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PBDW method for state estimation: Error analysis for noisy data and nonlinear formulation

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arXiv 2019年

作者： Gong, Helin Maday, Yvon Mula, Olga Taddei, Tommaso Science and Technology on Reactor System Design Technology Laboratory Nuclear Power Institute of China Chengdu610041 China Paris75005 France Institut Universitaire de France Paris75005 France Université Paris-Dauphine PSL Research University CNRS UMR 7534 CEREMADE Paris75016 France IMB UMR 5251 Univ. Bordeaux Talence33400 France Inria Bordeaux Sud-Ouest Team MEMPHIS Talence33400 France

We present an error analysis and further numerical investigations of the Parameterized-Background Data-Weak (PBDW) formulation to variational Data Assimilation (state estimation), proposed in [Y Maday, AT Patera, JD Penn, M Yano, Int J Numer Meth Eng, 102(5), 933-965]. The PBDW algorithm is a state estimation method involving reduced models. It aims at approximating an unknown function utrueliving in a highdimensional Hilbert space from M measurement observations given in the form ym= m(utrue), m = 1, ⋯, M, where mare linear functionals. The method approximates utruewith u = z + η. The background Z belongs to an N-dimensional linear space ZNbuilt from reduced modelling of a parameterized mathematical model, and the update η belongs to the space UMspanned by the Riesz representers of (1, ⋯, M). When the measurements are noisy - i.e., ym= m(utrue) + ϵmwith ϵmbeing a noise term - the classical PBDW formulation is not robust in the sense that, if N increases, the reconstruction accuracy degrades. In this paper, we propose to address this issue with an extension of the classical formulation, which consists in searching for the background z either on the whole ZNin the noise-free case, or on a well-chosen subset KN⊂ ZNin presence of noise. The restriction to KNmakes the reconstruction be nonlinear and is the key to make the algorithm significantly more robust against noise. We further present an a priori error and stability analysis, and we illustrate the efficiency of the approach on several numerical examples. Copyright © 2019, The Authors. All rights reserved.

关键词： Parameterization

A Dual-Band Multilayer Heterogeneous Frequency Selective Surface with Miniaturized Unit Cell

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A Dual-Band Multilayer Heterogeneous Frequency Selective Sur...

IEEE International Conference on Computational Electromagnetics (ICCEM)

作者： Yichun Cui Shengjun Zhang Jiaqi Liu Xin liu Hui Xue Borong Zhang National Key Laboratory of Science and Technology on Test Physics and Numerical Mathematics Beijing China National Key Laboratory of Science and Technology on Test Physics and Numerical Mathematics Beijing 100076 China Beijing Institute of System Engineering Beijing China

ISBN: (纸本)9781538612422

In terms that most researches about Frequency Selective Surface (FSS) concentrate on single layer structure design or FSS with one fundamental mode, a multilayer heterogeneous dual-band frequency selective surface composed of slot FSS, dielectric medium, patch FSS is proposed. This FSS possess miniaturized unit cell with dimension of 6×6mm 2 , it acts as a dual-band filter in given bands while behaving as an entire reflector in others. Results show that this dual-band frequency selective surface has narrow transmission bandwidths near 8.5GHz and 19.5GHz and flat rejection bands except for that. The structure exhibits excellent stability for oblique incident angles and provides polarization-independent response with compact design which moves the operating bands away from grating lobes. A method to adjust the element's size is proposed as well based on basic elements when given pass band frequency changed.

关键词： electromagnetic wave polarisation frequency selective surfaces microwave filters multilayers frequency selective surfaces electromagnetic wave polarisation Microwave filters unit cell multilayers Dual band belt cleaner compact design

Formation control for multiple agents with local measurements: Continuous-time and sampled-data-based cases

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arXiv 2019年

作者： Wang, Chen Li, Shuai Xia, Weiguo Sun, Jinan Xie, Guangming National Engineering Research Center for Software Engineering Peking University Beijing100871 China Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education School of Control Science and Engineering Dalian University of Technology Dalian116024 China State Key Laboratory of Turbulence and Complex Systems Intelligent Biomimetic Design Lab College of Engineering Peking University Beijing100871 China

