000001	0.0	0.0	0.000001
2050	0.000051	0.0	0.0	0.0	0.0	0.0	0.000051	0.0	0.000022	0.0	...	0.000002	0.000004	0.0	0.0	0.000004	0.000002	0.000001	0.0	0.0	0.000001

36 rows × 5240 columns

Executing "monte_carlo_uncertainty.py"

In order to execute this script, one has to adjust the settings in the beginning of the file so they are the same as the used ones in "mone_carlo_simulations.py" and "monte_carlo_evaluation.py". The path to the results has to be defined. Then the file is ready to be executed.

The file calculates for all considered years the spearman correlation and the normalized spearman square correlation between all inputs and the total in-use stock, the total hibernating stock, the total disposal flow, and the total export flow.

The results are written into the files "monte_carlo_results" (results of mentioned stocks and flows over years and runs), "speaman_results_abs" (spearman correlation between inputs and outputs over years) and "spearman_results_normalized" (normalized spareman square correlation between inputs and outputs over years).

%run monte_carlo_uncertainty.py

Calculate spearman correlation between inputs and:
['total_use_stock', 'total_hoarding_stock', 'to_disposal_flow', 'U.B hoarding stock', 'U.A use stock', 'total_export', 'total_disposal']
Year 1 of 36

c:\Users\rapha\.conda\envs\master_thesis\lib\site-packages\scipy\stats\stats.py:4484: SpearmanRConstantInputWarning: An input array is constant; the correlation coefficient is not defined.
  warnings.warn(SpearmanRConstantInputWarning())

Year 2 of 36
Year 3 of 36
Year 4 of 36
Year 5 of 36
Year 6 of 36
Year 7 of 36
Year 8 of 36
Year 9 of 36
Year 10 of 36
Year 11 of 36
Year 12 of 36
Year 13 of 36
Year 14 of 36
Year 15 of 36
Year 16 of 36
Year 17 of 36
Year 18 of 36
Year 19 of 36
Year 20 of 36
Year 21 of 36
Year 22 of 36
Year 23 of 36
Year 24 of 36
Year 25 of 36
Year 26 of 36
Year 27 of 36
Year 28 of 36
Year 29 of 36
Year 30 of 36
Year 31 of 36
Year 32 of 36
Year 33 of 36
Year 34 of 36
Year 35 of 36
Year 36 of 36
Export Monte Carlo results
Export spearman absolute results
Export spearman normalized results

The following cell shows a part of the table displaying the normalized square spearmen correlation.

with open(
    'monte_carlo_results/proof_of_concept/spearman_results_normalized.pkl',
     'rb') as f:
    spearman_results_normalized_pd= pickle.load(f)
spearman_results_normalized_pd

