KrigingPOD

class KrigingPOD(*args)

Kriging based POD.

Available constructor:

KrigingPOD(inputSample, outputSample, detection, noiseThres, saturationThres, boxCox)

Parameters:

inputSample2-d sequence of float

Vector of the input values. The first column must correspond with the defect sizes.

outputSample2-d sequence of float

Vector of the signals, of dimension 1.

detectionfloat

Detection value of the signal.

noiseThresfloat

Value for low censored data. Default is None.

saturationThresfloat

Value for high censored data. Default is None

boxCoxbool or float

Enable or not the Box Cox transformation. If boxCox is a float, the Box Cox transformation is enabled with the given value. Default is False.

Methods

computeDetectionSize(probabilityLevel[, ...])	Compute the detection size for a given probability level.
drawBoxCoxLikelihood([name])	Draw the loglikelihood versus the Box Cox parameter.
drawPOD([probabilityLevel, confidenceLevel, ...])	Draw the POD curve.
drawValidationGraph([name])	Draw the validation graph of the metamodel.
getBasis()	Accessor to the kriging basis.
getBoxCoxParameter()	Accessor to the Box Cox parameter.
getCovarianceModel()	Accessor to the kriging covariance model.
getDefectSizes()	Accessor to the defect size where POD is computed.
getDistribution()	Accessor to the parameters distribution.
getInitialStartSize()	Accessor to the size of the multi start algorithm.
getKrigingResult()	Accessor to the kriging result.
getPODCLModel([confidenceLevel])	Accessor to the POD model at a given confidence level.
getPODModel()	Accessor to the POD model.
getQ2()	Accessor to the Q2 value.
getSamplingSize()	Accessor to the Monte Carlo sampling size.
getSimulationSize()	Accessor to the simulation size.
getVerbose()	Accessor to the verbosity.
run()	Build the POD models.
setBasis(basis)	Accessor to the kriging basis.
setCovarianceModel(covarianceModel)	Accessor to the kriging covariance model.
setDefectSizes(size)	Accessor to the defect size where POD is computed.
setDistribution(distribution)	Accessor to the parameters distribution.
setInitialStartSize(size)	Accessor to the size of the multi start algorithm.
setKrigingResult(result)	Accessor to the kriging result.
setSamplingSize(size)	Accessor to the Monte Carlo sampling size.
setSimulationSize(size)	Accessor to the simulation size.
setVerbose(verbose)	Accessor to the verbosity.

Warning

The first column of the input sample must corresponds with the defects sample.

Notes

This class aims at building the POD based on a kriging model. No assumptions are required for the residuals with this method. The POD are computed by simulating conditional prediction. For each, a Monte Carlo simulation is performed. The accuracy of the Monte Carlo simulation is taken into account using the TCL.

The return POD model corresponds with an interpolate function built with the POD values computed for the given defect sizes. The default values are 20 defect sizes between the minimum and maximum value of the defect sample. The defect sizes can be changed using the method setDefectSizes.

The default kriging model is built with a linear basis only for the defect size and constant otherwise. The covariance model is an anisotropic squared exponential model. Parameters are estimated using a Multi Start TNC algorithm, the 100 initial starting points are defined according to a Sobol sequence .

For advanced use, all parameters can be defined thanks to dedicated set methods. Moreover, if the user has already built a kriging result, it can be given as parameter using the method setKrigingResult, then the POD is computed based on this kriging result.

A progress bar is shown if the verbosity is enabled. It can be disabled using the method setVerbose.

computeDetectionSize(probabilityLevel, confidenceLevel=None)

Compute the detection size for a given probability level.

Parameters:

probabilityLevelfloat

The probability level for which the defect size is computed.

confidenceLevelfloat

The confidence level associated to the given probability level the defect size is computed. Default is None.

Returns:

resultcollection of openturns.PointWithDescription

A PointWithDescription containing the detection size computed at the given probability level and confidence level if provided.

drawBoxCoxLikelihood(name=None)

Draw the loglikelihood versus the Box Cox parameter.

Parameters:

namestring

name of the figure to be saved with transparent option sets to True and bbox_inches=’tight’. It can be only the file name or the full path name. Default is None.

Returns:

figmatplotlib.figure

Matplotlib figure object.

axmatplotlib.axes

Matplotlib axes object.

Notes

This method is available only when the parameter boxCox is set to True.

drawPOD(probabilityLevel=None, confidenceLevel=None, defectMin=None, defectMax=None, nbPt=100, name=None)

Draw the POD curve.

Parameters:

probabilityLevelfloat

The probability level for which the defect size is computed. Default is None.

confidenceLevelfloat

The confidence level associated to the given probability level the defect size is computed. Default is None.

defectMin, defectMaxfloat

Define the interval where the curve is plotted. Default : min and max values of the input sample.

nbPtint

The number of points to draw the curves. Default is 100.

namestring

name of the figure to be saved with transparent option sets to True and bbox_inches=’tight’. It can be only the file name or the full path name. Default is None.

