臺灣博碩士論文加值系統

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.

Table of Contents

Chinese Abstract i
English Abstract ii
Acknowledgement iii
Table of Contents iv
List of Tables vi
List of Figures vii
Chapter 1 Introduction 1
1.1 Objective 2
1.2 Thesis Outline 3
Chapter 2 Review of Structural Health Monitoring 5
2.1 Introduction 5
2.2 Global Health Monitoring 6
2.3 Local Health Monitoring 10
2.4 Fractal Analysis 11
2.4.1 Detrended Fluctuation Analysis (DFA) 12
2.4.2 Detrended Cross-Correlation Analysis (DCCA) 14
Chapter 3 The Proposed SHM Method 15
3.1 Long-Range Correlation 16
3.2 Detrended Fluctuation Analysis (DFA) 17
3.3 Detrended Cross-Correlation Analysis (DCCA) 21 3.4 The Proposed Damage Index 23
3.5 The Proposed Structural Health Monitoring Flowchart 26
Chapter 4 Experimental Verification 30
4.1 Introduction 30
4.2 Experimental Setup 30
4.3 Wired Sensor and Configuration 31
4.4 Damage Simulation 32
4.5 Data Analysis 34
Chapter 5 Experimental Result and Discussion 53
5.1 Detrended Fluctuation Analysis (DFA) Result 54
5.2 Damage Condition 57
5.3 Detrended Cross Correlation analysis (DCCA) Result 59
5.4 Damage Location 60
5.5 Damage Index 63
5.6 Comparison with Other Methods 66
Chapter 6 Conclusion and Future Work 102
6.1 Conclusion 102
6.2 Future work 104

