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On an algorithm for solving Fredholm integrals of the first kind

STATISTICS AND COMPUTING 2019年第4期29卷 645-654页

作者： Chae, Minwoo Martin, Ryan Walker, Stephen G. Case Western Reserve Univ Dept Math Appl Math & Stat Cleveland OH 44106 USA North Carolina State Univ Dept Stat Raleigh NC 27695 USA Univ Texas Austin Dept Math Austin TX 78712 USA

In this paper we use an iterative algorithm for solving Fredholm equations of the first kind. The basic algorithm and convergence properties are known under certain conditions, but we provide a simpler convergence proof without requiring the restrictive conditions that have previously been needed. Several examples of independent interest are given, including mixing density estimation and a first passage time density function involving Brownian motion. We also develop the basic algorithm to include functions which are not necessarily non-negative and, again, present illustrations.

关键词： Brownian motion first passage time Convergence Expectation-maximization iterative algorithm Mixture model

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Plasma boundary reconstruction in JET by magnetic measurements

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FUSION ENGINEERING AND DESIGN 2019年 146卷 2074-2077页

作者： Chiariello, Andrea Gaetano Formisano, Alessandro Ledda, Francesco Martone, Raffaele Murari, Andrea Pizzo, Francesco Terranova, David Univ Campania L Vanvitelli Dept Engn Aversa CE Italy Culham Sci Ctr JET Eurofus Consortium Abingdon OX14 3DB Oxon England Consorzio RFX Padua Italy

The reconstruction of the plasma boundary is a critical issue in the monitoring and control of fusion devices. The problem can be solved by the solution of force balance magneto-hydro-dynamic equations but, unfortunately, the computing burden can be not compatible with the needs of the on-line control. Advanced electromagnetic modelling of the plasma, based on surface equivalent currents recently proposed, can be a compromise between accuracy and promptness especially when a fully 3D treatment is necessary or foreseen. A procedure able to take advantage of the magnetic measurements to provide a plasma boundary reconstruction is here presented. The paper includes the illustration of a first assessment carried out on the JET by using the data of a standard axisymmetric shot, with the aim to check the coherence between the experimental evidence and the numerical procedure.

关键词： Plasma boundary Last closed magnetic surface iterative algorithm Inverse problems

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Improving energy saving of crude oil distillation units with optimal operations

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JOURNAL OF CLEANER PRODUCTION 2020年 263卷

作者： Yang, Kunru Liu, Shirun He, Chang Zhang, Bingjian Chen, Qinglin Pan, Ming Sch Chem Engn & Technol Guangzhou Peoples R China Sun Yat Sen Univ Sch Mat Sci & Engn Guangzhou 510275 Peoples R China

As the most energy intensive sector in refinery industry, crude oil distillation unit can affect the overall energy consumption of a plant by up to 20%. Improving energy saving is an important factor of cleaner production and environmental impacts for crude oil distillation units. Many technologies regarding retrofit of heat exchanger network and optimal operations have been proposed to increase the energy and economic efficiencies of crude oil distillation units in the last decades. However, it is still a challenge of implementing traditional methods in practice, for instance, retrofitting are commonly restricted by process topology, safety and maintenance constraints and may lead to high capital costs because of considerable civil works;while operation models usually suffers from the computational difficulty caused by complex unit performances. To deal with the above problems, this paper presents an optimal operation strategy for improving energy efficiency of crude oil distillation units without any structural modifications. First, detailed process operations are formulated and expressed as a complex nonlinear programming model, which is then solved with a double-loop algorithm. The objective of the proposed method is to minimize process energy utilization while retain its economic benefit. This work provides an efficient tool to help engineers handily adjust process key parameters to achieve higher energy saving than the traditional approaches, especially up to 1.06 MWof energy reduction without additional retrofit investment in an industrial case. This is also equivalent to 2800 tons of CO2 emission reduction per year, and thus intensifying the overall sustainability profile of the crude oil distillation processes. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Crude oil distillation units (CDUs) Energy saving Optimal operations Nonlinear programming iterative algorithm

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Fairness-Based Superframe Design and Resource Allocation for Dynamic Rate Adaptation in DVB-RCS2 Satellite Systems

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IEEE COMMUNICATIONS LETTERS 2019年第11期23卷 2046-2049页

作者： Jung, Dong-Hyun Shin, Min-Su Ryu, Joon-Gyu Elect & Telecommun Res Inst Satellite Technol Res Grp Daejeon 34129 South Korea

In this letter, we consider a satellite communication system, where a gateway and multiple return channel satellite terminals (RCSTs) exchange information via a satellite based on the DVB-RCS2 standard. Transmission rate adaptation is used to deal with dynamic condition of return channels from the RCSTs. A joint superframe design and resource allocation problem is formulated to maximize Jain's fairness index. To overcome the high-computational complexity to obtain the optimal solution of the problem, we decompose the joint problem into two-level hierarchical problems and propose iterative algorithms to solve them. Simulation results show that the optimal solution of two-level hierarchical problems is very close to that of the joint problem, and that the proposed algorithms have low-computational complexity at the price of reduced fairness.

