去趨勢波動分析和非趨勢互相關分析在結構健康監測中的應用

Abstract

摘要

現今碎形理論已廣泛運用在工程領域的研究上。在生醫領域中，如人的步態分析、心率變化性、心電圖(electrocardiogram, ECG)、腦電圖(electroencephalogram, EEG)和DNA分析，使用碎形理論皆能分辨健康和生病的狀態，在其他領域之研究上一樣也能區分。在土木工程中，碎形理論經常用於評估混凝土與鋼筋表層之破壞狀態，由於其可靠且可行之技術能判別不規則、複雜、無規律之現象。本研究提出一套結構健康診斷系統之應用:去趨勢波動分析法(Detrended Fluctuation Analysis, DFA)與去趨勢互相關分析法(Detrended Cross-Correlation Analysis, DCCA)。DFA是一個即使趨勢所引起之非穩態及噪音，能夠有系統的決定時間序列的長期相關之常用方法。隨著DFA的一般化，DCCA為比較2組資料來獲得長期相關之資訊，故稱之為互相關。接著，在國家地震工程中心(NCREE)使用7層標竿結構進行實驗驗證。透過量測結構物之微震訊號，本研究使用碎形理論來評估破壞程度與破壞位置。DFA結果中的重要參數-Hurst指數為結構物之破壞程度。此外，藉由使用DCCA分析不同樓層之互相關訊號可檢測破壞位置。雖然破壞位置可容易的識別出來，仍有分類錯誤之誤差。因此由DCCA方法中去趨勢協方差之結果提出破壞指數(Damage Index)，來提高SHM系統之效率和準確度以識別結構物的破壞位置。從結果來看，破壞程度與破壞位置可有效的與透過Hurst指數及破壞指數有著87.5%準確率進行識別。因本系統僅需於破壞發生前量測一組初始值之微震訊號，所提出的SHM方法應用在實際監測系統上是可行的。

關鍵字:結構健康監測、碎形理論、去趨勢波動分析法、去趨勢互相關分析法

ABSTRACT

Fractal analyses have been widely used in engineering fields of study. Recent studies in the biomedical engineering, namely analysis of human gait, human heart rate variability, electrocardiogram (ECG) and electroencephalogram (EEG), and DNA analysis have shown that the proposed method is able to differentiate between healthy and pathological condition as well as in the other fields of study. In civil engineering, the proposed method is frequently used to identify the concrete and steel surface damage assessments due to its viable technique for interpreting irregular, complex, and disordered natural phenomenon. This study proposes applications of structural health monitoring (SHM) called Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA). DFA is a well-known method that can systematically determine the long-range correlation of time series even with the present of non-stationarities and noise caused by trends. As the generalization of the DFA, DCCA is the method obtaining the information about long-range correlation between two recorded data which then called cross-correlation. A seven-story benchmark structure at National Center for Earthquake Engineering (NCREE) is employed for experimental verification. By measuring the ambient vibration signal from the structure, fractal analyses are adopted to assess two goals of this study which are damage condition and location. Hurst exponent as the result of DFA is the important parameter to represent damage condition of the structure. Furthermore, the damage location can be detected by analyzing the cross-correlation signals of different floors via a DCCA analysis. Although the damage location can be easily detected, misclassifications still occur. Therefore, a damage index is proposed by detrended covariance as the result from DCCA method to improve the efficiency and accuracy of the SHM system to detect the possible damage location in the structure. Based on the results, the damage condition and location can be effectively assessed by Hurst exponent and a damage index by the accuracy 87,5% respectively. As only the ambient vibration signal is required with a set of initial reference measurements, the proposed SHM methods are promising applications in the practical implementation of monitoring system.

Keywords: structural health monitoring; fractal; detrended fluctuation analysis; detrended cross-correlation analysis.