The seismic response of a wide variety of structures, from small but irreplaceable museum exhibits to large bridge systems, is characterized by rocking. In addition, rocking motion is increasingly being used as a seismic protective strategy to limit the amount of seismic actions (moments) developed at the base of structures. However, rocking is a highly nonlinear phenomenon governed by non-smooth dynamic phases that make its prediction difficult. This study presents an alternative approach to rocking estimation based on a physics-informed convolutional neural network (PICNN). By training a group of PICNNs using limited datasets obtained from numerical simulations and encoding the known physics into the PICNNs, important predictive benefits are obtained relieving difficulties associated with over-fitting and minimizing the requirement for a large training database. Two models are created depending on the validation of the deep PICNN: the first model assumes that state variables including rotations and angular velocities are available, while the second model is useful when only acceleration measurements are known. The analysis is initiated by implementing K-means clustering. This is followed by a detailed statistical assessment and a comparative analysis of the response-histories of a rocking block. It is observed that the deep PICNN is capable of effectively estimating the seismic rocking response history when the rigid block does not overturn.

Physics-informed neural networks (PINNs), which are a recent development and incorporate physics-based knowledge into neural networks (NNs) in the form of constraints (e.g., displacement and force boundary conditions, and governing equations) or loss function, offer promise for generating digital twins of physical systems and processes. Although recent advances in PINNs have begun to address the challenges of structural health monitoring, significant issues remain unresolved, particularly in modeling the governing physics through partial differential equations (PDEs) under temporally variable loading. This paper investigates potential solutions to these challenges. Specifically, the paper will examine the performance of PINNs enforcing boundary conditions and utilizing sensor data from a limited number of locations within it, demonstrated through three case studies. Case Study 1 assumes a constant uniformly distributed load (UDL) and analyzes several setups of PINNs for four distinct simulated measurement cases obtained from a finite element model. In Case Study 2, the UDL is included as an input variable for the NNs. Results from these two case studies show that the modeling of the structure’s boundary conditions enables the PINNs to approximate the behavior of the structure without requiring satisfaction of the PDEs across the whole domain of the plate. In Case Study (3), we explore the efficacy of PINNs in a setting resembling real-world conditions, wherein the simulated measurment data incorporate deviations from idealized boundary conditions and contain measurement noise. Results illustrate that PINNs can effectively capture the overall physics of the system while managing deviations from idealized assumptions and data noise.

Despite the growing availability of sensing and data in general, we remain unable to fully characterize many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture human activity are unmatched in our engineered world, and, even in cases where data could be referred to as “big,” they will rarely hold information across operational windows or life spans. This paper pursues the combination of machine learning technology and physics-based reasoning to enhance our ability to make predictive models with limited data. By explicitly linking the physics-based view of stochastic processes with a data-based regression approach, a derivation path for a spectrum of possible Gaussian process models is introduced and used to highlight how and where different levels of expert knowledge of a system is likely best exploited. Each of the models highlighted in the spectrum have been explored in different ways across communities; novel examples in a structural assessment context here demonstrate how these approaches can significantly reduce reliance on expensive data collection. The increased interpretability of the models shown is another important consideration and benefit in this context.

In a Model Predictive Control (MPC) setting, the precise simulation of the behavior of the system over a finite time window is essential. This application-oriented benchmark study focuses on a robot arm that exhibits various nonlinear behaviors. For this arm, we have a physics-based model with approximate parameter values and an open benchmark dataset for system identification. However, the long-term simulation of this model quickly diverges from the actual arm’s measurements, indicating its inaccuracy. We compare the accuracy of black-box and purely physics-based approaches with several physics-informed approaches. These involve different combinations of a neural network’s output with information from the physics-based model or feeding the physics-based model’s information into the neural network. One of the physics-informed model structures can improve accuracy over a fully black-box model.

An approach for the identification of discontinuous and nonsmooth nonlinear forces, as those generated by frictional contacts, in mechanical systems that can be approximated by a single-degree-of-freedom model is presented. To handle the sharp variations and multiple motion regimes introduced by these nonlinearities in the dynamic response, the partially known physics-based model and noisy measurements of the system’s response to a known input force are combined within a switching Gaussian process latent force model (GPLFM). In this grey-box framework, multiple Gaussian processes are used to model the unknown nonlinear force across different motion regimes and a resetting model enables the generation of discontinuities. The states of the system, nonlinear force, and regime transitions are inferred by using filtering and smoothing techniques for switching linear dynamical systems. The proposed switching GPLFM is applied to a simulated dry friction oscillator and an experimental setup consisting of a single-storey frame with a brass-to-steel contact. Excellent results are obtained in terms of the identified nonlinear and discontinuous friction force for varying: (i) normal load amplitudes in the contact; (ii) measurement noise levels, and (iii) number of samples in the datasets. Moreover, the identified states, friction force, and sequence of motion regimes are used for evaluating: (1) uncertain system parameters; (2) the friction force–velocity relationship, and (3) the static friction force. The correct identification of the discontinuous nonlinear force and the quantification of any remaining uncertainty in its prediction enable the implementation of an accurate forward model able to predict the system’s response to different input forces.

The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases.