关键词： Resource management Indexes Satellites Logic gates Computational complexity iterative methods Satellite communication system DVB-RCS2 superframe design resource allocation iterative algorithm

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A thermal resistance network model based on three-dimensional structure

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MEASUREMENT 2019年 133卷 439-443页

作者： Han, Lei Tong, Zhenyang Southeast Univ Key Lab MEMS Minist Educ Nanjing 210096 Jiangsu Peoples R China

A thermal resistance network model based on three-dimensional structure is proposed in this paper. In a chip package newly developed method (three-dimensional stacked package), the thermal distribution management is essential. In order to improve the thermal design of a chip package structure, a thermal resistance network model of temperature distribution is established based on the thermal resistance network and the principle of spherical wall heat conduction. The principle of spherical wall heat conduction is adopted to calculate the complete 3-D temperature distribution at arbitrary position. For the analysis of the thermal resistance of thermal convection, the convection coefficient is calculated based on iterative algorithm. When the heating power arises from 0.27 W to 2.18 W, the errors between the calculation results and the experimental results are less than 5%. The experimental results validate the calculation results well. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Thermal resistance network model Three dimension iterative algorithm Thermal distribution

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Multi-objective steady-state optimization for a complex bioprocess in glycerol metabolism

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RESULTS IN CONTROL AND OPTIMIZATION 2021年 4卷

作者： Xu, Gongxian Zhang, Yijia Zhang, Jingshuo Bohai Univ Sch Math Sci Jinzhou 121013 Peoples R China Bohai Univ Dept Journal Jinzhou 121013 Peoples R China

This paper addresses the multi -objective steady-state optimization of a complex nonlinear system in glycerol metabolism. In the bioconversion system, we consider some mechanisms including the regulation for dha regulon, enzyme -catalytic kinetics, the inhibition of intracellular 3-hydroxypropionaldehyde (3-HPA), and so on. Firstly, we propose several new multi -objective steady-state optimization problems. These problems can simultaneously optimize any two of the following objectives: (1) minimization of the intracellular 3-HPA concentration;(2) maximization of the production rate of extracellular 1,3-propanediol (1,3-PDO);(3) maximization of the conversion rate of extracellular glycerol to extracellular 1,3-PDO;(4) maximization of the conversion rate of extracellular glycerol. Then a hybrid optimization method is proposed to solve the presented complex multi -objective problems. This optimization method couples a deterministic interior point approach and a stochastic genetic algorithm in the framework of normal -boundary intersection (NBI) method. After solving the proposed multi -objective problems of the addressed bioconversion system, we finally obtain their approximate Pareto optimal sets. The analysis for the attained optimization results is given. And a comparative study is also presented.

关键词： Bioprocess Steady-state optimization Multi-objective iterative algorithm Hybrid method

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Hybrid Model of Gravitational Fields Around Small Bodies for Efficient Trajectory Propagations

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2020年第2期43卷 232-249页

作者： Wei, Bingwei Shang, Haibin Qiao, Dong Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China Beijing Inst Technol Key Lab Dynam & Control Flight Vehicle Beijing 100081 Peoples R China

When modeling the gravitational fields around small bodies, the highly irregular shapes of such objects make it difficult to balance accuracy with efficiency. In this paper, a novel and general hybrid model for evaluating the gravity of a small body is proposed with the aim of reducing errors and the computational cost. The hybrid model separates dominant effects and smaller undulations. The dominant effects are represented by the gravity-best-fit ellipsoid, which is generated by solving an optimization problem in the sense of minimizing the contribution of undulations. The undulations are then approximated using the serendipity interpolation technique, which is computationally efficient. Furthermore, a discretization scheme for the region of interest is developed, and this guarantees the evaluation of gravity in the close proximity of a small body. Based on this discretization strategy, a rapid element tracking scheme is developed to improve the efficiency of trajectory propagations. The most remarkable advantage of this tracking strategy is that the runtime for identifying elements remains the same when the region of interest is arbitrarily broadened. Simulations on asteroids 1999KW4 and 1620 Geographos show that the hybrid model is highly accurate and around 196 times faster than the conventional polyhedral model.

