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Infrastructure systems are critical in modern communities but are highly susceptible to various natural and man-made disasters. Efficient post-disaster recovery requires repair-scheduling approaches under the limitation of capped resources that need to be shared across the system. Existing approaches, including component ranking methods, greedy evolutionary algorithms, and data-driven machine learning models, face various limitations when tested within such a context. To tackle these issues, we propose a novel approach to optimize post-disaster recovery of infrastructure systems by leveraging Deep Reinforcement Learning (DRL) methods and incorporating a specialized resilience metric to lead the optimization. The system topology is represented adopting a graph-based structure, where the system's recovery process is formulated as a sequential decision-making problem. Deep Q-learning algorithms are employed to learn optimal recovery strategies by mapping system states to specific actions, as for instance which component ought to be repaired next, with the goal of maximizing long-term recovery from a resilience-oriented perspective. To demonstrate the efficacy of our proposed approach, we implement this scheme on the example of post-earthquake recovery optimization for an electrical substation system. We assess different deep Q-learning algorithms to this end, namely vanilla Deep Q-Networks (DQN), Double DQN(DDQN), Duel DQN, and duel DDQN, demonstrating superiority of the DDQN for the considered problem. A further comparative analysis against baseline methods during testing reveals the superior performance of the proposed method in terms of both optimization effect and computational cost, rendering this an attractive approach in the context of resilience enhancement and rapid response and recovery., Comment: 35 pages, 17 figures

The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based principles and can be derived from corresponding governing equations, often of differential equation form. However, complex system characteristics, such as nonlinearities and energy dissipation mechanisms, often imply that such models are approximative and often imprecise. This challenge is further compounded in SHM, where sensor data is often sparse, making it difficult to fully observe the system's states. To address these issues, this paper explores the use of Physics-Informed Neural Networks (PINNs), a class of physics-enhanced machine learning (PEML) techniques, for the identification and estimation of dynamical systems. PINNs offer a unique advantage by embedding known physical laws directly into the neural network's loss function, allowing for simple embedding of complex phenomena, even in the presence of uncertainties. This study specifically investigates three key applications of PINNs: state estimation in systems with sparse sensing, joint state-parameter estimation, when both system response and parameters are unknown, and parameter estimation within a Bayesian framework to quantify uncertainties. The results demonstrate that PINNs deliver an efficient tool across all aforementioned tasks, even in presence of modelling errors. However, these errors tend to have a more significant impact on parameter estimation, as the optimization process must reconcile discrepancies between the prescribed model and the true system behavior. Despite these challenges, PINNs show promise in dynamical system modeling, offering a robust approach to handling uncertainties.

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM construction, schemes that allow to retain a portion of the physics tend to enhance the interpretability and generalization of ROMs. However, physics-based techniques can adversely scale when dealing with nonlinear systems that feature parametric dependencies. This study introduces a generative physics-based ROM that is suited for nonlinear systems with parametric dependencies and is additionally able to quantify the confidence associated with the respective estimates. A main contribution of this work is the conditioning of these parametric ROMs to features that can be derived from monitoring measurements, feasibly in an online fashion. This is contrary to most existing ROM schemes, which remain restricted to the prescription of the physics-based, and usually a priori unknown, system parameters. Our work utilizes conditional Variational Autoencoders to continuously map the required reduction bases to a feature vector extracted from limited output measurements, while additionally allowing for a probabilistic assessment of the ROM-estimated Quantities of Interest. An auxiliary task using a neural network-based parametrization of suitable probability distributions is introduced to re-establish the link with physical model parameters. We verify the proposed scheme on a series of simulated case studies incorporating effects of geometric and material nonlinearity under parametric dependencies related to system properties and input load characteristics.