The importance of automating pavement maintenance tasks for highway systems has garnered interest from both industry and academia. Despite significant research efforts and promising demonstrations being devoted to reaching a level of semi-automation featuring digital sensing and inspection, site maintenance work still requires manual processes using special vehicles and equipment, reflecting a clear gap to transition to fully autonomous maintenance. This paper reviews the current progress in pavement maintenance automation in terms of inspection and repair operations, followed by a discussion of three key technical challenges related to robotic sensing, control, and actuation. To address these challenges, we propose a conceptual solution we term Autonomous Maintenance Plant (AMP), mainly consisting of five modules for sensing, actuation, control, power supply, and mobility. This AMP concept is part of the “Digital Roads” project’s cyber-physical platform where a road digital twin (DT) is created based on its physical counterpart to enable real-time condition monitoring, sensory data processing, maintenance decision making, and repair operation execution. In this platform, the AMP conducts high-resolution survey and autonomous repair operations enabled (instructed) by the road DT. This process is unmanned and completely autonomous with an expectation to create a fully robotized highway pavement maintenance system.

In the present work, neural networks are applied to formulate parametrized hyperelastic constitutive models. The models fulfill all common mechanical conditions of hyperelasticity by construction. In particular, partially input convex neural network (pICNN) architectures are applied based on feed-forward neural networks. Receiving two different sets of input arguments, pICNNs are convex in one of them, while for the other, they represent arbitrary relationships which are not necessarily convex. In this way, the model can fulfill convexity conditions stemming from mechanical considerations without being too restrictive on the functional relationship in additional parameters, which may not necessarily be convex. Two different models are introduced, where one can represent arbitrary functional relationships in the additional parameters, while the other is monotonic in the additional parameters. As a first proof of concept, the model is calibrated to data generated with two differently parametrized analytical potentials, whereby three different pICNN architectures are investigated. In all cases, the proposed model shows excellent performance.

Alarm flood classification (AFC) methods are crucial in assisting human operators to identify and mitigate the overwhelming occurrences of alarm floods in industrial process plants, a challenge exacerbated by the complexity and data-intensive nature of modern process control systems. These alarm floods can significantly impair situational awareness and hinder decision-making. Existing AFC methods face difficulties in dealing with the inherent ambiguity in alarm sequences and the task of identifying novel, previously unobserved alarm floods. As a result, they often fail to accurately classify alarm floods. Addressing these significant limitations, this paper introduces a novel three-tier AFC method that uses alarm time series as input. In the transformation stage, alarm floods are subjected to an ensemble of convolutional kernel-based transformations (MultiRocket) to extract their characteristic dynamic properties, which are then fed into the classification stage, where a linear ridge regression classifier ensemble is used to identify recurring alarm floods. In the final novelty detection stage, the local outlier probability (LoOP) is used to determine a confidence measure of whether the classified alarm flood truly belongs to a known or previously unobserved class. Our method has been thoroughly validated using a publicly available dataset based on the Tennessee-Eastman process. The results show that our method outperforms two naive baselines and four existing AFC methods from the literature in terms of overall classification performance as well as the ability to optimize the balance between accurately identifying alarm floods from known classes and detecting alarm flood classes that have not been observed before.

The intersection of physics and machine learning has given rise to the physics-enhanced machine learning (PEML) paradigm, aiming to improve the capabilities and reduce the individual shortcomings of data- or physics-only methods. In this paper, the spectrum of PEML methods, expressed across the defining axes of physics and data, is discussed by engaging in a comprehensive exploration of its characteristics, usage, and motivations. In doing so, we present a survey of recent applications and developments of PEML techniques, revealing the potency of PEML in addressing complex challenges. We further demonstrate the application of select such schemes on the simple working example of a single degree-of-freedom Duffing oscillator, which allows to highlight the individual characteristics and motivations of different “genres” of PEML approaches. To promote collaboration and transparency, and to provide practical examples for the reader, the code generating these working examples is provided alongside this paper. As a foundational contribution, this paper underscores the significance of PEML in pushing the boundaries of scientific and engineering research, underpinned by the synergy of physical insights and machine learning capabilities.

In practice, nondestructive testing (NDT) procedures tend to consider experiments (and their respective models) as distinct, conducted in isolation, and associated with independent data. In contrast, this work looks to capture the interdependencies between acoustic emission (AE) experiments (as meta-models) and then use the resulting functions to predict the model hyperparameters for previously unobserved systems. We utilize a Bayesian multilevel approach (similar to deep Gaussian Processes) where a higher-level meta-model captures the inter-task relationships. Our key contribution is how knowledge of the experimental campaign can be encoded between tasks as well as within tasks. We present an example of AE time-of-arrival mapping for source localization, to illustrate how multilevel models naturally lend themselves to representing aggregate systems in engineering. We constrain the meta-model based on domain knowledge, then use the inter-task functions for transfer learning, predicting hyperparameters for models of previously unobserved experiments (for a specific design).

Effectively controlling systems governed by partial differential equations (PDEs) is crucial in several fields of applied sciences and engineering. These systems usually yield significant challenges to conventional control schemes due to their nonlinear dynamics, partial observability, high-dimensionality once discretized, distributed nature, and the requirement for low-latency feedback control. Reinforcement learning (RL), particularly deep RL (DRL), has recently emerged as a promising control paradigm for such systems, demonstrating exceptional capabilities in managing high-dimensional, nonlinear dynamics. However, DRL faces challenges, including sample inefficiency, robustness issues, and an overall lack of interpretability. To address these challenges, we propose a data-efficient, interpretable, and scalable Dyna-style model-based RL framework specifically tailored for PDE control. Our approach integrates Sparse Identification of Nonlinear Dynamics with Control within an Autoencoder-based dimensionality reduction scheme for PDE states and actions (AE+SINDy-C). This combination enables fast rollouts with significantly fewer environment interactions while providing an interpretable latent space representation of the PDE dynamics, facilitating insight into the control process. We validate our method on two PDE problems describing fluid flows—namely, the 1D Burgers equation and 2D Navier–Stokes equations—comparing it against a model-free baseline. Our extensive analysis highlights improved sample efficiency, stability, and interpretability in controlling complex PDE systems.