result_item	total_use_stock										...	total_disposal
sheet	MaTrace_initial_inflow										...	Reuse_storage_time_3
column	share										...	scale			shape
item	portable batteries	mobility batteries	hydroprocessing catalysts coke	hydroprocessing catalysts poisoning	hydroformylation catalysts	pet precursors catalysts	dissipative uses	hard metals	magnets	other metallic uses	...	e-bikes	power tools	others	smartphones	mobile phones	tablets	laptops	e-bikes	power tools	others
0	2.045029	0.114251	0.081801	0.138889	0.033126	0.138889	0.016901	0.012695	0.001878	0.012695	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
1	1.986973	0.039561	0.062895	0.081441	0.039561	0.179560	0.003664	0.021613	0.000673	0.000075	...	0.391401	0.346062	0.415117	0.439530	0.192605	0.004272	0.019618	0.263753	0.054494	0.025198
2	1.887136	0.012615	0.032919	0.021573	0.012615	0.151159	0.012615	0.026947	0.003658	0.006046	...	0.292899	0.022749	1.229923	0.009525	0.740630	0.009525	0.003857	0.173882	0.107761	0.028416
3	1.887136	0.012615	0.032919	0.021573	0.012615	0.151159	0.012615	0.026947	0.003658	0.006046	...	0.104374	0.047651	1.430971	0.055580	0.603906	0.009225	0.214161	0.140970	0.027523	0.040332
4	1.887136	0.012615	0.032919	0.021573	0.012615	0.151159	0.012615	0.026947	0.003658	0.006046	...	0.000757	0.052555	0.236201	0.037082	0.333742	0.010175	0.333742	0.091571	0.070717	0.758888
5	1.949861	0.081918	0.021740	0.039793	0.009102	0.195656	0.006093	0.003686	0.001881	0.003686	...	0.056047	0.387566	0.479825	0.366038	0.184595	0.142156	0.387566	0.199972	0.129240	0.324829
6	1.949861	0.081918	0.021740	0.039793	0.009102	0.195656	0.006093	0.003686	0.001881	0.003686	...	0.079654	0.122956	0.221262	0.290311	0.122956	0.389787	0.254616	0.175620	0.111253	0.053322
7	1.956062	0.228274	0.021809	0.055012	0.000679	0.092442	0.012753	0.000075	0.000075	0.012753	...	0.245442	0.000730	0.077973	0.194812	0.068237	0.301914	0.099394	0.111078	0.164304	0.000081
8	1.812508	0.063447	0.001886	0.000075	0.009129	0.103281	0.009129	0.003697	0.012750	0.006111	...	0.348333	0.038704	0.063979	0.228272	0.265484	0.038704	0.193869	0.000088	0.285143	0.285143
9	1.887136	0.012615	0.032919	0.021573	0.012615	0.151159	0.012615	0.026947	0.003658	0.006046	...	0.614613	0.135698	0.004372	0.097157	0.075031	0.004372	0.197080	0.047196	0.475435	0.214209
10	1.769097	0.000663	0.005964	0.008910	0.021281	0.206843	0.000074	0.061928	0.000074	0.008910	...	0.614613	0.135698	0.004372	0.097157	0.075031	0.004372	0.197080	0.047196	0.475435	0.214209
11	1.643312	0.001850	0.001850	0.003627	0.053960	0.177721	0.000666	0.101333	0.000074	0.016654	...	0.619059	0.104962	0.072059	0.117300	0.045326	0.014480	0.240683	0.104962	0.318826	0.117300
12	1.331594	0.053264	0.038651	0.003580	0.089504	0.190040	0.021116	0.289992	0.005918	0.038651	...	0.705611	0.092792	0.129602	0.092792	0.019172	0.024625	0.221627	0.081885	0.338192	0.053255
13	1.331594	0.053264	0.038651	0.003580	0.089504	0.190040	0.021116	0.289992	0.005918	0.038651	...	0.486022	0.124682	0.247971	0.112222	0.013854	0.051234	0.230264	0.124682	0.112222	0.023690
14	1.305751	0.021333	0.090426	0.021333	0.039049	0.207352	0.080387	0.207352	0.008932	0.062080	...	0.133836	0.009634	0.630646	0.023009	0.023009	0.009634	0.223644	0.086703	0.001990	0.049761
15	1.049711	0.001853	0.352918	0.101480	0.026760	0.071236	0.071236	0.275826	0.001853	0.012527	...	0.040197	0.055395	1.004931	0.027431	0.012842	0.001900	0.321046	0.017097	0.001900	0.012842
16	1.049711	0.001853	0.352918	0.101480	0.026760	0.071236	0.071236	0.275826	0.001853	0.012527	...	0.000075	0.244924	1.031938	0.033245	0.012740	0.054955	0.446954	0.012740	0.000075	0.016962
17	1.049711	0.001853	0.352918	0.101480	0.026760	0.071236	0.071236	0.275826	0.001853	0.012527	...	0.009178	0.182117	1.110530	0.021921	0.006144	0.033450	0.382363	0.033450	0.009178	0.040125
18	1.200942	0.012583	0.334245	0.091212	0.000670	0.054280	0.016753	0.137674	0.001861	0.000074	...	0.006119	0.166885	1.336367	0.009141	0.033317	0.027273	0.262982	0.039965	0.033317	0.047217
