arXiv subjects

Eleni Chatzi

Publications and source records attributed to Eleni Chatzi.

At least 73 records · Page 4Linked to original sources

arXiv2022

A Graded Metamaterial for Broadband and High-capability Piezoelectric Energy Harvesting

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.

physics.app-ph↗

arXiv2022

A framework for quantifying the value of vibration-based structural health monitoring

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.

stat.AP↗

arXiv2022

On off-line and on-line Bayesian filtering for uncertainty quantification of structural deterioration

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.

stat.CO↗

arXiv2022

Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty

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.

cs.LG↗

arXiv2022

Which Model to Trust: Assessing the Influence of Models on the Performance of Reinforcement Learning Algorithms for Continuous Control Tasks

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.

cs.LG↗

arXiv2022

Nonlinear Reduced Order Modelling of Soil Structure Interaction Effects via LSTM and Autoencoder Neural Networks

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.

cs.CE↗

arXiv2021

An adapted deflated conjugate gradient solver for robust extended/generalised finite element solutions of large scale, 3D crack propagation problems

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.

cs.CE↗

arXiv2021

Mitigation of Rayleigh-like waves in granular media via multi-layer resonant metabarriers

In this work, we experimentally and numerically investigate the propagation and attenuation of vertically polarized surface waves in an unconsolidated granular medium equipped with small-scale metabarriers of different depths, i.e., arrays composed of one, two, and three embedded layers of sub-wavelength resonators. Our findings reveal how such a multi-layer arrangement strongly affects the attenuation of the surface wave motion within and after the barrier. When the surface waves collide with the barriers, the wavefront is back-scattered and steered downward underneath the oscillators. Due to the stiffness gradient of the granular medium, part of the wavefield is then rerouted to the surface level after overcoming the resonant array. Overall, the in-depth insertion of additional layers of resonators leads to a greater and broader band wave attenuation when compared to the single layer case.

physics.geo-ph↗

arXiv2021

Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks

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.

cs.CE↗

arXiv2021

Moment fitted cut spectral elements for explicit analysis of guided wave propagation

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.

cs.CE↗

arXiv2021

Relational VAE: A Continuous Latent Variable Model for Graph Structured Data

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.

cs.CE↗

arXiv2021

On the Potential of Dynamic Substructuring Methods for Model Updating

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.

cs.CE↗

arXiv2021

Value of information from vibration-based structural health monitoring extracted via Bayesian model updating

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.

stat.AP↗

arXiv2021

Foundations of Population-Based SHM, Part IV: The Geometry of Spaces of Structures and their Feature Spaces

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.

stat.ML↗

arXiv2020

Remaining Useful Life Estimation Under Uncertainty with Causal GraphNets

In this work, a novel approach for the construction and training of time series models is presented that deals with the problem of learning on large time series with non-equispaced observations, which at the same time may possess features of interest that span multiple scales. The proposed method is appropriate for constructing predictive models for non-stationary stochastic time series.The efficacy of the method is demonstrated on a simulated stochastic degradation dataset and on a real-world accelerated life testing dataset for ball-bearings. The proposed method, which is based on GraphNets, implicitly learns a model that describes the evolution of the system at the level of a state-vector rather than of a raw observation. The proposed approach is compared to a recurrent network with a temporal convolutional feature extractor head (RNN-tCNN) which forms a known viable alternative for the problem context considered. Finally, by taking advantage of recent advances in the computation of reparametrization gradients for learning probability distributions, a simple yet effective technique for representing prediction uncertainty as a Gamma distribution over remaining useful life predictions is employed.

cs.LG↗

arXiv2020

On Dynamic Substructuring of Systems with Localised Nonlinearities

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.

cs.CE↗

arXiv2020

On the use of Nonlinear Normal Modes for Nonlinear Reduced Order Modelling

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.

math.NA↗

arXiv2020

A local basis approximation approach for nonlinear parametric model order reduction

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.

math.NA↗