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Generalized gradient projection neural networks for nonsmooth optimization problems

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Science China(Information Sciences) 2010年第5期53卷 990-1005页

作者： LI GuoCheng 1 , SONG ShiJi 2.? & WU Cheng 2.1 department of Mathematics, beijing Information Science and Technology{2., beijing 100192. China 2.department of automation, tsinghua university, beijing 100084, China 1. department of Mathematics Beijing Information Science and Technology University Beijing 100192 China2. Department of Automation Tsinghua University Beijing 100084 China

Generalized gradient projection neural network models are proposed to solve nonsmooth convex and nonconvex nonlinear programming problems over a closed convex subset of R n . By using Clarke’s generalized gradient, the neural network modeled by a differential inclusion is developed, and its dynamical behavior and optimization capabilities both for convex and nonconvex problems are rigorously analyzed in the framework of nonsmooth analysis and the differential inclusion theory. First for nonconvex optimization problems, the quasi convergence results similar to those achieved by previous work are proved. For convex optimization problems, the global convergence results are proved, i.e. any trajectory of the neural network converges to an asymptotically stable equilibrium point, which is an optimal solution of the primal problem whenever it exists. This result remains valid even if the initial condition is chosen outside the feasible set. In addition, an asymptotic control result involving a Tykhonov like regularization shows that any trajectory of the revised neural network can be forced to converge toward a particular optimal solution of the primal problem. Finally, two simulation optimization algorithms for solving the optimization and control problems are designed respectively, and three typical simulation experiments are illustrated to present the accuracy and efficiency of theoretical convergence results of this paper.

关键词： nonsmooth optimization problem generalized gradient projection networks differential inclu sions convergence

Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation

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Science China(Physics,Mechanics & Astronomy) 2005年第4期48卷 496-512页

作者： LI Zhihui1,2. ZHANG Hanxin1 & FU Song2.⒈ National Laboratory for CFD, Hypervelocity Aerodynamics Institute,China Aerodynamics Research and Development Center,Mianyang 62.000,China 2.department of Engineering Mechanics,tsinghua{2.,beijing 100084,China 1. National Laboratory for CFD Hypervelocity Aerodynamics Institute China Aerodynamics Research and Development Center 621000 Mianyang China 2. department of Engineering Mechanics Tsinghua University 100084 Beijing China

The gas-kinetic unified algorithm using Boltzmann model equation have been extended and developed to solve the micro-scale gas flows in Poiseuille-like micro-channels from Micro-Electro-Mechanical Systems (MEMS). The numerical modeling of the gas kinetic boundary conditions suitable for micro-scale gas flows is presented. To test the present method, the classical Couette flows with various Knudsen numbers, the gas flows from short microchannels like plane Poiseuille and the pressure-driven gas flows in two-dimensional short microchannels have been simulated and compared with the approximate solutions of the Boltzmann equation, the related DSMC results, the modified N-S solutions with slip-flow boundary theory, the gas-kinetic BGK-Burnett solutions and the experimental data. The comparisons show that the present gas-kinetic numerical algorithm using the mesoscopic Boltzmann simplified velocity distribution function equation can effectively simulate and reveal the gas flows in microchannels. The numerical experience indicates that this method may be a powerful tool in the numerical simulation of micro-scale gas flows from MEMS.

关键词： Boltzmann model equation, discrete velocity ordinate method, finite-difference scheme, Couette flow, Poiseuille flow, gas flow in short-microchannel.

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Density-functional formula for strongly correlated systems

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Progress in Natural Science:Materials International 2005年第5期15卷 395-401页

作者： WANG Huaiyu1*, HAN Rushan2.and CHEN Nanxian1(1. department of Physics, tsinghua university,{2., China 2. department of Physics, Peking university, beijing 100871, China) department of Physics Tsinghua University Beijing 100084 China department of Physics Peking University Beijing 100871 China

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.

关键词： density-functional theory strongly correlated systems doubly-occupied orbital two-particle wave function self-consistent equations.

