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Regression is a fundamental prediction task common in data-centric engineering applications that involves learning mappings between continuous variables. In many engineering applications (e.g., structural health monitoring), feature-label pairs used to learn such mappings are of limited availability, which hinders the effectiveness of traditional supervised machine learning approaches. This paper proposes a methodology for overcoming the issue of data scarcity by combining active learning (AL) for regression with hierarchical Bayesian modeling. AL is an approach for preferentially acquiring feature-label pairs in a resource-efficient manner. In particular, the current work adopts a risk-informed approach that leverages contextual information associated with regression-based engineering decision-making tasks (e.g., inspection and maintenance). Hierarchical Bayesian modeling allow multiple related regression tasks to be learned over a population, capturing local and global effects. The information sharing facilitated by this modeling approach means that information acquired for one engineering system can improve predictive performance across the population. The proposed methodology is demonstrated using an experimental case study. Specifically, multiple regressions are performed over a population of machining tools, where the quantity of interest is the surface roughness of the workpieces. An inspection and maintenance decision process is defined using these regression tasks, which is in turn used to construct the active-learning algorithm. The novel methodology proposed is benchmarked against an uninformed approach to label acquisition and independent modeling of the regression tasks. It is shown that the proposed approach has superior performance in terms of expected cost—maintaining predictive performance while reducing the number of inspections required.

Abstract 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. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for 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.

Population-based structural health monitoring (PBSHM) systems use data from multiple structures to make inferences of health states. An area of PBSHM that has recently been recognized for potential development is the use of multitask learning (MTL) algorithms that differ from traditional single-task learning. This study presents an application of the MTL approach, Joint Feature Selection with LASSO, to provide automatic feature selection. The algorithm is applied to two structural datasets. The first dataset covers a binary classification between the port and starboard side of an aircraft tailplane, for samples from two aircraft of the same model. The second dataset covers normal and damaged conditions for pre- and postrepair of the same aircraft wing. Both case studies demonstrate that the MTL results are interpretable, highlighting features that relate to structural differences by considering the patterns shared between tasks. This is opposed to single-task learning, which improved accuracy at the cost of interpretability and selected features, which failed to generalize in previously unobserved experiments.

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 the 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, and reliability communities, and provide directions to researchers and practitioners working towards more pervasive monitoring-based decision-support.

Abstract Offshore wind power has been in the spotlight among renewable energy sources. The current trends of increased power ratings and longer blades come together with the aim to reduce energy costs by design optimisation. The standard approach to deal with uncertainties in wind‐turbine design has been by the use of characteristic values and safety factors. This paper focusses on modelling the effect of structural and aerodynamic uncertainties in blades. First, the uncertainties in laminate properties are characterised and propagated in a blade structural model by means of a Monte Carlo simulation. Wind tunnel measurement data are then used to define the variability in lift and drag coefficients for both clean and rough aerofoil behaviour, which is then used to extrapolate rough behaviours throughout the blade. A stochastic spatial interpolation parameter is used to define the evolution of the degradation level. The combined effect and the variance contribution of these two uncertainty sources in turbine loads is finally defined by aeroelastic turbine simulation. This research aims to provide a framework to deal with uncertainties in wind‐turbine blade design and understand their effects in turbine behaviour.

Non-linear analysis is of increasing importance in wind energy engineering as a result of their exposure in extreme conditions and the ever-increasing size and slenderness of wind turbines. Whilst modern computing capabilities facilitate execution of complex analyses, certain applications which require multiple or real-time analyses remain a challenge, motivating adoption of accelerated computing schemes, such as reduced order modelling (ROM) methods. Soil structure interaction (SSI) simulations fall in this class of problems, with the non-linear restoring force significantly affecting the dynamic behaviour of the turbine. In this work, we propose a ROM approach to the SSI problem using a recently developed ROM methodology. We exploit a data-driven non-linear ROM methodology coupling an autoencoder with long short-term memory (LSTM) neural networks. The ROM is trained to emulate a steel monopile foundation constrained by non-linear soil and subject to forces and moments at the top of the foundation, which represent the equivalent loading of an operating turbine under wind and wave forcing. The ROM well approximates the time domain and frequency domain response of the Full Order Model (FOM) over a range of different wind and wave loading regimes, whilst reducing the computational toll by a factor of 300. We further propose an error metric for capturing isolated failure instances of the ROM.

