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Modern wind turbines are large and slender dynamical structures with a fatigue loading profile of complex nature. The guarantee of their structural integrity is paramount for materializing cost efficient and more reliable wind energy. The measurement of the global dynamic response and loads of wind turbines is fundamental for achieving this goal. However, an industry-wide, cost-effective direct sensing framework is yet to arise. Moreover, deploying physical sensors and measurement systems on every structural component of interest of a wind turbine induces prohibitive costs in deployment, maintenance and data management. Considering that direct fluid-structure interaction simulations on a farm level are not computationally feasible, the preferred path for structural response estimation on wind farms has been surrogate modelling. Within this landscape, new model architectures have risen in recent years which are able to take into account graph structured data (i.e. non-euclidean data). Wind turbines positioned in a farm, where there is a layout- and topology-dependant interplay of aerodynamic wake affecting the loading profile and power production, lend themselves perfectly to this paradigm. Thus, in this contribution, we introduce the use of graph neural networks (GNN) for layout agnostic saptio-temporal joint modelling of fatigue loads effects, rotor-averaged wind speed and power production on individual turbines of wind farms. To this end, we generate stochastic dependent samples of inflow conditions for wind speed, wind direction, wind shear and nacelle yaw angles. Additionally, wind farm layouts are randomly generated based on different geometric shapes (rectangle, triangle, ellipse and sparse circles) with random parametrization (varying orientations, length/width ratio) for different numbers of turbines and minimal distance (based on the rotor diameter). Both the arbitrary layouts and the random inflow conditions are used as inputs for PyWake, a wind farm simul

This study presents a robot-assisted solution for the automated identification of bridge frequencies and high-spatial-resolution mode shapes using a minimal number of sensors. The proposed approach employs programmable wheeled robots, whose movement can be remotely controlled, as the mobile platform carrying accelerometers. The output-only frequency domain decomposition (FDD) algorithm is adopted for use with the proposed stop-and-go mobile sensing scheme, resulting in the identification of frequencies and high-resolution mode shapes. The solution was verified via two numerical case studies and was validated on a full-scale test of a footbridge. The results reveal that the frequencies and high-resolution shapes of the excited structural modes are identified successfully using only two accelerometers, confirming the satisfactory practicality and efficiency of the proposed solution.

Previous studies have demonstrated a great potential of prestressed strengthening of structures employing iron-based shape memory alloys (Fe-SMAs). A bonded Fe-SMA strengthening solution with partial activation has been proposed. However, an analytical model for assessing the strengthening efficiency was lacking, due to the unique nature of the employed prestressing mechanism involving heating. In this study, a symmetric strengthening model and an asymmetric strengthening model are developed to analyze the prestress level in steel and glass beams and plates strengthened by bonded Fe-SMA strips. The asymmetric strengthening model is then modified to analyze reinforced concrete (RC) beams strengthened by embedded Fe-SMA rebars. Recovery stress at different activation temperatures, the influence of the activation temperature on the adhesive bond, as well as the prestress loss resulting from the deformation of substrate elements and adhesive joints are taken into account. The predicted strains and deflections in the parent structure closely approximate the experimental measurements that appear in current literature. A parametric study and a sensitivity analysis are then conducted to assess the impact of the four influential features on the final prestress level, and their impact is ranked in the following order: recovery stress ≈ Fe-SMA width > activation length > bonded anchorage length. Based on these findings, a design strategy, in line with Eurocode 0, for the bonded/embedded Fe-SMA strengthening system is proposed. Finally, some perspectives on potential areas for future research are offered.

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

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 with Alternating Frequency Time and numerical continuation techniques, the finite nonlinear metamaterial is accurately modeled. The resulting nonlinear frequency response reveals the bandgap is both amplitude-dependent and broadened. Furthermore, the nonlinear interaction between the local resonators and the mode shapes of the host beam is discussed, which leads to efficient modal frequency dissipation ability. The theoretical results are validated experimentally. By embedding the nonlinear damping effect into locally resonant metamaterials, wideband and shock wave attenuation of the proposed metamaterial is achieved, which opens new possibilities for versatile metamaterials beyond the conventional bandgap ranges of their linear counterparts. © 2023 The Author(s)

