Search results for "Uncertainty quantification"
showing 10 items of 29 documents
Stochastic Galerkin method for cloud simulation
2018
AbstractWe develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. The developed stochastic Galerkin method combines the space-time approximation obtained by a suitable finite volume method with a spectral-type approximation based on the generalized polynomial chaos expansion in the stochastic space. The resulting numerical scheme yields a second-order accurate approximation in both space and time and exponential convergence in the stochastic space. Our numerical results…
Autonomous ultrasonic inspection using Bayesian optimisation and robust outlier analysis
2020
The use of robotics is beginning to play a key role in automating the data collection process in Non Destructive Testing (NDT). Increasing the use of automation quickly leads to the gathering of large quantities of data, which makes it inefficient, perhaps even infeasible, for a human to parse the information contained in them. This paper presents a solution to this problem by making the process of NDT data acquisition an autonomous one as opposed to an automatic one. In order to achieve this, the robotic data acquisition task is treated as an optimisation problem, where one seeks to find locations with the highest indication of damage. The resulting algorithm combines damage detection tech…
Predictive Model Markup Language (PMML) Representation of Bayesian Networks: An Application in Manufacturing
2018
International audience; Bayesian networks (BNs) represent a promising approach for the aggregation of multiple uncertainty sources in manufacturing networks and other engineering systems for the purposes of uncertainty quantification, risk analysis, and quality control. A standardized representation for BN models will aid in their communication and exchange across the web. This article presents an extension to the predictive model markup language (PMML) standard for the representation of a BN, which may consist of discrete variables, continuous variables, or their combination. The PMML standard is based on extensible markup language (XML) and used for the representation of analytical models…
Uncertainty quantification on a spatial Markov-chain model for the progression of skin cancer
2019
AbstractA spatial Markov-chain model is formulated for the progression of skin cancer. The model is based on the division of the computational domain into nodal points, that can be in a binary state: either in ‘cancer state’ or in ‘non-cancer state’. The model assigns probabilities for the non-reversible transition from ‘non-cancer’ state to the ‘cancer state’ that depend on the states of the neighbouring nodes. The likelihood of transition further depends on the life burden intensity of the UV-rays that the skin is exposed to. The probabilistic nature of the process and the uncertainty in the input data is assessed by the use of Monte Carlo simulations. A good fit between experiments on mi…
Uncertainty quantification in simulations of epidemics using polynomial chaos.
2012
Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equa…
Gaussian Process Regression (GPR) Representation in Predictive Model Markup Language (PMML)
2017
International audience; This paper describes Gaussian process regression (GPR) models presented in predictive model markup language (PMML). PMML is an extensible-markup-language (XML) -based standard language used to represent data-mining and predictive analytic models, as well as pre- and post-processed data. The previous PMML version, PMML 4.2, did not provide capabilities for representing probabilistic (stochastic) machine-learning algorithms that are widely used for constructing predictive models taking the associated uncertainties into consideration. The newly released PMML version 4.3, which includes the GPR model, provides new features: confidence bounds and distribution for the pred…
Automated Uncertainty Quantification Through Information Fusion in Manufacturing Processes
2017
International audience; Evaluation of key performance indicators (KPIs) such as energy consumption is essential for decision-making during the design and operation of smart manufacturing systems. The measurements of KPIs are strongly affected by several uncertainty sources such as input material uncertainty, the inherent variability in the manufacturing process, model uncertainty, and the uncertainty in the sensor measurements of operational data. A comprehensive understanding of the uncertainty sources and their effect on the KPIs is required to make the manufacturing processes more efficient. Towards this objective, this paper proposed an automated methodology to generate a hierarchical B…
Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters
2020
[EN] In spite of its simple formulation via a nonlinear differential equation, the Gompertz model has been widely applied to describe the dynamics of biological and biophysical parts of complex systems (growth of living organisms, number of bacteria, volume of infected cells, etc.). Its parameters or coefficients and the initial condition represent biological quantities (usually, rates and number of individual/particles, respectively) whose nature is random rather than deterministic. In this paper, we present a complete uncertainty quantification analysis of the randomized Gomperz model via the computation of an explicit expression to the first probability density function of its solution s…
Computational nuclear quantum many-body problem: The UNEDF project
2013
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. The primary focus of the project was on constructing, validating, and applying an optimized nuclear energy density functional, which entailed a wide range of pioneering developments in microscopic nuclear structure and reactions, algorithms, high-performance computing, and uncertainty quantification. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF scien…
A Dempster-Shafer Theory-based approach to the Failure Mode, Effects and Criticality Analysis (FMECA) under epistemic uncertainty: application to the…
2017
Abstract Failure Mode and Effects Analysis (FMEA) is a safety and reliability analysis tool widely used for the identification of system/process potential failures, their causes and consequences. When aimed at the failure modes prioritization, FMEA is named Failure Mode, Effects and Criticality Analysis (FMECA). In the latter case, failure modes are commonly prioritized by means of the Risk Priority Number (RPN) that has been widely criticized to have several shortcomings. Firstly, in the presence of multiple experts supplying different and uncertain judgments on risk parameters, RPN is not able to deal with such a kind of information. Therefore, the present paper proposes the Dempster-Shaf…