pyrvt.motions¶

Random vibration theory (RVT) based motions.

The module attribute DEFAULT_CALC is used to control the default peak factor calculator is one is not provided when a class is initialized.

pyrvt.motions.sort_increasing(*args)[source]

Sort arrays such that they are increasing.

Check if the first array is is increasing, if not reverse the order. Same operation is applied to additional arrays.

Parameters:: *args (array_like) – arrays to be re-ordered.
Returns:: tuple containing sorted numpy.ndarray’s.
Return type:: tuple
Raises:: NotImplementedError – If first array is not monotonic.

pyrvt.motions.log_spaced_values(lower, upper, per_decade=512)[source]

Generate values with constant log-spacing.

Parameters:

lower (float) – lower end of the range.
upper (float) – upper end of the range.
per_decade (int, optional) – number of points per decade. Default is 512 points per decade.

Returns:

values – Log-spaced values.

Return type:

numpy.ndarray

pyrvt.motions.calc_sdof_tf(freqs, osc_freq, osc_damping)[source]

Single-degree-of-freedom transfer function.

When applied on the acceleration Fourier amplitude spectrum, it provides the pseudo-spectral acceleration.

Parameters:

freqs (array_like) – Frequencies at which the transfer function should be calculated (Hz).
osc_freq (float) – Frequency of the oscillator (Hz).
osc_damping (float) – Fractional damping of the oscillator (decimal).

Returns:

Complex valued transfer function.

Return type:

numpy.ndarray

class pyrvt.motions.RvtMotion(freqs=None, fourier_amps=None, duration=None, peak_calculator=None, calc_kwds=None)[source]

Bases: object

Random vibration theory motion.

Parameters:

freqs (array_like, optional) – Frequency array (Hz).
fourier_amps (array_like, optional) – Absolute value of acceleration Fourier amplitudes.
duration (float, optional) – Ground motion duration (sec).
peak_calculator (Calculator, optional) – Peak calculator to use. If None, then the default peak calculator is used. The peak calculator may either be specified by a [pyrvt.peak_calculators.Calculator][] instance, or created by the abbreviation of the calculator using [pyrvt.peak_calculators.get_peak_calculator][].
calc_kwds (dict, optional) – Keywords to be passed during the creation the peak calculator. These keywords are only required for some peak calculators.

__init__(freqs=None, fourier_amps=None, duration=None, peak_calculator=None, calc_kwds=None)[source]

Initialize the class.

Parameters:

freqs (ArrayLike | None)
fourier_amps (ArrayLike | None)
duration (float | None)
peak_calculator (str | Calculator | None)
calc_kwds (dict | None)

Return type:

None

property freqs: ndarray: Frequency values (Hz).

property fourier_amps: ndarray: Acceleration Fourier amplitude values (g-sec).

property duration: float: Duration of the ground motion for RVT analysis.

classmethod from_fas(fas, peak_calculator=None, calc_kwds=None)[source]

Build an RvtMotion from any object exposing a Fourier-spectrum shape.

Parameters:

fas (object) – Any object exposing freqs [Hz], fourier_amps [g-sec], and duration [sec] attributes (e.g. an instance of a pygmm.fourier_spectrum model, or a pygmm.contracts.FourierSpectrum dataclass).
peak_calculator (str | Calculator | None) – Forwarded to RvtMotion.
calc_kwds (dict | None) – Forwarded to RvtMotion.

Return type:

RvtMotion

calc_osc_accels(osc_freqs, osc_damping=0.05, trans_func=None)[source]

Pseudo-acceleration spectral response of an oscillator.

Parameters:

osc_freqs (float) – Frequency of the oscillator (Hz).
osc_damping (float) – Fractional damping of the oscillator (dec). For example, 0.05 for a damping ratio of 5%.
trans_func (array_like, optional) – Transfer function to be applied to motion prior calculation of the oscillator response.

Returns:

spec_accels – Peak pseudo-spectral acceleration of the oscillator

Return type:

numpy.ndarray

property angular_freqs: ndarray: Angular frequency values (rad/sec).

property pgv: float: Peak ground velocity (cm/sec).

property pga: float: Peak ground acceleration (g).

property arias_intensity: float: Arias intensity (m/s).

property cav: float: Cumulative absolute velocity (m/s).

calc_pgv(tf=None)[source]

Compute the peak ground velocity.