The Population-Based Structural Health Monitoring (PBSHM) paradigm has recently emerged as a promising approach to enhance data-driven assessment of engineering structures by facilitating transfer learning between structures with some degree of similarity. In this work, we apply this concept to the automated modal identification of structural systems. We introduce a Graph Neural Network (GNN)-based deep learning scheme to identify modal properties, including natural frequencies, damping ratios, and mode shapes of engineering structures based on the Power Spectral Density (PSD) of spatially-sparse vibration measurements. Systematic numerical experiments are conducted to evaluate the proposed model, employing two distinct truss populations that possess similar topological characteristics but varying geometric (size, shape) and material (stiffness) properties. The results demonstrate that, once trained, the proposed GNN-based model can identify modal properties of unseen structures within the same structural population with good efficiency and acceptable accuracy, even in the presence of measurement noise and sparse measurement locations. The GNN-based model exhibits advantages over the classic Frequency Domain Decomposition (FDD) method in terms of identification speed, as well as against an alternate Multi-Layer Perceptron (MLP) architecture in terms of identification accuracy, rendering this a promising tool for PBSHM purposes.

The task of open-set domain generalization (OSDG) involves recognizing novel classes within unseen domains, which becomes more challenging with multiple modalities as input. Existing works have only addressed unimodal OSDG within the meta-learning framework, without considering multimodal scenarios. In this work, we introduce a novel approach to address Multimodal Open-Set Domain Generalization (MM-OSDG) for the first time, utilizing self-supervision. To this end, we introduce two innovative multimodal self-supervised pretext tasks: Masked Cross-modal Translation and Multimodal Jigsaw Puzzles. These tasks facilitate the learning of multimodal representative features, thereby enhancing generalization and open-class detection capabilities. Additionally, we propose a novel entropy weighting mechanism to balance the loss across different modalities. Furthermore, we extend our approach to tackle also the Multimodal Open-Set Domain Adaptation (MM-OSDA) problem, especially in scenarios where unlabeled data from the target domain is available. Extensive experiments conducted under MM-OSDG, MM-OSDA, and Multimodal Closed-Set DG settings on the EPIC-Kitchens and HAC datasets demonstrate the efficacy and versatility of the proposed approach. Our source code is available at https://github.com/donghao51/MOOSA., Comment: Accepted by ECCV 2024, code: https://github.com/donghao51/MOOSA

Detecting out-of-distribution (OOD) samples is important for deploying machine learning models in safety-critical applications such as autonomous driving and robot-assisted surgery. Existing research has mainly focused on unimodal scenarios on image data. However, real-world applications are inherently multimodal, which makes it essential to leverage information from multiple modalities to enhance the efficacy of OOD detection. To establish a foundation for more realistic Multimodal OOD Detection, we introduce the first-of-its-kind benchmark, MultiOOD, characterized by diverse dataset sizes and varying modality combinations. We first evaluate existing unimodal OOD detection algorithms on MultiOOD, observing that the mere inclusion of additional modalities yields substantial improvements. This underscores the importance of utilizing multiple modalities for OOD detection. Based on the observation of Modality Prediction Discrepancy between in-distribution (ID) and OOD data, and its strong correlation with OOD performance, we propose the Agree-to-Disagree (A2D) algorithm to encourage such discrepancy during training. Moreover, we introduce a novel outlier synthesis method, NP-Mix, which explores broader feature spaces by leveraging the information from nearest neighbor classes and complements A2D to strengthen OOD detection performance. Extensive experiments on MultiOOD demonstrate that training with A2D and NP-Mix improves existing OOD detection algorithms by a large margin. Our source code and MultiOOD benchmark are available at https://github.com/donghao51/MultiOOD., Comment: NeurIPS 2024 spotlight. Code and MultiOOD benchmark: https://github.com/donghao51/MultiOOD

