sdynpy.signal_processing.sdynpy_frf_inverse.pinv_by_tikhonov

pinv_by_tikhonov(frf_matrix, regularization_weighting_matrix=None, regularization_parameter=None)[source]

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

Inverse of the supplied FRF matrix

Return type

np.ndarray

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, https://doi.org/10.1016/S0022-460X(02)01203-8.

2

Wikipedia, “Ridge regression”. https://en.wikipedia.org/wiki/Ridge_regression