Gledson Rodrigo Tondo

Gledson Rodrigo Tondo, Sebastian Rau, Igor Kavrakov et al.

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.

Gledson Rodrigo Tondo, Igor Kavrakov, Guido Morgenthal

Long-span bridges are subjected to a multitude of dynamic excitations during their lifespan. To account for their effects on the structural system, several load models are used during design to simulate the conditions the structure is likely to experience. These models are based on different simplifying assumptions and are generally guided by parameters that are stochastically identified from measurement data, making their outputs inherently uncertain. This paper presents a probabilistic physics-informed machine-learning framework based on Gaussian process regression for reconstructing dynamic forces based on measured deflections, velocities, or accelerations. The model can work with incomplete and contaminated data and offers a natural regularization approach to account for noise in the measurement system. An application of the developed framework is given by an aerodynamic analysis of the Great Belt East Bridge. The aerodynamic response is calculated numerically based on the quasi-steady model, and the underlying forces are reconstructed using sparse and noisy measurements. Results indicate a good agreement between the applied and the predicted dynamic load and can be extended to calculate global responses and the resulting internal forces. Uses of the developed framework include validation of design models and assumptions, as well as prognosis of responses to assist in damage detection and structural health monitoring.

Gledson Rodrigo Tondo, Sebastian Rau, Igor Kavrakov et al.

A physics-informed machine learning model, in the form of a multi-output Gaussian process, is formulated using the Euler-Bernoulli beam equation. Given appropriate datasets, the model can be used to regress the analytical value of the structure's bending stiffness, interpolate responses, and make probabilistic inferences on latent physical quantities. The developed model is applied on a numerically simulated cantilever beam, where the regressed bending stiffness is evaluated and the influence measurement noise on the prediction quality is investigated. Further, the regressed probabilistic stiffness distribution is used in a structural health monitoring context, where the Mahalanobis distance is employed to reason about the possible location and extent of damage in the structural system. To validate the developed framework, an experiment is conducted and measured heterogeneous datasets are used to update the assumed analytical structural model.

Gledson Rodrigo Tondo, Igor Kavrakov, Guido Morgenthal

Accurate modeling of aerodynamic loads is essential for understanding and predicting the responses of complex structural systems. However, these models often rely on simplifications of the true physical forces, introducing assumptions that can limit their accuracy. Validating such models becomes particularly challenging in the presence of noisy or incomplete data. To address this, we introduce a probabilistic physics-informed machine learning approach designed to reconstruct the underlying aerodynamic loads from noisy measurements of structural dynamic responses. The model avoids overfitting, eliminates the need for regularization schemes, and allows for the use of heterogeneous and multi-fidelity data during the training process. The efficacy of the approach is demonstrated through the reconstruction of aerodynamic loads on the Great Belt East Bridge, simulated under a linear unsteady assumption. Results show a strong agreement between true and predicted loads, particularly related to root mean squared errors, magnitude, phase angle and peak values of the signals. The method for load reconstructing holds broad applicability, such as modeling validation, future load estimation, and structural damage prognosis.

Paula Apollonia Wunderlich, Gledson Rodrigo Tondo, Guido Morgenthal

With the rapid advancement of computer technologies enabling fast calculations of complex structures, numerical methods have become a central tool in engineering sciences, while physical models have increasingly receded into the background. Nevertheless, owing to their clarity and comprehensibility, these former engineering tools remain of great value and their use can still be highly relevant today. At the example of the scale model of the Lillebælt Bridge -- developed by the Copenhagen engineers Christen Ostenfeld and Wriborg Jønson and given for research purposes to the Bauhaus-Universität Weimar -- this paper illustrates how physical models can still serve as useful instruments in research and teaching. By applying operational modal analysis, the natural frequencies and damping ratios of the bridge model are experimentally determined, which in turn can serve as reference data for the calibration and validation of numerical models.

Leonie Heller, Christopher Taube, Gledson Rodrigo Tondo et al.

