應用線上子空間系統識別法於結構勁度之即時量化評估

Application of Online Recursive Subspace Identification on Structural Stiffness Assessment and Quantification

陳俊達(Jun-Da Chen)

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(2017年)

https://doi.org/10.6342/NTU201701137

摘要

本研究的主要目的為利用遞迴式子空間識別法進行結構於地震外力作用當下的線上系統識別，並運用於本研究提出之結構損傷識別理論，即時識別結構物的損傷位置、損傷時間，並量化損傷情況；本研究中所定義的損傷特指為結構勁度之折減。
全文總共可分成三大部分:第一，利用多重輸入多重輸出之遞迴式子空間識別法分析加速度訊號，識別結構物的模態參數(模態頻率、阻尼比、振態) 於地震歷時中的變化。第二，將模態參數運用於本文提出的二階段結構損傷識別理論；第一階段建立代表結構物的簡化有限元素模型，第二階段計算出模型內各元素於地震歷時中的勁度折減量。第三，將遞迴式子空間識別法與二階段結構損傷識別理論分別應用於振動台實驗的量測資料與實際結構物的地震監測訊號進行驗證。
在遞迴式子空間識別法部分，本研究針對識別所需的使用者自訂參數提出設定建議，並經實際分析驗證由此自訂參數可得到正確的識別結果。本文比較四種不同遞迴式子空間識別法的識別表現與計算時間；其中可分為(1)採用固定長度移動資料視窗之方法，與(2)採用不斷新增資料點並需引進遺忘因子的擴大資料視窗之方法，由識別結果發現，具遺忘因子的識別法在追蹤模態參數變化方面有較好的成效。另外，以斜投影為基礎的二種方法有較穩定的模態參數識別結果。而在數值分析的計算時間方面，儘管本文所介紹的四種遞迴式系統識別方法在實務應用的例子中均有能力達到線上系統識別的效果，但以正交投影為基礎的二種方法能花費較少的運算時間；其中又以本文首次提出的一種遞迴式子空間識別法 (RSI-EIVPAST-Orthogonal) 能夠在遞迴運算中節省最多的數值計算量，因此能在即時系統識別過程中花費最少的分析時間。
在二階段結構損傷識別理論部分，結構物在有限的感測器分佈限制之下，能由健康狀態下識別的模態參數於第一階段建立簡化的有限元素模型，再於第二階段中由地震歷時中即時識別的模態參數以有效模型修正法不斷更新結構模型，或以元素損壞指標法不斷計算歷時中各時間點的元素損壞指標，兩種策略經實際分析驗證均可有效量化各元素的勁度折減量。
本研究透過建議之使用者自訂參數執行遞迴式子空間識別法，將線上識別之模態參數運用於二階段結構損傷識別理論，可於地震外力作用的過程中成功識別結構勁度損傷的位置與時間，並量化損傷情況。

關鍵字

遞迴式子空間識別法 ； 線上系統識別 ； 即時系統識別 ； 結構損傷識別 ； 模型更新 ； 損傷指標 ； 勁度折減

並列摘要

The purpose of this research is to implement recursive subspace identification (RSI) methods for online system identification during earthquake excitation to real-time localize, quantify the structural damage, and also detect the time of damage occurrence. In this paper, the definition of damage is the reduction of structural stiffness induced by seismic events.
This research can be divided into three major parts: First, using multiple input/multiple output (MIMO) RSI methods to analyze the acceleration responses and identify the change of modal parameters (i.e. modal frequencies, damping ratios, mode shapes) within the time history. Second, applying the RSI-identified modal parameters on the proposed two-stage damage detection algorithm; in the 1st stage, building up a simplified finite element model for the reference state of the structure, and in the 2nd stage, computing the stiffness reduction of each element within the earthquake for the target structure. Third, carrying out the RSI methods and two-stage damage detection algorithm using the measurements collected from three structures under shaking table tests and from three practical buildings in Taiwan, respectively.
This research proposes the guidelines on assigning the user-defined parameters required for RSI methods, and the assigned parameters are verified by the analysis to be capable of deriving correct identification results through RSI. The paper also compares 4 different kinds of RSI methods on their performances of identification and computational time. They can be categorized into two major types of methods: (1) methods adopting a fixed-length moving data window technique, and (2) methods using an enlarged data window skill that keeps appending new data points with a forgetting factor. Through this study, it is found that the RSI methods with forgetting factor provide a better tracking ability on the change of modal parameters. In addition, RSI methods based on oblique projection derive more stable identified results, while RSI methods based on orthogonal projection have less computational time; however, all of the presented RSI methods have potentials for real-time system identification. Among them, RSI-EIVPAST-Orthogonal is newly developed by this research for the first time, which utilizes a SVD renewing algorithm, EIV-PAST, in its recursive calculation, and it is proved to be the method taking the least computational time.
In the proposed two-stage damage detection algorithm, one can establish a simplified FE model using healthy modal parameters identified by RSI methods in the 1st stage, and then in the 2nd stage, take advantage of the following identified modal parameters to update the model by efficient model correction method (EMCM), or compute element damage index on each time instant by element damage index method (EDIM); these two strategies are proved by both the experimental and practical analysis to derive reasonable stiffness reduction in each element efficiently.
This research online identifies modal parameters through the RSI methods by suggested user-defined parameters, and then applies them on the proposed two-stage damage detection algorithm to successfully localize and quantify the damage due to stiffness reduction, and also efficiently detect the time of damage occurrence during the earthquake excitation.

並列關鍵字

Recursive Subspace Identification ； Online System Identification ； Real-time System Identification ； Structural Damage Detection ； Model Updating ； Damage Index ； Reduction of Stiffness

參考文獻

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