Detecting cosmic gamma rays at high rates is the key to time-resolve the acceleration of particles within some of the most powerful events in the universe. Time-resolving the emission of gamma rays from merging celestial bodies, apparently random bursts of gamma rays, recurring novas in binary systems, flaring jets from active galactic nuclei, clocking pulsars, and many more became a critical contribution to astronomy. For good timing on account of high rates, we would ideally collect the naturally more abundant, low energetic gamma rays in the domain of one giga electronvolt in large areas. Satellites detect low energetic gamma rays but only in small collecting areas. Cherenkov telescopes have large collecting areas but can only detect the rare, high energetic gamma rays. To detect gamma rays with lower energies, Cherenkov-telescopes need to increase in precision and size. But when we push the concept of the -- far/tele -- seeing Cherenkov telescope accordingly, the telescope's physical limits show more clearly. The narrower depth-of-field of larger mirrors, the aberrations of mirrors, and the deformations of mirrors and mechanics all blur the telescope's image. To overcome these limits, we propose to record the -- full/plenum -- Cherenkov-light field of an atmospheric shower, i.e. recording the directions and impacts of each individual Cherenkov photon simultaneously, with a novel class of instrument. This novel Cherenkov plenoscope can turn a narrow depth-of-field into the perception of depth, can compensate aberrations, and can tolerate deformations. We design a Cherenkov plenoscope to explore timing by detecting low energetic gamma rays in large areas., Comment: An interdisciplinary effort investigated by physicists and civil engineers. For simulations, see https://github.com/cherenkov-plenoscope. 28 pages, 25 figures, 50 references, 100% motivation. Log:(2024 February 09) Add journal reference, update email and affiliations

The automated discovery of constitutive laws forms an emerging research area, that focuses on automatically obtaining symbolic expressions describing the constitutive behavior of solid materials from experimental data. Existing symbolic/sparse regression methods rely on the availability of libraries of material models, which are typically hand-designed by a human expert using known models as reference, or deploy generative algorithms with exponential complexity which are only practicable for very simple expressions. In this paper, we propose a novel approach to constitutive law discovery relying on formal grammars as an automated and systematic tool to generate constitutive law expressions. Compliance with physics constraints is partly enforced a priori and partly empirically checked a posteriori. We deploy the approach for two tasks: i) Automatically generating a library of valid constitutive laws for hyperelastic isotropic materials; ii) Performing data-driven discovery of hyperelastic material models from displacement data affected by different noise levels. For the task of automatic library generation, we demonstrate the flexibility and efficiency of the proposed methodology in avoiding hand-crafted features and human intervention. For the data-driven discovery task, we demonstrate the accuracy, robustness and significant generalizability of the proposed methodology.

To maximize its value, the design, development and implementation of Structural Health Monitoring (SHM) should focus on its role in facilitating decision support. In this position paper, we offer perspectives on the synergy between SHM and decision-making. We propose a classification of SHM use cases aligning with various dimensions that are closely linked to the respective decision contexts. The types of decisions that have to be supported by the SHM system within these settings are discussed along with the corresponding challenges. We provide an overview of different classes of models that are required for integrating SHM in the decision-making process to support management and operation and maintenance of structures and infrastructure systems. Fundamental decision-theoretic principles and state-of-the-art methods for optimizing maintenance and operational decision-making under uncertainty are briefly discussed. Finally, we offer a viewpoint on the appropriate course of action for quantifying, validating and maximizing the added value generated by SHM. This work aspires to synthesize the different perspectives of the SHM, Prognostic Health Management (PHM), and reliability communities, and deliver a roadmap towards monitoring-based decision support.

Anomaly detection (AD) is essential in identifying rare and often critical events in complex systems, finding applications in fields such as network intrusion detection, financial fraud detection, and fault detection in infrastructure and industrial systems. While AD is typically treated as an unsupervised learning task due to the high cost of label annotation, it is more practical to assume access to a small set of labeled anomaly samples from domain experts, as is the case for semi-supervised anomaly detection. Semi-supervised and supervised approaches can leverage such labeled data, resulting in improved performance. In this paper, rather than proposing a new semi-supervised or supervised approach for AD, we introduce a novel algorithm for generating additional pseudo-anomalies on the basis of the limited labeled anomalies and a large volume of unlabeled data. This serves as an augmentation to facilitate the detection of new anomalies. Our proposed algorithm, named Nearest Neighbor Gaussian Mixup (NNG-Mix), efficiently integrates information from both labeled and unlabeled data to generate pseudo-anomalies. We compare the performance of this novel algorithm with commonly applied augmentation techniques, such as Mixup and Cutout. We evaluate NNG-Mix by training various existing semi-supervised and supervised anomaly detection algorithms on the original training data along with the generated pseudo-anomalies. Through extensive experiments on 57 benchmark datasets in ADBench, reflecting different data types, we demonstrate that NNG-Mix outperforms other data augmentation methods. It yields significant performance improvements compared to the baselines trained exclusively on the original training data. Notably, NNG-Mix yields up to 16.4%, 8.8%, and 8.0% improvements on Classical, CV, and NLP datasets in ADBench. Our source code is available at https://github.com/donghao51/NNG-Mix.

