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نتیجه جستجو - Discretization

تعداد مقالات یافته شده: 25
ردیف عنوان نوع
1 A hybrid Hermite WENO scheme for hyperbolic conservation laws
طرح WENO هیبریدی ترکیبی برای قوانین حفاظت از چربی خون-2020
In this paper, we propose a hybrid finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for solving one and two dimensional hyperbolic conservation laws, which would be the fifth order accuracy in the one dimensional case, while is the fourth order accuracy for two dimensional problems. The zeroth-order and the first-order moments are used in the spatial reconstruction, with total variation diminishing Runge-Kutta time discretization. Unlike the original HWENO schemes [28,29]using different stencils for spatial discretization, we borrow the thought of limiter for discontinuous Galerkin (DG) method to control the spurious oscillations, after this procedure, the scheme would avoid the oscillations by using HWENO reconstruction nearby discontinuities, and using linear approximation straightforwardly in the smooth regions is to increase the efficiency of the scheme. Moreover, the scheme still keeps the compactness as only immediate neighbor information is needed in the reconstruction. A collection of benchmark numerical tests for one and two dimensional cases are performed to demonstrate the numerical accuracy, high resolution and robustness of the proposed scheme.
Keywords: Hermite WENO scheme | Hyperbolic conservation laws | Discontinuous Galerkin method | Limiter
مقاله انگلیسی
2 Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws
Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws-2020
Using the theoretical framework of algebraic flux correction and invariant domain preserving schemes, we introduce a monolithic approach to convex limiting in continuous finite element schemes for linear advection equations, nonlinear scalar conservation laws, and hyperbolic systems. In contrast to flux-corrected transport (FCT) algorithms that apply limited antidiffusive corrections to bound-preserving low-order solutions, our new limiting strategy exploits the fact that these solutions can be expressed as convex combinations of bar states belonging to a convex invariant set of physically admissible solutions. Each antidiffusive flux is limited in a way which guarantees that the associated bar state remains in the invariant set and preserves appropriate local bounds. There is no free parameter and no need for limit fluxes associated with the consistent mass matrix of time derivative term separately. Moreover, the steady-state limit of the nonlinear discrete problem is well defined and independent of the pseudo-time step. In the case study for the Euler equations, the components of the bar states are constrained sequentially to satisfy local maximum principles for the density, velocity, and specific total energy in addition to positivity preservation for the density and pressure. The results of numerical experiments for standard test problems illustrate the ability of built-in convex limiters to resolve steep fronts in a sharp and nonoscillatory manner.
Keywords: Hyperbolic conservation laws | Positivity preservation | Invariant domains | Finite elements | Algebraic flux correction | Convex limiting
مقاله انگلیسی
3 On rule acquisition methods for data classification in heterogeneous incomplete decision systems
روش های اکتساب قانون برای طبقه بندی داده ها در سیستم های تصمیم گیری ناقص ناهمگن-2020
In the age of big data, lots of data obtained is low-quality data characterized by heterogeneousness and incompleteness, referred to as heterogeneous incomplete decision systems (HIDSs) in this paper. Data classification is an important task in machine learning, with the ability to discover valuable knowledge hidden in HIDSs. However, systematic studies on data classification in HIDSs are rarely reported. Especially, there is a lack of adaptive classification methods for HIDSs, which can deal directly with heterogeneous incomplete data and do not require prior discretization of numerical attributes or filling in missing values. In this paper, a unified representation model, called parameterized tolerance granulation model (PTGM), is proposed to deal with heterogeneous incomplete data. And the principle of an adaptive granulation method of constructing appropriate PTGMs is also described using difference-based collaborative optimization. Based on PTGMs, decision logic language is used to describe classifiers consisting of decision rules satisfying given conditions. Then, a discernibility function-based and a heuristic function-based classification methods are proposed to obtain all optimized rule sets (classifiers) and to generate a particular optimized rule set, respectively. The heuristic function-based method is actually an adaptive classification method, which can deal directly with heterogeneous incomplete data. Furthermore, detailed theoretical analyses are given to illustrate the correctness and effectiveness of the proposed methods. The experimental results show that the proposed methods are effective and have obvious advantages in directly handling heterogeneous incomplete data.
