Wave spectra

ffpack.lsm.waveSpectra.gaussianSwellSpectrum(w, wp, Hs, sigma)

Gaussian Swell spectrum, typically used to model long period swell seas [Guidance2016A].

Parameters

  • w (scalar) – Wave frequency.

  • wp (scalar) – Peak wave frequency.

  • Hs (scalar) – Significant wave height.

  • sigma (scalar) – peakedness parameter for Gaussian spectral width.

Returns

rst – The wave spectrum density value at wave frequency w.

Return type

scalar

Raises

ValueError – If w is not a scalar. If wp is not a scalar. If Hs is not a scalar. If sigma is not a scalar.

Examples

>>> from ffpack.lsm import gaussianSwellSpectrum
>>> w = 0.02
>>> wp = 0.51
>>> Hs = 20
>>> sigma = 0.07
>>> rst = gaussianSwellSpectrum( w, wp, Hs, sigma )

References

Guidance2016A

Guidance Notes on Selecting Design Wave by Long Term Stochastic Method

ffpack.lsm.waveSpectra.isscSpectrum(w, wp, Hs)

ISSC spectrum, also known as Bretschneider or modified Pierson-Moskowitz.

Parameters

  • w (scalar) – Wave frequency.

  • wp (scalar) – Peak wave frequency.

  • Hs (scalar) – Significant wave height.

Returns

rst – The wave spectrum density value at wave frequency w.

Return type

scalar

Raises

ValueError – If w is not a scalar. If wp is not a scalar. If Hs is not a scalar.

Examples

>>> from ffpack.lsm import isscSpectrum
>>> w = 0.02
>>> wp = 0.51
>>> Hs = 20
>>> rst = isscSpectrum( w, wp, Hs )
ffpack.lsm.waveSpectra.jonswapSpectrum(w, wp, alpha=0.0081, beta=1.25, gamma=3.3, g=9.81)

JONSWAP (Joint North Sea Wave Project) spectrum is an empirical relationship that defines the distribution of energy with frequency within the ocean.

Parameters

  • w (scalar) – Wave frequency.

  • wp (scalar) – Peak wave frequency.

  • alpha (scalar, optional) – Intensity of the Spectra.

  • beta (scalar, optional) – Shape factor, fixed value 1.25.

  • gamma (scalar, optional) – Peak enhancement factor.

  • g (scalar, optional) – Acceleration due to gravity, a constant. 9.81 m/s2 in SI units.

Returns

rst – The wave spectrum density value at wave frequency w.

Return type

scalar

Raises

ValueError – If w is not a scalar. If wp is not a scalar.

Examples

>>> from ffpack.lsm import jonswapSpectrum
>>> w = 0.02
>>> wp = 0.51
>>> rst = jonswapSpectrum( w, wp, alpha=0.0081, beta=1.25, gamma=3.3, g=9.81 )
ffpack.lsm.waveSpectra.ochiHubbleSpectrum(w, wp1, wp2, Hs1, Hs2, lambda1, lambda2)

Ochi-Hubble spectrum covers shapes of wave spectra associated with the growth and decay of a storm, including swells. [Guidance2016B].

Parameters

  • w (scalar) – Wave frequency.

  • wp1 (scalar) – Peak wave frequency.

  • wp2 (scalar) – Peak wave frequency.

  • Hs1 (scalar) – Significant wave height.

  • Hs2 (scalar) – Significant wave height.

  • lambda1 (scalar) –

  • lambda2 (scalar) –

Returns

rst – The wave spectrum density value at wave frequency w.

Return type

scalar

Raises

ValueError – If w is not a scalar. If wp1 or wp2 is not a scalar. If Hs1 or Hs2 is not a scalar. If lambda1 or lambda2 is not a scalar. If wp1 is not smaller than wp2.

Notes

Hs1 should normally be greater than Hs2 since most of the wave energy tends to be associated with the lower frequency component.

