arXiv subjects

Keith Worden

Publications and source records attributed to Keith Worden.

41 records · Page 3Linked to original sources

arXiv2021

A probabilistic risk-based decision framework for structural health monitoring

Obtaining the ability to make informed decisions regarding the operation and maintenance of structures, provides a major incentive for the implementation of structural health monitoring (SHM) systems. Probabilistic risk assessment (PRA) is an established methodology that allows engineers to make risk-informed decisions regarding the design and operation of safety-critical and high-value assets in industries such as nuclear and aerospace. The current paper aims to formulate a risk-based decision framework for structural health monitoring that combines elements of PRA with the existing SHM paradigm. As an apt tool for reasoning and decision-making under uncertainty, probabilistic graphical models serve as the foundation of the framework. The framework involves modelling failure modes of structures as Bayesian network representations of fault trees and then assigning costs or utilities to the failure events. The fault trees allow for information to pass from probabilistic classifiers to influence diagram representations of decision processes whilst also providing nodes within the graphical model that may be queried to obtain marginal probability distributions over local damage states within a structure. Optimal courses of action for structures are selected by determining the strategies that maximise expected utility. The risk-based framework is demonstrated on a realistic truss-like structure and supported by experimental data. Finally, a discussion of the risk-based approach is made and further challenges pertaining to decision-making processes in the context of SHM are identified.

stat.AP↗

arXiv2021

Structured Machine Learning Tools for Modelling Characteristics of Guided Waves

The use of ultrasonic guided waves to probe the materials/structures for damage continues to increase in popularity for non-destructive evaluation (NDE) and structural health monitoring (SHM). The use of high-frequency waves such as these offers an advantage over low-frequency methods from their ability to detect damage on a smaller scale. However, in order to assess damage in a structure, and implement any NDE or SHM tool, knowledge of the behaviour of a guided wave throughout the material/structure is important (especially when designing sensor placement for SHM systems). Determining this behaviour is extremely diffcult in complex materials, such as fibre-matrix composites, where unique phenomena such as continuous mode conversion takes place. This paper introduces a novel method for modelling the feature-space of guided waves in a composite material. This technique is based on a data-driven model, where prior physical knowledge can be used to create structured machine learning tools; where constraints are applied to provide said structure. The method shown makes use of Gaussian processes, a full Bayesian analysis tool, and in this paper it is shown how physical knowledge of the guided waves can be utilised in modelling using an ML tool. This paper shows that through careful consideration when applying machine learning techniques, more robust models can be generated which offer advantages such as extrapolation ability and physical interpretation.

stat.ML↗

arXiv2020

A Bayesian methodology for localising acoustic emission sources in complex structures

In the field of structural health monitoring (SHM), the acquisition of acoustic emissions to localise damage sources has emerged as a popular approach. Despite recent advances, the task of locating damage within composite materials and structures that contain non-trivial geometrical features, still poses a significant challenge. Within this paper, a Bayesian source localisation strategy that is robust to these complexities is presented. Under this new framework, a Gaussian process is first used to learn the relationship between source locations and the corresponding difference-in-time-of-arrival values for a number of sensor pairings. As an acoustic emission event with an unknown origin is observed, a mapping is then generated that quantifies the likelihood of the emission location across the surface of the structure. The new probabilistic mapping offers multiple benefits, leading to a localisation strategy that is more informative than deterministic predictions or single-point estimates with an associated confidence bound. The performance of the approach is investigated on a structure with numerous complex geometrical features and demonstrates a favourable performance in comparison to other similar localisation methods.

cs.LG↗

arXiv2020

On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression

This paper presents the use of spike-and-slab (SS) priors for discovering governing differential equations of motion of nonlinear structural dynamic systems. The problem of discovering governing equations is cast as that of selecting relevant variables from a predetermined dictionary of basis variables and solved via sparse Bayesian linear regression. The SS priors, which belong to a class of discrete-mixture priors and are known for their strong sparsifying (or shrinkage) properties, are employed to induce sparse solutions and select relevant variables. Three different variants of SS priors are explored for performing Bayesian equation discovery. As the posteriors with SS priors are analytically intractable, a Markov chain Monte Carlo (MCMC)-based Gibbs sampler is employed for drawing posterior samples of the model parameters; the posterior samples are used for variable selection and parameter estimation in equation discovery. The proposed algorithm has been applied to four systems of engineering interest, which include a baseline linear system, and systems with cubic stiffness, quadratic viscous damping, and Coulomb damping. The results demonstrate the effectiveness of the SS priors in identifying the presence and type of nonlinearity in the system. Additionally, comparisons with the Relevance Vector Machine (RVM) - that uses a Student's-t prior - indicate that the SS priors can achieve better model selection consistency, reduce false discoveries, and derive models that have superior predictive accuracy. Finally, the Silverbox experimental benchmark is used to validate the proposed methodology.

stat.ME↗

arXiv2020

Considering discrepancy when calibrating a mechanistic electrophysiology model

Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterise uncertainty in model inputs and how that propagates through to outputs or predictions. In this perspective piece we draw attention to an important and under-addressed source of uncertainty in our predictions -- that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes (GPs) and autoregressive-moving-average (ARMA) models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided.

stat.CO↗