19	0.971130	0.033540	0.549488	0.182605	0.040232	0.012853	0.009202	0.093166	0.027455	0.012853	...	0.016798	0.194181	1.360613	0.012617	0.039493	0.062786	0.151179	0.032923	0.102205	0.039493
20	1.022361	0.209790	0.442806	0.062810	0.054445	0.000075	0.001867	0.054445	0.016804	0.125545	...	0.000075	0.062887	1.444752	0.032976	0.102369	0.016825	0.102369	0.000075	0.165181	0.016825
21	1.079578	0.292661	0.351060	0.012461	0.021310	0.001843	0.000074	0.046085	0.001843	0.177042	...	0.000075	0.062887	1.444752	0.032976	0.102369	0.016825	0.102369	0.000075	0.165181	0.016825
22	1.079578	0.292661	0.351060	0.012461	0.021310	0.001843	0.000074	0.046085	0.001843	0.177042	...	0.001882	0.047050	1.102184	0.114502	0.166295	0.016938	0.126547	0.047050	0.211463	0.012722
23	0.962534	0.424015	0.379993	0.016961	0.092341	0.003694	0.000075	0.006106	0.021785	0.262400	...	0.013193	0.000078	1.032383	0.041295	0.056908	0.022560	0.085011	0.056908	0.329816	0.001952
24	0.893307	0.569097	0.400676	0.054812	0.102932	0.006090	0.003684	0.000075	0.000075	0.126391	...	0.035755	0.029269	0.860146	0.013702	0.023431	0.059105	0.050673	0.068186	0.456058	0.003973
25	0.893307	0.569097	0.400676	0.054812	0.102932	0.006090	0.003684	0.000075	0.000075	0.126391	...	0.069717	0.029926	0.627457	0.036558	0.069717	0.051811	0.036558	0.183122	0.598940	0.010031
26	0.752894	0.666098	0.274632	0.000664	0.311830	0.001845	0.001845	0.039043	0.003616	0.239795	...	0.069717	0.029926	0.627457	0.036558	0.069717	0.051811	0.036558	0.183122	0.598940	0.010031
27	0.752894	0.666098	0.274632	0.000664	0.311830	0.001845	0.001845	0.039043	0.003616	0.239795	...	0.010066	0.069961	0.688879	0.113884	0.090592	0.036686	0.014059	0.113884	0.545796	0.000749
28	0.880273	0.697121	0.136994	0.003630	0.294067	0.026747	0.001852	0.062310	0.000074	0.224125	...	0.073177	0.119119	0.438626	0.054382	0.019578	0.025146	0.002175	0.119119	0.887607	0.010528
29	0.880273	0.697121	0.136994	0.003630	0.294067	0.026747	0.001852	0.062310	0.000074	0.224125	...	0.045704	0.145232	0.485978	0.038101	0.072659	0.083027	0.006998	0.190849	0.916575	0.006998
30	0.880273	0.697121	0.136994	0.003630	0.294067	0.026747	0.001852	0.062310	0.000074	0.224125	...	0.045704	0.145232	0.485978	0.038101	0.072659	0.083027	0.006998	0.190849	0.916575	0.006998
31	0.880273	0.697121	0.136994	0.003630	0.294067	0.026747	0.001852	0.062310	0.000074	0.224125	...	0.031193	0.242715	0.435574	0.006999	0.105848	0.118290	0.045709	0.261379	1.064612	0.002160
32	0.779623	0.663220	0.123532	0.016535	0.176442	0.021238	0.012419	0.016535	0.008892	0.238759	...	0.044414	0.253974	0.472267	0.002099	0.114939	0.061206	0.024264	0.052474	0.856461	0.018891
33	0.779623	0.663220	0.123532	0.016535	0.176442	0.021238	0.012419	0.016535	0.008892	0.238759	...	0.044414	0.253974	0.472267	0.002099	0.114939	0.061206	0.024264	0.052474	0.856461	0.018891
34	0.779623	0.663220	0.123532	0.016535	0.176442	0.021238	0.012419	0.016535	0.008892	0.238759	...	0.066528	0.108296	0.626600	0.022862	0.076021	0.017799	0.013369	0.006408	0.684189	0.160190
35	0.779623	0.663220	0.123532	0.016535	0.176442	0.021238	0.012419	0.016535	0.008892	0.238759	...	0.066528	0.108296	0.626600	0.022862	0.076021	0.017799	0.013369	0.006408	0.684189	0.160190

36 rows × 3787 columns

Using this data, one can create plots displaying the contribution of an input to the uncertainty of an output. The following graph is not representative since only 10 runs were conducted.

graph_pd = spearman_results_normalized_pd.groupby(level=[0,1,2], axis = 1).sum()

graph_pd = graph_pd['U.A use stock'].copy()
graph_pd.columns = ['_'.join(col) for col in graph_pd.columns]
graph_pd


dic_legend = {'n_initial_products_Share': r'$\eta$: Initial inflow distribution',
'n_use_1_in_use_Weibull scale': r'$S_{Uk}$: Weibull scale',
'n_use_1_in_use_Weibull shape': r'$S_{Uk}$: Weibull shape',
'reuse_split_split': r'$\delta$: Split portable batteries to products'
}
handles_names_list = []

fig, ax = plt.subplots()
stacks = ax.stackplot(graph_pd.index, graph_pd.transpose().to_numpy())

plt.ylabel('Normalized square of Spearman\'s rank correlation in %')
plt.xlabel('Year')

Text(0.5, 0, 'Year')