Grey-box Models for Structural Dynamics Lizzy Cross , Tim Rogers, - PowerPoint PPT Presentation

Grey-box Models for Structural Dynamics Lizzy Cross , Tim Rogers, Ramon Fuentes, Haichen Shi, Chandula Wickramrachchi, Keith Worden

Talk overview • Structural Health Monitoring: approaches that don’t look like system identification • A manufacturing digression • Loads monitoring for lifetime assessment • Motivation for grey-box modelling • Some results • Next steps 2 / Dynamics Research Group, University of Sheffield

Structural Health Monitoring Main Aim: the development of diagnostic systems capable of detecting structural degradation in an automated, online manner  Damage detection, localisation, classification  Prognosis: remaining useful life  Understanding performance Advantages: Increased safety and efficiency 3 / Dynamics Research Group, University of Sheffield

Current Research Research Themes Application Areas  Vibration-based SHM  Aerospace Structures  Composite Materials  Guided Waves  Acoustic Emission  Ground Vehicles  Vision-based SHM  Civil Infrastructure  Wind Energy  Machine Learning  Statistical Methods  Machining  Model-driven SHM  Offshore Structures 4 / Dynamics Research Group, University of Sheffield

Managing the changing environment A key challenge is variability in operating conditions, how can we detect damage when everything else is changing as well? 0.485 Deck 44m from Saltash end Deck 62m from Saltash end Deck 80m from Saltash end 2 Deck 98m from Saltash end Deck 112m from Saltash end 0.48 Deck 123m from Saltash end Top of Plymouth side tower Top of Plymouth tower, south Top of Plymouth tower, north 0.475 1.5 Normalised displacement 0.47 1 0.465 0.46 0.5 0.455 0 0.45 0 5 10 15 20 25 30 35 40 45 50 20 40 60 80 100 120 140 160 data point reference Cross, Elizabeth J., Keith Worden, and Qian Chen. "Cointegration: a novel approach for the removal of environmental trends in structural health monitoring data." Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences . The Royal Society, 2011 . 5 / Dynamics Research Group, University of Sheffield

Managing the changing environment Cointegration – removing common trends without measurement of the environment 15 Deck 44m from Saltash end Deck 62m from Saltash end Deck 80m from Saltash end 2 10 Deck 98m from Saltash end Deck 112m from Saltash end Deck 123m from Saltash end Cointegrated residual amplitude Top of Plymouth side tower Top of Plymouth tower, south Top of Plymouth tower, north 5 1.5 Normalised displacement 0 1 -5 0.5 -10 0 20 40 60 80 100 120 140 160 data point reference -15 0 20 40 60 80 100 120 140 160 data point reference Cross, Elizabeth J., Keith Worden, and Qian Chen. "Cointegration: a novel approach for the removal of environmental trends in structural health monitoring data." Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences . The Royal Society, 2011 . 6 / Dynamics Research Group, University of Sheffield

Managing the changing environment Cointegration – removing common trends via linear combination 3 30 2 20 Normalised displacement (Easting) cointegrated residual amplitude 1 10 0 0 -1 -10 -2 -20 -3 0 500 1000 1500 2000 2500 3000 -30 0 500 1000 1500 2000 2500 3000 3500 data point data point reference Cross, Elizabeth J., Keith Worden, and Qian Chen. "Cointegration: a novel approach for the removal of environmental trends in structural health monitoring data." Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences . The Royal Society, 2011 . 7 / Dynamics Research Group, University of Sheffield

Managing the changing environment 30 15 10 20 5 cointegrated residual amplitude cointegrated residual amplitude 0 10 -5 0 -10 -15 -10 -20 -25 -20 -30 -35 -30 0 500 1000 1500 2000 2500 3000 3500 0 500 1000 1500 2000 2500 3000 3500 data point reference data point reference Cross, Elizabeth J., Keith Worden, and Qian Chen. "Cointegration: a novel approach for the removal of environmental trends in structural health monitoring data." Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences . The Royal Society, 2011 . 8 / Dynamics Research Group, University of Sheffield

Managing the changing environment Cointegration isn’t suitable when variables have a nonlinear relationship 13 12 11 10 Natural frequency (Hz) 9 8 7 6 5 4.5 4 3 0 500 1000 1500 2000 2500 3000 4.4 3500 4000 data point reference 4.3 1st eigen-frequency 4.2 4.1 4 Shi, H., Worden, K., & Cross, E. J. (2018). A regime-switching 3.9 cointegration approach for removing environmental and operational variations in structural health monitoring. Mechanical Systems and 3.8 Signal Processing , 103 , 381-397. -10 -5 0 5 10 15 20 Temperature - o C 9 / Dynamics Research Group, University of Sheffield