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 physics-enhanced machine learning 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 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 real-world scenarios, achieving domain generalization (DG) presents significant challenges as models are required to generalize to unknown target distributions. Generalizing to unseen multi-modal distributions poses even greater difficulties due to the distinct properties exhibited by different modalities. To overcome the challenges of achieving domain generalization in multi-modal scenarios, we propose SimMMDG, a simple yet effective multi-modal DG framework. We argue that mapping features from different modalities into the same embedding space impedes model generalization. To address this, we propose splitting the features within each modality into modality-specific and modality-shared components. We employ supervised contrastive learning on the modality-shared features to ensure they possess joint properties and impose distance constraints on modality-specific features to promote diversity. In addition, we introduce a cross-modal translation module to regularize the learned features, which can also be used for missing-modality generalization. We demonstrate that our framework is theoretically well-supported and achieves strong performance in multi-modal DG on the EPIC-Kitchens dataset and the novel Human-Animal-Cartoon (HAC) dataset introduced in this paper. Our source code and HAC dataset are available at https://github.com/donghao51/SimMMDG., Comment: NeurIPS 2023

Engineers are often faced with the decision to select the most appropriate model for simulating the behavior of engineered systems, among a candidate set of models. Experimental monitoring data can generate significant value by supporting engineers toward such decisions. Such data can be leveraged within a Bayesian model updating process, enabling the uncertainty-aware calibration of any candidate model. The model selection task can subsequently be cast into a problem of decision-making under uncertainty, where one seeks to select the model that yields an optimal balance between the reward associated with model precision, in terms of recovering target Quantities of Interest (QoI), and the cost of each model, in terms of complexity and compute time. In this work, we examine the model selection task by means of Bayesian decision theory, under the prism of availability of models of various refinements, and thus varying levels of fidelity. In doing so, we offer an exemplary application of this framework on the IMAC-MVUQ Round-Robin Challenge. Numerical investigations show various outcomes of model selection depending on the target QoI., Comment: Submitted to IMAC-XLII conference (2024), Orlando, Florida, USA

With the rapid evolution of the wind energy sector, there is an ever-increasing need to create value from the vast amounts of data made available both from within the domain, as well as from other sectors. This article addresses the challenges faced by wind energy domain experts in converting data into domain knowledge, connecting and integrating it with other sources of knowledge, and making it available for use in next generation artificially intelligent systems. To this end, this article highlights the role that knowledge engineering can play in the process of digital transformation of the wind energy sector. It presents the main concepts underpinning Knowledge-Based Systems and summarises previous work in the areas of knowledge engineering and knowledge representation in a manner that is relevant and accessible to domain experts. A systematic analysis of the current state-of-the-art on knowledge engineering in the wind energy domain is performed, with available tools put into perspective by establishing the main domain actors and their needs and identifying key problematic areas. Finally, guidelines for further development and improvement are provided.

In this paper, we incorporate the effect of nonlinear damping with the concept of locally resonant metamaterials to enable vibration attenuation beyond the conventional bandgap range. The proposed design combines a linear host cantilever beam and periodically distributed inertia amplifiers as nonlinear local resonators. The geometric nonlinearity induced by the inertia amplifiers causes an amplitude-dependent nonlinear damping effect. Through the implementation of both modal superposition and numerical harmonic methods the finite nonlinear metamaterial is accurately modelled. The resulting nonlinear frequency response reveals the bandgap is both amplitude-dependent and broadened. Furthermore, the modal frequencies are also attenuated due to the nonlinear damping effect. The theoretical results are validated experimentally. By embedding the nonlinear damping effect into locally resonant metamaterials, wideband attenuation of the proposed metamaterial is achieved, which opens new possibilities for versatile metamaterials beyond the limit of their linear counterparts.