Keywords: Rough set | Heterogeneous incomplete decision | systems | Rule acquisition | Data classification | Reduction
مقاله انگلیسی
4 Exponential stability analysis of quaternion-valued neural networks with proportional delays and linear threshold neurons: Continuous-time and discrete-time cases
تجزیه و تحلیل ثبات نمایی شبکه های عصبی کواترنیونی با تأخیر متناسب و نورون های آستانه خطی: موارد زمان گسسته و زمان پیوسته-2020
A class of quaternion-valued neural networks (QVNNs) with proportional delays and linear threshold neu- rons is proposed in this paper. First, by employing Halanay inequality technique and matrix measure method, the global exponential stability of continuous-time QVNNs with proportional delays and linear threshold neurons is studied, and some sufficient conditions are derived to guarantee global exponential stability of the studied continuous-time systems. Then, the discrete-time analogues of the continuous- time QVNNs with proportional delays and linear threshold neurons are formulated and investigated by using the semi-discretization method. The discrete-time analogues are equivalent to the considered continuous-time neural networks, and possess the convergence behaviors of the considered continuous- time systems without any limitation applied to the discretization step size. Finally, some numerical ex- amples are presented to ensure the effectiveness and correctness of the theoretical results obtained
Keywords: Exponential stability | Continuous-time | Discrete-time | Quaternion-valued neural networks | (QVNNs) | Proportional delays | Linear threshold neurons
مقاله انگلیسی
5 Parametric study on reinforcement learning optimized energy management strategy for a hybrid electric vehicle
مطالعه پارامتری در مورد یادگیری تقویت استراتژی مدیریت انرژی بهینه شده برای یک وسیله نقلیه الکتریکی هیبریدی-2020
An efficient energy split among different source of energy has been a challenge for existing hybrid electric vehicle (HEV) supervisory control system. It requires an optimized energy use of internal combustion engine and electric source such as battery, fuel cell, ultracapacitor, etc. In recent years, Reinforcement Learning (RL) based energy management strategy (EMS) has emerged as one of the efficient control strategies. The effectiveness Reinforcement Learning method largely depends on optimized parameter selections. However, a thorough parametric study still lacks in this field. It is a fundamental step for efficient implementation of the RLbased EMS. Different from existing RL-based EMS literature, this study conducts a parametric study on several key factors during the RL-based EMS development, including: (1) state types and number of states, (2) states and action discretization, (3) exploration and exploitation, and (4) learning experience selection. The main results show that learning experience selection can effectively reduce the vehicle fuel consumption. The study of the states and action discretization show that the vehicle fuel consumption reduces as action discretization increases while increasing the states discretization is detrimental to the fuel consumption. Moreover, the increasing number of states improves fuel economy. With the help of the proposed parametric analysis, the RL-based EMS can be easily adapted to other power split problems in a HEV application.
Keywords: Reinforcement learning | Q-learning | Energy management strategy | Hybrid electric vehicle
مقاله انگلیسی
6 Dual incremental fuzzy schemes for frequent itemsets discovery in streaming numeric data
طرح های فازی افزایشی دوگانه برای کشف مکرر آیتم ها در جریان داده های عددی-2020
Discovering frequent itemsets is essential for finding association rules, yet too computa- tional expensive using existing algorithms. It is even more challenging to find frequent itemsets upon streaming numeric data. The streaming characteristic leads to a challenge that streaming numeric data cannot be scanned repetitively. The numeric characteristic requires that streaming numeric data should be pre-processed into itemsets, e.g., fuzzy- set methods can transform numeric data into itemsets with non-integer membership val- ues. This leads to a challenge that the frequency of itemsets are usually not integer. To overcome such challenges, fast methods and stream processing methods have been ap- plied. However, the existing algorithms usually either still need to re-visit some previous data multiple times, or cannot count non-integer frequencies. Those existing algorithms re-visiting some previous data have to sacrifice large memory spaces to cache those pre- vious data to avoid repetitive scanning. When dealing with big streaming data nowadays, such large-memory requirement often goes beyond the capacity of many computers. Those existing algorithms unable to count non-integer frequencies would be very inaccurate in estimating the non-integer frequencies of frequent itemsets if used with integer approxi- mation of frequency-counting. To solve the aforementioned issues, in this paper we propose two incremental schemes for frequent itemsets discovery that are capable to work efficiently with streaming nu- meric data. In particular, they are able to count non-integer frequency without re-visiting any previous data. The key of our schemes to the benefits in efficiency is to extract essen- tial statistics that would occupy much less memory than the raw data do for the ongoing streaming data. This grants the advantages of our schemes 1) allowing non-integer count- ing and thus natural integration with a fuzzy-set discretization method to boost robustness and anti-noise capability for numeric data, 2) enabling the design of a decay ratio for dif- ferent data distributions, which can be adapted for three general stream models: landmark, damped and sliding windows, and 3) achieving highly-accurate fuzzy-item-sets discovery with efficient stream-processing. Experimental studies demonstrate the efficiency and effectiveness of our dual schemes with both synthetic and real-world datasets.
Keywords: Incremental algorithm | Data stream mining | Frequent itemsets | Without re-visiting
مقاله انگلیسی
7 Energy management strategy to reduce pollutant emissions during the catalyst light-off of parallel hybrid vehicles
استراتژی مدیریت انرژی برای کاهش انتشار آلاینده ها در هنگام خاموش شدن کاتالیزور وسایل نقلیه هیبریدی موازی-2020
The transportation sector is a major contributor to both air pollution and greenhouse gas emissions. Hybrid electric vehicles can reduce fuel consumption and CO2 emissions by optimizing the energy management of the powertrain. The purpose of this study is to examine the trade-off between regulated pollutant emissions and hybrid powertrain efficiency. The thermal dynamics of the three-way catalyst are taken into account in order to optimize the light-off. Experimental campaigns are conducted on a spark-ignition engine to introduce simplified models for emissions, exhaust gas temperature, catalyst heat transfers and efficiency. These models are used to determine the optimal distribution of a power request between the thermal engine and the electric motor with three-dimensional dynamic programming and a weighted objective function. A pollution-centered scenario is compared with a consumption-centered scenario for various driving cycles. The optimal torque distribution for the emissions-centered scenario on the world harmonized light-duty vehicles test cycle shows an 8–33% decrease in pollutant emissions while the consumption remains stable (0.1% increase). The consistency of the results is analyzed with respect to the discretization parameters, driving cycle, electric motor and battery sizing, as well as emission and catalyst models. The control strategies are promising but will have to be adapted to online engine control where the driving cycle and the catalyst efficiency are uncertain..
