應用奇值分解進行時間序列模式的階數估算

On the Application of Singular Value Decomposition to Order Estimation of Time Series Model

柯文俊(Wen-Jiunn Ko) ； 洪振發(Chen-Far Hung)

《中華民國振動與噪音工程學會論文集》 1996 (1996/04) Pp. 203-214

https://doi.org/10.30028/CSSVANNUAL.199604.0203

摘要

本文應用奇值分解技術進行時間序列模式的階數估算。依據奇值及奇值比之大小，奇值分解將資料矩陣(Data Matrix)之所有奇值區隔爲兩群，其一爲模態奇值(Modal SV)，另一爲雜訊奇值(Noise SV)。在傳統的時間序列中，應用如AIC、BIC與FPE等準則之最小化而判定模式，其函數曲線係由低階連續往高階尋求合適模式中嵌合而成，運算過程非常複雜。因過度高估模式遭致虛假模態而產生缺陷。為了避免這些缺陷，奇值分解技術將資料矩陣分解為模態成份與雜訊成份，此舉將使我們排除傳統階數估算因高估模式階數所帶來的虛假模態，而能適當的改善模態振頻與阻泥比的估算精確度。最後；爲了驗證本法的適當性與可考靠性，多組自由振動資料在多組訊號雜訊比下進行數值模擬。

並列摘要

A singular value decomposition (SVD) technique is proposed for the order estimation of time series model. In this mothods, all singular values of data matrix can be separated into two smaller SV groups, one is modal SV the other is noise SV, by means of the magnitude of SV and SV ratio (SVR). In the conventional order estimation methods of time series model, the order predicated by minimization of AIC, BIC or FPE criteria, which are the continuous fitting curves consisted of the infomation from lower to higher models. The processes are very complicate and may incur the spurious modes due to overdetermination of model order In order to avoid the shortcoming, a SVD technique is proposed, which decomposes the data matrix into a modal component and a noise component, the model order will be reduced without incurring the spurious modes and the precision of predicated modal frequencies and damping ratio are adequatelly improved. Finally, to demostrate the validity and adequacy of the method, mamy sets data of free response are tested with various signal noise ratio.

並列關鍵字

SVD ； SV ； ORDER ESTIMATION ； TIME SERIES MODEL