We study the formation control problem for a group of mobile agents in a plane, in which each agent is modeled as a kinematic point and can only use the local measurements in its local frame. The agents are required to maintain a geometric pattern while keeping a desired distance to a static/moving target. The prescribed formation is a general one which can be any geometric pattern, and the neighboring relationship of the N-agent system only has the requirement of containing a directed spanning tree. To solve the formation control problem, a distributed controller is proposed based on the idea of decoupled design. One merit of the controller is that it only uses each agent's local measurements in its local frame, so that a practical issue that the lack of a global coordinate frame or a common reference direction for real multi-robot systems is successfully solved. Considering another practical issue of real robotic applications that sampled data is desirable instead of continuous-time signals, the sampled-data based controller is developed. Theoretical analysis of the convergence to the desired formation is provided for the multiagent system under both the continuous-time controller with a static/moving target and the sampled-data based one with a static target. Numerical simulations are given to show the effectiveness and performance of the controllers. Copyright © 2019, The Authors. All rights reserved.

关键词： Multi agent systems

Noise Model Analysis of MEMS Gyroscope Circuit Control system

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Noise Model Analysis of MEMS Gyroscope Circuit Control Syste...

2018 International Conference on Mathematics, Modelling, Simulation and Algorithms（MMSA2018）

作者： Yuxian Liu Ting Chen Chunhua He GuangDong ShunDe Innovation Design Institute National Key Laboratory of Science and Technology on Micro/Nano Fabrication Institute of Microelectronics

ISBN: (纸本)9781510863064

The detection signal of MEMS resonant gyroscope is very weak, and it is sensitively affected by the mechanical structure and the noise of the detection circuit. Noise is an important parameter which affecting gyroscope resolution, angle random walk coefficient and zero partial stability. In this paper, the noise model is established for the front-end solitary circuit, filter circuit, ADC/DAC and other key circuit modules of the gyro control system drive closed loop and sense closed loop, through the mathematical theory, the paper deduces the noise of the key circuit module, instructs the control system parameter design, and gives the corresponding simulation results.

关键词： MEMS gyroscope noise model front-end circuit filter ADC/DAC

Virtual Reality Oriented Modeling and Simulation of Water-dropping From Helicopter

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Virtual Reality Oriented Modeling and Simulation of Water-dr...

作者： Yangnanbing Han Hu Liu Yongliang Tian Zhengyuan Chen Zhengxin Nie School of Aeronautical Science & Engineering Beihang University State Key Laboratory of Virtual Reality Technology and System Aircraft Advanced Design Technology Key Laboratory of Ministry of Industry and Information Technology College Of Aerospace Engineering Nanjing University of Aeronautics and Astronautics

Fire-fight helicopter is the core of forest aviation *** virtual reality technology to train the crew of helicopter can improve their skill to put out fire efficiently and reduce property ***,current methods of visualizing water-dropping of helicopter in virtual environment cannot simultaneously ensure real-time performance and *** the one hand,the existing visualization methods,which have been widely used,are often just visual imitations and cannot reflect the physical laws of *** the other hand,complex computations are required for the general fluid modeling method,which cannot meet the requirement of real-time response in a VR *** is of great significance to establish a simulation-oriented model of water-dropping from helicopter for achieving realistic water visualization and further increasing the fidelity and immersion of the virtual *** this paper,we demonstrate an effective approach to establish a water-dropping model of helicopter and visualize it in a VR system,simulating physical laws and virtual effects at the same time.

关键词： Aerial firefighting Helicopter Visualization Water-dropping model

Optimal design of a High-power Friction Brake Based on Improved Genetic Algorithm 36

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Optimal Design of a High-power Friction Brake Based on Impro...

第36届中国控制会议

作者： LI Pengfei WANG Guangsen ZHANG Xiangming MA Mingzhong National Key Laboratory of Science and Technology on Vessel Integrated Power System Naval Univ. of Engineering

ISBN: (纸本)9781538629185

For the emergency braking of a large-capacity inertia flywheel energy storage system, this paper refers to a rapid braking scheme based on the friction brake. However, its difficulty lies in the design of a high power brake, which includes temperature, volume, power and so on. The present multi-objective optimization algorithm is not available for engineers due to its complicated design, much difficulty in implementation, and time-consuming calculation. Therefore, this paper has proposed an improved genetic algorithm to solve multiple constraints, which can be changed into a problem of common constraint. Moreover the algorithm is convenient for designers because of its ideal convergence, universality and flexibility. The prototype testing proves the braking scheme of the large-capacity flywheel energy storage system to be feasible and the optimized algorithm for the friction brake to be effective, which can play a certain guiding role in engineering practice.

