On a Stochastic Regularization Technique for Ill-Conditioned Linear Systems

Open Engineering

Moura Henrique Gomes¹  Junior Edson Costa²  Rispoli Vinicius Carvalho³  Lenzi Arcanjo⁴ 

[1] Engineering College, Laboratory of Noise Vibration and Harshness, University of Brasilia at GamaBrasilia, Brazil;Engineering College, Laboratory of instrumentation, Signal and Image Processing, University of Brasilia at GamaBrasilia, Brazil;Engineering College, University of Brasilia at GamaBrasilia, Brazil;Laboratory of Vibration and Acoustics, Federal University of Santa CatarinaBrasilia, Brazil;

关键词: force identification problems;    inverse problems;    regularization;    random matrices;   

DOI  :  10.1515/eng-2019-0008

来源: DOAJ

【 摘 要 】

Knowledge about the input–output relations of a system can be very important in many practical situations in engineering. Linear systems theory comes from applied mathematics as an efficient and simple modeling technique for input–output systems relations. Many identification problems arise from a set of linear equations, using known outputs only. It is a type of inverse problems, whenever systems inputs are sought by its output only. This work presents a regularization method, called random matrix method, which is able to reduce errors on the solution of ill-conditioned inverse problems by introducing modifications into the matrix operator that rules the problem. The main advantage of this approach is the possibility of reducing the condition number of the matrix using the probability density function that models the noise in the measurements, leading to better regularization performance. The method described was applied in the context of a force identification problem and the results were compared quantitatively and qualitatively with the classical Tikhonov regularization method. Results show the presented technique provides better results than Tikhonov method when dealing with high-level ill-conditioned inverse problems.

【 授权许可】

Unknown