Specific Quantities Of Interest Research Articles

A new modelling framework for predator-prey interactions: A case study of an aphid-ladybeetle system

The significance of the relationship between data and models in ecology cannot be overstated. Over the past few decades, numerous techniques have been developed and applied in the study of ecological systems. One such technique is the Bayesian calibration of model parameters, which draws from Bayes' theorem to incorporate prior knowledge in estimating parameter values and quantifying their uncertainty. In this study, we establish a Bayesian framework for analysing ecological time series and apply it to a specific case of aphid-ladybeetle predation. To accomplish this, we construct and assess six mathematical models consisting of ordinary differential equations. These models encompass three phenomenological models and three data-driven models. To gain insights into the behaviour of the models concerning a specific quantity of interest, namely aphid abundance, we conduct a sensitivity analysis of the parameters. Subsequently, we compare the outputs of the models by employing model selection techniques. Based on our analysis, the best-performing model is a phenomenological one that incorporates a Holling's type II functional response. We believe that this framework has the potential for application and extension to other ecological systems, thereby enhancing our understanding of these intricate systems.

Building a certified reduced basis for coupled thermo-hydro-mechanical systems with goal-oriented error estimation

A goal-oriented a-posteriori error estimator is developed for transient coupled thermo-hydro-mechanical (THM) parametric problems solved with a reduced basis approximation. The estimator assesses the error in some specific Quantity of Interest (QoI). The goal-oriented error estimate is derived based on explicitly-computed weak residual of the primal problem and implicitly-computed adjoint solution associated with the QoI. The time-dependence of the coupled THM system poses an additional complexity as the auxiliary adjoint problem evolves backwards in time. The error estimator guides a greedy adaptive procedure that constructs progressively an optimal reduced basis by smartly selecting snapshot points over a given parametric training sample. The reduced basis obtained is used to drastically reduce the coupled system spatial degrees of freedom by several orders of magnitude. The computational gain obtained from the developed methodology is demonstrated through applications in 2D and 3D parametrized problems simulating the evolution of coupled THM processes in rock masses.

A Method for the Prediction of Extreme Ship Responses Using Design-Event Theory and Computational Fluid Dynamics

The design of a naval vessel requires accurate estimation of the extreme loads and motions that it will experience during its lifetime. Operation in large seaways in which the ship-wave interaction is highly nonlinear and transient leads to design events such as maximum internal loads due to global wave bending, local slamming loads, extreme roll, combinations of the global wave bending and local slamming, and many others. In this article, a method is presented that allows for nonlinear analysis to be used to predict events with user-specified rareness. The core of the method combines probability, frequency, and time-domain analyses to generate short time-window sea environments that lead to extreme dynamical events. The Office of Naval Research Tumblehome geometry is analyzed for the extreme roll angle when advancing in stern quartering irregular seas. 1. Introduction The design of a naval vessel requires accurate estimation of extreme loads and motions that it will experience during its lifetime. Specific quantities of interest are the maximum slamming load during wet-deck impact, maximum acceleration at different locations on the vessel, maximum green-water load on the bow structure or helicopter deck, maximum roll angle, or frequency of occurrence of capsize, to name a few. It is important to recognize that a ship lifetime is decades long, and the exposure time in different severe storms over the lifetime is of the order of weeks, if not months. Furthermore, because of the random nature of the sea and, hence, the dynamical response of the ship, the extreme response is also random and should be characterized statistically. This means that a single lifetime realization in a given seaway by either model tests or numerical simulation only gives one sample of the extreme response, and multiple lifetime realizations are required to characterize the extreme response.

Anomalous electron transport in Hall-effect thrusters: Comparison between quasi-linear kinetic theory and particle-in-cell simulations

Kinetic drift instabilities have been implicated as a possible mechanism leading to anomalous electron cross-field transport in E × B discharges, such as Hall-effect thrusters. Such instabilities, which are driven by the large disparity in electron and ion drift velocities, present a significant challenge to modelling efforts without resorting to time-consuming particle-in-cell (PIC) simulations. Here, we test aspects of quasi-linear kinetic theory with 2D PIC simulations with the aim of developing a self-consistent treatment of these instabilities. The specific quantities of interest are the instability growth rate (which determines the spatial and temporal evolution of the instability amplitude), and the instability-enhanced electron-ion friction force (which leads to “anomalous” electron transport). By using the self-consistently obtained electron distribution functions from the PIC simulations (which are in general non-Maxwellian), we find that the predictions of the quasi-linear kinetic theory are in good agreement with the simulation results. By contrast, the use of Maxwellian distributions leads to a growth rate and electron-ion friction force that is around 2–4 times higher, and consequently significantly overestimates the electron transport. A possible method for self-consistently modelling the distribution functions without requiring PIC simulations is discussed.

Uncertainty quantification in LES of a turbulent bluff-body stabilized flame

We address the forward uncertainty quantification problem in large eddy simulation (LES) of a turbulent non-premixed hydrocarbon flame, focusing on parametric uncertainty. More specifically, we examine the effect of uncertainty in the Smagorinsky coefficient and turbulent Prandtl and Schmidt numbers on specific quantities of interest. To conduct this analysis 25 LES simulations are performed, from which a surrogate model is built, based on polynomial chaos expansion, for the quantities of interest. This enables global sensitivity analysis and forward propagation of uncertainty, providing marginal and joint distributions on the quantities of interest. A non-intrusive method is used to construct the surrogate models, avoiding the need to modify the deterministic LES forward solver. The accuracy of the surrogates is examined using global error measures. The results provide insights into the underlying structure of the LES simulation, the impact of varying parameters on specific observables, and correlations among different quantities of interest.