Partially Observable Markov Decision Processes (POMDPs) can model complex sequential decision-making problems under stochastic and uncertain environments. A main reason hindering their broad adoption in real-world applications is the lack of availability of a suitable POMDP model or a simulator thereof. Available solution algorithms, such as Reinforcement Learning (RL), require the knowledge of the transition dynamics and the observation generating process, which are often unknown and non-trivial to infer. In this work, we propose a combined framework for inference and robust solution of POMDPs via deep RL. First, all transition and observation model parameters are jointly inferred via Markov Chain Monte Carlo sampling of a hidden Markov model, which is conditioned on actions, in order to recover full posterior distributions from the available data. The POMDP with uncertain parameters is then solved via deep RL techniques with the parameter distributions incorporated into the solution via domain randomization, in order to develop solutions that are robust to model uncertainty. As a further contribution, we compare the use of transformers and long short-term memory networks, which constitute model-free RL solutions, with a model-based/model-free hybrid approach. We apply these methods to the real-world problem of optimal maintenance planning for railway assets.

Digital technologies can be used to gather accurate information about the behavior of structural components for improving systems design, as well as for enabling advanced Structural Health Monitoring strategies. New avenues for achieving automated and continuous structural assessment are opened up via development of virtualization approaches delivering so-called Digital Twins, i.e., digital mirrored representations of physical. In this framework, the main motivation of this work stems from the existing challenges in the implementation and deployment of a real-time predictive framework for virtualization of dynamic systems. Kalman-based filters are usually employed in this context to address the task of joint input-state prediction in structural dynamics. A Gaussian Process Latent Force Model (GPLFM) approach is exploited in this work to construct flexible data-driven a priori models for the unknown inputs, which are then coupled with a mechanistic model of the structural component under study for input-state estimation. The use of GP regression for this task overcomes the limitations of the conventional random-walk model, thus limiting the necessity of offline user-dependent calibration of this type of data assimilation methods. This paper proposes the use of alternative covariance functions for GP regression in structural dynamics. A theoretical analysis of the GPLFMs linked to the investigated covariance functions is offered. The outcome of this study provides insights into the applicability of each covariance type for GP-based input-state estimation. The proposed framework is validated via an illustrative simulated example, namely a 3 Degrees of Freedom system subjected to an array of different loading scenarios. Additionally, the performance of the method is experimentally assessed on the task of joint input-state estimation during testing of a 3D-printed scaled wind turbine blade.

Prognostic Health Management aims to predict the Remaining Useful Life (RUL) of degrading components/systems utilizing monitoring data. These RUL predictions form the basis for optimizing maintenance planning in a Predictive Maintenance (PdM) paradigm. We here propose a metric for assessing data-driven prognostic algorithms based on their impact on downstream PdM decisions. The metric is defined in association with a decision setting and a corresponding PdM policy. We consider two typical PdM decision settings, namely component ordering and/or replacement planning, for which we investigate and improve PdM policies that are commonly utilized in the literature. All policies are evaluated via the data-based estimation of the long-run expected maintenance cost per unit time, using monitored run-to-failure experiments. The policy evaluation enables the estimation of the proposed metric. We employ the metric as an objective function for optimizing heuristic PdM policies and algorithms' hyperparameters. The effect of different PdM policies on the metric is initially investigated through a theoretical numerical example. Subsequently, we employ four data-driven prognostic algorithms on a simulated turbofan engine degradation problem, and investigate the joint effect of prognostic algorithm and PdM policy on the metric, resulting in a decision-oriented performance assessment of these algorithms.

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition, however, such methods can become inefficient or fail in the case of parameteric or strongly nonlinear models. Such limitations are usually tackled via a library of local reduction bases each of which being valid for a given parameter vector. The success of such methods, however, is strongly reliant upon the method used to relate the parameter vectors to the local bases, this is typically achieved using clustering or interpolation methods. We propose the replacement of these methods with a Variational Autoencoder (VAE) to be used as a generative model which can infer the local basis corresponding to a given parameter vector in a probabilistic manner. The resulting VAE-boosted parametric ROM \emph{VpROM} still retains the physical insights of a projection-based method but also allows for better treatment of problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

