Search results for "Uncertainty quantification"

Uncertainty assessment of a model for biological nitrogen and phosphorus removal: Application to a large wastewater treatment plant

2012

Abstract In the last few years, the use of mathematical models in WasteWater Treatment Plant (WWTP) processes has become a common way to predict WWTP behaviour. However, mathematical models generally demand advanced input for their implementation that must be evaluated by an extensive data-gathering campaign, which cannot always be carried out. This fact, together with the intrinsic complexity of the model structure, leads to model results that may be very uncertain. Quantification of the uncertainty is imperative. However, despite the importance of uncertainty quantification, only few studies have been carried out in the wastewater treatment field, and those studies only included a few of …

Handling the epistemic uncertainty in the selective maintenance problem

2020

Abstract Nowadays, both continuous and discontinuous operating systems require higher and higher reliability levels in order to avoid the occurrence of dangerous or even disastrous consequences. Accordingly, the definition of appropriate maintenance policies and the identification of components to be maintained during the planned system’s downtimes are fundamental to ensure the reliability maximization. Therefore, the present paper proposes a mathematical programming formulation of the selective maintenance problem with the aim to maximize the system’s reliability under an uncertain environment. Specifically, the aleatory model related to the components’ failure process is well known, where…

First-order linear differential equations whose data are complex random variables: Probabilistic solution and stability analysis via densities

2022

[EN] Random initial value problems to non-homogeneous first-order linear differential equations with complex coefficients are probabilistically solved by computing the first probability density of the solution. For the sake of generality, coefficients and initial condition are assumed to be absolutely continuous complex random variables with an arbitrary joint probability density function. The probability of stability, as well as the density of the equilibrium point, are explicitly determined. The Random Variable Transformation technique is extensively utilized to conduct the overall analysis. Several examples are included to illustrate all the theoretical findings.

A perspective on Gaussian processes for Earth observation

2019

Earth observation (EO) by airborne and satellite remote sensing and in-situ observations play a fundamental role in monitoring our planet. In the last decade, machine learning and Gaussian processes (GPs) in particular has attained outstanding results in the estimation of bio-geo-physical variables from the acquired images at local and global scales in a time-resolved manner. GPs provide not only accurate estimates but also principled uncertainty estimates for the predictions, can easily accommodate multimodal data coming from different sensors and from multitemporal acquisitions, allow the introduction of physical knowledge, and a formal treatment of uncertainty quantification and error pr…

Compressed Particle Methods for Expensive Models With Application in Astronomy and Remote Sensing

2021

In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model selection or uncertainty quantification. Bayesian inference requires the approximation of complicated integrals involving (often costly) posterior distributions. Generally, this approximation is obtained by means of Monte Carlo (MC) methods. In order to reduce the computational cost of the corresponding technique, surrogate models (also called emulators) are often employed. Another alternative approach is the so-called Approximate Bayesian Computation (ABC) sc…

Epistemic uncertainty in fault tree analysis approached by the evidence theory

2012

Abstract Process plants may be subjected to dangerous events. Different methodologies are nowadays employed to identify failure events, that can lead to severe accidents, and to assess the relative probability of occurrence. As for rare events reliability data are generally poor, leading to a partial or incomplete knowledge of the process, the classical probabilistic approach can not be successfully used. Such an uncertainty, called epistemic uncertainty, can be treated by means of different methodologies, alternative to the probabilistic one. In this work, the Evidence Theory or Dempster–Shafer theory (DST) is proposed to deal with this kind of uncertainty. In particular, the classical Fau…

An urban drainage stormwater quality model: model development and uncertainty quantification

2010

Summary The evaluation of urban stormwater quality is of relevant importance for urban drainage, and mathematical models may be of great interest in this respect. To date, several detailed mathematical models are available to predict stormwater quantity–quality characteristics in urban drainage systems. However, only a few models take sewer sediments into account, considering their cohesive-like properties that influence the build-up process of the pollutant load. Furthermore, the model data requirements, especially for the quality aspects, are extensive, which limit their applicability and affect model results with large uncertainty. Uncertainty analysis provides a measure or index regardi…

Bayesian approach for uncertainty quantification in water quality modelling: The influence of prior distribution

2010

Summary Mathematical models are of common use in urban drainage, and they are increasingly being applied to support decisions about design and alternative management strategies. In this context, uncertainty analysis is of undoubted necessity in urban drainage modelling. However, despite the crucial role played by uncertainty quantification, several methodological aspects need to be clarified and deserve further investigation, especially in water quality modelling. One of them is related to the “a priori” hypotheses involved in the uncertainty analysis. Such hypotheses are usually condensed in “a priori” distributions assessing the most likely values for model parameters. This paper explores…

Special Section on Fractional Operators in the Analysis of Mechanical Systems Under Stochastic Agencies

2017

Uncertainty propagation within the UNEDF models

2016

The parameters of the nuclear energy density have to be adjusted to experimental data. As a result they carry certain uncertainty which then propagates to calculated values of observables. In the present work we quantify the statistical uncertainties of binding energies, proton quadrupole moments, and proton matter radius for three UNEDF Skyrme energy density functionals by taking advantage of the knowledge of the model parameter uncertainties. We find that the uncertainty of UNEDF models increases rapidly when going towards proton or neutron rich nuclei. We also investigate the impact of each model parameter on the total error budget.