Examples

>>> from ffpack.lsm import ochiHubbleSpectrum
>>> w = 0.02
>>> wp1 = 0.4
>>> wp2 = 0.51
>>> Hs1 = 20
>>> Hs2 = 15
>>> lambda1 = 7
>>> lambda2 = 10
>>> rst = ochiHubbleSpectrum( w, wp1, wp2, Hs1, Hs2, lambda1, lambda2 )

References

Guidance2016B

Guidance Notes on Selecting Design Wave by Long Term Stochastic Method

ffpack.lsm.waveSpectra.piersonMoskowitzSpectrum(w, Uw, alpha=0.0081, beta=0.74, g=9.81)

Pierson Moskowitz spectrum is an empirical relationship that defines the distribution of energy with frequency within the ocean.

Parameters

  • w (scalar) – Wave frequency.

  • Uw (scalar) – Wind speed at a height of 19.5m above the sea surface.

  • alpha (scalar, optional) – Intensity of the Spectra.

  • beta (scalar, optional) – Shape factor.

  • g (scalar, optional) – Acceleration due to gravity, a constant. 9.81 m/s2 in SI units.

Returns

rst – The wave spectrum density value at wave frequency w.

Return type

scalar

Raises

ValueError – If w is not a scalar. If wp is not a scalar.

Examples

>>> from ffpack.lsm import piersonMoskowitzSpectrum
>>> w = 0.51
>>> Uw = 20
>>> rst = piersonMoskowitzSpectrum( w, Uw, alpha=0.0081,
...                                 beta=1.25, g=9.81 )

Wind spectra

ffpack.lsm.windSpectra.apiSpectrum(f, u0, z=10)

API spectrum is implemented according to [API2007].

Parameters

  • f (scalar) – Frequency ( Hz ).

  • u0 (scalar) – 1 hour mean wind speed ( m/s ) at 10 m above sea level.

Returns

rst – Power spectrum density ( m^2 s^-2 Hz^-1 ).

Return type

scalar

Raises

ValueError – If n is not a scalar. If uz is not a scalar.

Examples

>>> from ffpack.lsm import apiSpectrum
>>> f = 2
>>> u0 = 10
>>> rst = apiSpectrum( f, u0 )

References

API2007

API, 2007. Recommended practice 2A-WSD (RP 2A-WSD): Recommnded practice for planning, designing and constructing fixed offshore platforms - working stress design.

ffpack.lsm.windSpectra.davenportSpectrumWithDragCoef(n, delta1, kappa=0.005, normalized=True)

Davenport spectrum in the original paper by Davenport [Davenport1961].

Parameters

  • n (scalar) – Frequency ( Hz ) when normalized=False. Normalized frequency when normalized=True.

  • delta1 (scalar) – Velocity ( m/s ) at standard reference height of 10 m.

  • kappa (scalar, optional) – Drag coefficient referred to mean velocity at 10 m. Default value 0.005 corresponding to open unobstructed country [Davenport1961]. The recommended value for heavilly built-up urban centers with tall buildings is 0.05. The recommended value for country broken by low clustered obstructions is between 0.015 and 0.02.

  • normalized (bool, optional) – If normalized is set to False, the power spectrum density will be returned.

Returns

rst – Power spectrum density ( m^2 s^-2 Hz^-1 ) when normalized=False. Normalized power spectrum density when normalized=True.

Return type

scalar

Raises

ValueError – If n is not a scalar. If delta1 is not a scalar.

Examples

>>> from ffpack.lsm import davenportSpectrumWithDragCoef
>>> n = 2
>>> delta1 = 10
>>> rst = davenportSpectrumWithDragCoef( n, delta1, kappa=0.005,
...                                      normalized=True )

References

Davenport1961(1,2)

Davenport, A.G., 1961. The spectrum of horizontal gustiness near the ground in high winds. Quarterly Journal of the Royal Meteorological Society, 87(372), pp.194-211.

ffpack.lsm.windSpectra.davenportSpectrumWithRoughnessLength(n, uz, z=10, z0=0.03, normalized=True)

Davenport spectrum in the paper by Hiriart et al. [Hiriart2001].

Parameters

  • n (scalar) – Frequency ( Hz ) when normalized=False. Normalized frequency when normalized=True.

  • uz (scalar) – Mean wind speed ( m/s ) measured at height z.

  • z (scalar, optional) – Height above the ground ( m ), default to 10 m.