Sensing the fluid flow around an arbitrary geometry entails extrapolating from the physical quantities perceived at its surface in order to reconstruct the features of the surrounding fluid. This is a challenging inverse problem, yet one that if solved could have a significant impact on many engineering applications. The exploitation of such an inverse logic has gained interest in recent years with the advent of widely available cheap but capable MEMS-based sensors. When combined with novel data-driven methods, these sensors may allow for flow reconstruction around immersed structures, benefiting applications such as unmanned airborne/underwater vehicle path planning or control and structural health monitoring of wind turbine blades. In this work, we train deep reversible Graph Neural Networks (GNNs) to perform flow sensing (flow reconstruction) around two-dimensional aerodynamic shapes: airfoils. Motivated by recent work, which has shown that GNNs can be powerful alternatives to mesh-based forward physics simulators, we implement a Message-Passing Neural Network to simultaneously reconstruct both the pressure and velocity fields surrounding simulated airfoils based on their surface pressure distributions, whilst additionally gathering useful farfield properties in the form of context vectors. We generate a unique dataset of Computational Fluid Dynamics simulations by simulating random, yet meaningful combinations of input boundary conditions and airfoil shapes. We show that despite the challenges associated with reconstructing the flow around arbitrary airfoil geometries in high Reynolds turbulent inflow conditions, our framework is able to generalize well to unseen cases.

Structural Health Monitoring (SHM) describes a process for inferring quantifiable metrics of structural condition, which can serve as input to support decisions on the operation and maintenance of infrastructure assets. Given the long lifespan of critical structures, this problem can be cast as a sequential decision making problem over prescribed horizons. Partially Observable Markov Decision Processes (POMDPs) offer a formal framework to solve the underlying optimal planning task. However, two issues can undermine the POMDP solutions. Firstly, the need for a model that can adequately describe the evolution of the structural condition under deterioration or corrective actions and, secondly, the non-trivial task of recovery of the observation process parameters from available monitoring data. Despite these potential challenges, the adopted POMDP models do not typically account for uncertainty on model parameters, leading to solutions which can be unrealistically confident. In this work, we address both key issues. We present a framework to estimate POMDP transition and observation model parameters directly from available data, via Markov Chain Monte Carlo (MCMC) sampling of a Hidden Markov Model (HMM) conditioned on actions. The MCMC inference estimates distributions of the involved model parameters. We then form and solve the POMDP problem by exploiting the inferred distributions, to derive solutions that are robust to model uncertainty. We successfully apply our approach on maintenance planning for railway track assets on the basis of a "fractal value" indicator, which is computed from actual railway monitoring data.

Accurate structural response prediction forms a main driver for structural health monitoring and control applications. This often requires the proposed model to adequately capture the underlying dynamics of complex structural systems. In this work, we utilize a learnable Extended Kalman Filter (EKF), named the Neural Extended Kalman Filter (Neural EKF) throughout this paper, for learning the latent evolution dynamics of complex physical systems. The Neural EKF is a generalized version of the conventional EKF, where the modeling of process dynamics and sensory observations can be parameterized by neural networks, therefore learned by end-to-end training. The method is implemented under the variational inference framework with the EKF conducting inference from sensing measurements. Typically, conventional variational inference models are parameterized by neural networks independent of the latent dynamics models. This characteristic makes the inference and reconstruction accuracy weakly based on the dynamics models and renders the associated training inadequate. In this work, we show that the structure imposed by the Neural EKF is beneficial to the learning process. We demonstrate the efficacy of the framework on both simulated and real-world structural monitoring datasets, with the results indicating significant predictive capabilities of the proposed scheme., Comment: Accepted for publication in Structural Health Monitoring

Intelligent data-driven monitoring procedures hold enormous potential for ensuring safe operation and optimal management of the railway infrastructure in the face of increasing demands on cost and efficiency. Numerous studies have shown that the track stiffness is one of the main parameters influencing the evolution of degradation that drives maintenance processes. As such, the measurement of track stiffness is fundamental for characterizing the performance of the track in terms of deterioration rate and noise emission. This can be achieved via low-cost On Board Monitoring (OBM) sensing systems (i.e., axle-box accelerometers) that are mounted on in-service trains and enable frequent, real-time monitoring of the railway infrastructure network. Acceleration-based stiffness indicators have seldom been considered in monitoring applications. In this work, the use of a Vold-Kalman filter is proposed, for decomposing the signal into periodic wheel and track related excitation--response pairs functions. We demonstrate that these components are in turn correlated to operational conditions, such as wheel out-of-roundness and rail type. We further illustrate the relationship between the track stiffness, the measured wheel-rail forces and the sleeper passage amplitude, which can ultimately serve as an indicator for predictive track maintenance and prediction of track durability.

