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inverse problem and Variation Method to Optimize Cascade Heat Exchange Network in Central Heating System

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Journal of Thermal Science 2017年第6期26卷 545-551页

作者： ZHANG Yin WEI Zhiyuan ZHANG Yinping WANG Xin College of Architecture and Environment Sichuan University Department of Building Science Tsinghua University

Urban heating in northern China accounts for 40% of total building energy usage. In central heating systems, heat is often transferred from heat source to users by the heat network where several heat exchangers are installed at heat source, substations and terminals respectively. For given overall heating capacity and heat source tempera- tore, increasing the terminal fluid temperature is an effective way to improve the thermal performance of such cascade heat exchange network for energy saving. In this paper, the mathematical optimization model of the cas- cade heat exchange network with three-stage heat exchangers in series is established. Aim at maximizing the cold fluid temperature for given hot fluid temperature and overall heating capacity, the optimal heat exchange area dis- tribution and the medium fluids＇ flow rates arc determined through inverse problem and variation method. The preliminary results show that the heat exchange areas should be distributed equally for each heat exchanger. It al- so indicates that in order to improve the thermal performance of the whole system, more heat exchange areas should be allocated to the heat exchanger whore flow rate difference between two fluids is relatively small. This work is important for guiding the optimization design of practical cascade heating systems.

关键词： District heating Heat exchanger Thermal performance optimization inverse problem Lagrange variation

inverse problem METHOD FOR WATER ENVIRONMENT TOTAL CAPACITY CONTROL OF A TIDAL RIVER

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Journal of Hydrodynamics 2005年第3期17卷 323-329页

作者： WANGDao-zeng ZHAOYu-feng LINWei-qing ShanghaiInstituteofAppliedMathematicsandMechanics ShanghaiUniversityShanghai200072China ShanghaiAcademeofEnvironmentalScience Shanghai200233China

In this paper, an improved method for water environment total capacity control of tidal rivers was presented. The maximal capacity of point pollution sources for the Huangpu River was computed by this method, and the result was compared with the practically observed data. The numerical result shows that the method is effective and efficient.

关键词： inverse problem tidal river PST-BFGS method point source pollution Huangpu River

inverse problem of bottom slope design for aerator devices

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Journal of Hydrodynamics 2013年第5期25卷 805-808页

作者：吴建华樊博许唯临 College of Water Conservancy and Hydropower Engineering Hohai University State Key Laboratory of Hydraulics and Mountain River Engineering Sichuan University

Air entrainment is an effective approach to protect release works from cavitation damage. The traditional method of aerator device designs is that, for given flow conditions, the geometries of the aerator device are designed and then the effec（s are experimentally tested for cavitation damage control. The present paper proposes an inverse problem method of determining the bottom slopes in front of and behind an aerator if the requirements of air entrainment, flow conditions and some of aerator geometric parameters are given. An RBF neural network model is developed and the relevant bottom slopes are calculated in different conditions of flow and geometry on the basis of the data of 19 aerator devices from different discharge tunnels with safe operation. The case study shows that the methodology provides an effective way to design aerator devices under given target conditions.

关键词： air entrainment bottom slope inverse problem neural network discharge ttmnel

inverse problem of a Tumor Model

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Journal of Donghua University(English Edition) 2010年第5期27卷 649-655页

作者：魏英超陶有山郭谦 College of Science Donghua University Mathematics & Science College Shanghai Normal University

This paper considers a model for the growth of a solid tumor with a single anticancer agent *** model is a free boundary problem of a nonlinear reaction-diffusion-advection equation,where the free boundary is the surface of the *** multicellular spheroids are routinely used as in vitro(i.e.,outside live organisms)models of cancer growth and they can be observed and controlled in the laboratory,the following inverse problem is studied:given observed dynamics of tumor growth,a certain parameter is *** Lipschitz stability of solutions to the above-mentioned inverse problem is established,and this inverse problem is solved by control *** methods for solving the inverse problem are also given.

