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

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

Oct 26, 2022 111 likes •459 views

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 dont look like system identification A

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Grey-box Models for Structural Dynamics

Lizzy Cross, Tim Rogers, Ramon Fuentes, Haichen Shi, Chandula Wickramrachchi, Keith Worden

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2 / Dynamics Research Group, University of Sheffield

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
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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

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Research Themes

  • Vibration-based SHM
  • Guided Waves
  • Acoustic Emission
  • Vision-based SHM
  • Machine Learning
  • Statistical Methods
  • Model-driven SHM

4 / Dynamics Research Group, University of Sheffield

Application Areas

  • Aerospace Structures
  • Composite Materials
  • Ground Vehicles
  • Civil Infrastructure
  • Wind Energy
  • Machining
  • Offshore Structures

Current Research

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A key challenge is variability in operating conditions, how can we detect damage when everything else is changing as well?

5 / Dynamics Research Group, University of Sheffield

Managing the changing environment

20 40 60 80 100 120 140 160 0.5 1 1.5 2 data point reference Normalised displacement Deck 44m from Saltash end Deck 62m from Saltash end Deck 80m from Saltash end Deck 98m from Saltash end Deck 112m from Saltash end Deck 123m from Saltash end Top of Plymouth side tower Top of Plymouth tower, south Top of Plymouth tower, north

5 10 15 20 25 30 35 40 45 50 0.45 0.455 0.46 0.465 0.47 0.475 0.48 0.485

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.

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Cointegration – removing common trends without measurement of the environment

6 / Dynamics Research Group, University of Sheffield

Managing the changing environment

20 40 60 80 100 120 140 160 0.5 1 1.5 2 data point reference Normalised displacement Deck 44m from Saltash end Deck 62m from Saltash end Deck 80m from Saltash end Deck 98m from Saltash end Deck 112m from Saltash end Deck 123m from Saltash end Top of Plymouth side tower Top of Plymouth tower, south Top of Plymouth tower, north

20 40 60 80 100 120 140 160

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5 10 15 data point reference Cointegrated residual amplitude 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.

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Cointegration – removing common trends via linear combination

7 / Dynamics Research Group, University of Sheffield

Managing the changing environment

500 1000 1500 2000 2500 3000

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1 2 3 data point Normalised displacement (Easting) 500 1000 1500 2000 2500 3000 3500

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10 20 30 data point reference cointegrated residual amplitude

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.

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500 1000 1500 2000 2500 3000 3500

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10 20 30 data point reference cointegrated residual amplitude

8 / Dynamics Research Group, University of Sheffield

500 1000 1500 2000 2500 3000 3500

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5 10 15 data point reference cointegrated residual amplitude

Managing the changing environment

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.

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Cointegration isn’t suitable when variables have a nonlinear relationship

9 / Dynamics Research Group, University of Sheffield

Managing the changing environment

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5 10 15 20 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 Temperature - oC 1st eigen-frequency

500 1000 1500 2000 2500 3000 3500 4000 3 4 5 6 7 8 9 10 11 12 13 data point reference Natural frequency (Hz)

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.

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10 / Dynamics Research Group, University of Sheffield

Managing the changing environment

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.

Gaussian Process Regression 𝑦1 = 𝑔 𝑌 + 𝜁

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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

11 / Dynamics Research Group, University of Sheffield

Managing the changing environment

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.

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12 / 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.

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13 / 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.

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14 / 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.

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15 / 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.

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16 / Dynamics Research Group, University of Sheffield

Using GPs for loads monitoring

3800 4000 4200 4400 4600 4800 5000 5200 5400

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1 2 3 4 5 data point Normalised side stay load GP prediction (reduced inputs) measurement 3 confidence intervals

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.

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17 / Dynamics Research Group, University of Sheffield

Wave loading prediction

Wave loading assessment is critical to gain an accurate picture

  • f 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

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18 / 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.

