Quantifying the Relations of Closely-Spaced Modes by Signal Subspace Correlation Method

以訊號次空間關聯法量化具相近頻率模組之關係

程安邦(An-Pan Chemg)

《中華民國振動與噪音工程學會論文集》 1998 (1998/05) Pp. 153-160

https://doi.org/10.30028/CSSVANNUAL.199805.0153

摘要

本文旨在以向量空間關聯性的方法來分析兩個相近頻率模組的關係。這個方法稱為「訊號次空間關聯法」。為筆者數年前所提出，當時並已推導適用於輕阻尼之概略解。由於訊號次空間含有頻率與阻尼的資料，而本法可以找出不同模組的相互關係，並藉用其相關矩陣（即次空間之內積）的「奇值」（由奇值分解法而來）大小判斷其相近的程度。當兩組訊號次空間相同時，奇值等於一：當二者頻率漸遠時，奇值則隨之下降趨於零。事實上，本法可以用來偵測結構體的變化。本文提出的理論解在假設取樣頻率高於自然頻率數倍以上時可適用於所有次阻尼的模組，因此較過去的研究結果更為完整。有關於此法的理論推導，特性、優點等，將會於本文中一一介紹，並有一些模擬結果供參考與比較。

關鍵字

模態參數 ； 訊號次空間 ； 奇值分解法

並列摘要

This article presents an analytical formulation or correlating signal subspaces of two closed-spaced vibration modes. A methodology, called Signal Subspace Correlation (SSC), is introduced. Since a signal subspace contains modal Information, such as damping ratio and natural frequency, this approach reveals how closely-spaced modes affect each other In terms of SSC matrix. The singular values of the correlation matrix tell how close the modes are. For Identical modes, the singular values are exactly one, and the singular values drop to zero as the modes move away from each other. In fact, the SSC approach can be used to detect structural changes and quantify modal relations. The results of this work are valid for under-damping modes provided that the sampling rate is sufficiently higher than the natural frequencies of interest. The characteristics and advantages of the SSC methodology will also be explained followed by some numerical examples.