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or mechanical structures), which are typically high-dimensional in nature. In the scope of physics-informed machine learning, this paper proposes a framework -- termed Neural Modal ODEs -- to integrate physics-based modeling with deep learning for modeling the dynamics of monitored and high-dimensional engineered systems. Neural Ordinary Differential Equations -- Neural ODEs are exploited as the deep learning operator. In this initiating exploration, we restrict ourselves to linear or mildly nonlinear systems. We propose an architecture that couples a dynamic version of variational autoencoders with physics-informed Neural ODEs (Pi-Neural ODEs). An encoder, as a part of the autoencoder, learns the abstract mappings from the first few items of observational data to the initial values of the latent variables, which drive the learning of embedded dynamics via physics-informed Neural ODEs, imposing a modal model structure on that latent space. The decoder of the proposed model adopts the eigenmodes derived from an eigen-analysis applied to the linearized portion of a physics-based model: a process implicitly carrying the spatial relationship between degrees-of-freedom (DOFs). The framework is validated on a numerical example, and an experimental dataset of a scaled cable-stayed bridge, where the learned hybrid model is shown to outperform a purely physics-based approach to modeling. We further show the functionality of the proposed scheme within the context of virtual sensing, i.e., the recovery of generalized response quantities in unmeasured DOFs from spatially sparse data., Comment: Accepted for publication in Data-Centric Engineering

This work studies a broadband graded metamaterial, which integrates the piezoelectric energy harvesting function targeting low-frequency structural vibrations, lying below 100 Hz. The device combines a graded metamaterial with beam-like resonators, piezoelectric patches and a self-powered piezoelectric interface circuit for energy harvesting. Based on the mechanical and electrical lumped parameters, an integrated model is proposed to investigate the power performance of the proposed design. Thorough numerical simulations were conducted to analyse the spatial frequency separation capacity and the slow-wave phenomenon of the graded metamaterial for broadband and high-capability piezoelectric energy harvesting. Experiments with realistic vibration sources show that the harvested power of the proposed design yields a five-fold increase with respect to conventional harvesting solutions based on single cantilever harvesters. Our results reveal the significant potential on exploitation of graded metamaterials for energy-efficient vibration-powered devices.

Data-informed predictive maintenance planning largely relies on stochastic deterioration models. Monitoring information can be utilized to update sequentially the knowledge on time-invariant deterioration model parameters either within an off-line (batch) or an on-line (recursive) Bayesian framework. With a focus on the quantification of the full parameter uncertainty, we review, adapt and investigate selected Bayesian filters for parameter estimation: an on-line particle filter, an on-line iterated batch importance sampling filter, which performs Markov chain Monte Carlo (MCMC) move steps, and an off-line MCMC-based sequential Monte Carlo filter. A Gaussian mixture model is used to approximate the posterior distribution within the resampling process in all three filters. Two numerical examples serve as the basis for a comparative assessment of off-line and on-line Bayesian estimation of time-invariant deterioration model parameters. The first case study considers a low-dimensional, nonlinear, non-Gaussian probabilistic fatigue crack growth model that is updated with sequential crack monitoring measurements. The second high-dimensional, linear, Gaussian case study employs a random field to model corrosion deterioration across a beam, which is updated with sequential measurements from sensors. The numerical investigations provide insights into the performance of off-line and on-line filters in terms of the accuracy of posterior estimates and the computational cost, when applied to problems of different nature, increasing dimensionality and varying sensor information amount. Importantly, they show that a tailored implementation of the on-line particle filter proves competitive with the computationally demanding MCMC-based filters. Suggestions on the choice of the appropriate method in function of problem characteristics are provided.

