Real Time Integral-Based Structural Health Monitoring

1. Real Time Integral-Based Structural Health Monitoring • I. Singh-Levett1, C. E. Hann1J. G. Chase1, B.L. Deam2 ,J.B. Mander2 • 1Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand • 2Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand

2. Introduction • Structural Health Monitoring (SHM) compares a structures condition relative to a baseline state to identify damage • Determining the existence, location and degree of damage is critical after a major event to aid recovery/response • Visual and localized inspection methods can be complicated or time consuming • Just knowing its damaged and having to go check out how much is ok, but requires manpower that may not be available. • Main goal = autonomous ability to determine basic level and location of damage to make a reliable safety/service estimate remotely Current SHM Techniques: • Modal parameter estimation • insensitive to localized damage and sensitive to noise • more suitable to linear structures • Flexibility based methods • computationally intense, not suitable for real-time • Time series methods • Many variations on the above …

3. Benefits of Real-Time SHM • Immediate assessment of instrumented structures • Infer state of non-instrumented structures using fragility relationships • Optimization of response and recovery • Reduction of social and economic impacts and costs

4. Integral SHM – Minimum Requirements • Measurements: • Ground and structural accelerations • Relatively very low frequency displacement (GPS, fibre-Optics or Storey-Drift Extensometers) • Method uses simple Bouc-Wen non-linear model including permanent displacements • Integral-based fitting method • Reformulated D.E.’s in terms of integration of measured/estimated motion • Linear least squares, very fast  real-time capability • Robust to noise and modelling error

5. Non-Linear Structural Model Permanent displacement is represented by • Bouc-Wen Hysteresis Model: Equation of Relative Motion: = Displacement = Velocity = Acceleration = Ground Acceleration = Hysteretic Displacement - for simulation, Bouc-Wen Hysteresis - for fitting, constant piecewise function  model independent M = Mass Matrix C = Damping Matrix Ke = Elastic Stiffness Matrix Kh = Hysteretic Stiffness Matrix

6. Displacement and Velocity via Integration & Correction • To use the model you need all the response quantities, but .. You didn’t measure them • The displacement is initially approximated by double integration of acceleration • Displacement is measured at up to 1-10 Hz • Drift error is corrected every 0.1-1.0 s with measured displacement • However: this gives a discontinuity in displacement every 0.1-1.0 s • Piecewise C(1) continuous cubic curves are fitted to the corrected displacements to “smooth out” the joins at 0.1s intervals. • The velocity and acceleration computed by numerical differentiation of corrected displacements • Important step as ensures displacement, velocity and acceleration are precisely related by differentiation • Otherwise solution is corrupted by the discontinuities

7. Parameter Identification • Integrate of the Equations of Motion (2x) • Discretise changes in stiffness and Bouc-Wen plastic terms • Identify stiffness and permanent displacement from revised equation of motion: = Estimated Velocity = Estimated Displacement = Estimated Acceleration = linear stiffness = permanent displacement parameter

8. Result = Least Squares Solution • Enabled by piecewise parameter variation

9. Algorithm Output • Least squares procedure yields solution vector: • Can calculate estimated permanent displacement from results and Bouc-Wen formulation:

10. Fitting Algorithm Overview • Measure displacement at low sampling rate and acceleration at high rate • Low = 1-10Hz • High = 1+ kHz • Estimate displacement via 2x-integration at high sampling rate • Correct high frequency displacement using low frequency displacement, and obtain velocity and acceleration. • Create system of linear equations by piecewise discretisation of unknowns over time at useful rates/intervals of expected change • Find unknowns using linear least squares • Estimate permanent displacements from results • Repeat for all time periods of interest

11. Results – Simulated Data • Single DOF system with linear stiffness of 39.58N/m – 1s Period • 10% uniformly distributed noise on all measurements • Stiffness identified over 2s intervals, permanent displacement over 0.4s intervals

12. Generalises to MDOF • 1-DOF algorithm is generalised for N-DOF situation Bottom Storey Intermediate Storeys Top Storey • Taking a cumulative sum removes unknowns (by telescoping terms) giving a generalised equation for any storey w :

13. Non-Linear Frame • Four storey structure designed to demonstrate dynamic response • Replaceable plastic hinges • 1/5th scale structure subjected to El Centro record

14. Steel Frame - Stiffness • Identified stiffness compares well to pushover analysis results • Similar behaviour observed for all storeys • Discrepancy in final stiffness value attributed to strain hardening and strain rate effects

15. Steel Frame - Yielding • Initial and final residual deformations are accurately captured • Two major yields identified, both occur during peaks in displacement • Final residual deformation identified to within 1.5% of true value for all storeys

16. Re-simulation – The ultimate check • Structural response is re-simulated using the fitted parameters • Accurate re-simulation validates method and shows fitted parameters are realistic

17. Conclusions • The algorithm is able to accurately identify stiffness and permanent displacement in a non-linear steel frame structure and in many simulated structures with significant random noise • The algorithm has also been applied to recognize different regimes of motion of a hybrid rocking structure • Relatively minimal computations are required making the method very suitable for real-time implementation • Could be run on 10-20 MIPS • i.e. your fancy cell phone does more work