arXiv subjects

Johannes Hendriks

Publications and source records attributed to Johannes Hendriks.

9 recordsLinked to original sources

arXiv2023

A Bayesian Filtering Algorithm for Gaussian Mixture Models

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after both the time and measurement updates. In addition, a square-root implementation of the unified algorithm is presented and this algorithm is profiled on several simulated systems. This includes the state estimation for two non-linear systems that are strictly outside the class considered in this paper.

stat.ML↗

arXiv2021

Practical Bayesian System Identification using Hamiltonian Monte Carlo

This paper considers Bayesian parameter estimation of dynamic systems using a Markov Chain Monte Carlo (MCMC) approach. The Metroplis-Hastings (MH) algorithm is employed, and the main contribution of the paper is to examine and illustrate the efficacy of a particular proposal density based on energy preserving Hamiltonian dynamics, which results in what is known in the statistics literature as ``Hamiltonian Monte--Carlo'' (HMC). The very significant utility of this approach is that, as will be illustrated, it greatly reduces (almost to the point of elimination) the typically very high correlation in the Metropolis--Hastings chain which has been observed by several authors to restrict the application of the MH approach to only very low dimension model structures. The paper illustrates how the HMC approach may be applied to both significant dimension linear and nonlinear model structures, even when the system order is unknown, and using both simulated and real data.

stat.AP↗

arXiv2021

Intragranular Strain Estimation in Far-Field Scanning X-ray Diffraction using a Gaussian Processes

A new method for estimation of intragranular strain fields in polycrystalline materials based on scanning three-dimensional X-ray diffraction data (scanning-3DXRD) is presented and evaluated. Given an apriori known anisotropic compliance, the regression method enforces the balance of linear and angular momentum in the linear elastic strain field reconstruction. By using a Gaussian Process (GP), the presented method can yield a spatial estimate of the uncertainty of the reconstructed strain field. Furthermore, constraints on spatial smoothness can be optimised with respect to measurements through hyperparameter estimation. These three features address weaknesses discussed for previously existing scanning-3DXRD reconstruction methods and, thus, offers a more robust strain field estimation. The method is twofold validated; firstly by reconstruction from synthetic diffraction data and, secondly, by reconstruction of previously studied tin (Sn) grain embedded in a polycrystalline specimen. Comparison against reconstructions achieved by a recently proposed algebraic inversion technique is also presented. It is found that the GP regression consistently produces reconstructions with lower root mean squared errors, mean absolute errors and maximum absolute errors across all six components of strain.

cond-mat.mtrl-sci↗

arXiv2021

Linearly Constrained Neural Networks

We present a novel approach to modelling and learning vector fields from physical systems using neural networks that explicitly satisfy known linear operator constraints. To achieve this, the target function is modelled as a linear transformation of an underlying potential field, which is in turn modelled by a neural network. This transformation is chosen such that any prediction of the target function is guaranteed to satisfy the constraints. The approach is demonstrated on both simulated and real data examples.

stat.ML↗

arXiv2020

Variational State and Parameter Estimation

This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this work, a variational approach is used to provide an assumed density which approximates the desired, intractable, distribution. The approach is deterministic and results in an optimisation problem of a standard form. Due to the parametrisation of the assumed density selected first- and second-order derivatives are readily available which allows for efficient solutions. The proposed method is compared against state-of-the-art Hamiltonian Monte Carlo in two numerical examples.

stat.ML↗

arXiv2020

Bayesian Non-parametric Bragg-edge Fitting for Neutron Transmission Strain Imaging

Energy resolved neutron transmission techniques can provide high-resolution images of strain within polycrystalline samples allowing the study of residual strain and stress in engineered components. Strain is estimated from such data by analysing features known as Bragg-edges for which several methods exist. It is important for these methods to provide both accurate estimates of strain and an accurate quantification the associated uncertainty. Our contribution is twofold. First, we present a numerical simulation analysis of these existing methods, which shows that the most accurate estimates of strain are provided by a method that provides inaccurate estimates of certainty. Second, a novel Bayesian non-parametric method for estimating strain from Bragg-edges is presented. The numerical simulation analysis indicates that this method provides both competitive estimates of strain and accurate quantification of certainty, two demonstrations on experimental data are then presented.

cs.CE↗

arXiv2019

Deep kernel learning for integral measurements

Deep kernel learning refers to a Gaussian process that incorporates neural networks to improve the modelling of complex functions. We present a method that makes this approach feasible for problems where the data consists of line integral measurements of the target function. The performance is illustrated on computed tomography reconstruction examples.

stat.ML↗

arXiv2018

Probabilistic modelling and reconstruction of strain

This paper deals with modelling and reconstruction of strain fields, relying upon data generated from neutron Bragg-edge measurements. We propose a probabilistic approach in which the strain field is modelled as a Gaussian process, assigned a covariance structure customised by incorporation of the so-called equilibrium constraints. The computational complexity is significantly reduced by utilising an approximation scheme well suited for the problem. We illustrate the method on simulations and real data. The results indicate a high potential and can hopefully inspire the concept of probabilistic modelling to be used within other tomographic applications as well.

physics.data-an↗

arXiv2018

Tomographic Reconstruction of Two-Dimensional Residual Strain Fields from Bragg-Edge Neutron Imaging

Bragg-edge strain imaging from energy-resolved neutron transmission measurements poses an interesting tomography problem. The solution to this problem will allow the reconstruction of detailed triaxial stress and strain distributions within polycrystalline solids from sets of Bragg-edge strain images. Work over the last decade has provided some solutions for a limited number of special cases. In this paper, we provide a general approach to reconstruction of an arbitrary system based on a least squares process constrained by equilibrium. This approach is developed in two- dimensions before being demonstrated experimentally on two samples using the RADEN instrument at the J-PARC spallation neutron source in Japan. Validation of the resulting reconstructions is provided through a comparison to conventional constant wavelength strain measurements carried out on the KOWARI engineering diffractometer within ANSTO in Australia. The paper concludes with a discussion on the range of problems to be addressed in a three-dimensional implementation.

physics.app-ph↗