Multiscale Surrogate Modeling and Uncertainty Quantification for Periodic Composite Structures

Computational modeling of the structural behavior of continuous fiber composite materials often takes into account the periodicity of the underlying micro-structure. A well established method dealing with the structural behavior of periodic micro-structures is the so- called Asymptotic Expansion Homogenization (AEH). By considering a periodic perturbation of the material displacement, scale bridging functions, also referred to as elastic correctors, can be derived in order to connect the strains at the level of the macro-structure with micro- structural strains. For complicated inhomogeneous micro-structures, the derivation of such functions is usually performed by the numerical solution of a PDE problem - typically with the Finite Element Method. Moreover, when dealing with uncertain micro-structural geometry and material parameters, there is considerable uncertainty introduced in the actual stresses experienced by the materials. Due to the high computational cost of computing the elastic correctors, the choice of a pure Monte-Carlo approach for dealing with the inevitable material and geometric uncertainties is clearly computationally intractable. This problem is even more pronounced when the effect of damage in the micro-scale is considered, where re-evaluation of the micro-structural representative volume element is necessary for every occurring damage. The novelty in this paper is that a non-intrusive surrogate modeling approach is employed with the purpose of directly bridging the macro-scale behavior of the structure with the material behavior in the micro-scale, therefore reducing the number of costly evaluations of corrector functions, allowing for future developments on the incorporation of fatigue or static damage in the analysis of composite structural components.Comment: Appeared in UNCECOMP 201

Machine Learning for Structural Health Assessment under Uncertainty: with applications in Wind Energy

The engineering sub-discipline of Structural Health Monitoring (SHM) promises that actionable insights on the current and future structural condition of monitored structures (e.g., wind turbines, bridges or critical components such as bearings) can be achieved through sensing and the subsequent inference of suited computational models. The main tools of SHM are system identification and computation, with the possible incorporation of physics-based models. Wind energy generation is an important factor in directly mitigating climate change by facilitating the reduction of energy production-related carbon emissions. The viability of wind energy projects, hinges upon the ratio of the expected long-term power produced, to the cost of installation, operation, repair, and maintenance of wind turbines. By forecasting and detecting damages and potential degradation of wind turbines in a timely and robust manner, a core target of SHM, repair and maintenance-associated downtimes can be reduced, thus improving the long-term viability of wind energy infrastructure. Currently, available SHM techniques underperform when dealing with very high-dimensional and high-volume data and often under-deliver due to simplifications for computational convenience of probabilistic and model-form assumptions underlying them. Through the course of the last two decades, Machine Learning (ML), and in particular Deep Learning, routinely proves to be a superior approach to flexible function approximation when adequate amounts of data are available. Moreover, in the last decade, scalable and effective techniques have emerged for the representation of uncertainty directly from data via the use of deep neural networks. This dissertation introduces these deep learning tools, to SHM problems, with a particular focus on wind energy applications. In data-driven methods, and in particular, in deep learning, the underlying structure of problems is often neglected, since the main expectation is that these models discover the hidden structure directly from data. This approach often introduces spurious correlations between variables and negatively affects generalization. In addressing this issue, this thesis proposes a technique that allows for the flexible exploitation of known, or partially known, relations of entities involved in a problem (relational inductive biases), termed Graph Neural Networks (GNNs). The first application introduced in this thesis in chapter 5, is the application of variational Bayesian deep neural networks for the distribution of cross-section fatigue estimates available in finite element simulation meshes. The proposed technique is useful in estimating the distribution of fatigue estimates on turbine blade cross-sections, from coarse SCADA information and fatigue simulations, to enable long-term fatigue accumulation prediction under uncertainty. A problem in wind-energy related SHM, where it is of use to incorporate the problem structure, is the modeling of the statistics of operational data of turbines in a farm, where encoding the relative position of turbines in the learning algorithm is an mportant relational inductive bias. This case is treated in chapter 6. The technique is demonstrated in real and simulated farm data, demonstrating generalization in novel farm geometries for the simulated data. It is shown that the proposed technique comprises a combination of other recently proposed approaches to learning on data from stochastic processes, and shows good generalization on a synthetic benchmark example for one-dimensional Gaussian process regression. In chapter 7, a supervised learning problem where the incorporation of geometric relations plays a key role is presented. The problem treats the fusion of data from an arbitrarily positioned set of sensors and, in particular, sensors deployed on a beam of circular cross-section. The relative position of the sensors needs to be incorporated in the learning procedure since in order to infer the position of a defect, it needs to be taken into account jointly with the sensor readings. The developed technique performs well with a relatively small number of training examples and incorporates variational Bayesian neural network layers that allow for representing the uncertainty in the learned model. In chapter 8, predictive data-driven models are developed for addressing the ultimate step of the SHM hierarchy, i.e., the problem of remaining useful life (RUL) estimation. The models are trained on time series corresponding to synthetic and real data on degradation of critical structural/industrial components, namely bearings. Through the use of graph networks, predictive models that operate on irregularly sampled data, which do not process the time series in a sequential manner are developed. Although the actual bearings where this method was employed do not correspond to bearings from wind turbines, the developed techniques are straightforwardly transferable to real use-cases. The proposed GNN techniques cover supervised (predictive tasks, such as localization), unsupervised (deep latent variable modeling for the distribution of operational data), and semi-supervised learning (i.e., data imputation for operational data). The dissertation concludes in chapter 9, where further applications and possible extensions of this work are discussed