  • z0 (scalar, optional) – Roughness length ( m ), default to 0.03 m corresponding to open exposure case in [Ho2003].

  • normalized (bool, optional) – If normalized is set to False, the power spectrum density will be returned.

Returns

rst – Power spectrum density ( m^2 s^-2 Hz^-1 ) when normalized=False. Normalized power spectrum density when normalized=True.

Return type

scalar

Raises

ValueError – If n is not a scalar. If uz is not a scalar.

Examples

>>> from ffpack.lsm import davenportSpectrumWithRoughnessLength
>>> n = 2
>>> uz = 10
>>> rst = davenportSpectrumWithRoughnessLength( n, uz, z=10, z0=0.03,
...                                             normalized=True )

References

Hiriart2001

Hiriart, D., Ochoa, J.L. and Garcia, B., 2001. Wind power spectrum measured at the San Pedro Mártir Sierra. Revista Mexicana de Astronomia y Astrofisica, 37(2), pp.213-220.

Ho2003

Ho, T.C.E., Surry, D. and Morrish, D.P., 2003. NIST/TTU cooperative agreement-windstorm mitigation initiative: Wind tunnel experiments on generic low buildings. London, Canada: BLWTSS20-2003, Boundary-Layer Wind Tunnel Laboratory, Univ. of Western Ontario.

ffpack.lsm.windSpectra.ec1Spectrum(n, uz, sigma=0.03, z=10, tcat=0, normalized=True)

EC1 spectrum is implemented according to Annex B [EN1991-1-42005].

Parameters

  • n (scalar) – Frequency ( Hz ) when normalized=False. Normalized frequency when normalized=True.

  • uz (scalar) – Mean wind speed ( m/s ) measured at height z.

  • sigma (scalar, optional) – Standard derivation of wind.

  • z (scalar, optional) – Height above the ground ( m ), default to 10 m.

  • tcat (scalar, optional) – Terrain category, could be 0, 1, 2, 3, 4 Default to 0 (sea or coastal area exposed to the open sea) in EC1 Table 4.1.

  • normalized (bool, optional) – If normalized is set to False, the power spectrum density will be returned.

Returns

rst – Power spectrum density ( m^2 s^-2 Hz^-1 ) when normalized=False. Normalized power spectrum density when normalized=True.

Return type

scalar

Raises

ValueError – If n is not a scalar. If uz is not a scalar. If tcat is not int or not within range of 0 to 4

Examples

>>> from ffpack.lsm import ec1Spectrum
>>> n = 2
>>> uz = 10
>>> rst = ec1Spectrum( n, uz, sigma=0.03, z=10, tcat=0, normalized=True )

References

EN1991-1-42005

EN1991-1-4, 2005. Eurocode 1: Actions on structures.

ffpack.lsm.windSpectra.iecSpectrum(f, vhub, sigma=0.03, z=10, k=1, normalized=True)

IEC spectrum is implemented according to [IEC2005].

Parameters

  • f (scalar) – Frequency ( Hz ) when normalized=False. Normalized frequency when normalized=True.

  • vhub (scalar) – Mean wind speed ( m/s ).

  • sigma (scalar, optional) – Standard derivation of the turblent wind speed component.

  • z (scalar, optional) – Height above the ground ( m ), default to 10 m.

  • k (scalar, optional) – Wind speed direction, could be 1, 2, 3 ( 1 = longitudinal, 2 = lateral, and 3 = upward ) Default to 1 (longitudinal).

  • normalized (bool, optional) – If normalized is set to False, the power spectrum density will be returned.

Returns

rst – Single-sided velocity component power spectrum density ( m^2 s^-2 Hz^-1 ) when normalized=False. Normalized single-sided velocity component power spectrum density when normalized=True.

Return type

scalar

Raises

ValueError – If n is not a scalar. If uz is not a scalar. If k is not int or not within range of 1 to 3

Examples

>>> from ffpack.lsm import iecSpectrum
>>> n = 2
>>> vhub = 10
>>> rst = iecSpectrum( n, vhub, sigma=0.03, z=10, k=1, normalized=True )

References

IEC2005

IEC, 2005. IEC 61400-1, Wind turbines - Part 1: Design requirements.

