The frequencysignal module#

Handle frequency-domain stress signals for pyLife workflows.

Provide helpers for smoothing frequency-indexed power spectral densities before spectral comparison or frequency-domain fatigue assessment.

Warning

This module is not considered finalized even though it is part of pylife-2.0. Breaking changes might occur in upcoming minor releases.

class pylife.stress.frequencysignal.psdSignal(df)[source]#

Handle routines for frequency-indexed PSD signals.

The class stores a pandas data frame schema where the index is a frequency index in Hz and each column contains one power spectral density, e.g. in MPa²/Hz for a stress signal. The current methods are also used as legacy unbound helpers with a pandas.DataFrame as self.

Parameters:

df (pandas.DataFrame) – Frequency-domain signal with frequency index in Hz and PSD columns.

Notes

The RMS value follows the one-sided PSD convention

\[x_\mathrm{rms} = \sqrt{\int_0^\infty S_{xx}(f)\,df}.\]

Examples

>>> from pylife.stress.frequencysignal import psdSignal
>>> psd = pd.DataFrame({"stress": [1.0, 1.0]}, index=[1.0, 2.0])
>>> round(float(psdSignal.rms_psd(psd).iloc[0]), 6)
1.0
psd_smoother(fsel, factor_rms_nodes=0.5)[source]#

Smooth a PSD by optimizing values at selected frequency nodes.

Replace a dense frequency-indexed PSD by a compact node-based representation. The optimization balances preservation of the RMS value against preservation of the PSD values at the selected nodes.

Parameters:

  • fsel (array_like) – Frequency nodes in Hz used for the smoothed PSD.

  • factor_rms_nodes (float, optional) – Weighting factor between node-value error and RMS error. 0 considers only the error of node PSD values, while 1 considers only the RMS error. Default is 0.5.

Returns:

Smoothed PSD with frequency index in Hz. The index contains the original minimum frequency, unique selected nodes, and the original maximum frequency.

Return type:

pandas.DataFrame

Notes

For every input column, the optimized node PSD values minimize

\[\alpha \frac{(r_\mathrm{in} - r_\mathrm{smooth})^2} {r_\mathrm{in}^2} + (1 - \alpha) \frac{\lVert \log_{10}(S_\mathrm{node}/H) \rVert^2} {\lVert \log_{10}(S_\mathrm{node}) \rVert^2},\]

where \(\alpha\) is factor_rms_nodes and \(H\) are the optimized node values.

rms_psd()[source]#

Compute the RMS value of every PSD column.

Returns:

Root mean square value of each column, in the unit of the square root of the PSD unit times Hz, e.g. MPa for a stress PSD given in MPa²/Hz. The index holds the original column names.

Return type:

pandas.Series

Notes

The PSD is first resampled onto 2048 logarithmically spaced frequency points between the smallest and the largest frequency of the index and then integrated with the trapezoidal rule,

\[x_\mathrm{rms} = \sqrt{\int_{f_\mathrm{min}}^{f_\mathrm{max}} S_{xx}(f)\,df}.\]

Examples

>>> from pylife.stress.frequencysignal import psdSignal
>>> psd = pd.DataFrame({"stress": [1.0, 1.0]}, index=[1.0, 2.0])
>>> round(float(psdSignal.rms_psd(psd).iloc[0]), 6)
1.0