Analysis - Calibration¶

Calibrating a generic model for given data, ie identifying model parameters so that the result of the model was in some sense the closest measured data.

Configuration¶

WrappedAction

Workflow of calibrated model

Parameters

List of parameters

name: Name of parameter in calibration and inside of model
group: Group of parameter
bounds: Upper and lower bound of parameter
init_value: Init value of parameter
offset, scale: Body param. = scale * tuned param. + offset; default offset = 0.0, scale = 1.0
fixed: If True then parameter is fixed in init value
log_transform: If True with parameter is internally operated as log10(parameter value)
tied_params: Parameters used in tied_expression
tied_expression: Python expression, may use other parameters (defined in tied_params), this parameter is not calibrated

Observations

List of observations

name: Name of observation
group: Group of observation
weight: Observation weight in target function
upper_bound:: If computed value is greater than this parameter, special penalization is applied
lower_bound:: If computed value is smaller than this parameter, special penalization is applied

AlgorithmParameters

Define approximation of derivatives, for each group of parameters.

group:: Parameter group
diff_inc_rel: Step for derivation eval relative
diff_inc_abs: Step for derivation eval absolute

TerminationCriteria

Define criteria for termination of calibration process.

n_lowest, tol_lowest: Stop if difference of min and max from n_lowest min values of objective function
n_from_lowest: Stop if n iterations without improvement
n_param_change, tol_rel_param_change: Stop if max relative change of parameter form last n_param_change is lower than tol_rel_param_change (must be satisfied for all parameters). If parameter is log transformed relative change is measured on log10 its value (this will be changed in future versions).
n_max_steps: Maximum number of iterations to perform

MinimizationMethod

Sets minimalization method. Must be one of:

L-BFGS-B - Limited-memory Broyden–Fletcher–Goldfarb–Shanno with bounds

SLSQP - Sequential Least SQuares Programming

BoundsType

Sets type of bounds of parameters. Must be one of:

hard - use bounds from underlying SciPy minimize

soft - use penalization if parameter go out of bounds

Calibration input¶

observations: Struct of individual observations

Calibration output¶

optimisation

Sequence of individual iterations:

converge_reason

Reason of convergence

cumulative_n_evaluation

Number of evaluation of criterial functon

residual

Criterial function in this iteration

observations

measured_value: Desired value
model_value: Observation value corresponding to input parameters
residual: Difference between measured_value and model_value
sensitivity: Sensitivity of observation j is the magnitude of the j’th row of the Jacobian multiplied by the weight associated with that observation; this magnitude is then divided by the number of adjustable parameters. It is thus a measure of the sensitivity of that observation to all parameters involved in the parameter estimation process.

parameters

parameter_type: Type of parameter, is one of Free, Tied, Fixed, Frozen
value: Parameter value in this iteration
interval_estimate: Not implemented yet
sensitivity: Sensitivity of the i’th parameter is the normalised (with respect to the number of observations) magnitude of the column of the Jacobian matrix pertaining to that parameter, with each element of that column multiplied by the weight pertaining to the respective observation.
relative_sensitivity: The relative sensitivity of a parameter is obtained by multiplying its sensitivity by the magnitude of the value of the parameter. It is thus a measure of the changes in model outputs that are incurred by a fractional change in the value of the parameter.

result

n_iter: Number of iterations
converge_reason: Reason of convergence
residual: Criterial function after calibration

Objective function¶

As objective function is used sum over individual observation of square of difference between measured value and modeled value multiplied by square of observation weight.