Managing the changing environment 𝑦 1 = 𝑔 𝑌 + 𝜁 Gaussian Process Regression Shi, H., Worden, K., & Cross, E. J. (2018). A regime-switching cointegration approach for removing environmental and operational variations in structural health monitoring. Mechanical Systems and Signal Processing , 103 , 381-397. 10 / Dynamics Research Group, University of Sheffield

Managing the changing environment Dirichlet Process for online clustering Alternatively we could take a clustering approach. The DP allows us to cluster online without needing to know the number (and size of) the clusters a-priori Rogers, T. J., Worden, K., Fuentes, R., Dervilis, N., Tygesen, U. T., & Cross, E. J. (2019). A Bayesian non-parametric clustering approach for semi- supervised Structural Health Monitoring. Mechanical Systems and Signal Processing , 119 , 100-119. 11 / Dynamics Research Group, University of Sheffield

In-process monitoring Detecting faults in composite lay-up during ATP trials at the AMRC Fuentes, R., Cross, E. J., Ray, N., Dervilis, N., Guo, T., & Worden, K. (2017). In-Process Monitoring of Automated Carbon Fibre Tape Layup Using Ultrasonic Guided Waves. In Special Topics in Structural Dynamics, Volume 6 (pp. 179-188). Springer, Cham. 12 / Dynamics Research Group, University of Sheffield

Robotic Inspection for NDT Fuentes, R., Mineo, C., Pierce, S. G., Worden, K., & Cross, E. J. (2019). A probabilistic compressive sensing framework with applications to ultrasound signal processing. Mechanical Systems and Signal Processing , 117 , 383-402. Fuentes, R., Worden, K., Antoniadou, I, Mineo, C.,Pierce, S. G., & Cross, E. J. (2017, September). Compressive sensing for direct time of flight estimation in ultrasound-based NDT. In 11th International Workshop on Structural Health Monitoring . 13 / Dynamics Research Group, University of Sheffield

Using GPs for loads monitoring Using a small number of sensors can we predict the fatigue accrual on aerospace components? Holmes, G., Sartor, P., Reed, S., Southern, P., Worden, K., & Cross, E. (2016). Prediction of landing gear loads using machine learning techniques. Structural Health Monitoring , 15 (5), 568-582. Fuentes, R., Cross, E., Halfpenny, A., Worden, K., & Barthorpe, R. J. (2014, July). Aircraft parametric structural load monitoring using gaussian process regression. In EWSHM-7th European workshop on structural health monitoring . 14 / Dynamics Research Group, University of Sheffield

Using GPs for loads monitoring • A Gaussian Process allows prediction giving an error ~1.2% Fuentes, R., Cross, E., Halfpenny, A., Worden, K., & Barthorpe, R. J. (2014, July). Aircraft parametric structural load monitoring using Gaussian process regression. In EWSHM-7th European workshop on structural health monitoring . 15 / Dynamics Research Group, University of Sheffield

Using GPs for loads monitoring 5 GP prediction (reduced inputs) measurement 4 3  confidence intervals 3 Normalised side stay load 2 1 0 -1 -2 -3 -4 3800 4000 4200 4400 4600 4800 5000 5200 5400 data point Holmes, G., Sartor, P., Reed, S., Southern, P., Worden, K., & Cross, E. (2016). Prediction of landing gear loads using machine learning techniques. Structural Health Monitoring , 15 (5), 568-582. 16 / Dynamics Research Group, University of Sheffield

Wave loading prediction Wave loading assessment is critical to gain an accurate picture of fatigue accrual in offshore structures These are challenging conditions in which to instrument and measure System identification is made significantly harder by the fact that some structures have natural frequencies close to the dominant wave frequency 17 / Dynamics Research Group, University of Sheffield

Wave loading prediction GP-NARX for wave loading prediction • Prediction of wave loading from particle velocity and acceleration • Lag selection selected through evolutionary algorithm, posterior likelihood of a validation set (MPO) used for cost function • Test NMSE: 14.6% • Improvement over Morison’s equation, NMSE 19.5% Worden, K., Rogers, T., & Cross, E. J. (2017). Identification of nonlinear wave forces using Gaussian process NARX models. In Nonlinear Dynamics, Volume 1 (pp. 203-221). Springer, Cham. 18 / Dynamics Research Group, University of Sheffield