Modal‐based goal‐oriented error assessment for timeline‐dependent quantities in transient dynamics

SUMMARYThis article presents a new approach to assess the error in specific quantities of interest in the framework of linear elastodynamics. In particular, a new type of quantities of interest (referred as timeline‐dependent quantities) is proposed. These quantities are scalar time‐dependent outputs of the transient solution, which are better suited to time‐dependent problems than the standard scalar ones, frozen in time. The proposed methodology furnishes error estimates for both the standard scalar and the new timeline‐dependent quantities of interest. The key ingredient is the modal‐based approximation of the associated adjoint problems, which allows efficiently computing and storing the adjoint solution.The approximated adjoint solution is readily post‐processed to produce an enhanced solution, requiring only one spatial post‐process for each vibration mode and using the time‐harmonic hypothesis to recover the time dependence. Thus, the proposed goal‐oriented error estimate consists in injecting this enhanced adjoint solution into the residual of the direct problem. The resulting estimate is very well suited for transient dynamic simulations because the enhanced adjoint solution is computed before starting the forward time integration of the direct problem. Thus, the cost of the error estimate at each time step is very low. Copyright © 2013 John Wiley & Sons, Ltd.

Control of modeling errors in the coupling of linear transport and diffusion models

We consider in this paper the initial-boundary value problem for the 1D neutron transport equation with isotropic scattering, set in some bounded interval with inflow boundary conditions. The usual parabolic scaling yields the diffusive limit. A surrogate model, coupling transport and diffusion equations, is then introduced in order to accurately assess the value of specific quantities of interest. The control of the quality of the computation (with respect to such a quantity of interest) is performed by means of an approach for modeling error estimation combined with an adaptive strategy to control the surrogate model, if necessary.

Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems

A goal-oriented analysis of linear, stochastic advection–diffusion models is presented which provides both a method for solution verification as well as a basis for improving results through adaptation of both the mesh and the way random variables are approximated. A class of model problems with random coefficients and source terms is cast in a variational setting. Specific quantities of interest are specified which are also random variables. A stochastic adjoint problem associated with the quantities of interest is formulated and a posteriori error estimates are derived. These are used to guide an adaptive algorithm which adjusts the sparse probabilistic grid so as to control the approximation error. Numerical examples are given to demonstrate the methodology for a specific model problem.

Near-crack-tip measurements within an Arlequin modeling for the numerical evaluation of far-field quantities of interest

As a possible solution to this issue, we propose here to use the Arlequin framework [BEN98, BEN05] to mix experimental data measured in the vicinity of the local phenomenon with a global numerical model suited for the prediction of a specific quantity of interest. Let us recall here that the Arlequin method is a versatile numerical approach which, as shown in Figure 1, allows for the superposition and coupling of different models on a specific zone, typically a surface or a volume.

A goal-oriented field measurement filtering technique for the identification of material model parameters

The post-processing of experiments with nonuniform fields is still a challenge: the information is often much richer, but its interpretation for identification purposes is not straightforward. However, this is a very promising field of development because it would pave the way for the robust identification of multiple material parameters using only a small number of experiments. This paper presents a goal-oriented filtering technique in which data are combined into new output fields which are strongly correlated with specific quantities of interest (the material parameters to be identified). Thus, this combination, which is nonuniform in space, constitutes a filter of the experimental outputs, whose relevance is quantified by a quality function based on global variance analysis. Then, this filter is optimized using genetic algorithms.

Reliability of computational science

AbstractToday's computers allow us to simulate large, complex physical problems. Many times the mathematical models describing such problems are based on a relatively small amount of available information such as experimental measurements. The question arises whether the computed data could be used as the basis for decision in critical engineering, economic, and medicine applications. The representative list of engineering accidents occurred in the past years and their reasons illustrate the question. The paper describes a general framework for verification and validation (V&V) which deals with this question. The framework is then applied to an illustrative engineering problem, in which the basis for decision is a specific quantity of interest, namely the probability that the quantity does not exceed a given value. The V&V framework is applied and explained in detail. The result of the analysis is the computation of the failure probability as well as a quantification of the confidence in the computation, depending on the amount of available experimental data. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 753–784, 2007

Estimation of Modeling Error in Computational Mechanics

We review and extend the theory and methodology of a posteriori error estimation and adaptivity for modeling error for certain classes of problems in linear and nonlinear mechanics. The basic idea is that for a given collection of physical phenomena a rich class of mathematical models can be identified, including models that are sufficiently refined and validated that they satisfactorily capture the events of interest. These fine models may be intractable, too complex to solve by existing means. Coarser models are therefore used. Moreover, as is frequently the case in applications, there are specific quantities of interest that are sought which are functionals of the solution of the fine model. In this paper, techniques for estimating modeling errors in such quantities of interest are developed. Applications to solid and fluid mechanics are presented.

Monte Carlo simulation for evaluating retail wheeling effects

Abstract A Monte Carlo simulation method for evaluating retail-wheeling effects on power systems is formulated and solution methods are presented. The effects of wheeling on operating cost, transmission losses, and system security are considered. For a specific operating condition, the effects are quantified by the sensitivity of specific quantities of interest with respect to power wheeling level. Quantities of interest are total operating cost, transmission losses and security, which is quantified with several indices. This model is utilized within a Monte Carlo simulation to calculate probability distribution functions of the incremental effects of wheeling on operating cost, transmission losses, and system security. The model and solution methods are applied on an example power system and the results are presented.