Ultrasonic guided waves offer a convenient and practical approach to structural health monitoring and non-destructive evaluation. A key property of guided waves is the fully defined relationship between central frequency and propagation characteristics (phase velocity, group velocity and wavenumber)—which is described using dispersion curves. For many guided wave-based strategies, accurate dispersion curve information is invaluable, such as group velocity for localisation. From experimental observations of dispersion curves, a system identification procedure can be used to determine the governing material properties. As well as returning an estimated value, it is useful to determine the distribution of these properties based on measured data. A method of simulating samples from these distributions is to use the iterative Markov-Chain Monte Carlo (MCMC) procedure, which allows for freedom in the shape of the posterior. In this work, a scanning-laser Doppler vibrometer is used to record the propagation of Lamb waves in a unidirectional-glass-fibre composite plate, and dispersion curve data for various propagation angles are extracted. Using these measured dispersion curve data, the MCMC sampling procedure is performed to provide a Bayesian approach to determining the dispersion curve information for an arbitrary plate. The distribution of the material properties at each angle is discussed, including the inferred confidence in the predicted parameters. The percentage errors of the estimated values for the parameters were 10–15 points larger when using the most likely estimates, as opposed to calculating from the posterior distributions, highlighting the advantages of using a probabilistic approach.

A framework is proposed for generative models as a basis for digital twins or mirrors of structures. The proposal is based on the premise that deterministic models cannot account for the uncertainty present in most structural modeling applications. Two different types of generative models are considered here. The first is a physics-based model based on the stochastic finite element (SFE) method, which is widely used when modeling structures that have material and loading uncertainties imposed. Such models can be calibrated according to data from the structure and would be expected to outperform any other model if the modeling accurately captures the true underlying physics of the structure. The potential use of SFE models as digital mirrors is illustrated via application to a linear structure with stochastic material properties. For situations where the physical formulation of such models does not suffice, a data-driven framework is proposed, using machine learning and conditional generative adversarial networks (cGANs). The latter algorithm is used to learn the distribution of the quantity of interest in a structure with material nonlinearities and uncertainties. For the examples considered in this work, the data-driven cGANs model outperforms the physics-based approach. Finally, an example is shown where the two methods are coupled such that a hybrid model approach is demonstrated.

One of the main problems in data-based Structural Health Monitoring (SHM), is the scarcity of measured data corresponding to damage states in the structures of interest. One approach to solving this problem is to develop methods of transferring health inferences and information between structures in an identified population—Population-based SHM (PBSHM). In the case of homogenous populations (sets of nominally-identical structures, like in a wind farm), the idea of the form has been proposed which encodes information about the ideal or typical structure together with information about variations across the population. In the case of sets of disparate structures—heterogeneous populations—transfer learning appears to be a powerful tool for sharing inferences, and is also applicable in the homogenous case. In order to assess the likelihood of transference being meaningful, it has proved useful to develop an abstract representation framework for spaces of structures, so that similarities between structures can formally be assessed; this framework exploits tools from graph theory. The current paper discusses all of these very recent developments and provides illustrative examples.

The current work introduces a novel combination of two Bayesian tools, Gaussian Processes (GPs), and the use of the Approximate Bayesian Computation (ABC) algorithm for kernel selection and parameter estimation for machine learning applications. The combined methodology that this research article proposes and investigates offers the possibility to use different metrics and summary statistics of the kernels used for Bayesian regression. The presented work moves a step toward online, robust, consistent, and automated mechanism to formulate optimal kernels (or even mean functions) and their hyperparameters simultaneously offering confidence evaluation when these tools are used for mathematical or engineering problems such as structural health monitoring (SHM) and system identification (SI).