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 synergy between monitoring and prognostics enables data-informed predictions of the future condition of deteriorating engineering systems. These predictions form the basis for Predictive Maintenance planning. In this thesis, we develop a framework for quantifying the Value of Information from Structural Health Monitoring. Various computational aspects related to Bayesian filtering are investigated. Lastly, a decision-oriented metric for assessing prognostic algorithms is proposed., Die Synergie zwischen Monitoring und Prognostik ermöglicht datengestützte Vorhersagen über den zukünftigen Zustand von technischen Systemen im Hinblick auf eine Predictive Maintenance Planung. In dieser Arbeit entwickeln wir einen Rahmen für die Quantifizierung des Value of Information aus dem Structural Health Monitoring. Es werden rechnerische Aspekte der Bayes'schen Filterung untersucht. Schließlich wird eine entscheidungsorientierte Metrik zur Bewertung von Prognosealgorithmen vorgeschlagen.

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.

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 and from other sectors. This article addresses the challenges faced by wind energy domain experts in converting data into domain knowledge, connecting and integrating them with other sources of knowledge, and making them available for use in next-generation artificial intelligence systems. To this end, this article highlights the role that knowledge engineering can play in the 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 wind energy 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, as well as identifying key problematic areas. Finally, recommendations for further development and improvement are provided.

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: Code and MultiOOD benchmark: https://github.com/donghao51/MultiOOD

The prestressed strengthening of structures via use of bonded iron-based shape memory alloys (Fe-SMAs) has proven promising, albeit with concerns regarding the temperature dependency of the adhesive properties. In this study, the effect of activation temperature and generated prestress are investigated experimentally. Six Fe-SMA-to-steel adhesively bonded joints, comprising different Fe-SMA strips (non-prestrained and prestrained) and activation strategies (full activation and partial activation), were prepared, activated via electrical resistance heating, and tested under quasi-static loading. It is found that the bond–slip behavior of a joint with activation can be modeled by that of an equivalent non-activated joint. The generated prestress influences the full-range behavior by raising the base tensile stress level of the Fe-SMA strip, with negligible effects on further aspects of the full-range behavior. With the increasing activation temperature, the fracture energy is initially increased and eventually reduced, while the bond capacity and effective bond length are retained almost constant.

Various structures exhibit time-varying modal properties driven by short-term variability of environmental and operational conditions, which can cause considerable short-term variations in the modal characteristics, and modal damping, in particular. This study focuses on short-term damping estimation based on operational response measurements, for which a Gaussian process time-dependent auto-regressive moving average time series model is proposed. The model coefficients are represented by basis functions which express dependence on influencing environmental and operational variables, to account for various phenomena driving the time-varying nature of the modal characteristics. The method is verified by estimating short-term damping from the response of a simulated two-mode model. The applicability of the method for more complex cases is demonstrated by estimating the short-term damping of a multi-megawatt wind turbine in operation (and during an extreme wind gust) by means of its simulated edgewise blade response. The results demonstrate that the proposed method offers an enabling approach towards short-term damping and natural frequency estimation based on response measurements.

The implementation of Structural Health Monitoring (SHM) offers the prospect for sustainable and safe service-life extension of existing bridges, a large portion of which is approaching the end of their nominal life. Many SHM frameworks for civil infrastructure address timely damage detection and identification. However, the scarcity of case studies on real damaged bridges hinders the generalized application of SHM in practice. In this contribution, monitoring data from a four-day campaign on the Ponte-Moesa bridge, a three-span concrete box-girder bridge, is presented as a benchmark for data-driven damage diagnosis schemes. The monitoring data, covering accelerations from ambient and forced vibrations, contains the reference state after concluding the service life along with several gradually increasing dam-age states, including drilling holes and cutting reinforcement rebars and prestressed cables. The potential of damage-sensitive features to identify damage is presented and the uncertainties, resulting from the environmental and operational conditions and sensor malfunctioning, pertaining to robust damage detection are discussed. Drawing from real bridge monitoring data, a range of prospects and open challenges of vibration-based SHM for bridges are reviewed., Peer Reviewed, Objectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats Sostenibles, Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructura, Postprint (published version)

