Latent degradation indicators estimation and prediction : a Monte Carlo approach

Asset health inspections can produce two types of indicators: (1) direct indicators (e.g. the thickness of a brake pad, and the crack depth on a gear) which directly relate to a failure mechanism; and (2) indirect indicators (e.g. the indicators extracted from vibration signals and oil analysis data) which can only partially reveal a failure mechanism. While direct indicators enable more precise references to asset health condition, they are often more difficult to obtain than indirect indicators. The state space model provides an efficient approach to estimating direct indicators by using indirect indicators. However, existing state space models to estimate direct indicators largely depend on assumptions such as, discrete time, discrete state, linearity, and Gaussianity. The discrete time assumption requires fixed inspection intervals. The discrete state assumption entails discretising continuous degradation indicators, which often introduces additional errors. The linear and Gaussian assumptions are not consistent with nonlinear and irreversible degradation processes in most engineering assets. This paper proposes a state space model without these assumptions. Monte Carlo-based algorithms are developed to estimate the model parameters and the remaining useful life. These algorithms are evaluated for performance using numerical simulations through MATLAB. The result shows that both the parameters and the remaining useful life are estimated accurately. Finally, the new state space model is used to process vibration and crack depth data from an accelerated test of a gearbox. During this application, the new state space model shows a better fitness result than the state space model with linear and Gaussian assumption.

A sequential Monte Carlo approach to design for population pharmacokinetics studies

Here we present a sequential Monte Carlo approach that can be used to find optimal designs. Our focus is on the design of phase III clinical trials where the derivation of sampling windows is required, along with the optimal sampling schedule. The search is conducted via a particle filter which traverses a sequence of target distributions artificially constructed via an annealed utility. The algorithm derives a catalogue of highly efficient designs which, not only contain the optimal, but can also be used to derive sampling windows. We demonstrate our approach by designing a hypothetical phase III clinical trial.

A sequential Monte Carlo approach to the sequential design for discriminating between rival continuous data models

Here we present a sequential Monte Carlo approach to Bayesian sequential design for the incorporation of model uncertainty. The methodology is demonstrated through the development and implementation of two model discrimination utilities; mutual information and total separation, but it can also be applied more generally if one has different experimental aims. A sequential Monte Carlo algorithm is run for each rival model (in parallel), and provides a convenient estimate of the marginal likelihood (of each model) given the data, which can be used for model comparison and in the evaluation of utility functions. A major benefit of this approach is that it requires very little problem specific tuning and is also computationally efficient when compared to full Markov chain Monte Carlo approaches. This research is motivated by applications in drug development and chemical engineering.

Adaptive sequential Monte Carlo approach for real-time applications

This paper presents an adaptive Sequential Monte Carlo approach for real-time applications. Sequential Monte Carlo method is employed to estimate the states of dynamic systems using weighted particles. The proposed approach reduces the run-time computation complexity by adapting the size of the particle set. Multiple processing elements on FPGAs are dynamically allocated for improved energy efficiency without violating real-time constraints. A robot localisation application is developed based on the proposed approach. Compared to a non-adaptive implementation, the dynamic energy consumption is reduced by up to 70% without affecting the quality of solutions. © 2012 IEEE.

Is the pinning of ordinary dislocations in γ-TiAl intrinsic or extrinsic in nature? A combined atomistic and kinetic Monte Carlo approach

We address the question of the observed pinning of 1/2

Anisotropic seismic inversion using a multigrid Monte Carlo approach

We propose a new approach for the inversion of anisotropic P-wave data based on Monte Carlo methods combined with a multigrid approach. Simulated annealing facilitates objective minimization of the functional characterizing the misfit between observed and predicted traveltimes, as controlled by the Thomsen anisotropy parameters (epsilon, delta). Cycling between finer and coarser grids enhances the computational efficiency of the inversion process, thus accelerating the convergence of the solution while acting as a regularization technique of the inverse problem. Multigrid perturbation samples the probability density function without the requirements for the user to adjust tuning parameters. This increases the probability that the preferred global, rather than a poor local, minimum is attained. Undertaking multigrid refinement and Monte Carlo search in parallel produces more robust convergence than does the initially more intuitive approach of completing them sequentially. We demonstrate the usefulness of the new multigrid Monte Carlo (MGMC) scheme by applying it to (a) synthetic, noise-contaminated data reflecting an isotropic subsurface of constant slowness, horizontally layered geologic media and discrete subsurface anomalies; and (b) a crosshole seismic data set acquired by previous authors at the Reskajeage test site in Cornwall, UK. Inverted distributions of slowness (s) and the Thomson anisotropy parameters (epsilon, delta) compare favourably with those obtained previously using a popular matrix-based method. Reconstruction of the Thomsen epsilon parameter is particularly robust compared to that of slowness and the Thomsen delta parameter, even in the face of complex subsurface anomalies. The Thomsen epsilon and delta parameters have enhanced sensitivities to bulk-fabric and fracture-based anisotropies in the TI medium at Reskajeage. Because reconstruction of slowness (s) is intimately linked to that epsilon and delta in the MGMC scheme, inverted images of phase velocity reflect the integrated effects of these two modes of anisotropy. The new MGMC technique thus promises to facilitate rapid inversion of crosshole P-wave data for seismic slownesses and the Thomsen anisotropy parameters, with minimal user input in the inversion process.

