sdynpy.signal_processing.sdynpy_frf_inverse.pinv_by_tikhonov

• Module: sdynpy.signal_processing.sdynpy_frf_inverse

• Source: GitHub

Signature¶

def sdynpy.signal_processing.sdynpy_frf_inverse.pinv_by_tikhonov(frf_matrix, regularization_weighting_matrix=None, regularization_parameter=None)

Computes the pseudo-inverse of an FRF matrix via Tikhonov regularization

Parameters¶

• frf_matrix : NDArray Transfer function as an np.ndarray, should be organized such that the frequency is the first axis, the responses are the second axis, and the references are the third axis

• regularization_weighting_matrix : sdpy.Matrix or np.ndarray, optional Matrix used to weight input degrees of freedom in the regularization, the default is identity. This can be a 3D matrix such that the the weights are different for each frequency line. The matrix should be sized [number of lines, number of references, number of references], where the number of lines either be one (the same weights at all frequencies) or the length of the abscissa (for the case where a 3D matrix is supplied).

• regularization_parameter : float or np.ndarray, optional Scaling parameter used on the regularization weighting matrix. A vector of regularization parameters can be provided so the regularization is different at each frequency line. The vector must match the length of the abscissa in this case (either be size [num_lines,] or [num_lines, 1]).

Returns¶

• np.ndarray

• Inverse of the supplied FRF matrix

Raises¶

• Exception

• If a regularization parameter isn’t supplied

• Warning

• If a 2D regularization weighting matrix is supplied when a vector of regularization parameters is supplied

Notes¶

Tikhonov regularization is being done via the SVD method (details on Wikipedia or in the paper by Tithe and Thompson).

References¶

.. [1] A.N. Tithe, D.J. Thompson, The quantification of structure-borne transmission pathsby inverse methods. Part 2: Use of regularization techniques, Journal of Sound and Vibration, Volume 264, Issue 2, 2003, Pages 433-451, ISSN 0022-460X, Thite & Thompson (2003). .. [2] Wikipedia, “Ridge regression”. Ridge regression