The identification of influence surfaces (ISs) for bridge structures offers an efficient tool for understanding traffic loads and assessing structural conditions. In general, ISs of a real bridge can be identified through calibration tests using calibration vehicles with known weights moving across the bridge. However, the existing methods face difficulties in considering comprehensive factors, such as the lateral movement, speed variation, and track width of the calibration vehicle, as well as bridge dynamic effects. These factors inevitably introduce inaccuracies into the task of identification. To comprehensively consider these factors, this study proposes a deep learning-based method that combines deep multilayer perceptrons (MLPs) and computer vision (CV), with deep MLP adopted to identify bridge ISs and CV employed to obtain the position coordinates of the calibration vehicle's wheels. A series of numerical simulations and field experiments on an in-service bridge were carried out to validate the proposed framework and compare it against a broadly established method to such an end-Quilligan's method. The results show the accuracy, robustness, and practicability of the proposed framework.

The estimation of the flow conditions throughout a modern wind farm is a relevant albeit complex problem involving several different modelling scales. In this context, recent years have seen the rise of the demand - normally industry-driven - of quick, computationally inexpensive, wind farm flow field simulators upon which further calculations might be undertaken (e.g. power output, fatigue loads, etc.). Naturally, the trustworthiness of such models hinges upon their ability to accurately estimate wakes, under the evident trade-off between computational time and accuracy. One such simulator that has been recently gaining traction within the wind community is PyWake, a Python-based flow solver, with several possible add-ons and modularity options. Based on runs from PyWake, this contribution studies the applicability of graph neural networks (GNN) as a simultaneous wind turbine fleet, wind inflow and loads surrogate. As graphs are discrete mathematical sets of dependent objects, one can see how the layout-dependent interaction between wind turbines’ aerodynamics, from which wake arises, lends itself to be modelled as a graph. Thus, we introduce the use of GNNs for layout-agnostic joint modelling of rotor-averaged wind speed, turbulence intensity, power production and damage equivalent loads (DEL) on individual turbines of wind farms. To this end, probabilistic samples of inflow conditions from a Weibull distribution for wind speed, uniform wind direction and conditional normal distributions of wind shear and nacelle yaw angles are generated as main inflow properties in the numerical simulations. Additionally, arbitrary wind farm layouts are created based on varied geometric shapes with random parametrization (varying orientations, length/width ratio). Both the arbitrary layouts and the random inflow conditions are then used as inputs for PyWake. PyWake’s output, namely, rotor averaged wind speed, turbulence intensity, power production and DELs of each individual wind

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 article, 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.

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.

We propose a new variational autoencoder (VAE) with physical constraints capable of learning the dynamics of Multiple Degree of Freedom (MDOF) dynamic systems. Standard variational autoencoders place greater emphasis on compression than interpretability regarding the learned latent space. We propose a new type of encoder, based on the recently developed Hamiltonian Neural Networks, to impose symplectic constraints on the inferred a posteriori distribution. In addition to delivering robust trajectory predictions under noisy conditions, our model is capable of learning an energy-preserving latent representation of the system. This offers new perspectives for the application of physics-informed neural networks on engineering problems linked to dynamics. © 2023, The Author(s).

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.

Optimal sensor placement (OSP) strategies in complex engineering systems aim to maximize the information gain from data by optimizing the location, type and number of the sensors or the actuators. It is used as a guide for assessing the structural condition, detecting damages and supporting the decision-making regarding structural health, safety and performance. In this work, a Bayesian optimal experimental design framework is used to optimize the type, location and number of sensors in composite wind turbine blades (WTB) excited by wind loads. The framework is based on a modal expansion technique for virtual sensing under output-only vibration measurements and on information theory for quantifying the information contained in a sensor configuration. The optimal sensor configuration optimizes a utility function associated with the expected Kullback-Leibler divergence (KL-div) between the prior and posterior distribution of the predictions at the virtual sensing (Ercan and Papadimitriou, Sensors 21:3400, 2021). The design variables include the location, type and number of sensors.