关键词： friction brake genetic algorithm multi-objective optimization penalty function

A third order gas-kinetic scheme for unstructured grid

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arXiv 2018年

作者： Li, Ji Zhong, Chengwen Zhuo, Congshan National Key Laboratory of Science and Technology on Aerodynamic Design and Research Northwestern Polytechnical University Xi'an Shaanxi710072 China

In our study, a compact third order gas-kinetic scheme is constructed for unstructured grid which is combined the compact least-square reconstruction (CLS) method. The CLS method can achieve arbitrary high order compact reconstruction using the stencil from the whole computational domain implicitly. A large sparse linear system resulted from the CLS reconstruction method is solved by applying the generalized minimal residual algorithm (GMRES), and the Reverse-Cuthill-McKee (RCM) algorithm and the incomplete lower-upper (ILU) factorization method are implemented to accelerate the convergence of the iterative method. Different from the traditional flux solver, the BGK based gas-kinetic scheme is in the nature of spatial and temporal accuracy. Applying the second order expansion to the distribution function, the third order flux solver can be obtained directly. The accuracy of present method is validated by several numerical cases such as the advection of density perturbation problem, Sod shock wave problem, Lax shock tube test case, Shu-Osher problem, shock-vortex interaction, and lid-driven cavity flow. The advantages of this high order gas-kinetic scheme are exhibited in some benchmarks including incompressible flow and supersonic compressible flow, inviscid flow and viscous *** Codes 82C40, 76M12 Copyright © 2018, The Authors. All rights reserved.

关键词： Viscous flow

A conservative implicit scheme for steady state solutions of diatomic gas flow in all flow regimes

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arXiv 2018年

作者： Yuan, Ruifeng Zhong, Chengwen National Key Laboratory of Science and Technology on Aerodynamic Design and Research Northwestern Polytechnical University Xi'an Shaanxi710072 China

An implicit scheme for steady state solutions of diatomic gas flow is presented. The method solves the Rykov model equation in the finite volume discrete velocity method (DVM) framework, in which the translational and rotational degrees of freedom are taken into ac-count. At the cell interface, a difference scheme of the model equation is used to construct a multiscale ux (similar to discrete unified gas-kinetic scheme (DUGKS)), so that the cell size is not constrained by the cell Knudsen (Kn) number. The physical local time step is implemented to preserve the multiscale property in the nonuniform mesh case. The implicit macroscopic prediction technique is adopted to find a predicted equilibrium state at each time level and the implicit macroscopic governing equation is solved along with the implicit microscopic system. Furthermore, an efficient integral error compensation technique is applied, which makes the scheme conservative and allows more exible discretization for particle velocity space. In the test cases, the unstructured velocity-space mesh is used, the present method is proved to be efficient and accurate. Copyright © 2018, The Authors. All rights reserved.

关键词： Degrees of freedom (mechanics)

Meso-macro scale model for dynamic fracture of functional graded material 14

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Meso-macro scale model for dynamic fracture of functional gr...

14th International Conference on Fracture, ICF 2017

作者： Bai, Xiaoming Shi, Kaikai Guo, Licheng Zheng, Liangang Science and Technology on Reactor System Design Technology Laboratory Nuclear Power Institute of China Chengdu610213 China Department of Astronautic Science and Mechanics Harbin Institute of Technology Harbin150001 China

A meso-macro scale model for dynamic fracture of functional graded material is proposed in present work. The dynamic piecewise-exponential (DPE) model is extended to the meso-macro scale by the data mining method. With present model, the influence of meso-scale design parameters on macro-scale fracture behaviors can be investigated conveniently. Thus, the material design procedures and the fracture analysis of FGM are connected. © 2017 ICF 2017 - 14th International Conference on Fracture. All rights reserved.

关键词： Fracture