協方差型隨機子空間識別法之應用

Application of Covariance Driven Stochastic Subspace Identification Method

劉奕成(Yi-Cheng Liu)

指導教授 ： 羅俊雄

國立臺灣大學/工學院/土木工程學研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.00497

摘要

本研究目的是探討隨機子空間識別法（Stochastic Subspace Identification, SSI）在只有結構微震反應的量測下，於土木結構系統識別及損壞診斷上的應用範疇。在離線分析的應用上，可將於不同矩陣維度識別出之系統極點（system poles）繪製成穩定圖，以達正確識別結構震態的目的。在此研究的前半段，首先將對隨機子空間識別法搭配穩定圖的識別效果做研究，在不同情況諸如：訊號之雜訊、非線性、時變性與間隔緊密頻率等因素之甘擾下，比較各種隨機子空間識別法對此等甘擾因素之敏感度。接下來，協方差型隨機子空間識別法（Covariance driven Stochastic Subspace Identification, SSI-COV）將應用在廣州電視塔（Canton Tower）的系統識別工作，其為一座大型挑高細長結構，並為結構健康監測之標杆問題。除此之外，奇異譜分析法（Singular Spectrum Analysis, SSA）將以「前置子空間濾波器」的概念與協方差型隨機子空間識別法結合，名為「SSA-SSI-COV」識別法，除了能有效提昇資料解析能力，更提供一個能決定系統識別之最佳系統維度的做法。
研究的第二部份是針對系統震態參數之線上識別與損壞診斷技巧的開發，以遞迴式協方差型隨機子空間識別法（Recursive Covariance-driven Stochastic Subspace identification, RSSI-COV）為主體，並搭配延伸工具變項─投影近似子空間追蹤演算法（Extended Instrumental Variable – Projection Approximation Subspace Tracking algorithm, EIV-PAST）達成線上更新子空間的目地。另外，一個可供線上作業之子空間前置濾波器─「遞迴式奇異譜分析法（recursive Singular Spectrum, rSSA）」的開發與搭配，可有效減低雜訊對實地結構識別品質之影響，提昇線上分析的穩定性。此兩種子空間技術將透過時變性系統之數值模擬與實地試驗數據得到驗証，並從中取得可靠的識別模型控制參數。最後，它們將被應用在三個結構震態追縱的實驗上：（1）三層樓鋼構試體瞬時勁度折減之震動台實驗，（2）單層雙跨鋼筋混凝土結構之震動台試驗，此兩者皆以結構受到地震作用下之輸出反應做線上震態識別。最後，（3）橋樑沖刷實驗之損壞診斷與預警之應用。

關鍵字

隨機子空間識別 ； 協方差型 ； 系統識別 ； 結構健康監測 ； 遞歸式隨機子空間識別 ； 遞歸式奇異譜分析 ； 廣州電視塔

並列摘要

In this research the application of output-only system identification technique known as Stochastic Subspace Identification (SSI) algorithms in civil structures is carried out. With the aim of finding accurate modal parameters of the structure in off-line analysis, a stabilization diagram is constructed by plotting the identified poles of the system with increasing the size of data matrix. A sensitivity study of the implementation of SSI through stabilization diagram is firstly carried out, different scenarios such as noise effect, nonlinearity, time-varying systems and closely-spaced frequencies are considered. Comparison between different SSI approaches was also discussed. In the following, the identification task of a real large scale structure: Canton Tower, a benchmark problem for structural health monitoring of high-rise slender structures is carried out, for which the capacity of Covariance-driven SSI algorithm (SSI-COV) will be demonstrated. The introduction of a subspace preprocessing algorithm known as Singular Spectrum Analysis (SSA) can greatly enhance the identification capacity, which in conjunction with SSI-COV is called the SSA-SSI-COV method, it also allows the determination of the best system order.
The objective of the second part of this research is to develop on-line system parameter estimation and damage detection technique through Recursive Covariance-driven Stochastic Subspace identification (RSSI-COV) approach. The Extended Instrumental Variable version of Projection Approximation Subspace Tracking algorithm (EIV-PAST) is taking charge of the system-related subspace updating task. To further reduce the noise corruption in field experiments, the data pre-processing technique called recursive Singular Spectrum Analysis technique (rSSA) is developed to remove the noise contaminant measurements, so as to enhance the stability of data analysis. Through simulation study as well as the experimental research, both RSSI-COV and rSSA-SSI-COV method are applied to identify the dynamic behavior of systems with time-varying characteristics, the reliable control parameters for the model are examined. Finally, these algorithms are applied to track the evolution of modal parameters for: (1) shaking table test of a 3-story steel frame with instantaneous stiffness reduction. (2) Shaking table test of a 1-story 2-bay reinforced concrete frame, both under earthquake excitation, and at last, (3) damage detection and early warning of an experimental steel bridge under continuous scour.

並列關鍵字

Stochastic Subspace Identification ； Covariance Driven ； System Identification ； Structural Health Monitoring ； Recursive Stochastic Subspace Identification ； Recursive Singular Spectrum Analysis ； Canton Tower

參考文獻

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