An iterated multiplicative regularization for force reconstruction problems

Aucejo, Mathieu; Smet, Olivier de

doi:10.1016/j.jsv.2018.09.020

Cited by 6 publications

(7 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is in general no closed-form solution to problem P2. 5 However, several analytical results can be obtained when X and N are distributed according to a generalized Gaussian. From now on, the Gaussian case will be considered only, as it contains the essence of the idea (the generalized Gaussian case will be briefly addressed in section 5.1).…”

Section: Mmap Estimatementioning

confidence: 99%

“…This is recognized equal to the square-root L-curve defined with scaling function f = √ in equation (5). The associated optimal regularization parameter is…”

Section: L-curve With Inverse Gamma Priorsmentioning

confidence: 99%

“…The L-curve is a plot of the norm of the residuals with respect to the norm of the solution as a function of the regularization parameter. Specifically, upon introducing some monotonically increasing scale function f, it is the curve γ defined by the parametric equation γ : R + → R 2 ; λ → γ = ζ(λ) = f(T(X(λ))) η(λ) = f(U(X(λ))), (5) with X(λ) as defined in equation (4).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Bayesian interpretation of the L-curve

Antoni¹,

Idier²,

Bourguignon³

2023

Inverse Problems

View full text Add to dashboard Cite

The L-curve is a popular heuristic to tune Tikhonov regularization in linear inverse problems. This paper shows how it naturally arises when the problem is solved from a Bayesian perspective. Specifically, it establishes that the L-curve is a graphical way of searching for the maximum aposteriori solution after marginalization over the priors. The framework is general enough to enclose the classical (linear, logarithmic and square-root) L-curves as particular cases and to allow the design of new L-curves. It also explicitly accounts for the dimensions of the inverse problem (number of observations versus number of unknowns) in regularization. Elaborating on this framework, new criteria for locating the corner of the L-curve are discovered, such as the ``minimum speed on the curve'' and the ``maximum angular speed'', and conditions are established for their equivalence with the maximum curvature and the marginalized maximum aposteriori. All results are supported by numerical experiments. Experiments also show that the Bayesian L-curve rooted on appropriate priors can succeed in inverse problems where the classical L-curve is prone to fail.

show abstract

Section: Mmap Estimatementioning

confidence: 99%

“…This is recognized equal to the square-root L-curve defined with scaling function f = √ in equation (5). The associated optimal regularization parameter is…”

Section: L-curve With Inverse Gamma Priorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Bayesian interpretation of the L-curve

Antoni¹,

Idier²,

Bourguignon³

2023

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…To further improve the identification accuracy, in the follow-up studies, some other regularization methods [ 18 ], such as the function expansion method [ 20 , 21 , 22 ], multiplicative regularization [ 23 , 24 ], sparse regularization [ 25 , 26 , 27 , 28 ], and so on [ 29 , 30 , 31 , 32 ], are introduced into the force identification problem. In particular, for the time-varying external force, it is usually not sparse in the time domain.…”

Section: Introductionmentioning

confidence: 99%

Identification of Time-Varying External Force Using Group Sparse Regularization and Redundant Dictionary

Liu

2022

Sensors

View full text Add to dashboard Cite

How to accurately identify unknown time-varying external force from measured structural responses is an important engineering problem, which is critical for assessing the safety condition of the structure. In the context of a few available accelerometers, this paper proposes a novel time-varying external force identification method using group sparse regularization based on the prior knowledge in the redundant dictionary. Firstly, the relationship between time-varying external force and acceleration responses is established, and a redundant dictionary is designed to create a sparse expression of external force. Then, the relevance of atoms in the redundant dictionary is revealed, and this prior knowledge is used to determine the group structures of atoms. As a result, a force identification governing equation is formulated, and the group sparse regularization is reasonably introduced to ensure the accuracy of the identified results. The contribution of this paper is that the group structures of atoms are reasonably determined based on prior knowledge, and the complexity in the process for identifying external force from measured acceleration responses is reduced. Finally, the effectiveness of the proposed method is demonstrated by numerical simulations and an experimental structure. The illustrated results show that, compared with the force identification method based on the standard l1-norm regularization, the proposed method can further improve the identified accuracy of unknown external force and greatly enhance the computational efficiency for the force identification problem.

show abstract

“…The approach can locate the force whose location does not coincide with the nodes of the mesh in a fast, iterative manner. Aucejo and De Smet (2018) presented an original iterated multiplicative regularization based on the iterated Tikhonov regularization. This method takes prior knowledge of the signals into account and does not need to choose the regularization parameters.…”

Section: Introductionmentioning

confidence: 99%

A novel method for force identification based on filter and FEM

Zheng

Wang

2019

Journal of Vibration and Control

View full text Add to dashboard Cite

Force identification plays a vital role in vibration control and structural health monitoring. Force identification is an inverse problem to determine the excitation load from the responses. In general, the inverse problem has strong ill-posedness and ill-condition, especially in the case of low signal-to-noise ratio. Singular value decomposition and Tikhonov regularization are widely used for the reconstruction of the input force. Nevertheless, the anti-noise performance and accuracy of the two methods are still unsatisfactory. In this paper, we present a novel method for force identification based on a filter and the finite element method (FEM). The filter is used to suppress the noise of the input signals. FEM is introduced to reduce the discretization error and the regularization parameters are optimized by the genetic algorithm. After the signal is filtered, the characteristics of the signal will be changed. Especially, the initial and the last segments of the input signal will be lost. These changes may make the identified force inaccurate, even more inaccurate than the force identified with no filtering. To deal with this problem, cubic spline interpolation and a nonlinear autoregressive neural network are introduced to repair the input signals. Finally, three numerical examples and experiments are used to verify the superiority of the method.

show abstract

An iterated multiplicative regularization for force reconstruction problems

Cited by 6 publications

References 35 publications

A Bayesian interpretation of the L-curve

A Bayesian interpretation of the L-curve

Identification of Time-Varying External Force Using Group Sparse Regularization and Redundant Dictionary

A novel method for force identification based on filter and FEM

Contact Info

Product

Resources

About