The likelihood module

class pylife.materialdata.woehler.analyzers.likelihood.Likelihood(fatigue_data)[source]
likelihood_finite(SD, k, N_E, TN)[source]
likelihood_infinite(SD, TS)[source]

Produces the likelihood functions that are needed to compute the endurance limit and the scatter in load direction. The likelihood functions are represented by a cummalative distribution function. The likelihood function of a runout is 1-Li(fracture).

Parameters:
  • variables – The start values to be optimized. (Endurance limit SD, Scatter in load direction 1/TS)
  • zone_inf – The data that our log-likelihood function takes in. This data is found in the infinite zone.
  • load_cycle_limit – The dependent variable that our model requires, in order to seperate the fractures from the runouts.
Returns:

Sum of the log likelihoods. The negative value is taken since optimizers in statistical packages usually work by minimizing the result of a function. Performing the maximum likelihood estimate of a function is the same as minimizing the negative log likelihood of the function.
Return type:

neg_sum_lolli
likelihood_total(SD, TS, k, N_E, TN)[source]

Produces the likelihood functions that are needed to compute the parameters of the woehler curve. The likelihood functions are represented by probability and cummalative distribution functions. The likelihood function of a runout is 1-Li(fracture). The functions are added together, and the negative value is returned to the optimizer.

Parameters:
  • SD – Endurnace limit start value to be optimzed, unless the user fixed it.
  • TS – The scatter in load direction 1/TS to be optimzed, unless the user fixed it.
  • k – The slope k_1 to be optimzed, unless the user fixed it.
  • N_E – Load-cycle endurance start value to be optimzed, unless the user fixed it.
  • TN – The scatter in load-cycle direction 1/TN to be optimzed, unless the user fixed it.
  • fractures – The data that our log-likelihood function takes in. This data represents the fractured data.
  • zone_inf – The data that our log-likelihood function takes in. This data is found in the infinite zone.
  • load_cycle_limit – The dependent variable that our model requires, in order to seperate the fractures from the runouts.
Returns:

Sum of the log likelihoods. The negative value is taken since optimizers in statistical packages usually work by minimizing the result of a function. Performing the maximum likelihood estimate of a function is the same as minimizing the negative log likelihood of the function.
Return type:

neg_sum_lolli