Machine Learning of Structural Aerodynamics: Physics-enhanced Data-Driven Modelling

• Applicant: Dr.-Ing. Igor Kavrakov
• Subject Area: Applied Mechanics, Statics and Dynamics ; Structural Engineering, Building Informatics and Construction Operation ; Fluid Mechanics
• Term: from 2021 to 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 491258960

• Final Report Year: 2025

Final Report Abstract

Recent advancements in data-driven aeroelasticity have been inspired by the wealth of data available in wind engineering practice. The project explores physics-enhanced machine learning for nonlinear structural aerodynamics, applicable in both design and service stages. A novel aerodynamic force methodology was developed by combining Gaussian Process (GP) regression with a quasi-steady model, where the GP model compensates for missing physics, and the quasi-steady model enhances robustness. A training procedure incorporating random gust and motion angles was devised, and the method was validated using analytical aerodynamics of a flat plate and Computational Fluid Dynamics (CFD) simulations of the Great Belt Bridge deck. The physics-enhanced GP model effectively predicts broadband buffeting and flutter responses, capturing aerodynamic nonlinearity and fluid memory effects. However, it lacks interpretability and has limitations for certain phenomena (e.g., aerodynamic frequency modulation) due to the absence of an auto-regressive structure. A Bayesian method for equation discovery, leveraging stochastic variational inference and GPs, was introduced to address nonstationary dynamical systems. This method enables model discovery by employing a double-Cauchy parameter prior on a function library, resulting in a parsimonious, interpretable state-space model. The method was validated on standard dynamical systems in wind engineering, including the Van der Pol oscillator and Hopf bifurcation. Its particular suitability for noisy data, which is prevalent in wind engineering, was demonstrated compared to other methods. Additionally, physics-informed GP models were developed for Timoshenko beams, Kirchhoff plates, and latent dynamical forces. These models use GP priors on observed mechanical quantities (e.g., displacements) and integrate mechanical models with heterogeneous data to infer probability densities of unobserved quantities (e.g., wind loads) and/or parameters (e.g., flexural rigidity). Numerical and physical experiments validated these models, including numerical determination flexural rigidity of a simply supported plate and estimating dynamic forces on a small-scale Little Belt Bridge model. These methods can enable online updates of the GP force models using response measurements. In conclusion, this project demonstrates how physics-enhanced data-driven methods improve structural aerodynamic modeling, both in structural design and service. The findings are relevant to the design and monitoring of long-span bridges and tall towers, benefiting both academia and industry.

Publications

• A physics-informed machine learning model for reconstruction of dynamic loads. IABSE Reports, 119, 315-322. International Association for Bridge and Structural Engineering (IABSE).
  Tondo, Gledson Rodrigo; Kavrakov, Igor & Morgenthal, Guido
  
• Aerodynamic force reconstruction using physicsinformed Gaussian processes. In 16th International Conference on Wind Engineering (ICWE16), Florence, Italy, 27-31 Aug 2023
  Tondo, G., Kavrakov, I. & Morgenthal, G.
  
• Gaussian Process Modelling of Nonlinear Aerodynamic Forces Acting on Bluff Bodies. In 16th International Conference on Wind Engineering (ICWE16), Florence, Italy, 27-31 Aug 2023
  Kavrakov, I., McRobie, A. & Morgenthal, G.,
  
• PIGPTimoshenkoBeam (Source code to [J4].)
  Tondo, G., Kavrakov, I. & Morgenthal, G.
  
• Simulating bluff body aeroelasticity using Gaussian Processes. In Wind Engineering Society (WES) Day, Southampton, United Kingdom, 26 June 2023
  Kavrakov, I.
  
• Stochastic stiffness identification and response estimation of Timoshenko beams via physics-informed Gaussian processes. Probabilistic Engineering Mechanics, 74, 103534.
  Tondo, Gledson Rodrigo; Rau, Sebastian; Kavrakov, Igor & Morgenthal, Guido
  
• AeroGPBuff (Source code to [J1].)
  Kavrakov, I., Morgenthal, G. & McRobie, A.
  
• Bridge Maintenance, Safety, Management, Digitalization and Sustainability. CRC Press.
  Jensen, Jens Sandager; Frangopol, Dan M. & Schmidt, Jacob Wittrup
  
• Buffeting Analysis of Structures using Gaussian Processes with Semi-analytical Priors. SSRN Electronic Journal.
  Kavrakov, Igor
  
• Data-driven aeroelastic analyses of structures in turbulent wind conditions using enhanced Gaussian Processes with aerodynamic priors. Journal of Wind Engineering and Industrial Aerodynamics, 253, 105848.
  Kavrakov, Igor; Morgenthal, Guido & McRobie, Allan
  
• The Lefkandi-Toumba Building as a timberframed structure. EXARC Journal
  Coucouzeli, A., McRobie, A. & Kavrakov, I.
  
• Efficient dynamic modal load reconstruction using physics-informed Gaussian processes based on frequency-sparse Fourier basis functions. Mechanical Systems and Signal Processing, 225, 112295.
  Tondo, Gledson Rodrigo; Kavrakov, Igor & Morgenthal, Guido
  
• PIGPDynamicModalLoadReconstruction (Source code to [J3].)
  Tondo, G., Kavrakov, I. & Morgenthal, G.
  
• PlateGP (Source code to [J2].)
  Kavrakov, I., Tondo, G. & Morgenthal, G.
  
• Stochastic Inference of Plate Bending from Heterogeneous Data: Physics-Informed Gaussian Processes via Kirchhoff–Love Theory. Journal of Engineering Mechanics, 151(4).
  Kavrakov, Igor; Tondo, Gledson Rodrigo & Morgenthal, Guido