mean phase deviation (MPD) indicator

[Ayubirad]

Dear @twmacro

Please have look at the following paper and the mean phase deviation (MPD) indicator. I think it is a useful measure alongside other modal indicators to distinguish physical modes (generally MPD < 0.3 is good):

Here's the code to implement MPD:

def mean_phase_deviation(u):
    """Mean phase deviation of mode vector u

    Mean phase deviation (MPD) is the deviation in phase from the mean
    phase and is a measure of mode shape complexity.

    Arguments
    ---------
    u : 1darray[complex]
        Mode shape vector

    Returns
    -------
    float
        Mean phase deviation of the mode vector

    References
    ----------
    [Reynders2012] Reynders, E., Houbrechts, J., De Roeck, G., 2012.
        Fully automated (operational) modal analysis. Mechanical
        Systems and Signal Processing 29, 228–250.
        https://doi.org/10.1016/j.ymssp.2012.01.007
    """
    u = np.asarray(u)
    U, s, VT = np.linalg.svd(np.c_[u.real, u.imag])
    V = VT.T
    w = np.abs(u)
    num = u.real*V[1, 1] - u.imag*V[0, 1]
    den = np.sqrt(V[0, 1]**2+V[1, 1]**2)*np.abs(u)
    return np.sum(w*np.arccos(np.abs(num/den))) / np.sum(w)

Best regards,
Ayubirad

[twmacro]

Thank you very much, @Ayubirad! I have the paper now, and I'll definitely check it out. :-)

Best regards,
Tim

[dfdffbdf]

Thank you