关键词： tumors free boundary problem inverse problem stability control theory

Preliminary Study of the Feasibility of inverse problem Algorithms Used for Arc Magnetic Measurement Method

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Plasma Science and Technology 2010年第2期12卷 200-203页

作者：汪倩李兴文宋浩永荣命哲 State Key Laboratory of Electrical Insulation and Power Equipment Xi'an Jiaotong University

Non-contact magnetic measurement method is an effective way to study the air arc behavior experimentally. One of the crucial techniques is to solve an inverse problem for the electromagnetic field. This study is devoted to investigating different algorithms for this kind of inverse problem preliminarily, including the preconditioned conjugate gradient method, penalty function method and genetic algorithm. The feasibility of each algorithm is analyzed. It is shown that the preconditioned conjugate gradient method is valid only for few arc segments, the estimation accuracy of the penalty function method is dependent on the initial conditions, and the convergence of genetic algorithm should be studied further for more segments in an arc current.

关键词： arc magnetic measurement electromagnetic field inverse problem

An approach to estimating and extrapolating model error based on inverse problem methods:towards accurate numerical weather prediction

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Chinese Physics B 2014年第8期23卷 669-677页

作者：胡淑娟邱春雨张利云黄启灿于海鹏丑纪范 College of Atmospheric Sciences Lanzhou University School of Mathematics and Statistics Lanzhou University

Model error is one of the key factors restricting the accuracy of numerical weather prediction （NWP）. Considering the continuous evolution of the atmosphere, the observed data （ignoring the measurement error） can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers＇ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.

关键词： numerical weather prediction model error past data inverse problem

THE inverse problem OF CENTROSYMMETRICMATRICES WITH A SUBMATRIX CONSTRAINT

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Journal of Computational Mathematics 2004年第4期22卷 535-544页

作者： Zhen-yunPeng Xi-yanHu LeiZhang DepartmentofMathematics HunanUniversityofScienceandTechnologyXiangtan411201China (CollegeofMathematicsandEconometrics HunanUniversityChangsha410082China

By using Moore-Penrose generalized inverse and the general singular value decomposition of matrices, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the centrosymmetric solutions with a submatrix constraint of matrix inverse problem AX = B. In addition, in the solution set of corresponding problem, the expression of the optimal approximation solution to a given matrix is derived.

关键词： Matrix norm Centrosymmetric matrix inverse problem Optimal approximation

inverse problem for adaptive SIR model:Application to COVID-19 in Latin America

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Infectious Disease Modelling 2022年第1期7卷 134-148页

作者： Tchavdar T.Marinov Rossitza S.Marinova Department of Natural Sciences Southern University at New OrleansNew OrleansLA70126USA Department of Mathematical and Physical Sciences Concordia University of EdmontonEdmontonABT5B 4E4Canada

This work presents a method for solving an Adaptive Susceptible-Infected-Removed(ASIR)epidemic model with time-dependent transmission and removal *** COVID-19 data as of March 2021 are used for identifying the rates from an inverse *** estimated rates are used to solve the adaptive SIR system for the spread of the infectious *** method simultaneously solves the problem for the time-dependent rates and the unknown functions of the A-SIR *** results show the spread of COVID-19 in the World,Argentina,Brazil,Colombia,Dominican Republic,and *** of the reported affected by the disease individuals from the available real data and the values obtained with the A-SIR model demonstrate how well the model simulates the dynamic of the infectious disease.

关键词： inverse problem SIR epidemic Model Coefficient identification Time-dependent transmission and removal rates COVID-19

An inverse problem for Maxwell's Equations in Anisotropic Media

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Chinese Annals of Mathematics,Series B 2007年第1期28卷 35-54页

作者： Masahiro YAMAMOTO Graduate School of Mathematical Sciences The University of Tokyo 3-8-1 Komaba Meguro Tokyo 153Japan

The authors consider Maxwell＇s equations for an isomagnetic anisotropic and inhomogeneous medium in two dimensions, and discuss an inverse problem of determining the permittivity tensor （ε1,ε2,ε2,ε3 ） and the permeability μ in the constitutive relations from a finite number of lateral boundary measurements. Applying a Carleman estimate, the authors prove an estimate of the Lipschitz type for stability, provided that ε1,ε2,ε3,μ satisfy some a priori conditions.

关键词： Anisotropic media inverse problem Maxwell's equations Carleman estimate Lipschitz stability