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Challenges from the data-driven perspective

Common challenges arising from these problems

  • A lack of training data that covers the
  • perating envelope
  • Relationships that change depending on
  • perational conditions
  • Sparse sensor networks with reliability

problems

19 / Dynamics Research Group, University of Sheffield

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Challenges from the physics-based modelling perspective

Common challenges arising from these problems

  • High fidelity models have a high level of

complexity and are very expensive to run

  • Validation of these models is a significant

challenge

  • Model updating strategies also a significant

challenge

  • Loading assumptions still necessary

20 / Dynamics Research Group, University of Sheffield

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Grey-box modelling

21 / Dynamics Research Group, University of Sheffield

Philosophy

  • Consider a grey-box to be a combination of a

physics-based model and a data-based model

  • Start with the simplest physics that are well

understood and can be validated

  • Increase flexibility via machine learning/data-

driven models

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Grey-box modelling

22 / Dynamics Research Group, University of Sheffield

Key elements

  • That the model formulations should be based on

structured elicitation from experts

  • Uncertainties are quantified
  • Outputs will be distributions
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Grey-box modelling

23 / Dynamics Research Group, University of Sheffield

Key research questions to address

  • Model formulation/architecture
  • Optimal balance of exploratory power between the two

components

  • How to validate these models
  • How to incorporate predictive distributions for use in a

predictive maintenance strategy

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24 / Dynamics Research Group, University of Sheffield

Some history

Cascaded tanks benchmark

Worden, K., Barthorpe, R. J., Cross, E. J., Dervilis, N., Holmes, G. R., Manson, G., & Rogers, T. J. (2018). On evolutionary system identification with applications to nonlinear

  • benchmarks. Mechanical Systems and Signal Processing, 112, 194-232.
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25 / Dynamics Research Group, University of Sheffield

Wave loading

Morison’s + GP-NARX

Full model predicted outputs from the grey-box model Full model predicted output from the black-box GP- NARX model

14% improvement over Morison’s, 5% over GP-NARX

“A Grey-Box Model for Wave Force Prediction” T.J. Rogers, K. Worden, U. T. Tygesen, E. J. Cross 2018/9, 1st International Conference on Structural Integrity for Offshore Energy Industry

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26 / Dynamics Research Group, University of Sheffield

Latent force models

Latent force models – model the unknown force with a GP

  • State space model of SDOF/MDOF system
  • 𝑉~𝐻𝑄(0, 𝑙(𝑢, 𝑢’))

Rogers, T., K. Worden, G. Manson, U. Tygesen, and E. Cross. 2018. “A Bayesian filtering approach to operational modal analysis with recovery of forcing signals,” in ISMA 2018 - International Conference on Noise and Vibration Engineering and US

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27 / Dynamics Research Group, University of Sheffield

Latent force models

Latent force models – model the unknown force with a GP

  • Temporal GP in state space formulation
  • Combined

Rogers, T., K. Worden, G. Manson, U. Tygesen, and E. Cross. 2018. “A Bayesian filtering approach to operational modal analysis with recovery of forcing signals,” in ISMA 2018 - International Conference on Noise and Vibration Engineering and US

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28 / Dynamics Research Group, University of Sheffield

Latent force models

Latent force models – model the unknown force with a GP

  • MCMC for parameter estimation (M,C,K and GP hyperparameters)

Rogers, T., K. Worden, G. Manson, U. Tygesen, and E. Cross. 2018. “A Bayesian filtering approach to operational modal analysis with recovery of forcing signals,” in ISMA 2018 - International Conference on Noise and Vibration Engineering and US

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29 / Dynamics Research Group, University of Sheffield

Latent force models

  • SDOF force reconstruction

Rogers, T., K. Worden, G. Manson, U. Tygesen, and E. Cross. 2018. “A Bayesian filtering approach to operational modal analysis with recovery of forcing signals,” in ISMA 2018 - International Conference on Noise and Vibration Engineering and US

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Conclusions

30 / Dynamics Research Group, University of Sheffield

Key research questions to address

  • Model formulation/architecture
  • Optimal balance of exploratory power between the two

components

  • How to validate these models
  • How to incorporate predictive distributions for use in a

predictive maintenance strategy

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Laboratory for Verification and Validation

Our latest facility enables controlled testing of components and full scale structures in a range of environments

  • 3 environmental chamber
  • Wind and rain simulation
  • 3 x 2 m shake table
  • 12m wave tank
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Laboratory for Verification and Validation

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Thanks for listening 