Sensitivity analysis

This section presents the functions useful for sensitivity analysis of parametric inventories, and the generation of simplified algebraic models.

One at a time

lca_algebraic.oat_matrix(model: Activity, impacts, functional_unit: float | Expr = 1, n=10, title='Impact variability (% of mean)', name_type=NameType.LABEL)

This function generates a heat map of relative the variance of impacts for each parameter varying along its min/max values.

Parameters

model:

Root activity of the inventory

impacts:

Impact variabilityList of impact methods keys (tuples)

functional_unit:

Float value of expression by which to divide each impact.

lca_algebraic.oat_dashboard(model, impacts, functional_unit: float | Expr = 1, func_unit_name='kWh', **kwparams)

This function runs a “one at a time” analysis on the selected param.

It makes each parameter vary on its min:max range, while keeping other parameters at their default values.

It returns an interactive dashboard.

Parameters

model :

Root activity of the inventory

methods :

List of methods keys (tuple)

functional_unit:

Value of sympy expression by which to divide the impacts

func_unit_name:

Name of the physical unit of the functional unit, for display

figsize:

Size of figure fro graphs : (15, 15 by default)

figspace:

Space between figures for graphs : (0.5, 0.5) by default

sharex:

Shared X axes ? True by default

Returns

An interactive dashboard with selection of a parameter and graphs of impacts.

GSA / Sobol analysis

lca_algebraic.incer_stochastic_dashboard(model: Activity, methods, n=1024, var_params=None, functional_unit=typing.Union[float, sympy.core.expr.Expr], **kwparams)

This function runs a monte carlo & Sobol analysis (GSA) on a parametric model and displays a dashboard with results.

Parameters

model:

The root activity of your inventory

methods:

List of impact methods keys (tuples)

var_params:

Optional list of parameters to vary. By default, all the parameters that are not marked as FIXED will be varyed.

functional_unit:

Float value or Sympy expression by which to divide the impacts

figsize:

Size of figure for violin plots : (15, 15) by default

figspace:

Space between violin graphs (0.5, 0.5) by default

sharex:

Share X axe for violin graph : True by default

Returns

An interactive dashboard with 4 tabs :

• Violin graphs with distributions of impacts

• Bar graph with relative variance of impacts

• A heatmap amtrix of Sobol indices for each paramter x impact method

• A detailed table with all values

Simplified models

lca_algebraic.sobol_simplify_model(model: Activity, methods, min_ratio=0.8, functional_unit=1, n=2048, var_params=None, fixed_mode='median', num_digits=3, simple_sums=True, simple_products=True) → List[LambdaWithParamNames]

Computes Sobol indices and selects main parameters for explaining sensibility of at least ‘min_ratio’, Then generates simplified models for those parameters.

The other parameters are replaced by their mean or median values.

Also the term contributing to less than 1% of variation in sums and products are removed.

Decimal numbers are rounded to 3 digits.

Parameters

model:

Root activity of the inventory

methods:

List of impact methods to consider

min_ratio:

[0, 1] minimum amount of first order variation (sum of S1) to explain; 0.8 (80%) by default.

var_params:

Optional list of parameters to vary. If not provided, all parameters vary.

fixed_mode :

What to replace minor parameters with : MEDIAN by default

simple_sums:

If true (default) remove terms in sums that are lower than 1%

simple_products:

If true (default) remove terms in products that contribute to less than 1% to variation

num_digits:

Number of decimal places to round decimal number to (default 3)

Returns

List of LambdaWithParamNames, one per impact. The class LambdaWithParamNames wraps the simplified expression together with the list of required parameters and compiled lambda functions for fast evaluation.

The core simplified expresion may be access with res[i].expr

Examples

>>> res = sobol_simplify_model(
>>>     model=total_inventory,
>>>     methods=[climate_change],
>>>     functional_unit=total_energy) # Holds a sympy expression computing the total energy

>>> print(res[0].expr) # Dispalt the simplified expression

lca_algebraic.compare_simplified(model: Activity, methods, simpl_lambdas, functional_unit=1, func_unit_name='', scales=None, unit_overrides=None, nb_cols=2, height=10, width=15, textboxright=0.6, r2_height=0.65, residuals=False, **kwargs)

Compare distribution of simplified model with full model.

This functions runs the same monte caarlo random sample as input and feed it to oboth simplified models and full model. It displays graphs and metrics comparing the two.

Parameters

model:

Root activity of the inventory

methods :

List of impact methods

functional_unit:

Float value or sympy expression by whicxh to devide the impacts

func_unit_name:

Name of the physical functional unit

simpl_lambdas :

Simplified lambdas, as returned by sobol_simplify_model(…)

residuals :

If true, draw heat map of residuals, rather than distributions

nb_cols:

number of columns for displaying graphs

percentiles:

List of percentiles to compute [5, 95] by default