pystra.mc.CrudeMonteCarlo#

class CrudeMonteCarlo(analysis_options=None, limit_state=None, stochastic_model=None, point=None)[source]#

Bases: MonteCarlo

Crude Monte Carlo simulation (CMC)

The Crude Monte Carlo simulation (CMC) is the most simple form and corresponds to a direct application of Equation (24). A large number \(n\) of samples are simulated for the set of random variables \({\bf X}\). All samples that lead to a failure are counted \(n_f\) and after all simulations the probability of failure \(p_f\) may be estimated by [Faber2009]

\[\tilde{p}_f = \frac{n_f}{n}\]

Theoretically, an infinite number of simulations will provide an exact probability of failure. However, time and the power of computers are limited; therefore, a suitable amount of simulations \(n\) are required to achieve an acceptable level of accuracy.

Attributes:

analysis_option (AnalysisOption): Option for the structural analysis
limit_state (LimitState): Information about the limit state
stochastic_model (StochasticModel): Information about the model
point (vec): Design point for the simulation

Methods

`computeBeta`	Compute beta value
`computeBins`	Return an optimal amount of bins for a histogram
`computeCoefficientOfVariation`	Compute Coefficient of Variation
`computeFailureProbability`	Compute probability of failure
`computeLimitState`	Evaluate limit-state function
`computePercentDone`	Compute percent done
`computeRandomNumbers`	Compute random numbers
`computeResults`	Collect result of sampling
`computeSumUpdate`	Update summation
`computeTransformation`	Compute transformation from u to x space
`getBeta`	Returns the beta value
`getBins`	Returns the amount on bins
`getDistributionData`	Returns data for the failure
`getFailure`	Returns the probability of failure
`init_run`	Derived classes call this at top of their run()
`initializeVariables`	Initialization of the simulation variables
`run`
`setPoint`	Set design point
`showResults`	Show results and plots

initializeVariables()[source]#: Initialization of the simulation variables

showResults()[source]#: Show results and plots

computeBeta()#: Compute beta value

computeBins(samples)#

Return an optimal amount of bins for a histogram

Returns:

bins (int): Returns amount on bins

computeCoefficientOfVariation()#: Compute Coefficient of Variation

computeFailureProbability()#: Compute probability of failure

computeLimitState()#: Evaluate limit-state function

computePercentDone()#: Compute percent done

computeRandomNumbers()#: Compute random numbers

computeResults()#: Collect result of sampling

computeSumUpdate()#: Update summation

computeTransformation()#: Compute transformation from u to x space

Note

TODO: this method takes a lot of time, find some better solution.

getBeta()#

Returns the beta value

Returns:

beta (float): Returns the beta value

getBins()#

Returns the amount on bins

Returns:

bins (int): Returns the amount on bins (histogram)

getDistributionData()#

Returns data for the failure

Returns:

all_G (float): Returns data from the distribution

getFailure()#

Returns the probability of failure

Returns:

Pf (float): Returns the probability of failure

init_run()#: Derived classes call this at top of their run()

setPoint(point=None)#: Set design point