Sequence spectra

ffpack.lsm.sequenceSpectra.periodogramSpectrum(data, fs)

Power spectral density with scipy.signal.periodogram.

Parameters

  • data (1darray) – Sequence to calculate power spectral density.

  • fs (scalar) – Sampling frequency.

Returns

  • freq (1darray) – frequency components.

  • psd (1darray) – Power spectral density.

Raises

ValueError – If data is not a 1darray. If fs is not a scalar.

Examples

>>> from ffpack.lsm import periodogramSpectrum
>>> data = [ 2, 5, 3, 6, 2, 4, 1, 6, 1, 3, 1, 5, 3, 6, 3, 6, 4, 5, 2 ]
>>> fs = 2
>>> freq, psd = periodogramSpectrum( data, fs )
ffpack.lsm.sequenceSpectra.welchSpectrum(data, fs, nperseg=1024)

Power spectral density with scipy.signal.welch.

Parameters

  • data (1darray) – Sequence to calculate power spectral density.

  • fs (scalar) – Sampling frequency.

  • nperseg (scalar) – Length of each segment. Defaults to 1024.

Returns

  • freq (1darray) – frequency components.

  • psd (1darray) – Power spectral density.

Raises

ValueError – If data is not a 1darray. If fs is not a scalar.

Examples

>>> from ffpack.lsm import welchSpectrum
>>> data = [ 2, 5, 3, 6, 2, 4, 1, 6, 1, 3, 1, 5, 3, 6, 3, 6, 4, 5, 2 ]
>>> fs = 2
>>> freq, psd = welchSpectrum( data, fs, nperseg=1024 )

Cycle counting matrix

ffpack.lsm.cycleCountingMatrix.astmRainflowCountingMatrix(data, resolution=0.5)

Calculate ASTM rainflow counting matrix.

Parameters

  • data (1d array) – Sequence data to calculate rainflow counting matrix.

  • resolution (bool, optional) – The desired resolution to round the data points.

Returns

  • rst (2d array) – A matrix contains the counting results.

  • matrixIndexKey (1d array) – A sorted array contains the index keys for the counting matrix.

Raises

ValueError – If the data dimension is not 1. If the data length is less than 2.

Notes

The default round function will round half to even: 1.5, 2.5 => 2.0:

Examples

>>> from ffpack.lsm import astmRainflowCountingMatrix
>>> data = [ -2.0, 1.0, -3.0, 5.0, -1.0, 3.0, -4.0, 4.0, -2.0 ]
>>> rst, matrixIndexKey = astmRainflowCountingMatrix( data )
ffpack.lsm.cycleCountingMatrix.astmRainflowRepeatHistoryCountingMatrix(data, resolution=0.5)

Calculate ASTM simplified rainflow counting matrix for repeating histories.

Parameters

  • data (1d array) – Sequence data to calculate simplified rainflow counting matrix for repeating histories.

  • resolution (bool, optional) – The desired resolution to round the data points.

Returns

  • rst (2d array) – A matrix contains the counting results.

  • matrixIndexKey (1d array) – A sorted array contains the index keys for the counting matrix.

Raises

ValueError – If the data dimension is not 1. If the data length is less than 2.

Notes

The default round function will round half to even: 1.5, 2.5 => 2.0:

Examples

>>> from ffpack.lsm import astmRainflowRepeatHistoryCountingMatrix
>>> data = [ -2.0, 1.0, -3.0, 5.0, -1.0, 3.0, -4.0, 4.0, -2.0 ]
>>> rst, matrixIndexKey = astmRainflowRepeatHistoryCountingMatrix( data )
ffpack.lsm.cycleCountingMatrix.astmRangePairCountingMatrix(data, resolution=0.5)

Calculate ASTM range pair counting matrix.

Parameters

  • data (1d array) – Sequence data to calculate range pair counting matrix.

  • resolution (bool, optional) – The desired resolution to round the data points.

Returns

  • rst (2d array) – A matrix contains the counting results.

  • matrixIndexKey (1d array) – A sorted array contains the index keys for the counting matrix.