In the field of structural health monitoring (SHM), inverse problems which require repeated analyses are common. With the increase in the use of nonlinear models, the development of nonlinear reduced order modelling techniques is of paramount interest. Of considerable research interest, is the use of flexible and scalable machine learning methods which can learn to approximate the behaviour of nonlinear dynamic systems using input and output data. One such nonlinear system of interest, in the context of wind turbine structures, is the soil structure interaction (SSI) problem. Soil demonstrates strongly nonlinear behaviour with regards to its restoring force and has been shown to considerably influence the dynamic response of wind turbine structures. In this work, we demonstrate the application of a recently developed nonlinear reduced order modelling method, which leverages Autoencoder and LSTM neural networks, to a nonlinear soil structure interaction problem of a wind turbine monopile subject to realistic loading at the seabed level. The accuracy and efficiency of the methodology is compared to full order simulations carried out using Abaqus. The ROM was shown to have good fidelity and a considerable reduction in computational time for the system considered.

The difficulty in quantifying the benefit of Structural Health Monitoring (SHM) for decision support is one of the bottlenecks to an extensive adoption of SHM on real-world structures. In this paper, we present a framework for such a quantification of the value of vibration-based SHM, which can be flexibly applied to different use cases. These cover SHM-based decisions at different time scales, from near-real time diagnostics to the prognosis of slowly evolving deterioration processes over the lifetime of a structure. The framework includes an advanced model of the SHM system. It employs a Bayesian filter for the tasks of sequential joint deterioration state-parameter estimation and structural reliability updating, using continuously identified modal and intermittent visual inspection data. It also includes a realistic model of the inspection and maintenance decisions throughout the structural life-cycle. On this basis, the Value of SHM is quantified by the difference in expected total life-cycle costs with and without the SHM. We investigate the framework through application on a numerical model of a two-span bridge system, subjected to gradual and shock deterioration, as well as to changing environmental conditions, over its lifetime. The results show that this framework can be used as an a-priori decision support tool to inform the decision on whether or not to install a vibration-based SHM system on a structure, for a wide range of SHM use cases.

In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based on particle representations of probability densities and can be seamlessly generalized to any state-space representation. Within this context, a unified framework of the various Particle Filter (PF) alternatives is presented for the solution of state, state-parameter and input-state-parameter estimation problems on the basis of sparse measurements. The algorithmic steps of each filter are thoroughly presented and a simple illustrative example is utilized for the inference of i) unobserved states, ii) unknown system parameters and iii) unmeasured driving inputs.

An adapted deflation preconditioner is employed to accelerate the solution of linear systems resulting from the discretization of fracture mechanics problems with well-conditioned extended/generalized finite elements. The deflation space typically used for linear elasticity problems is enriched with additional vectors, accounting for the enrichment functions used, thus effectively removing low frequency components of the error. To further improve performance, deflation is combined, in a multiplicative way, with a block-Jacobi preconditioner, which removes high frequency components of the error as well as linear dependencies introduced by enrichment. The resulting scheme is tested on a series of non-planar crack propagation problems and compared to alternative linear solvers in terms of performance.

In this work, we investigate the dynamics and attenuation properties of a one-dimensional inertial amplified lattice with opposite chirality. The unit cell of the structure consists of a hollow-square plate connected to a ring through arch-like ligaments. The peculiar geometry and orientation of the links allow for coupling the axial and the torsional motion of the lattice, thus amplifying the inertia of the system. We develop both simplified analytical and numerical models of the building block to derive the complex dispersion relation of the infinite lattice. The structure supports a frequency-tailorable attenuation zone, whose lower bound is controlled by the second coupled axial-torsional mode. Laboratory measurements of the transmission spectrum on a 3D printed sample match very well with the analytical and numerical predictions, confirming the wide-band filtering properties of this lattice. We complete our investigation by developing and solving a constrained optimization model to obtain the optimized geometric parameters of the unit cell that minimize the bandgap opening frequency and, at the same time, fulfill structural requirements. In particular, the internal stresses induced by the self-weight of the structure are kept to a low by virtue of the employed design, with the aim to prevent plastic deformations and failure. The inertial amplification mechanism, proposed and investigated in this work, offers an efficient variant for the efficient design of materials and structures for vibration mitigation and shock protection., Comment: submitted to JSV