pyflange.stats

Sampler that generates random fatigue cases

Returns a sampler that yields random pyflange.fatigue.BoltFatigueAnalysis objects.

Evaluate the gap heigh probability distribution according to ref. [1].

The following example, creates a gap distribution and the calculates the 95% quantile of the gap height

from pyflange.gap import gap_height_distribution

D = 7.50      # Flange diameter in meters
u = 0.0014    # Flatness tolerance (non-dimensional)
L = 1.22      # Gap length
gap_dist = gap_height_distribution(D, u, L)     # a lognorm distribution object

u95 = gap_dist.ppf(0.95)    # PPF is the inverse of CDF. See scipy.stats.lognorm documentation.

Sampler based on a Log-Normal distribution.

Returns a log-normal distribution sampler with given mean value and coefficient of variation.

The following example creates a Log-Normal distribution sampler and generates three realizations.

samp = lognorm_sampler(12.0, 0.25)  # log-normal sampler sampler with 
                                    # mean value 12.0 and CoV = 0.25.

val1 = next(samp)   # A random value from the log-normal distribution
val2 = next(samp)   # Another random value from the log-normal distribution
val3 = next(samp)   # Yet another random value from the log-normal distribution

Sampler based on a Normal distribution.

Returns a normal distribution sampler with given mean value and coefficient of variation.

The following example creates a Normal distribution sampler and generates three realizations.

samp = norm_sampler(12.0, 0.25)   # normal sampler sampler with mean 12.0
                                  # and CoV = 0.25.

val1 = next(samp)   # A random value from the normal distribution
val2 = next(samp)   # Another random value from the normal distribution
val3 = next(samp)   # Yet another random value from the normal distribution

Generic distribution-based sampler.

Returns a generator that, at every next call returns a random realization of the passed random variable.

The following example creates a Normal distribution sampler and generates three realizations.

from scipy.stats import norm
ndist = norm(12.0, 2.0) # normal distribution with mean value 12 and standard deviation 2.

samp = sampler(ndist)   # sampler based on the ndist distribution

val1 = next(samp)       # A random value from ndist distribution
val2 = next(samp)       # Another random value from ndist distribution
val3 = next(samp)       # Yet another random value from ndist distribution

A sampler that yields random pyflange PolynomialLFlangeSegment objects.

Returns a sampler that yields random L-Flange segment objects, defined by the given deterministic parameters and the following random parameters which are generated according to ref. [1].

• preload (float), sampled from a Normal distribution with mean value given by the passed bolt_preload_ratio and CoV given by the passed bolt_preload_cov.
• gap_angle (float) and gap_height (float), given by the standard_gap_size_generator, created with flange diameter 2R and the given flange_flatness_tolerance.
• gap_shape_factor (float) sampled from a Normal distribution with mean value 1.0 and CoV=0.15
• tilt_angle (float) sampled from a log-normal distribution with mean value 0.1 deg and CoV=0.50.

The following example creates a L-Flange segment sampler and generates three random flange segments.

from math import pi
mm = 0.001
kN = 1000

from pyflange.bolts import StandardMetricBolt, RoundNut
N_BOLTS = 156

fseg_samp = standard_PolynomialLFlangeSegment_sampler (
        a = 150*mm,        # distance between inner face of the flange and center of the bolt hole
        b = 122*mm,        # distance between center of the bolt hole and center-line of the shell
        s =  54*mm,        # shell thickness
        t = 172*mm,        # flange thickness
        R = 4000*mm,       # shell outer curvature radius
        central_angle = 2*pi / N_BOLTS,  # angle subtended by the flange segment

        Zg = -18044*kN / N_BOLTS,      # load applied to the flange segment shell at rest

        # Bolt object representing the flange segment bolt
        bolt = StandardMetricBolt("M80", "10.9", shank_length=160*mm, 
                shank_diameter_ratio=76.1/80, stud=True),

        bolt_preload_ratio = 0.750,     # Ratio between mean preload Fp and Fy = As*fy.
        bolt_preload_cov = 0.03,        # Coefficient of variation of the bolt preload.

        Do = 86*mm,               # Bolt hole diameter
        washer = None,            # Bolt washer
        nut = RoundNut("M80"),    # Bolt nut

        flange_flatness_tolerance = 0.0014,   # 1.4 mm/m

        s_ratio = 1.0       # Ratio of bottom shell thickness over s. Default s_botom = s.
    )

fseg1 = next(fseg_samp)     # A random L-Flange segment object
fseg2 = next(fseg_samp)     # Another random L-Flange segment object
fseg3 = next(fseg_samp)     # Yet another random L-Flange segment object

Sampler that generates random bolt SN curves, according to ref. [2].

Returns a sampler that yields pyflange.fatigue.BoltFatigueCurve objects, having a reference stress range randomly generated from a normal distribution with mean value 62 MPa and CoV=0.10.

Sampler that generates random flange gaps according to ref. [1]

The following example creates a standard gap-size sampler and generate three realizations.

# Gap size sampler for 7.5 m falnge with flatness tolerance 1.4 mm/m
samp = standard_gap_size_sampler(7.5, 0.0014)

ga1, gh1 = next(samp)  # A random gap-anlge, gap-height pair
ga2, gh2 = next(samp)  # Another random gap-anlge, gap-height pair
ga3, gh3 = next(samp)  # Yet another random gap-anlge, gap-height pair

Sampler that generates a random markov matrix according to ref [2].

Returns a MarkovMatrix sampler that yields random Markov matrices having the same mean load values and number of cycles as the passed markov_matrix parameter, but random ranges multiplied by a random factor extracted by a normal distribution with mean value 1.0 and CoV equal to the passed range_CoV parameter.