Keywords: Hybrid electric vehicle | Energy management strategy | Dynamic programming | Catalyst thermal behavior | Fuel consumption | Pollutant emissions
مقاله انگلیسی
8 Rapid trajectory design in complex environments enabled by reinforcement learning and graph search strategies
طراحی مسیر سریع در محیط های پیچیده که با یادگیری تقویت و استراتژی های جستجوی نمودار امکان پذیر است-2020
Designing trajectories in dynamically complex environments is challenging and easily becomes intractable. Recasting the problem may reduce the design time and offer global solutions by leveraging phase space mapping patterns available as accessible regions, and the application of search techniques from combinatorics. A computationally efficient search process produces potential trajectory concepts to meet unique design requirements over a broad range of mission types, including low-thrust scenarios. A successful framework is summarized in terms of four components: (i) Accessible regions — establishing reachable regions within the design space for a given thruster/engine capability: (ii) Database exploitation — discretization of well known dynamical structures to form a searchable 2D or 3D volume or map: (iii) Automated pathfinding — exploiting machine learning techniques to determine the transport sequence to deliver an efficient path: (iv) Convergence/ optimization — once the transport sequence is determined as a globally efficient concept, it is optimized locally by traditional numerical strategies.
مقاله انگلیسی
9 FLEXI: A high order discontinuous Galerkin framework for hyperbolic–parabolic conservation laws
FLEXI: یک چارچوب بالا و ناپیوسته گالرکین برای قوانین مربوط به حفاظت بیش از حد-پارابولیک-2020
High order (HO) schemes are attractive candidates for the numerical solution of multiscale problems occurring in fluid dynamics and related disciplines. Among the HO discretization variants, discontinuous Galerkin schemes offer a collection of advantageous features which have lead to a strong increase in interest in them and related formulations in the last decade. The methods have matured sufficiently to be of practical use for a range of problems, for example in direct numerical and large eddy simulation of turbulence. However, in order to take full advantage of the potential benefits of these methods, all steps in the simulation chain must be designed and executed with HO in mind. Especially in this area, many commercially available closed-source solutions fall short. In this work, we therefore present the FLEXI framework, a HO consistent, opensource simulation tool chain for solving the compressible Navier–Stokes equations on CPU clusters. We describe the numerical algorithms and implementation details and give an overview of the features and capabilities of all parts of the framework. Beyond these technical details, we also discuss the important but often overlooked issues of code stability, reproducibility and user-friendliness. The benefits gained by developing an open-source framework are discussed, with a particular focus on usability for the open-source community. We close with sample applications that demonstrate the wide range of use cases and the expandability of FLEXI and an overview of current and future developments.
Keywords: Discontinuous Galerkin | High order | Large eddy simulation | Computational fluid dynamics | Open-source software | Shock capturing
مقاله انگلیسی
10 Machine-learning based error prediction approach for coarse-grid Computational Fluid Dynamics (CG-CFD)
رویکرد پیش بینی خطا مبتنی بر یادگیری ماشین برای دینامیک سیالات محاسباتی درشت-شبکه (CG-CFD)-2020
Computational Fluid Dynamics (CFD) is one of the modeling approaches essential to identifying the parameters that affect Containment Thermal Hydraulics (CTH) phenomena. While the CFD approach can capture the multidimensional behavior of CTH phenomena, its computational cost is high when modeling complex accident scenarios. To mitigate this expense, we propose reliance on coarse-grid CFD (CG-CFD). Coarsening the computational grid increases the grid-induced error thus requiring a novel approach that will produce a surrogate model predicting the distribution of the CG-CFD local error and correcting the fluid-flow variables. Given sufficiently fine-mesh simulations, a surrogate model can be trained to predict the CG-CFD local errors as a function of the coarse-grid local flow features. The surrogate model is constructed using Machine Learning (ML) regression algorithms. Two of the widely used ML regression algorithms were tested: Artificial Neural Network (ANN) and Random Forest (RF). The proposed CG-CFD method is illustrated with a three-dimensional turbulent flow inside a lid-driven cavity. We studied a set of scenarios to investigate the capability of the surrogate model to interpolate and extrapolate outside the training data range. The proposed method has proven capable of correcting the coarse-grid results and obtaining reasonable predictions for new cases (of different Reynolds number, different grid sizes, or larger geometries). Based on the investigated cases, we found this novel method maximizes the benefit of the available data and shows potential for a good predictive capability.
Keywords: Coarse grid (mesh) | CFD | Machine learning | Discretization error | Big data | Artificial neural network | Random forest | Data-driven
مقاله انگلیسی
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