Parameters:: tf (array_like, optional) – Transfer function to apply to the motion. If None, no transfer function is applied.
Returns:: pgv – Peak ground velocity (cm/sec).
Return type:: float

calc_pga(tf=None)[source]

Compute the peak ground acceleration.

Parameters:: tf (array_like, optional) – Transfer function to apply to the motion. If None, no transfer function is applied.
Returns:: pga – Peak ground acceleration (g).
Return type:: float

calc_arias_intensity(tf=None)[source]

Compute the Arias intensity.

Parameters:: tf (array_like, optional) – Transfer function to apply to the motion. If None, no transfer function is applied.
Returns:: arias_intensity – Arias intensity (m/s).
Return type:: float

calc_cav(tf=None)[source]

Compute the cumulative absolute velocity (CAV).

Uses an empirical regression on Arias intensity and duration based on observed ground motions.

Parameters:: tf (array_like, optional) – Transfer function to apply to the motion. If None, no transfer function is applied.
Returns:: cav – Cumulative absolute velocity (m/s).
Return type:: float

calc_peak(transfer_func=None, **kwds)[source]

Compute the peak response.

Parameters:: transfer_func (array_like, optional) – Transfer function to apply to the motion. If None, then no transfer function is applied.
Returns:: peak – Calculated peak
Return type:: float

calc_attenuation(min_freq, max_freq=None)[source]

Compute the site attenuation (κ) based on a log-linear fit.

Parameters:

min_freq (float) – minimum frequency of the fit (Hz).
max_freq (float, optional) – maximum frequency of the fit. If None, then the maximum frequency range is used.

Returns:

atten (float) – attenuation parameter.
r_sqr (float) – squared correlation coefficient of the fit (R²). See scipy.stats.linregress.
freqs (array_like) – selected frequencies
fitted (array_like) – fitted values

Return type:

tuple[float, float, ndarray, ndarray]

Notes

This function computes the site attenuation defined by Anderson & Hough (1984) [@anderson84] as:

$$ a(f) = A_0 exp(-pi kappa f) text( for ) f > f_E $$

for a single Fourier amplitude spectrum

class pyrvt.motions.CompatibleRvtMotion(osc_freqs, osc_accels_target, duration, osc_damping=0.05, window_len=None, peak_calculator=None, calc_kwds=None)[source]

Bases: RvtMotion

Response spectrum compatible RVT motion.

A [CompatibleRvtMotion][pyrvt.motions.CompatibleRvtMotion] object is used to compute a Fourier amplitude spectrum that is compatible with a target response spectrum.

Parameters:

osc_freqs (npt.ArrayLike)
osc_accels_target (npt.ArrayLike)
duration (float)
osc_damping (float)
window_len (int | None)
peak_calculator (str | peak_calculators.Calculator | None)
calc_kwds (dict | None)

property angular_freqs: ndarray: Angular frequency values (rad/sec).

property arias_intensity: float: Arias intensity (m/s).

calc_arias_intensity(tf=None)

Compute the Arias intensity.

Parameters:: tf (array_like, optional) – Transfer function to apply to the motion. If None, no transfer function is applied.
Returns:: arias_intensity – Arias intensity (m/s).
Return type:: float

calc_attenuation(min_freq, max_freq=None)

Compute the site attenuation (κ) based on a log-linear fit.

Parameters:

min_freq (float) – minimum frequency of the fit (Hz).
max_freq (float, optional) – maximum frequency of the fit. If None, then the maximum frequency range is used.

Returns:

atten (float) – attenuation parameter.
r_sqr (float) – squared correlation coefficient of the fit (R²). See scipy.stats.linregress.
freqs (array_like) – selected frequencies
fitted (array_like) – fitted values

Return type:

tuple[float, float, ndarray, ndarray]

Notes

This function computes the site attenuation defined by Anderson & Hough (1984) [@anderson84] as:

$$ a(f) = A_0 exp(-pi kappa f) text( for ) f > f_E $$

for a single Fourier amplitude spectrum

calc_cav(tf=None)

Compute the cumulative absolute velocity (CAV).