Fault prediction model based on evidential reasoning approach

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Science China(Information Sciences) 2010年第10期53卷 2032-2046页

作者： SI XiaoSheng 1,2., HU ChangHua 1 & ZHOU ZhiJie 1,2.1 Unit 302. Xi’an Institute of Hi-Tech, Shaanxi, Xi’an 71002., China 2.department of automation, tsinghua university,{2., China 1. Unit 302 Xi’an Institute of Hi-Tech Shaanxi Xi’an 710025 China2. Department of Automation Tsinghua University Beijing 100084 China

In order to deal with fault prediction problems that involve both quantitative and qualitative in-formation for nonlinear complex system, a new fault prediction model is established based on the evidential reasoning (ER) approach, and an optimal learning algorithm for training ER-based prediction model is pre-sented based on the mean square error (MSE) criterion. This prediction model inherits the advantages of ER approach, which can deal with precise data, incomplete data and fuzzy data with nonlinear characteristic. In this model, the input signals transformed using rule based information transformation technique, are aggregated by analytical ER approach, and then the outputs of prediction model are constructed according to the types of system outputs. In addition, two fault decision criteria are defined to conduct fault identification. To overcome the difficulty in determining model parameters accurately and subjectively, a nonlinear optimization model is constructed and the optimal parameters are obtained. Two experimental studies are conducted to evaluate the performance of the proposed model. The results show that the established prediction model and the presented parameters optimization methods can deal with fault prediction problem effectively.

关键词： fault prediction evidential reasoning belief distribution nonlinear optimization

Preparation of MWNTs/Al_2._3 composites and their mechanical and electrical properties

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Science China(Technological Sciences) 2005年第6期48卷 622-631页

作者： FAN Jinpeng1,2. ZHAO Daqing1,2. XU Zening1,2.& WU Minsheng1,2.1. department of Mechanical Engineering, tsinghua university,{2., China 2. Key Laboratory for Advanced Manufacturing by Materials Processing Technology, tsinghua university,{2., China 1. department of Mechanical Engineering Tsinghua University 100084 Beijing China 2. Key Laboratory for Advanced Manufacturing by Materials Processing Technology Tsinghua University 100084 Beijing China

The mechanical and electrical properties of MWNTs/Al2.3 composite prepared fabricated by hot pressing are investigated. The relation between properties and microstructure of composites is also discussed. With 4wt% MWNTs as reinforcement, the fracture toughness of composite obtained reaches 5.55 MPa·m1/2. which is 80% higher than that of pure Al2.3 obtained in the same conditions. The main toughening mechanism is CNTs’ pinning alumina grain boundaries, and the pullout of CNTs takes effect also. Through adding 2.t% MWNTs and altering the mix method, the fracture toughness of the composite obtained is 3.97 MPa·m1/2. Furthermore, the electrical resistivity is as low as 8.4×10?3 ?·m, decreasing by 14 orders of magnitude compared with pure alumina ceramics. The function of CNTs in composite is related to the distribution state of CNTs in composite, and the distribution state of CNTs in matrix is dependent on preparation procedures.

关键词： MWNTs, alumina, composite, fracture toughness, electrical properties.

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Parameter estimation for whole-body kinetic model of FDG metabolism

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Progress in Natural Science:Materials International 2006年第11期16卷 1164-1170页

作者： CUI Yunfeng~1, BAI Jing~1**, CHEN Yingmao~2.and TIAN Jiahe~2.1. department of Biomedical Engineering, tsinghua university,{2., China 2. department of Nuclear Medicine, General Hospital of PLA, beijing 100853, China) [a]department of Biomedical Engineering Tsinghua University Beijing China [b]department of Nuclear Medicine General Hospital of PLA Beijing China

Based on the radioactive tracer [ ~ 18 F]2.fluoro-2.deoxy-D-glucose （FDG）, positron emission tomography （PET）, and compartment model, the tracer kinetic study has become an important method to investigate the glucose metabolic kinetics in human body. In this work, the kinetic parameters of three-compartment and four-parameter model for the FDG metabolism in the tissues of myocardium, lung, liver, stomach, spleen, pancreas, and marrow were estimated through some dynamic FDG-PET experiments. Together with published brain and skeletal muscle parameters, a relatively complete whole-body model was presented. In the liver model, the dual blood supply from the hepatic artery and the portal vein to the liver was considered for parameter estimation, and the more accurate results were obtained using the dual-input rather than the single arterial-input. The established whole-body model provides the functional information of FDG metabolism in human body. It can be used to further investigate the glucose metabolism, and also be used for the simulation and visualization of FDG metabolic process in human body.

