Recovering the initial state of an infinite-dimensional system using observers

Let A be the generator of a strongly continuous semigroup T on the Hilbert space X, and let C be a linear operator from D(A) to another Hilbert space Y (possibly unbounded with respect to X, not necessarily admissible). We consider the problem of estimating the initial state z₀∈D(A) (with respect to the norm of X) from the output function y(t)=CT_tz₀, given for all t in a bounded interval [0,τ]. We introduce the concepts of estimatability and backward estimatability for (A,C) (in a more general way than currently available in the literature), we introduce forward and backward observers, and we provide an iterative algorithm for estimating z₀ from y. This algorithm generalizes various algorithms proposed recently for specific classes of systems and it is an attractive alternative to methods based on inverting the Gramian. Our results lead also to a very general formulation of Russell’s principle, i.e., estimatability and backward estimatability imply exact observability. This general formulation of the principle does not require T to be invertible. We illustrate our estimation algorithms on systems described by wave and Schrödinger equations, and we provide results from numerical simulations.     

Hull-form optimization in calm and rough water

The paper presents a formal methodology for the hull form optimization in calm and rough water using wash waves and selected dynamic responses, respectively. Parametric hull form modeling is used to generate the variant hull forms with some of the form parameters modified, which are evaluated in the optimization scheme based on evolutionary strategies. Rankine-source panel method and strip theories are used for the hydrodynamic evaluation. The methodology is implemented in the optimization of a double-chine, planing hull form. Furthermore, a dual-stage optimization strategy is applied on a modern fast displacement ferry. The effect of the selected optimization parameters is presented and discussed.     

生物电阻抗测量的理论探讨

通过生物阻抗测量的研究来分析血液动力学。方法:对阻抗容积描记术原理深入研究与验证,提出阻抗容积描记术原理的改进。改进的阻抗容积描记术原理是利用悬浮物质电导率原理和泊萧叶流量定律,从而找出影响测量精度的干扰信号—呼吸波引起波动,从理论中找到了影响脉搏波阻抗测量的因素。试验的结果表明利用理论的成果和方法实现血液动力学参数较高精度的无创检测。     

基于小波和人工智能技术的车辆无缝定位技术研究

基于自适应神经模糊逻辑推理系统(ANHS),在全球定位系统(GPS)信号阻塞时,为惯性导航系统(INS)提供位置和速度修正量以提高系统的精度和鲁棒性.首先用小波对数据信号进行降噪处理;然后设定INS的位置或速度作为ANHS的输入参数,经训练后输出相应修正量,训练期望值为经小波多分辨率分析得到的位置误差和速度误差.实验表明,无GPS信号时定位精度比同条件下卡尔曼滤波精度提高约40%,因此该方法可为车辆提供可靠有效的导航定位服务.     

Experion PKS与RTU、ESD通讯的实现

以塔里木油田迪那2气田为例,从Experion PKS与RTU、ESD的系统结构、硬件及软件组成情况入手,重点介绍了基于Modbus协议Experion PKS与RTU、ESD之间通讯的实现过程。     

Numerical method using cubic B-spline for the heat and wave equation

In the present paper, the cubic B-splines method is considered for solving one-dimensional heat and wave equations. A typical finite difference approach had been used to discretize the time derivative while the cubic B-spline is applied as an interpolation function in the space dimension. The accuracy of the method for both equations is discussed. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.     

S-states of helium-like ions

A simple Mathematica (version 7) code for computing S-state energies and wave functions of two-electron (helium-like) ions is presented. The elegant technique derived from the classical papers of Pekeris (1958, 1959, 1962, 1965, 1971) [1], [2] and [3] is applied. The basis functions are composed of the Laguerre functions. The method is based on the perimetric coordinates and specific properties of the Laguerre polynomials. Direct solution of the generalized eigenvalues and eigenvectors problem is used, distinct from the Pekeris works. No special subroutines were used, only built-in objects supported by Mathematica. The accuracy of the results and computation times depend on the basis size. The ground state and the lowest triplet state energies can be computed with a precision of 12 and 14 significant figures, respectively. The accuracy of the higher excited states calculations is slightly worse. The resultant wave functions have a simple analytical form, that enables calculation of expectation values for arbitrary physical operators without any difficulties. Only three natural parameters are required in the input.The above Mathematica code is simpler than the earlier version (Liverts and Barnea, 2010 [4]). At the same time, it is faster and more accurate.