Uses an empirical regression on Arias intensity and duration based on observed ground motions.

Parameters:: tf (array_like, optional) – Transfer function to apply to the motion. If None, no transfer function is applied.
Returns:: cav – Cumulative absolute velocity (m/s).
Return type:: float

calc_osc_accels(osc_freqs, osc_damping=0.05, trans_func=None)

Pseudo-acceleration spectral response of an oscillator.

Parameters:

osc_freqs (float) – Frequency of the oscillator (Hz).
osc_damping (float) – Fractional damping of the oscillator (dec). For example, 0.05 for a damping ratio of 5%.
trans_func (array_like, optional) – Transfer function to be applied to motion prior calculation of the oscillator response.

Returns:

spec_accels – Peak pseudo-spectral acceleration of the oscillator

Return type:

numpy.ndarray

calc_peak(transfer_func=None, **kwds)

Compute the peak response.

Parameters:: transfer_func (array_like, optional) – Transfer function to apply to the motion. If None, then no transfer function is applied.
Returns:: peak – Calculated peak
Return type:: float

calc_pga(tf=None)

Compute the peak ground acceleration.

Parameters:: tf (array_like, optional) – Transfer function to apply to the motion. If None, no transfer function is applied.
Returns:: pga – Peak ground acceleration (g).
Return type:: float

calc_pgv(tf=None)

Compute the peak ground velocity.

Parameters:: tf (array_like, optional) – Transfer function to apply to the motion. If None, no transfer function is applied.
Returns:: pgv – Peak ground velocity (cm/sec).
Return type:: float

property cav: float: Cumulative absolute velocity (m/s).

property duration: float: Duration of the ground motion for RVT analysis.

property fourier_amps: ndarray: Acceleration Fourier amplitude values (g-sec).

property freqs: ndarray: Frequency values (Hz).

classmethod from_fas(fas, peak_calculator=None, calc_kwds=None)

Build an RvtMotion from any object exposing a Fourier-spectrum shape.

Parameters:

fas (object) – Any object exposing freqs [Hz], fourier_amps [g-sec], and duration [sec] attributes (e.g. an instance of a pygmm.fourier_spectrum model, or a pygmm.contracts.FourierSpectrum dataclass).
peak_calculator (str | Calculator | None) – Forwarded to RvtMotion.
calc_kwds (dict | None) – Forwarded to RvtMotion.

Return type:

RvtMotion

property pga: float: Peak ground acceleration (g).

property pgv: float: Peak ground velocity (cm/sec).

__init__(osc_freqs, osc_accels_target, duration, osc_damping=0.05, window_len=None, peak_calculator=None, calc_kwds=None)[source]

Initialize the motion.

Parameters:

osc_freqs (array_like) – Frequencies of the oscillator response (Hz).
osc_accels_target (array_like) – Spectral acceleration of the oscillator at the specified frequencies (g).
duration (float) – Duration of the ground motion (sec).
osc_damping (float, optional) – Fractional damping of the oscillator (dec). Default value is 0.05 for a damping ratio of 5%.
window_len (int, optional) – Window length used for smoothing the computed Fourier amplitude spectrum. If None, then no smoothing is applied. The smoothing is applied as a moving average with a width of window_len.
peak_calculator (Calculator, optional) – Peak calculator to use. If None, then the default peak calculator is used. The peak calculator may either be specified by a [pyrvt.peak_calculators.Calculator][] object, or by the initials of the calculator using [pyrvt.peak_calculators.get_peak_calculator][].
calc_kwds (dict, optional) – Keywords to be passed during the creation the peak calculator. These keywords are only required for some peak calculators.

Return type:

None

classmethod from_response_spectrum(rs, duration, **kw)[source]

Create from any object with .periods, .spec_accels, .damping.

Duck-typed: accepts pygmm.contracts.ResponseSpectrum or any object with the same attributes.

Parameters:

rs – Response spectrum with .periods [s], .spec_accels [g], and .damping [decimal].
duration (float) – Ground-motion duration [s].
**kw – Forwarded to CompatibleRvtMotion (e.g. peak_calculator).

Return type:

CompatibleRvtMotion