Reference 106

Reference

[1] E. a. Johnson, H. F. Lam, L. S. Katafygiotis, and J. L. Beck, “Phase I IASC-ASCE Structural Health Monitoring Benchmark Problem Using Simulated Data,” J. Eng. Mech., 2004.
[2] H. F. Lam, L. S. Katafygiotis, and N. C. Mickleborough, “Application of a Statistical Model Updating Approach on Phase I of the IASC-ASCE Structural Health Monitoring Benchmark Study,” J. Eng. Mech., 2004.
[3] B. B. Mandelbrot, “The Fractal Geometry of Nature,” American Journal of Physics, 1983.
[4] C. K. Peng, S. Havlin, H. E. Stanley, and a L. Goldberger, “Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series.,” Chaos, 1995.
[5] S. Pikkujamsa, T. Makikallio, and L. Sourander, “Cardiac interbeat interval dynamics from childhood to senescence,” Circulation, 1999.
[6] D. Makowiec, R. Gała̧ska, A. Dudkowska, A. Rynkiewicz, and M. Zwierz, “Long-range dependencies in heart rate signals-revisited,” Phys. A Stat. Mech. its Appl., 2006.
[7] C. K. Peng, S. V Buldyrev, a L. Goldberger, S. Havlin, R. N. Mantegna, M. Simons, and H. E. Stanley, “Statistical properties of DNA sequences.,” Physica A, 1995.
[8] P. C. Ivanov, A. N. Amaral, and H. E. Stanley, “Multifractality in human heartbeat dynamics,”, 1999.
[9] S. Dutta, D. Ghosh, S. Chatterjee, and F. Hasselman, “Multifractal detrended fluctuation analysis of human gait diseases,”, 2013.
[10] H. Wang, L. Xiang, and R. B. Pandey, “A multifractal detrended fluctuation analysis ( MDFA ) of the Chinese growth enterprise market ( GEM ),” Physica A, 2012.
[11] D. Yang, C. Zhang, and Y. Liu, “Multifractal characteristic analysis of near-fault earthquake ground motions,” Soil Dyn. Earthq. Eng., 2015.
[12] B. Podobnik and H. E. Stanley, “Detrended cross-correlation analysis: A new method for analyzing two nonstationary time series,” Phys. Rev. Lett., 2008.
[13] E. B. S. Marinho, a. M. Y. R. Sousa, and R. F. S. Andrade, “Using Detrended Cross-Correlation Analysis in geophysical data,” Phys. A Stat. Mech. its Appl., 2013.
[14] B. Podobnik, Z. Q. Jiang, W. X. Zhou, and H. E. Stanley, “Statistical tests for power-law cross-correlated processes,” Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys., 2011.
[15] Ritter, “Aalborg Universitet Vibrational Based Inspection of Civil Engineering Structures Rytter , Anders,” 1993.
[16] W. Fan and P. Qiao, “Vibration-based Damage Identification Methods : A Review and Comparative Study,” 2011.
[17] C. R. Farrar and G. H. James, “System Identification From Ambient Vibration Measurements on a Bridge,” J. Sound Vib., 1997.
[18] a. K. Pandey, M. Biswas, and M. M. Samman, “Damage detection from changes in curvature mode shapes,” J. Sound Vib., 1991.
[19] M. M. Abdel Wahab and G. De Roeck, “Damage Detection in Bridges Using Modal Curvatures: Application To a Real Damage Scenario,” J. Sound Vib., 1999.
[20] P. C. Chang, A. Flatau, and S. C. Liu, “Review Paper: Health Monitoring of Civil Infrastructure,” Struct. Heal. Monit., 2003.
[21] M. Cao and P. Qiao, “Integrated wavelet transform and its application to vibration mode shapes for the damage detection of beam-type structures,” Smart Mater. Struct., 2008.
[22] A. Aktan and F. Catbas, “Development of a model health monitoring guide for major bridges,”, 2003.
[23] S. a Jang, S. Sim, and B. F. S. Jr, “Structural Damage Detection Using Static Strain Data.”
[24] R. Lopes and N. Betrouni, “Fractal and multifractal analysis : A review,” Med. Image Anal., 2009.
[25] J. W. Kantelhardt, J. W. Kantelhardt, E. Koscielny-Bunde, E. Koscielny-Bunde, H. H. a. Rego, H. H. a. Rego, S. Havlin, S. Havlin, A. Bunde, and A. Bunde, “Detecting long-range correlations with detrended uctuation analysis,” Phys. A Stat. Mech. its Appl., 2001.
[26] S. V. Buldyrev, N. V. Dokholyan, a. L. Goldberger, S. Havlin, C.-K. Peng, H. E. Stanley, and G. M. Viswanathan, “Analysis of DNA sequences using methods of statistical physics,” Phys. A Stat. Mech. its Appl., 1998.
[27] A. Bunde, S. Havlin, J. W. Kantelhardt, T. Penzel, J. H. Peter, and K. Voigt, “Correlated and uncorrelated regions in heart-rate fluctuations during sleep,” Phys. Rev. Lett., 2000.
[28] E. Koscielny-Bunde, H. Eduardo, Roman, “Long-range power-law correlations in local daily temperature fluctuations,” Philos. Mag. B, 1998.
[29] E. P. de Moura, a. P. Vieira, M. a S. Irmão, and a. a. Silva, “Applications of detrended-fluctuation analysis to gearbox fault diagnosis,” Mech. Syst. Signal Process., 2009.
[30] J. Liu, “Detrended fluctuation analysis of vibration signals for bearing fault detection,” 2011 IEEE Conf. Progn. Heal. Manag., 2011.
[31] W. C. Jun, G. Oh, and S. Kim, “Understanding volatility correlation behavior with a magnitude cross-correlation function,” Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys., 2006.
[32] J. C. Reboredo, M. a. Rivera-Castro, and G. F. Zebende, “Oil and US dollar exchange rate dependence: A detrended cross-correlation approach,” Energy Econ., 2014.
[33] J. W. Kantelhardt, “Fractal and Multifractal Time Series,”, 2008.
[34] D. Delignieres, S. Ramdani, L. Lemoine, K. Torre, M. Fortes, and G. Ninot, “Fractal analyses for ‘short’ time series: A re-assessment of classical methods,” J. Math. Psychol., 2006.
[35] R. Author, L. Review, L. Source, R. Statistical, and S. Stable, “Journal of the Royal Statistical Society. Series A (General),”, 2015.
[36] E. a F. Ihlen, “Introduction to multifractal detrended fluctuation analysis in Matlab,” Front. Physiol., 2012.
[37] J. W. Kantelhardt, E. Koscielny-Bunde, D. Rybski, P. Braun, A. Bunde, and S. Havlin, “Long-term persistence and multifractality of precipitation and river runoff records,” J. Geophys. Res. Atmos., 2006.
[38] T.-K. Lin and J.-C. Liang, “Application of multi-scale (cross-) sample entropy for structural health monitoring,” Smart Mater. Struct., 2015.