This study presents an automated robotic solution for identifying frequencies and high-resolution mode shapes of bridge structures. In this solution, a programmable wheeled robot, whose movement can be precisely and remotely controlled, acts as the mobile platform that carries an accelerometer, and another accelerometer is deployed on the tested structure as a stationary reference. By exploiting a mobile modal identification scheme, this study adopts an output-only frequency domain decomposition technique to extract frequencies and high-resolution mode shapes from the acceleration signals captured by both the mobile and stationary accelerometers. To validate the solution, a field test is conducted on a footbridge, where the frequencies and high-resolution shapes of the first two structural modes are successfully identified, using only two wireless accelerometers. This confirms the effectiveness and efficiency of the proposed solution. © 2023 IABSE. Published by American Chemical Society.

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 will be 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

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.

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.

This study establishes a subspace identification scheme to estimate bridge frequencies by processing the dynamic response of a traversing vehicle for two traverses over the target bridge. Specifically, this study discusses the feasibility of the Multivariable Output Error State Space (MOESP) method for vehicles with high speed and/or bridges with short characteristic lengths. To deal with the time-varying nature of the vehicle–bridge system, the study employs the singular value decomposition (SVD) based pseudo-inverse algorithm. The proposed scheme is numerically verified on synthetic datasets, which are attained via simulation of the vehicle–bridge interaction (VBI) problem, in order to obtain the vehicle response, which serves for application of the MOESP algorithm. The numerical experiments concern both a sprung mass vehicle and a more realistic multi-degree-of-freedom (MDOF) vehicle identifying a 3-span bridge. The results demonstrate that the proposed approach succeeds in identifying structural frequencies of the bridge even under assumption of high vehicle speeds and high levels of road surface roughness. © 2021

This study establishes a subspace identification scheme to estimate bridge frequencies by processing the dynamic response of a traversing vehicle for two traverses over the target bridge. Specifically, this study discusses the feasibility of the Multivariable Output Error State Space (MOESP) method for vehicles with high speed and/or bridges with short characteristic lengths. To deal with the time-varying nature of the vehicle–bridge system, the study employs the singular value decomposition (SVD) based pseudo-inverse algorithm. The proposed scheme is numerically verified on synthetic datasets, which are attained via simulation of the vehicle–bridge interaction (VBI) problem, in order to obtain the vehicle response, which serves for application of the MOESP algorithm. The numerical experiments concern both a sprung mass vehicle and a more realistic multi-degree-of-freedom (MDOF) vehicle identifying a 3-span bridge. The results demonstrate that the proposed approach succeeds in identifying structural frequencies of the bridge even under assumption of high vehicle speeds and high levels of road surface roughness. © 2021

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

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.

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.

The 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, which are typically high-dimensional in nature. In the scope of physics-informed machine learning, this article proposes a framework—termed neural modal ordinary differential equations (Neural Modal ODEs)—to integrate physics-based modeling with deep learning for modeling the dynamics of monitored and high-dimensional engineered systems. 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 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 Pi-Neural ODEs, imposing a modal model structure on that latent space. The decoder of the proposed model adopts the eigenmodes derived from an eigenanalysis 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 out perform a purely physics-based approach to modeling. We further show the functionality of the proposed scheme within the context of virtual sensing, that is, the recovery of generalized response quantities in unmeasured DOFs from spatially sparse data.

Real-Time Hybrid Substructuring (RTHS) is a cyber-physical testing method to analyze complex dynamical systems. This thesis covers three research topics related to RTHS: (i) an actuator control scheme is proposed that achieves high test fidelity and maintains test stability also for RTHS with contact (ii) a fidelity measure is established that is based on an experimental sensitivity analysis and (iii) an RTHS setup to test prosthetic feet is presented, where the amputee is modeled., Real-Time Hybrid Substructuring (RTHS) ist eine cyber-physische Testmethode zur Analyse komplexer dynamischer Systeme. Diese Arbeit umfasst drei Forschungsthemen im Zusammenhang mit RTHS: (i) die Implementierung moderner Regelungsalgorithmen, um eine hohe Testtreue und Teststabilität zu gewährleisten (ii) die Etablierung eines Fehlermaßes zur Ermittlung der Testtreue basierend auf einer experimentellen Sensitivitätsanalyse und (iii) die Vorstellung eines RTHS-Aufbaus zum Testen von Fußprothesen.

