Stochastic stiffness identification and response estimation of
  Timoshenko beams via physics-informed Gaussian processes
Gledson Rodrigo Tondo Sebastian Rau Igor Kavrakov Guido Morgenthal
Machine learning models trained with structural health monitoring data have
become a powerful tool for system identification. This paper presents a
physics-informed Gaussian process (GP) model for Timoshenko beam elements. The
model is constructed as a multi-output GP with covariance and cross-covariance
kernels analytically derived based on the differential equations for
deflections, rotations, strains, bending moments, shear forces and applied
loads. Stiffness identification is performed in a Bayesian format by maximising
a posterior model through a Markov chain Monte Carlo method, yielding a
stochastic model for the structural parameters. The optimised GP model is
further employed for probabilistic predictions of unobserved responses.
Additionally, an entropy-based method for physics-informed sensor placement
optimisation is presented, exploiting heterogeneous sensor position information
and structural boundary conditions built into the GP model. Results demonstrate
that the proposed approach is effective at identifying structural parameters
and is capable of fusing data from heterogeneous and multi-fidelity sensors.
Probabilistic predictions of structural responses and internal forces are in
closer agreement with measured data. We validate our model with an experimental
setup and discuss the quality and uncertainty of the obtained results. The
proposed approach has potential applications in the field of structural health
monitoring (SHM) for both mechanical and structural systems.