Program summary

Program title: TwoElAtomSL(SH)Catalogue identifier: AEHY_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHY_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 11 434No. of bytes in distributed program, including test data, etc.: 540 063Distribution format: tar.gzProgramming language: Mathematica 7.0Computer: Any PCOperating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux SUSE 11.0RAM:?¹⁰⁹ bytesClassification: 2.1, 2.2, 2.7, 2.9Nature of problem: The Schrödinger equation for atoms (ions) with more than one electron has not been solved analytically. Approximate methods must be applied in order to obtain the wave functions or another physical attributes from quantum mechanical calculations.Solution method: The S-wave function is expanded into a triple set of basis functions which are composed of the exponentials combined with the Laguerre polynomials in the perimetric coordinates. Using specific properties of the Laguerre polynomials, solution of the two-electron Schrödinger equation reduces to solving the generalized eigenvalues and eigenvector problem for the proper Hamiltonian. The unknown exponential parameter is determined by means of minimization of the corresponding eigenvalue (energy).Restrictions: First, the too large length of expansion (basis size) takes the too large computation time and operative memory giving no perceptible improvement in accuracy. Second, the number of shells Ω in the wave function expansion enables one to calculate the excited nS-states up to n=Ω+1 inclusive.Running time: 2–60 minutes (depends on basis size and computer speed).     

An explicit predictor-corrector solver with application to seismic wave modelling

Wave-equation-based forward modelling using explicit finite-difference methods is a standard technique for calculating synthetic seismograms. The stability criterion restricts the size of the time step. In this paper a predictor–corrector method for solving the wave equation is described which allows the use of a larger time step. A stability analysis of the method is also carried out. Parallel implementation of the algorithm is described for a distributed computing environment which makes use of MPI and PVM message passing calls for communication between processors.     

Validation metrics for response histories: perspectives and case studies

The quantified comparison of transient response results are useful to analysts as they seek to improve and evaluate numerical models. Traditionally, comparisons of time histories on a graph have been used to make subjective engineering judgments as to how well the histories agree or disagree. Recently, there has been an interest in quantifying such comparisons with the intent of minimizing the subjectivity, while still maintaining a correlation with expert opinion. This increased interest has arisen from the evolving formalism of validation assessment where experimental and computational results are compared to assess computational model accuracy. The computable measures that quantify these comparisons are usually referred to as validation metrics. In the present work, two recently developed metrics are presented, and their wave form comparative quantification is demonstrated through application to analytical wave forms, measured and computed free-field velocity histories, and comparison with Subject Matter Expert opinion.

Snap-stabilization and PIF in tree networks

The contribution of this paper is threefold. First, we present the paradigm of snap-stabilization. A snap- stabilizing protocol guarantees that, starting from an arbitrary system configuration, the protocol always behaves according to its specification. So, a snap-stabilizing protocol is a time optimal self-stabilizing protocol (because it stabilizes in 0 rounds). Second, we propose a new Propagation of Information with Feedback (PIF) cycle, called Propagation of Information with Feedback and Cleaning (). We show three different implementations of this new PIF. The first one is a basic cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h ²) rounds (where h is the height of the tree) due to some undesirable local states. The second algorithm improves the worst delay of the basic algorithm from O(h ²) to 1 round. The state requirement for the above two algorithms is 3 states per processor, except for the root and leaf processors that use only 2 states. Also, they work on oriented trees. We then propose a third snap-stabilizing PIF algorithm on un-oriented tree networks. The state requirement of the third algorithm depends on the degree of the processors, and the delay is at most h rounds. Next, we analyze the maximum waiting time before a PIF cycle can be initiated whether the PIF cycle is infinitely and sequentially repeated or launch as an isolated PIF cycle. The analysis is made for both oriented and un-oriented trees. We show or conjecture that the two best of the above algorithms produce optimal waiting time. Finally, we compute the minimal number of states the processors require to implement a single PIF cycle, and show that both algorithms for oriented trees are also (in addition to being time optimal) optimal in terms of the number of states. WARNING: The concept of snap-stabilization was first introduced in [12]. The concept evolved over the last eight years. We take this evolution in consideration in this paper, which includes the early results published in [10] and [12]. In particular, infinite repetition of computation cycles is a requirement of self-stabilizing systems. This is not required in snap-stabilization because snap-stabilization ensures that the first completed computation cycle is executed according to the specification of the problem. The correctness proofs conform to this basic property.