Deep CNNs and Adversarial Regularization for Fatigue Damage Failure Prediction of Concrete Anchors

Fatigue experiments present with large scatter even for identical specimens tested under controlled laboratory conditions. It has long been known that variations in the mechanical behavior of fatigued metals occur, such as hardening or softening and variations on the shape of hysteresis curves. In order to incorporate measurements in the fatigue life prediction of concrete anchors, a fully data-driven model, using load-displacement and acceleration data, was trained to predict directly the remaining cycles to failure for anchors embedded in cracked concrete loaded in variable amplitude fatigue

Remaining Useful Life Estimation for Engineered Systems Operating under Uncertainty with Causal GraphNets

In this work, a novel approach, termed GNN-tCNN, is presented for the construction and training of Remaining Useful Life (RUL) models. The method exploits Graph Neural Networks (GNNs) and deals with the problem of efficiently learning from time series with non-equidistant observations, which may span multiple temporal scales. 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 learns a model that describes the evolution of the system implicitly rather than at the raw observation level and is based on message-passing neural networks, which encode the irregularly sampled causal structure. The proposed approach is compared to a recurrent network with a temporal convolutional feature extractor head (LSTM-tCNN), which forms a viable alternative for the problem considered. Finally, by taking advantage of recent advances in the computation of reparametrization gradients for learning probability distributions, a simple, yet efficient, technique is employed for representing prediction uncertainty as a gamma distribution over RUL predictions.ISSN:1424-822

Conditional variational autoencoders for probabilistic wind turbine blade fatigue estimation using Supervisory, Control, and Data Acquisition data

Wind turbine fatigue estimation is based on time-consuming Monte Carlo simulations for various wind conditions, followed by cycle-counting procedures and the application of engineering damage models. The outputs of the fatigue simulations are large in volume and of high dimensionality, as they typically consist of estimates on finite-element computational meshes. The strain and stress tensor time series, which are the primary quantities of interest when considering the problem of fatigue estimation, are dictated by complex vibration characteristics due to the coupled effect of aerodynamics, structural dynamics, geometrically non-linear mechanics, and control. A Variational Auto-Encoder (VAE) is trained in order to model the probability distribution of the accumulated fatigue on the root cross-section of a simulated wind turbine blade. The VAE is conditioned on historical data that correspond to coarse wind-field measurement statistics, such as mean hub-height wind speed, standard deviation of hub-height wind speed and shear exponent. In the absence of direct measurements of structural loads, the proposed technique finds applications in making long-term probabilistic deterioration predictions from historical Supervisory, Control, and Data Acquisition (SCADA) data, while capturing the inherent aleatoric uncertainty due to the incomplete information on strain time series of the wind turbine structure, when only SCADA data statistics are available

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

Surrogate Modelling For Fatigue Damage of Wind-Turbine Blades Using Polynomial Chaos Expansions And Non-Negative Matrix Factorization

ISSN:2221-378