Returns:

figmatplotlib.figure

Matplotlib figure object.

axmatplotlib.axes

Matplotlib axes object.

drawValidationGraph(name=None)

Draw the validation graph of the metamodel.

Parameters:

namestring

name of the figure to be saved with transparent option sets to True and bbox_inches=’tight’. It can be only the file name or the full path name. Default is None.

Returns:

figmatplotlib.figure

Matplotlib figure object.

axmatplotlib.axes

Matplotlib axes object.

getBasis()

Accessor to the kriging basis.

Returns:

basisopenturns.Basis

The basis used as trend in the kriging model. Default is a linear basis for the defect and constant for the other parameters.

getBoxCoxParameter()

Accessor to the Box Cox parameter.

Returns:

lambdaBoxCoxfloat

The Box Cox parameter used to transform the data. If the transformation is not enabled None is returned.

getCovarianceModel()

Accessor to the kriging covariance model.

Returns:

covarianceModelopenturns.CovarianceModel

The covariance model in the kriging model. Default is an anisotropic Squared exponential covariance model.

getDefectSizes()

Accessor to the defect size where POD is computed.

Returns:

defectSizesequence of float

The defect sizes where the Monte Carlo simulation is performed to compute the POD.

getDistribution()

Accessor to the parameters distribution.

Returns:

distributionopenturns.JointDistribution

The input parameters distribution used for the Monte Carlo simulation. Default is a Uniform distribution for all parameters.

getInitialStartSize()

Accessor to the size of the multi start algorithm.

Returns:

sizeint

The number of multi start using the TNC algorithm to find the covariance parameters. Default is 100.

getKrigingResult()

Accessor to the kriging result.

Returns:

resultopenturns.KrigingResult

The kriging result.

getPODCLModel(confidenceLevel=0.95)

Accessor to the POD model at a given confidence level.

Parameters:

confidenceLevelfloat

The confidence level the POD must be computed. Default is 0.95

Returns:

PODModelClopenturns.Function

The function which computes the probability of detection for a given defect value at the confidence level given as parameter.

getPODModel()

Accessor to the POD model.

Returns:

PODModelopenturns.Function

The function which computes the probability of detection for a given defect value.

getQ2()

Accessor to the Q2 value.

Returns:

Q2float

The Q2 value computed analytically using Dubrule (1983) technique.

getSamplingSize()

Accessor to the Monte Carlo sampling size.

Returns:

sizeint

The size of the Monte Carlo simulation used to compute the POD for each defect size.

getSimulationSize()

Accessor to the simulation size.

Returns:

sizeint

The size of the simulation used to compute the confidence interval.

getVerbose()

Accessor to the verbosity.

Returns:

verbosebool

Enable or disable the verbosity. Default is True.

run()

Build the POD models.

Notes

This method build the kriging model. First the censored data are filtered if needed. The Box Cox transformation is performed if it is enabled. Then it builds the POD models : conditional samples are simulated for each defect size, then the distributions of the probability estimator (for MC simulation) are built. Eventually, a sample of this distribution is used to compute the mean POD and the POD at the confidence level.

setBasis(basis)

Accessor to the kriging basis.

Parameters:

basisopenturns.Basis

The basis used as trend in the kriging model.

setCovarianceModel(covarianceModel)

Accessor to the kriging covariance model.

Parameters:

covarianceModelopenturns.CovarianceModel

The covariance model in the kriging model.

setDefectSizes(size)

Accessor to the defect size where POD is computed.

Parameters:

defectSizesequence of float

The defect sizes where the Monte Carlo simulation is performed to compute the POD.

setDistribution(distribution)

Accessor to the parameters distribution.

Parameters:

distributionopenturns.JointDistribution

The input parameters distribution used for the Monte Carlo simulation.

setInitialStartSize(size)

Accessor to the size of the multi start algorithm.

Parameters:

sizeint

The number of multi start using the TNC algorithm to find the covariance parameters.

setKrigingResult(result)

Accessor to the kriging result.

Parameters:

resultopenturns.KrigingResult

The kriging result.

transformationopenturns.Function

The normalization transformation.

setSamplingSize(size)

Accessor to the Monte Carlo sampling size.

Parameters:

sizeint

The size of the Monte Carlo simulation used to compute the POD for each defect size.

setSimulationSize(size)

Accessor to the simulation size.

Parameters:

sizeint

The size of the simulation used to compute the confidence interval.

setVerbose(verbose)

Accessor to the verbosity.

Parameters:

verbosebool

Enable or disable the verbosity.