This study establishes a subspace identification scheme to estimate bridge frequencies by processing the dynamic response of a traversing vehicle for two traverses over the target bridge. Specifically, this study discusses the feasibility of the Multivariable Output Error State Space (MOESP) method for vehicles with high speed and/or bridges with short characteristic lengths. To deal with the time-varying nature of the vehicle–bridge system, the study employs the singular value decomposition (SVD) based pseudo-inverse algorithm. The proposed scheme is numerically verified on synthetic datasets, which are attained via simulation of the vehicle–bridge interaction (VBI) problem, in order to obtain the vehicle response, which serves for application of the MOESP algorithm. The numerical experiments concern both a sprung mass vehicle and a more realistic multi-degree-of-freedom (MDOF) vehicle identifying a 3-span bridge. The results demonstrate that the proposed approach succeeds in identifying structural frequencies of the bridge even under assumption of high vehicle speeds and high levels of road surface roughness. © 2021

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.

The need for algorithms able to solve Reinforcement Learning (RL) problems with few trials has motivated the advent of model-based RL methods. The reported performance of model-based algorithms has dramatically increased within recent years. However, it is not clear how much of the recent progress is due to improved algorithms or due to improved models. While different modeling options are available to choose from when applying a model-based approach, the distinguishing traits and particular strengths of different models are not clear. The main contribution of this work lies precisely in assessing the model influence on the performance of RL algorithms. A set of commonly adopted models is established for the purpose of model comparison. These include Neural Networks (NNs), ensembles of NNs, two different approximations of Bayesian NNs (BNNs), that is, the Concrete Dropout NN and the Anchored Ensembling, and Gaussian Processes (GPs). The model comparison is evaluated on a suite of continuous control benchmarking tasks. Our results reveal that significant differences in model performance do exist. The Concrete Dropout NN reports persistently superior performance. We summarize these differences for the benefit of the modeler and suggest that the model choice is tailored to the standards required by each specific application.

In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework targets the inference of the characteristics and latent structure of nonlinear dynamical systems from measurement data, where exact inference of latent variables is typically intractable. A recently surfaced option pertains to leveraging variational inference to perform approximate inference. In such a scheme, transition and emission functions of the system are parameterized via feed-forward neural networks (deep generative models). However, due to the generalized and highly versatile formulation of neural network functions, the learned latent space often lacks physical interpretation and structured representation. To address this, we bridge physics-based state space models with Deep Markov Models, thus delivering a hybrid modeling framework for unsupervised learning and identification of nonlinear dynamical systems. The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system by imposing physics-driven restrictions on the side of the latent space. We demonstrate the benefits of such a fusion in terms of achieving improved performance on illustrative simulation examples and experimental case studies of nonlinear systems. Our results indicate that the physics-based models involved in the employed transition and emission functions essentially enforce a more structured and physically interpretable latent space, which is essential for enhancing and generalizing the predictive capabilities of deep learning-based models., Comment: Accepted for publication in Mechanical Systems and Signal Processing

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer hardware. However, in certain use cases, such as uncertainty quantification or high precision real-time simulation, the computational cost remains a challenge. This necessitates the adoption of reduced-order modelling methods, which can reduce the computational toll of such nonlinear analyses. In this work, we propose a reduction scheme relying on the exploitation of an autoencoder as means to infer a latent space from output-only response data. This latent space, which in essence approximates the system's nonlinear normal modes (NNMs), serves as an invertible reduction basis for the nonlinear system. The proposed machine learning framework is then complemented via the use of long short term memory (LSTM) networks in the reduced space. These are used for creating an nonlinear reduced-order model (ROM) of the system, able to recreate the full system's dynamic response under a known driving input.

In this work, a method for the simulation of guided wave propagation in solids defined by implicit surfaces is presented. The method employs structured grids of spectral elements in combination to a fictitious domain approach to represent complex geometrical features through singed distance functions. A novel approach, based on moment fitting, is introduced to restore the diagonal mass matrix property in elements intersected by interfaces, thus enabling the use of explicit time integrators. Since this approach can lead to significantly decreased critical time steps for intersected elements, a "leap-frog" algorithm is employed to locally comply with this condition, thus introducing only a small computational overhead. The resulting method is tested through a series of numerical examples of increasing complexity, where it is shown that it offers increased accuracy compared to other similar approaches. Due to these improvements, components of interest for SHM-related tasks can be effectively discretized, while maintaining a performance comparable or only slightly worse than the standard spectral element method., Comment: 26 pages, 16 figures

