Nizar Lajnef

Xuyang Li, Hamed Bolandi, Talal Salem et al.

Structural monitoring for complex built environments often suffers from mismatch between design, laboratory testing, and actual built parameters. Additionally, real-world structural identification problems encounter many challenges. For example, the lack of accurate baseline models, high dimensionality, and complex multivariate partial differential equations (PDEs) pose significant difficulties in training and learning conventional data-driven algorithms. This paper explores a new framework, dubbed NeuralSI, for structural identification by augmenting PDEs that govern structural dynamics with neural networks. Our approach seeks to estimate nonlinear parameters from governing equations. We consider the vibration of nonlinear beams with two unknown parameters, one that represents geometric and material variations, and another that captures energy losses in the system mainly through damping. The data for parameter estimation is obtained from a limited set of measurements, which is conducive to applications in structural health monitoring where the exact state of an existing structure is typically unknown and only a limited amount of data samples can be collected in the field. The trained model can also be extrapolated under both standard and extreme conditions using the identified structural parameters. We compare with pure data-driven Neural Networks and other classical Physics-Informed Neural Networks (PINNs). Our approach reduces both interpolation and extrapolation errors in displacement distribution by two to five orders of magnitude over the baselines. Code is available at https://github.com/human-analysis/neural-structural-identification

Hamed Bolandi, Gautam Sreekumar, Xuyang Li et al.

Structural failures are often caused by catastrophic events such as earthquakes and winds. As a result, it is crucial to predict dynamic stress distributions during highly disruptive events in real time. Currently available high-fidelity methods, such as Finite Element Models (FEMs), suffer from their inherent high complexity. Therefore, to reduce computational cost while maintaining accuracy, a Physics Informed Neural Network (PINN), PINN-Stress model, is proposed to predict the entire sequence of stress distribution based on Finite Element simulations using a partial differential equation (PDE) solver. Using automatic differentiation, we embed a PDE into a deep neural network's loss function to incorporate information from measurements and PDEs. The PINN-Stress model can predict the sequence of stress distribution in almost real-time and can generalize better than the model without PINN.

Hamed Bolandi, Gautam Sreekumar, Xuyang Li et al.

Structural components are typically exposed to dynamic loading, such as earthquakes, wind, and explosions. Structural engineers should be able to conduct real-time analysis in the aftermath or during extreme disaster events requiring immediate corrections to avoid fatal failures. As a result, it is crucial to predict dynamic stress distributions during highly disruptive events in real-time. Currently available high-fidelity methods, such as Finite Element Models (FEMs), suffer from their inherent high complexity and are computationally prohibitive. Therefore, to reduce computational cost while preserving accuracy, a deep learning model, Neuro-DynaStress, is proposed to predict the entire sequence of stress distribution based on finite element simulations using a partial differential equation (PDE) solver. The model was designed and trained to use the geometry, boundary conditions and sequence of loads as input and predict the sequences of high-resolution stress contours. The performance of the proposed framework is compared to finite element simulations using a PDE solver.

Xuyang Li, Hamed Bolandi, Mahdi Masmoudi et al.

Structural health monitoring (SHM) ensures the safety and longevity of structures like buildings and bridges. As the volume and scale of structures and the impact of their failure continue to grow, there is a dire need for SHM techniques that are scalable, inexpensive, can operate passively without human intervention, and are customized for each mechanical structure without the need for complex baseline models. We present MIDAS, a novel "deploy-and-forget" approach for automated detection and localization of damage in structures. It is a synergistic integration of entirely passive measurements from inexpensive sensors, data compression, and a mechanics-informed autoencoder. Once deployed, MIDAS continuously learns and adapts a bespoke baseline model for each structure, learning from its undamaged state's response characteristics. After learning from just 3 hours of data, it can autonomously detect and localize different types of unforeseen damage. Results from numerical simulations and experiments indicate that incorporating the mechanical characteristics into the autoencoder allows for up to a 35% improvement in the detection and localization of minor damage over a standard autoencoder. Our approach holds significant promise for reducing human intervention and inspection costs while enabling proactive and preventive maintenance strategies. This will extend the lifespan, reliability, and sustainability of civil infrastructures.

Xuyang Li, Mahdi Masmoudi, Rami Gharbi et al.

Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics. A central challenge in using PDEs for real-world applications is to accurately infer the parameters, particularly when the parameters exhibit non-linear and spatiotemporal variations. Existing parameter estimation methods, such as sparse identification and physics-informed neural networks (PINNs), struggle in such cases, especially with nonlinear dynamics, multiphysics interactions, or limited observations of the system response. To address these challenges, we introduce Neptune, a general-purpose method capable of inferring parameter fields from sparse measurements of system responses. Neptune employs independent coordinate neural networks to continuously represent each parameter field in physical space or in state variables. Across various physical and biomedical problems, where direct parameter measurements are prohibitively expensive or unattainable, Neptune significantly outperforms existing methods, achieving robust parameter estimation from as few as 50 observations, reducing parameter estimation errors by two orders of magnitude and dynamic response prediction errors by a factor of ten compared to PINNs. Furthermore, Neptune exhibits superior extrapolation capabilities, enabling accurate predictions in regimes beyond training data where PINN fail. By facilitating reliable and data-efficient parameter inference, Neptune promises broad transformative impacts in engineering, healthcare, and beyond.