Automatic (operational) modal analysis for Stochastic Subspace Identification

對於線性非時變系統的監測，操作型模態分析在過去已被證明為一種有效的分析方式，隨機子空間識別法更是其中一強大的演算法。綜觀來說，此識別法所預測出的系統模態參數會被其統計上的不確定性所影響，如：不確定的量測噪音形式、不穩定的震動形式以及有限的量測點等等，所以其分析的結果將隱含著誤差。穩態圖能夠透過比較不同的系統階數幫助使用者識別正確的模態參數，換句話說，其能夠將具有物理意義的極點與奇異的極點分開供使用者參考。 在傳統隨機子空間識別法中，決定演算法的參數如：系統階數、漢克矩陣的列數以及清除奇異極點的準則值時，通常太過主觀。為了減少人為操作，此研究提出了一自動化的隨機子空間識別法。 首先，此自動化的演算法將套用至協方差型隨機子空間識別法。這裡使用一套系統化的檢視機制來選擇含有物理意義極點的準則值。第二，統計學的分群法將被應用於區分物理極點和奇異極點。最後，在穩態圖上不同系統階數上的每個模態極點將能算出其信賴區間，以幫助估計系統的自然頻率和阻尼比。此分析方法將應用於：(一)運作中的三垮鋼構橋、(二)橋樑沖刷實驗、(三)三層樓鋼構架之震動台實驗。其分別代表不同的系統狀態：(一)非時變系統、(二)時變系統、(三)非線性系統。 資料型子空間識別法以及頻率域分解法也將應用於此研究的量測資料作為參考。最後，結構物破壞檢測的方法將應用於更加深入的分析。總而言之，此研究證明了其所提出的自動型隨機子空間識別法應用於結構物健康檢測是一更穩定且高信賴度的方法。Operational modal analysis has been proven to be an efficient tool for the identification of liner-time-invariant system using multivariate measurements. In particular, Stochastic Subspace Identification (SSI) is one of the powerful algorithms in structural health monitoring (SHM). Generally, the estimated modal parameters through SSI may be afflicted with statistical uncertainty, e.g. undefined measurement noises, non-stationary excitation, environmental condition, finite number of data samples, and etc. Therefore, the identified results are subjected to variance errors. Accordingly, the concept of the system stabilization diagram can help users to identify the correct modes, i.e. through physical criteria to remove the spurious modes. Modal parameters can be estimated at successive model orders where the physical modes of the system are extracted and separated from the spurious modes. Another issue has been raised on the subjective judgement of selecting the pre-defined parameters, i.e. the modal orders, row length of data Hankel matrix and threshold values of criteria on stabilization diagram. To avoid relying on engineer judgment when conducting SSI, an automated SSI algorithm is developed and discussed in this thesis. First of all, the identification of modal parameters through covariance-driven stochastic subspace identification (SSI-COV) from the output-only measurements is applied with the automated scheme. A systematic way of investigation on the criteria for the stabilization diagram is presented. Secondly, a statistical approach is utilized to separate physical modes from spurious modes. Finally, the computation of uncertainty bounds for each mode with all model order in the stabilization diagram is presented to determine system natural frequencies and damping ratios. Demonstration of this study on the system identification of: (1) a three-span steel bridge under operation condition, (2) an experimental bridge scouring test and (3) a 3-story steel frame under a series of shaking table tests are presented. Each case study represented a different condition of system including: (1) a time-invariant system, (2) a time-variant system and (3) a nonlinear system, respectively. Several system identification tools such as the data-driven Subspace Identification (SI-DATA) and Frequency Domain Decomposition (FDD), are also applied to help users to recognize the results of the proposed algorithm. Moreover, further assessment of structural damage severity can be proceeded through damage detection methods. All in all, it is shown that the proposed new operation procedure for the automated covariance-driven stochastic subspace identification can enhance the robustness and reliability in structural health monitoring