Real-Time Structural Health Monitoring of Vibrating Systems

Cover
Title Page
Copyright Page
Preface
Acknowledgements
Table of Contents
Symbols
Part: I
	1. Introduction
		1.1 Need for SHM development
		1.2 Definitions
		1.3 Components of SHM
		1.4 Need for real-time SHM
		1.5 Motivation for this book
		1.6 Organization of the book
		References
	2. Mathematical Preliminaries
		2.1 Deterministic and random signals
		2.2 Fourier transform
		2.3 Frequency response function
		2.4 Impulse response function
		2.5 Power spectral density
		2.6 Eigenperturbation–a bird’s eye view
		2.7 Recursive covariance estimation in a higher order perturbation framework
		2.8 A note on eigenvalue sensitivity
		2.9 Gershgorin’s theorem
		2.10 Time series analysis
		2.11 Summary
		References
	3. Single-sensor Real Time Damage Detection Techniques: RSSA and its Variants
		3.1 Introduction
		3.2 Background
			3.2.1 Singular Spectrum Analysis (SSA)
			3.2.2 Multichannel Singular Spectrum Analysis (MSSA)
			3.2.3 RPCA in structural dynamics
		3.3 RMSSA-RPCA adaptive algorithm
		3.4 Framework of the RMSSA-RPCA algorithm
		3.5 Numerical models
			3.5.1 5-DOF linear structural system
			3.5.2 5-DOF Base-isolated structural system
		3.6 Damage identification results
			3.6.1 RSSA algorithm results: 5-DOF BW-system
			3.6.2 5-DOF linear system for RMSSA-RPCA algorithm
			3.6.3 5-DOF Base-isolated system
			3.6.4 Threshold for damage detectability of RMSSA-RPCA algorithm
		3.7 Robustness of the RMSSA-RPCA algorithm
			3.7.1 Damage detection in the presence of low frequency-operational noise
			3.7.2 Case study for the 5-DOF base isolated system using non-stationary excitation
			3.7.3 Comparison with RPCA algorithm
		3.8 Experimental verification
			3.8.1 Description of the setup and measurement program
			3.8.2 Results
		3.9 Conclusions
		References
	4. Multi-sensor Real Time Damage Detection Techniques (A): RPCA
		4.1 Motivation
		4.2 Problem formulation
		4.3 Recursive covariance estimation and FOEP
			4.3.1 RPCA: Theoretical development using POMs
		4.4 Real time condition indicators
			4.4.1 Recursive residual error (RRE)
				4.4.1.1 Temporal RRE
				4.4.1.2 Local RRE
			4.4.2 Recursive eigen vector change
			4.4.3 Outlier detection using correlation coefficient (ρ)
		4.5 Proposed algorithm
		4.6 Numerical example
			4.6.1 Structural model and simulation parameters
			4.6.2 Results for white noise input excitation
				4.6.2.1 Temporal damage detection results
				4.6.2.2 Spatial damage detection results
			4.6.3 Results for underdetermined case—white noise excitation
			4.6.4 Comparative study with batch PCA
			4.6.5 Results for El Centro ground excitation
		References
	5. Multi-sensor Real Time Damage Detection Techniques (B): RPCA-TVAR
		5.1 Motivation
		5.2 Background
		5.3 RPCA and structural dynamics: A POC based formulation
		5.4 TVAR modeling
		5.5 Damage sensitive features
			5.5.1 Time varying auto-regressive coefficients
			5.5.2 Recursive statistics on TVAR coefficients
		5.6 Proposed algorithm
		5.7 Numerical example
		5.8 Temporal damage detection results
			5.8.1 Spatial damage detection results
			5.8.2 Results for El Centro ground excitation
			5.8.3 Results for time-diluted damage
			5.8.4 Results for underdetermined case-white noise excitation
		5.9 Experimental study
		References
	6. Multi-sensor Real Time Damage Detection Techniques (B): Real Time Structural Damage Detection Using Recursive Canonical Correlation Analysis
		6.1 Motivation
		6.2 Background
		6.3 RCCA: Detailed derivation
		6.4 Recursive damage sensitive features
		6.5 Proposed algorithm
		6.6 Detection results using proposed algorithm
			6.6.1 Temporal damage detection studies for the B-W systems excited using white noise
				6.6.1.1 Temporal damage detection results for the 5 DOF B-W system
				6.6.1.2 Spatial damage detection results for the Bouc-Wen 5 dof model
			6.6.2 Detection results for the 5 DOF B-W system excited by El Centro ground motion
			6.6.3 Case study for an under determined system
			6.6.4 Case study of a 7 DOF B-W system excited using white noise
			6.6.5 A note on the effect of the increased DOF on the detection results using the proposed algorithm
			6.6.6 Case study for a strongly nonlinear system: A 5 DOF structure modeled with Duffing oscillator on its 3rd floor
			6.6.7 A case study with negligible non-linearity: Spatial damage detection
		6.7 Performance check of the proposed method against RPCA: A comparative study
			6.7.1 Case studies for the 5 DOF B-W system using white noise
				6.7.1.1 Case study for 15% global damage detection using 5 DOF B-W system
				6.7.1.2 Case study for 25% local damage detection using 5 DOF B-W system
			6.7.2 Case study for the 5 DOF B-W system excited using El Centro ground motion
		6.8 Experimental verifications
			6.8.1 Detection results for the experimental trials: A 164comparative study with RPCA
		References
	7. Real-time Modal Identification— RCCA Based Approach
		7.1 Motivation
		7.2 Background
			7.2.1 BSS based formulation of CCA
				7.2.1.1 PCA and structural dynamics
			7.2.2 Recursive covariance estimation and FOEP
		7.3 RCCA: Detailed derivation
		7.4 Proposed algorithm
		7.5 Model description
			7.5.1 5 DOF mass, spring and dashpot system: Model description
			7.5.2 5 DOF B-W model description
		7.6 Modal identification results
			7.6.1 Modal identification results using batch CCA
			7.6.2 Modal identification results using RCCA
			7.6.2.1 Recursive modal identification results for 5–DOF linear system
		7.7 Real time damage detection: An application of RCCA
			7.7.1 Recursive damage sensitive features
			7.7.2 Damage detection results for linear 5–DOF system
			7.7.3 Damage detection results for 5 DOF B-W system using RCCA
				7.7.3.1 Global damage detection results using the 5 DOF B-W system
				7.7.3.2 Local damage detection results using the 5 DOF B-W system
		7.8 Experimental verifications
			7.8.1 2 DOF shear building experimental setup
		References
Part: II
	8. Recursive SHM Practical Applications
		8.1 Introduction
		8.2 UCLA factor building—A general overview
		8.3 UCLAFB case study—RPCA-RRE
		8.4 UCLAFB case study—RPCA-TVAR
		8.5 UCLAFB case study—RSSA
		8.6 Case study for the IASC–ASCE benchmark structure
		8.7 Phase-I ASCE-SHM benchmark—A general overview
		References
	9. Conclusions and Future Prospects
		9.1 Summary
		9.2 Overview of Results and Contributions
		9.3 Future Prospects of Real-Time Monitoring
		9.4 Conclusions
		References
Index