Graph Networks (GNs) enable the fusion of prior knowledge and relational reasoning with flexible function approximations. In this work, a general GN-based model is proposed which takes full advantage of the relational modeling capabilities of GNs and extends these to probabilistic modeling with Variational Bayes (VB). To that end, we combine complementary pre-existing approaches on VB for graph data and propose an approach that relies on graph-structured latent and conditioning variables. It is demonstrated that Neural Processes can also be viewed through the lens of the proposed model. We show applications on the problem of structured probability density modeling for simulated and real wind farm monitoring data, as well as on the meta-learning of simulated Gaussian Process data. We release the source code, along with the simulated datasets., Comment: Code and simulated datasets will be released after finalization of peer review

Quantifying the value of the information extracted from a structural health monitoring (SHM) system is an important step towards convincing decision makers to implement these systems. We quantify this value by adaptation of the Bayesian decision analysis framework. In contrast to previous works, we model in detail the entire process of data generation to processing, model updating and reliability calculation, and investigate it on a deteriorating bridge system. The framework assumes that dynamic response data are obtained in a sequential fashion from deployed accelerometers, subsequently processed by an output-only operational modal analysis scheme for identifying the system's modal characteristics. We employ a classical Bayesian model updating methodology to sequentially learn the deterioration and estimate the structural damage evolution over time. This leads to sequential updating of the structural reliability, which constitutes the basis for a preposterior Bayesian decision analysis. Alternative actions are defined and a heuristic-based approach is employed for the life-cycle optimization. By solving the preposterior Bayesian decision analysis, one is able to quantify the benefit of the availability of long-term SHM vibrational data. Numerical investigations show that this framework can provide quantitative measures on the optimality of an SHM system in a specific decision context.

One of the requirements of the population-based approach to Structural Health Monitoring (SHM) proposed in the earlier papers in this sequence, is that structures be represented by points in an abstract space. Furthermore, these spaces should be metric spaces in a loose sense; i.e. there should be some measure of distance applicable to pairs of points; similar structures should then be close in the metric. However, this geometrical construction is not enough for the framing of problems in data-based SHM, as it leaves undefined the notion of feature spaces. Interpreting the feature values on a structure-by-structure basis as a type of field over the space of structures, it seems sensible to borrow an idea from modern theoretical physics, and define feature assignments as sections in a vector bundle over the structure space. With this idea in place, one can interpret the effect of environmental and operational variations as gauge degrees of freedom, as in modern gauge field theories. This paper will discuss the various geometrical structures required for an abstract theory of feature spaces in SHM, and will draw analogies with how these structures have shown their power in modern physics. In the second part of the paper, the problem of determining the normal condition cross section of a feature bundle is addressed. The solution is provided by the application of Graph Neural Networks (GNN), a versatile non-Euclidean machine learning algorithm which is not restricted to inputs and outputs from vector spaces. In particular, the algorithm is well suited to operating directly on the sort of graph structures which are an important part of the proposed framework for PBSHM. The solution of the normal section problem is demonstrated for a heterogeneous population of truss structures for which the feature of interest is the first natural frequency.

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses possible, certain use cases such as uncertainty quantification and real time high-precision simulation remain computationally challenging. This motivates the development of reduced order modelling methods, which can reduce the computational toll of simulations relying on mechanistic principles. The majority of existing reduced order modelling techniques involve projection onto linear bases. Such methods are well established for linear systems but when considering nonlinear systems their application becomes more difficult. Targeted schemes for nonlinear systems are available, which involve the use of multiple linear reduction bases or the enrichment of traditional bases. These methods are however generally limited to weakly nonlinear systems. In this work, nonlinear normal modes (NNMs) are demonstrated as a possible invertible reduction basis for nonlinear systems. The extraction of NNMs from output only data using machine learning methods is demonstrated and a novel NNM-based reduced order modelling scheme introduced. The method is demonstrated on a simulated example of a nonlinear 20 degree-of-freedom (DOF) system.