Raises

ValueError – If the data dimension is not 1. If the data length is less than 2.

Notes

The default round function will round half to even: 1.5, 2.5 => 2.0:

Examples

>>> from ffpack.lsm import astmRangePairCountingMatrix
>>> data = [ -2.0, 1.0, -3.0, 5.0, -1.0, 3.0, -4.0, 4.0, -2.0 ]
>>> rst, matrixIndexKey = astmRangePairCountingMatrix( data )
ffpack.lsm.cycleCountingMatrix.astmSimpleRangeCountingMatrix(data, resolution=0.5)

Calculate ASTM simple range counting matrix.

Parameters

  • data (1d array) – Sequence data to calculate range counting matrix.

  • resolution (bool, optional) – The desired resolution to round the data points.

Returns

  • rst (2d array) – A matrix contains the counting results.

  • matrixIndexKey (1d array) – A sorted array contains the index keys for the counting matrix.

Raises

ValueError – If the data dimension is not 1. If the data length is less than 2.

Notes

The default round function will round half to even: 1.5, 2.5 => 2.0.

Examples

>>> from ffpack.lsm import astmSimpleRangeCountingMatrix
>>> data = [ -2.0, 1.0, -3.0, 5.0, -1.0, 3.0, -4.0, 4.0, -2.0 ]
>>> rst, matrixIndexKey = astmSimpleRangeCountingMatrix( data )
ffpack.lsm.cycleCountingMatrix.fourPointCountingMatrix(data, resolution=0.5)

Calculate Four point cycle counting matrix.

Parameters

  • data (1d array) – Sequence data to calculate rainflow counting matrix.

  • resolution (bool, optional) – The desired resolution to round the data points.

Returns

  • rst (2d array) – A matrix contains the counting results.

  • matrixIndexKey (1d array) – A sorted array contains the index keys for the counting matrix.

Raises

ValueError – If the data dimension is not 1. If the data length is less than 2.

Notes

The default round function will round half to even: 1.5, 2.5 => 2.0:

Examples

>>> from ffpack.lsm import fourPointCountingMatrix
>>> data = [ -2.0, 1.0, -3.0, 5.0, -1.0, 3.0, -4.0, 4.0, -2.0 ]
>>> rst, matrixIndexKey = fourPointCountingMatrix( data )
ffpack.lsm.cycleCountingMatrix.johannessonMinMaxCountingMatrix(data, resolution=0.5)

Calculate Johannesson minMax cycle counting matrix.

Parameters

  • data (1d array) – Sequence data to calculate rainflow counting matrix.

  • resolution (bool, optional) – The desired resolution to round the data points.

Returns

  • rst (2d array) – A matrix contains the counting results.

  • matrixIndexKey (1d array) – A sorted array contains the index keys for the counting matrix.

Raises

ValueError – If the data dimension is not 1. If the data length is less than 2.

Notes

The default round function will round half to even: 1.5, 2.5 => 2.0:

Examples

>>> from ffpack.lsm import johannessonMinMaxCountingMatrix
>>> data = [ -2.0, 1.0, -3.0, 5.0, -1.0, 3.0, -4.0, 4.0, -2.0 ]
>>> rst, matrixIndexKey = johannessonMinMaxCountingMatrix( data )
ffpack.lsm.cycleCountingMatrix.rychlikRainflowCountingMatrix(data, resolution=0.5)

Calculate Rychlik rainflow counting matrix.

Parameters

  • data (1d array) – Sequence data to calculate rainflow counting matrix.

  • resolution (bool, optional) – The desired resolution to round the data points.

Returns

  • rst (2d array) – A matrix contains the counting results.

  • matrixIndexKey (1d array) – A sorted array contains the index keys for the counting matrix.

Raises

ValueError – If the data dimension is not 1. If the data length is less than 2.

Notes

The default round function will round half to even: 1.5, 2.5 => 2.0:

Examples

>>> from ffpack.lsm import rychlikRainflowCountingMatrix
>>> data = [ -2.0, 1.0, -3.0, 5.0, -1.0, 3.0, -4.0, 4.0, -2.0 ]
>>> rst, matrixIndexKey = rychlikRainflowCountingMatrix( data )