Multiplicative regularization

This paper implements a generalized multiplicative regularization for estimating the mechanical loads acting on a linear structure. The proposed strategy extends the ordinary multiplicative regularization, previously published by the authors, by introducing an extra tuning parameter, which is determined through an original iterative procedure...

In a paper, recently published in Mechanical Systems and Signal Processing, a multiplicative mixed-norm regularization has been introduced for solving space-frequency force reconstruction problems. Originally, the solution is obtained from an Iteratively Reweighted Least-Squares (IRLS) algorithm. However, as shown in this communication, such an algorithm exhibits a lack of robustness regarding the measurement noise level...

This paper introduces a multi-parameter multiplicative regularization for force reconstruction problems. This approach allows exploiting the local prior information available on the sources to identify, while determining the related regularization parameters in an elegant and efficient manner...

The multiplicative ℓ_q-regularization has been recently introduced in structural dynamics for solving force reconstruction problems. Practically, the resolution of this regularization strategy requires the implementation of an iterative procedure...

In time domain, force reconstruction problems are commonly solved from Tikhonov and LASSO regularizations. Practically, these approaches can lead to inaccurate reconstructions, if the sources to identify don't share the same space-time characteristics or the corresponding force vector doesn't exhibit the desired structure...

Tikhonov and LASSO regularizations are commonly used to solve force reconstruction problems in time domain. Unfortunately, these particular forms of additive regularization are not well adapted to tackle both localization and time reconstruction problems simultaneously, since they are generally restricted to the reconstruction of sources sharing the same space and time characteristics...

In presence of very noisy data, standard regularization methods generally fail in reconstructing satisfying solutions. To this end, iterated regularization techniques can be implemented. This class of regularization approaches can be seen as an iterative refinement of an initial solution obtained from classical regularization methods...

Dynamic forces reconstruction from vibration data is an ill-posed inverse problem. A standard approach to stabilize the reconstruction consists in using some prior information on the quantities to identify. This is generally done by including in the formulation of the inverse problem a regularization term as an additive or a multiplicative constraint...

Iterated Tikhonov regularization can be seen as an iterative refinement of an initial solution obtained by applying the standard Tikhonov regularization. This kind of approach is particularly suited when noisy data with low signal-to-noise ratio (SNR) are to be used...

We have recently proposed a multiplicative regularization to reconstruct mechanical forces acting on a structure from vibration measurements. This method does not require any selection procedure for choosing the regularization parameter, since the amount of regularization is automatically adjusted throughout an iterative resolution process...