Smooth decomposition of random fields

详细信息	查看全文 | 推荐本文 |

• 作者：Sergio Bellizzi^a ; ^{bellizzi@lma.cnrs-mrs.fr} ; Rubens Sampaio^b ; ^{rsampaio@puc-rio.br}
• 刊名：Journal of Sound and Vibration
• 出版年：2012
• 期刊代码：91_0022460x
• 类别：ph
• 出版时间：16 July, 2012
• 卷：331
• 期：15
• 页码：3509-3520
• 文件大小：480 K

摘要

The Smooth Decomposition (SD) method was introduced to analyze discrete-time signals and generalized to continuous-time vector-valued random processes. The SD is obtained solving a generalized eigenproblem defined from the covariance matrix of the random process and the covariance matrix of the associated time-derivative random process which defines the decomposition basis. This paper presents a new extension of the SD to continuous-time and continuous-space vector-valued random processes, classically named random fields. This generalization is a major step since one now deals with operators in infinite-dimensional spaces and not matrices. It is shown that in this new context the main properties of the SD are preserved. Applied to the responses of randomly excited continuous mechanical systems, the SD can be considered as an output-only analysis tool. Moreover, two natural orderings are defined to classify the decomposition terms which permit to interpret the SD in terms of modal analysis or in terms of Karhunen-Lo猫ve analysis.