The time-dependent deformation of concrete, particularly creep, remains a key challenge for reliable and material-efficient design. Experimental results show that tailored preloading, short-term loads exceeding the subsequent sustained load, can reduce both the magnitude and variability of creep strains which may be associated with beneficial microstructural changes. Building on these insights, this article employs Gaussian Process Regression (GPR) to calibrate analytical creep models, incorporating the effects of preloading intensity, timing, and concrete age into conventional predictions. The study pursues three main objectives: (i) calibrating a creep model using GPR based on experimental data, (ii) evaluating the impact of training data selection and preparation, and (iii) analysing model performance depending on the available experimental duration. The results demonstrate that GPR can improve model accuracy, quantify uncertainties, and support optimal test planning, while also enhancing understanding of preloading effects and contributing to more reliable and sustainable concrete creep predictions.

Gledson Rodrigo Tondo, Guido Morgenthal

Wind-traffic interactions strongly influence the dynamic response of long-span bridges, yet loads are often analysed independently. This work models concurrent wind and traffic and demonstrates that it differs from linear superposition. Traffic is synthesised from volumes, composition, and vehicle dynamics, with vehicles represented as 3D systems. Vehicle-pavement interaction adopts ISO roughness with transverse coherence, and wind turbulence follows the Kármán spectrum with Davenport coherence. A quasi-steady aerodynamic model supports time-history analysis under combined actions. Results indicate non-linear interactions that change response, revealing limitations of conventional design assumptions. The framework enables accurate performance assessment and informs serviceability criteria and design optimisation for long-span bridges.

Gledson Rodrigo Tondo, Igor Kavrakov, Guido Morgenthal

Knowledge of the force time history of a structure is essential to assess its behaviour, ensure safety and maintain reliability. However, direct measurement of external forces is often challenging due to sensor limitations, unknown force characteristics, or inaccessible load points. This paper presents an efficient dynamic load reconstruction method using physics-informed Gaussian processes (GP) based on frequency-sparse Fourier basis functions. The GP's covariance matrices are built using the description of the system dynamics, and the model is trained using structural response measurements. This provides support and interpretability to the machine learning model, in contrast to purely data-driven methods. In addition, the model filters out irrelevant components in the Fourier basis function by leveraging the sparsity of structural responses in the frequency domain, thereby reducing computational complexity during optimization. The trained model for structural responses is then integrated with the differential equation for a harmonic oscillator, creating a probabilistic dynamic load model that predicts load patterns without requiring force data during training. The model's effectiveness is validated through two case studies: a numerical model of a wind-excited 76-story building and an experiment using a physical scale model of the Lillebælt Bridge in Denmark, excited by a servo motor. For both cases, validation of the reconstructed forces is provided using comparison metrics for several signal properties. The developed model holds potential for applications in structural health monitoring, damage prognosis, and load model validation.

Igor Kavrakov, Gledson Rodrigo Tondo, Guido Morgenthal

Advancements in machine learning and an abundance of structural monitoring data have inspired the integration of mechanical models with probabilistic models to identify a structure's state and quantify the uncertainty of its physical parameters and response. In this paper, we propose an inference methodology for classical Kirchhoff-Love plates via physics-informed Gaussian Processes (GP). A probabilistic model is formulated as a multi-output GP by placing a GP prior on the deflection and deriving the covariance function using the linear differential operators of the plate governing equations. The posteriors of the flexural rigidity, hyperparameters, and plate response are inferred in a Bayesian manner using Markov chain Monte Carlo (MCMC) sampling from noisy measurements. We demonstrate the applicability with two examples: a simply supported plate subjected to a sinusoidal load and a fixed plate subjected to a uniform load. The results illustrate how the proposed methodology can be employed to perform stochastic inference for plate rigidity and physical quantities by integrating measurements from various sensor types and qualities. Potential applications of the presented methodology are in structural health monitoring and uncertainty quantification of plate-like structures.