Root Cause Analysis by a Combined Sparse Classification and Monte Carlo Approach

Classification methods with embedded feature selection capability are very appealing for the analysis of complex processes since they allow the analysis of root causes even when the number of input variables is high. In this work, we investigate the performance of three techniques for classification within a Monte Carlo strategy with the aim of root cause analysis. We consider the naive bayes classifier and the logistic regression model with two different implementations for controlling model complexity, namely, a LASSO-like implementation with a L1 norm regularization and a fully Bayesian implementation of the logistic model, the so called relevance vector machine. Several challenges can arise when estimating such models mainly linked to the characteristics of the data: a large number of input variables, high correlation among subsets of variables, the situation where the number of variables is higher than the number of available data points and the case of unbalanced datasets. Using an ecological and a semiconductor manufacturing dataset, we show advantages and drawbacks of each method, highlighting the superior performance in term of classification accuracy for the relevance vector machine with respect to the other classifiers. Moreover, we show how the combination of the proposed techniques and the Monte Carlo approach can be used to get more robust insights into the problem under analysis when faced with challenging modelling conditions.

Parallel Monte Carlo approach for integration of the rendering equation

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the rendering equation in the context of the parallel sampling scheme for hemisphere. Our aim is to apply this sampling scheme to stratified Monte Carlo integration method for parallel solving of the rendering equation. The domain for integration of the rendering equation is a hemisphere. We divide the hemispherical domain into a number of equal sub-domains of orthogonal spherical triangles. This domain partitioning allows to solve the rendering equation in parallel. It is known that the Neumann series represent the solution of the integral equation as a infinity sum of integrals. We approximate this sum with a desired truncation error (systematic error) receiving the fixed number of iteration. Then the rendering equation is solved iteratively using Monte Carlo approach. At each iteration we solve multi-dimensional integrals using uniform hemisphere partitioning scheme. An estimate of the rate of convergence is obtained using the stratified Monte Carlo method. This domain partitioning allows easy parallel realization and leads to convergence improvement of the Monte Carlo method. The high performance and Grid computing of the corresponding Monte Carlo scheme are discussed.

A new solution of the rendering equation with stratified Monte Carlo approach

This paper is turned to the advanced Monte Carlo methods for realistic image creation. It offers a new stratified approach for solving the rendering equation. We consider the numerical solution of the rendering equation by separation of integration domain. The hemispherical integration domain is symmetrically separated into 16 parts. First 9 sub-domains are equal size of orthogonal spherical triangles. They are symmetric each to other and grouped with a common vertex around the normal vector to the surface. The hemispherical integration domain is completed with more 8 sub-domains of equal size spherical quadrangles, also symmetric each to other. All sub-domains have fixed vertices and computable parameters. The bijections of unit square into an orthogonal spherical triangle and into a spherical quadrangle are derived and used to generate sampling points. Then, the symmetric sampling scheme is applied to generate the sampling points distributed over the hemispherical integration domain. The necessary transformations are made and the stratified Monte Carlo estimator is presented. The rate of convergence is obtained and one can see that the algorithm is of super-convergent type.

Quasi Monte Carlo approach with uniform separation for solving of the rendering equation, ICNAAM 2007

This paper is directed to the advanced parallel Quasi Monte Carlo (QMC) methods for realistic image synthesis. We propose and consider a new QMC approach for solving the rendering equation with uniform separation. First, we apply the symmetry property for uniform separation of the hemispherical integration domain into 24 equal sub-domains of solid angles, subtended by orthogonal spherical triangles with fixed vertices and computable parameters. Uniform separation allows to apply parallel sampling scheme for numerical integration. Finally, we apply the stratified QMC integration method for solving the rendering equation. The superiority our QMC approach is proved.

A Monte Carlo Approach for the Cook -Torrance Model

In this work we consider the rendering equation derived from the illumination model called Cook-Torrance model. A Monte Carlo (MC) estimator for numerical treatment of the this equation, which is the Fredholm integral equation of second kind, is constructed and studied.