关键词： compartment model FDG PET parameter estimation.

Improvement of the classification accuracy in discriminating diabetic retinopathy by multifocal electroretinogram analysis

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Progress in Natural Science:Materials International 2007年第8期17卷 913-918页

作者： Xu Jin~1 Hu Guangshu~(1**) Huang Houbin~2.(1.department of Biomedical Engineering,tsinghua{2.,beijing 100084,China 2.department of Ophthalmology,General Hospital of Chinese PLA,beijing 100853,China) [a]department of Biomedical Engineering Tsinghua University Beijing China [b]department of Ophthalmology General Hospital of Chinese PLA Beijing China

The multifocal electroretinogram (mfERG) is a newly developed electrophysiological *** this paper,a classifi- cation method is proposed for early diagnosis of the diabetic retinopathy using mfERG *** records were obtained from eyes of healthy individuals and patients with diabetes at different *** each mfERG record,103 local responses were *** value of each point on all the mfERG local responses was looked as one potential feature to classify the experimental *** sub- sets were selected from the feature space by comparing the inter-intra *** on the selected feature subset,Fisher's linear classi- fiers were *** the final classification decision of the record was made by voting all the classifiers' *** the method to classify all experimental subjects,very low error rates were *** crucial properties of the diabetic retinopathy classification method are also discussed.

关键词： diabetic retinopathy multifocal electroretinogram feature selection linear classifier

Study on an intelligent fault-tolerant technique for multiple satellite configured navigation under highly dynamic conditions

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Science China(Information Sciences) 2011年第3期54卷 529-541页

作者： WANG ShiCheng 1 , ZHAO Xin 1 , MIN HaiBo 1 , LIU ZhiGuo 1 & SI XiaoSheng 2.1 High-Tech Institute of Xi’an, Xi’an 71002., China 2.department of automation, tsinghua university,{2., China 1. High-Tech Institute of Xi’an Xi’an 710025 China2. Department of Automation Tsinghua University Beijing 100084 China

The probability of pseudo-range information being faulty will increase when there is increased noise in the receiver due to highly dynamic conditions. In this paper, an intelligent fault-tolerant federated Kalman filter (IFFKF) is presented to solve the problem of invalid position information as a result of the uncertainty in the category and quantity of failed satellites in a multiple configured satellite system. At the same time, a corresponding intelligent fault-tolerant system structure based on a cell-level fusion mode of operation was designed. Furthermore, a fault diagnosis strategy is proposed to deal with gradually or suddenly changing faults. By monitoring the residual and the residual rate, an observation quality gene is obtained using a fuzzy logic control system, and the local filter is adaptively adjusted on-line. Consequently, any filtering divergence arising from a gradually changing fault can, to a large extent, be prevented. The results show that the proposed algorithm and structure can achieve reliable positioning by fully utilizing new multiple satellites, monitoring and managing the gradual fault, as well as detecting and isolating any sudden fault in a synchronous manner. As such, the proposed algorithm has the potential to improve the reliability of a multiple satellite configured navigation system.

关键词： multiple satellite configured systems fuzzy logic control intelligent fault-tolerant filtering federated filtering fault detection and isolation

Extremal eigenvalues of measure differential equations with fixed variation

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Science China Mathematics 2010年第10期53卷 2573-2588页

作者： ZHANG MeiRong 1,2.1 department of Mathematical Sciences,tsinghua{2.,beijing 100084,China 2.Zhou Pei-Yuan Center for Applied Mathematics,tsinghua{2.,beijing 100084,China 1. department of Mathematical Sciences Tsinghua University Beijing 100084 China2. Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing 100084 China

In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely *** taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth *** results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.

关键词： measure differential equation eigenvalue extremal value weak* topology Frechét derivative sub-differential

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