slippy.surface.RandomPerezSurface

class slippy.surface.RandomPerezSurface(target_psd: numpy.ndarray, height_distribution: Optional[Union[scipy.stats._distn_infrastructure.rv_continuous, Sequence]] = None, accuracy: float = 0.001, max_it: int = 100, min_speed: float = 1e-10, generate: bool = False, grid_spacing: Optional[float] = None, exact: str = 'best')[source]

Surfaces with set height distribution and PSD found by the Perez method

Parameters

  • target_psd (np.ndarray) – The PSD which the surface will approximate, the shape of the surface will be the same as the psd array (the same number of points in each direction)

  • height_distribution ({scipy.stats.rv_continuous, sequence}) – Either a scipy.stats distribution or a sequence of the same size as the required output

  • accuracy (float, optional (1e-3)) – The accuracy required for the solution to be considered converged, see the notes of the discretise method for more information

  • max_it (int, optional (100)) – The maximum number of iterations used to discretise a realisation

  • min_speed (float, optional (1e-10)) – The minimum speed of the iterations, if the iterations are converging slower than this they are deemed not to converge

  • generate (bool, optional (False)) – If True the surface profile is found on instantiation

  • grid_spacing (float, optional (None)) – The distance between grid points on the surface

  • exact ({'psd', 'heights', 'best'}, optional ('best')) –

Notes

This method iterates between a surface with the exact right height distribution and one with the exact right PSD this method is not guaranteed to converge for all surfaces, for more details see the reference.

Examples

Making a surface with a normal height distribution and a given power spectra.

>>> import numpy as np
>>> import scipy.stats as stats
>>> import slippy.surface as s
>>> # making a surface with an exponential ACF as described in the original paper:
>>> beta = 10 # the drop off length of the acf
>>> sigma = 1 # the roughness of the surface
>>> qx = np.arange(-128,128)
>>> qy = np.arange(-128,128)
>>> Qx, Qy = np.meshgrid(qx,qy)
>>> Cq = sigma**2*beta/(2*np.pi*(beta**2+Qx**2+Qy**2)**0.5) # the PSD of the surface
>>> Cq = np.fft.fftshift(Cq)
>>> height_distribution = stats.norm()
>>> my_surface = s.RandomPerezSurface(target_psd = Cq, height_distribution=height_distribution,
>>>                                   grid_spacing=1,
>>>                                   generate=True)
>>> my_surface.show()

References

Based on the method and code given in:

Francesc Pérez-Ràfols, Andreas Almqvist, Generating randomly rough surfaces with given height probability distribution and power spectrum, Tribology International, Volume 131, 2019, Pages 591-604, ISSN 0301-679X, https://doi.org/10.1016/j.triboint.2018.11.020. (http://www.sciencedirect.com/science/article/pii/S0301679X18305607)

__init__(target_psd: numpy.ndarray, height_distribution: Optional[Union[scipy.stats._distn_infrastructure.rv_continuous, Sequence]] = None, accuracy: float = 0.001, max_it: int = 100, min_speed: float = 1e-10, generate: bool = False, grid_spacing: Optional[float] = None, exact: str = 'best')[source]

Methods

__init__(target_psd[, height_distribution, ...])

convert_coordinates(y_coord, x_coord)

discretise([return_new, accuracy, max_it, ...])

Discretise the surface with a realisation

find_summits([mask, four_nearest, ...])

Find summits after low pass filtering

get_acf([profile_in])

Find the auto correlation function of the surface

get_fft([profile_in])

Find the fourier transform of the surface

get_height_of_mat_vr(ratio[, void, mask, ...])

Find the height of a given material or void volume ratio

get_mat_vr(height[, void, mask, ratio])

Find the material or void volume ratio for a given height

get_points_from_extent([extent, ...])

Gets the grid points from the extent and the grid spacing

get_psd()

Find the power spectral density of the surface

get_summit_curvature([summits, mask, ...])

Get summit curvatures

interpolate(y_points, x_points[, mode, ...])

Easy memoized interpolation on surface objects

low_pass_filter(cut_off_freq[, return_copy])

Low pass FIR filter the surface profile

max_shape()

mesh(depth[, method, parameters])

Returns a Mesh object for the surface

resample([new_grid_spacing, return_profile, ...])

Resample or crop the profile by interpolation

roughness(parameter_name[, mask, ...])

Find areal roughness parameters

show([property_to_plot, plot_type, ax, ...])

Plot surface properties

subtract_polynomial(order[, mask])

Flatten the surface by subtracting a polynomial

wear(name, x_pts, y_pts, depth)

Add wear / geometry changes to the surface profile

Attributes

acf

The auto correlation function of the surface profile

dimensions

The number of spatial dimensions that

dist

extent

The overall dimensions of the surface in the same units as grid spacing

fft

The fast fourier transform of the surface

grid_spacing

The distance between grid points in the x and y directions

is_analytic

is_discrete

A bool flag, True if there is a profile present

mask

A mask used to exclude some values from analysis, a single float or an array of bool the same size as profile Either a boolean array of size self.size or a float of the value to be excluded

material

A material object describing the properties of the surface

moving_surface

profile

The height data for the surface profile

psd

The power spectral density of the surface

shape

The shape of the surface profile array, the number of points in each direction

size

The total number of points in the surface

surface_type

A description of the surface type

unworn_profile

wear_volumes