Dynamic substructuring (DS) methods encompass a range of techniques to decompose large structural systems into multiple coupled subsystems. This decomposition has the principle benefit of reducing computational time for dynamic simulation of the system. In this context, DS methods may form an essential component of hybrid simulation, wherein they can be used to couple physical and numerical substructures at reduced computational cost. Since most engineered systems are inherently nonlinear, particular potential lies in incorporating nonlinear methods in existing substructuring schemes which are largely linear methods. The most widely used and studied DS methods are classical linear techniques such as the Craig-Bampton (CB) method. However, as linear methods they naturally break down in the presence of nonlinearities. Recent advancements in substructuring have involved the development of enrichments to linear methods, which allow for some degree of nonlinearity to be captured. The use of mode shape derivatives has been shown to be able to capture geometrically non-linear effects as an extension to the CBmethod. Other candidates include the method of Finite Element Tearing and Interconnecting. In this work, a virtual hybrid simulation is presented in which a linear elastic vehicle frame supported on four nonlinear spring damper isolators is decomposed into separate domains. One domain consisting of the finite element model of the vehicle frame, which is reduced using the CB method. The second domain consists of the nonlinear isolators whose restoring forces are characterised by nonlinear spring and damper forces. Coupling between the models is carried out using a Lagrange multiplier method and time series simulations of the system are conducted and compared to the full global system with regards to simulation time and accuracy.

While purely data-driven assessment is feasible for the first levels of the Structural Health Monitoring (SHM) process, namely damage detection and arguably damage localization, this does not hold true for more advanced processes. The tasks of damage quantification and eventually residual life prognosis are invariably linked to availability of a representation of the system, which bears physical connotation. In this context, it is often desirable to assimilate data and models, into what is often termed a digital twin of the monitored system. One common take to such an end lies in exploitation of structural mechanics models, relying on use of Finite Element approximations. proper updating of these models, and their incorporation in an inverse problem setting may allow for damage quantification and localization, as well as more advanced tasks, including reliability analysis and fatigue assessment. However, this may only be achieved by means of repetitive analyses of the forward model, which implies considerable computational toll, when the model used is a detailed FE representation. In tackling this issue, reduced order models can be adopted, which retain the parameterisation and link to the parameters regulating the physical properties, albeit greatly reducing the computational burden. In this work a detailed FE model of a wind turbine tower is considered, reduced forms of this model are found using both the Craig Bampton and Dual Craig Bampton methods. These reduced order models are then used and compared in a Transitional Markov Chain Monte Carlo procedure to localise and quantify damage which is introduced to the system.

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction (pMOR) scheme for nonlinear structural dynamics, and the particular case of material nonlinearity. A physics-based parametric representation is developed, incorporating dependencies on system properties and/or excitation characteristics. The pMOR formulation relies on use of a Proper Orthogonal Decomposition applied to a series of snapshots of the nonlinear dynamic response. A new approach to manifold interpolation is proposed, with interpolation taking place on the reduced coefficient matrix mapping local bases to a global one. We demonstrate the performance of this approach firstly on the simple example of a shear-frame structure, and secondly on the more complex 3D numerical case study of an earthquake-excited wind turbine tower. Parametric dependence pertains to structural properties, as well as the temporal and spectral characteristics of the applied excitation. The developed parametric Reduced Order Model (pROM) can be exploited for a number of tasks including monitoring and diagnostics, control of vibrating structures, and residual life estimation of critical components., Comment: 23 pages, 28 figures

A common shortcoming of vibration-based damage localization techniques is that localized damages, i.e. small cracks, have a limited influence on the spectral characteristics of a structure. In contrast, even the smallest of defects, under particular loading conditions, cause localized strain concentrations with predictable spatial configuration. However, the effect of a small defect on strain decays quickly with distance from the defect, making strain-based localization rather challenging. In this work, an attempt is made to approximate, in a fully data-driven manner, the posterior distribution of a crack location, given arbitrary dynamic strain measurements at arbitrary discrete locations on a structure. The proposed technique leverages Graph Neural Networks (GNNs) and recent developments in scalable learning for Bayesian neural networks. The technique is demonstrated on the problem of inferring the position of an unknown crack via patterns of dynamic strain field measurements at discrete locations. The dataset consists of simulations of a hollow tube under random time-dependent excitations with randomly sampled crack geometry and orientation.