The previous few research-oriented posts (e.g. 1, 2, 3) have been fairly critical of Tikhonov regularization in a specific machine learning application being developed. This post explains the source of the problems with integrating this form of regularization into the algorithm, and demonstrates its successful application.
In previous versions of the modal analysis algorithm performed the following regression:

However, when Tikhonov Regularization is integrated into this already regularized regression, it produces:
If, instead, we perform the regression:

Current work involves this regularization technique, and explores the benefits of higher dimensional measurements for retrieving information about the forcing function. Still other current work thoroughly examines various distance measures for eigenvalue estimates in the context of forcing function estimation.