关键词： 4179 Toutatis iterative algorithm Spherical Harmonics Frozen Orbit Random Access Memory Finite Element Program Tetrahedral Element Probability Distribution Optimization algorithm Solar System

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A finite difference scheme for the nonlinear time-fractional partial integro-differential equation

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2020年第6期43卷 3392-3412页

作者： Guo, Jing Xu, Da Qiu, Wenlin Hunan Normal Univ Sch Math & Stat Minist Educ Key Lab Comp & Stochast Math Changsha 410081 Hunan Peoples R China

In this paper, a finite difference scheme is proposed for solving the nonlinear time-fractional integro-differential equation. This model involves two nonlocal terms in time, ie, a Caputo time-fractional derivative and an integral term with memory. The existence of numerical solutions is shown by the Leray-Schauder theorem. And we obtain the discrete L-2 stability and convergence with second order in time and space by the discrete energy method. Then the uniqueness of numerical solutions is derived. Moreover, an iterative algorithm is designed for solving the derived nonlinear system. Numerical examples are presented to validate the theoretical findings and the efficiency of the proposed algorithm.

关键词： existence and uniqueness finite difference scheme iterative algorithm nonlinear time-fractional integro-differential equation stability and convergence

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Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations

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CHAOS SOLITONS & FRACTALS 2020年 140卷

作者： Rabbani, Mohsen Das, Anupam Hazarika, Bipan Arab, Reza Islamic Azad Univ Sari Branch Dept Math Sari Iran Rajiv Gandhi Univ Dept Math Rono Hills Doimukh 791112 Arunachal Prade India Cotton Univ Dept Math Gauhati 781001 Assam India Gauhati Univ Dept Math Gauhati 781014 Assam India

The purpose of this article is to introduce a new tempered sequence space and obtain the measure of noncompactness in this space. Using the measure of noncompactness and generalized Darbo fixed point theorem, we discuss the existence of solutions of an infinite system of fractional differential equations. Also we provide an example to highlight and establish the importance of our main result. Finally, we approach the solution of the example with high accuracy, by a convergent iterative algorithm with the help of modified homotopy perturbation method. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Measure of noncompactness Tempered space Fractional differential equations Darbo fixed point theorem iterative algorithm Modified homotopy perturbation

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Cross-sectional photoacoustic tomography image reconstruction with a multi-curve integration model

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COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2020年 197卷 105731-105731页

作者： Qi, Li Huang, Shixian Li, Xipan Zhang, Shuangyang Lu, Lijun Feng, Qianjin Chen, Wufan Southern Med Univ Guangdong Prov Key Lab Med Image Proc 1023 Shatai Rd Guangzhou 510900 Guangdong Peoples R China Southern Med Univ Sch Biomed Engn 1023 Shatai Rd Guangzhou 510900 Guangdong Peoples R China

Background and objective: In acoustic inversion of photoacoustic tomography (PAT), an imaging model that precisely describes both the ultrasonic wave propagation and the detector properties is of crucial importance. Inspired by the multi-stripe integration model in clinical X-ray computed tomography systems, in this work, we introduce the Multi-Curve-Integration-based acoustic inversion for cross-sectional Photoacoustic Tomography (MCI-PAT). Methods: We assumed that in cross-sectional PAT system, the three-dimensional (3-D) wave propagation problem could be reduced to a two-dimensional (2-D) problem in a limited, yet sufficient field of view. Under such condition, the MCI-PAT imaging model is generated by integrating several circular acoustic curves, the centers of which are points evenly distributed on the finite-size ultrasonic transducer surface. In this way, the spatial detector response is taken into account, while its computational burden does not largely increase because the integration process is performed only on a 2-D plane. Results: As proven by simulation, phantom and in vivo small animal experiments, the MCI-PAT method leads to promising improvement in PAT image quality. Comparing to traditional imaging models that considered only a single acoustic curve, our proposed method successfully improved the visibility of small structures and achieved evident enhancement on signal-to-noise ratio. Conclusions: The performance of the MCI-PAT method demonstrates that for cross-sectional PAT, a 2-D simplification of the propagation of multiple photoacoustic waves is feasible. Due to its simplicity, our method can be used as an add-on to current system models considering only a single acoustic curve. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Photoacoustic tomography Image reconstruction iterative algorithm

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