Improved error bound for multivariate Chebyshev polynomial interpolation

ABSTRACT

Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties which provides tremendous application potential in mathematical finance. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For efficiency, a sharp error bound is essential, in particular for high-dimensional applications. For tensorized Chebyshev interpolation, we present an error bound that improves existing results significantly.     

An iterative method for suboptimal control of linear time-delayed systems

This article presents a new approach for solving the Optimal Control Problem (OCP) of linear time-delay systems with a quadratic cost functional. The proposed method can also be used for designing optimal control time-delay systems with disturbance. In this study, the Variational Iteration Method (VIM) is employed to convert the original Time-Delay Optimal Control Problem (TDOCP) into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Finally, Illustrative examples are included to demonstrate the validity and applicability of the technique.     

基于Legendre多项式的锂离子电池降阶模型

在Newman模型以及单粒子模型(SPM)的基础上,提出基于Legendre正交多项式的电池模型降阶算法;同时,将固液相物理量的分布纳入模型算法,在提高运算速度的情况下,保证运算精度。以磷酸铁锂(Li Fe PO4)正极锂离子电池为例,对导出的降阶模型进行仿真验证。与全阶模型相比,该模型所计算的电池状态量误差均能保持在2%下。     

Construction of a polynomial invariant annihilation attack of degree 7 for T-310

Abstract

Cryptographic attacks are typically constructed by black-box methods and combinations of simpler properties, for example in [Generalised] Linear Cryptanalysis. In this article, we work with a more recent white-box algebraic-constructive methodology. Polynomial invariant attacks on a block cipher are constructed explicitly through the study of the space of Boolean polynomials which does not have a unique factorisation and solving the so-called Fundamental Equation (FE). Some recent invariant attacks are quite symmetric and exhibit some sort of clear structure, or work only when the Boolean function is degenerate. As a proof of concept, we construct an attack where a highly irregular product of seven polynomials is an invariant for any number of rounds for T-310 under certain conditions on the long term key and for any key and any IV. A key feature of our attack is that it works for any Boolean function which satisfies a specific annihilation property. We evaluate very precisely the probability that our attack works when the Boolean function is chosen uniformly at random.     

利用分段三次多项式提取山谷线和山脊线

通过利用分段三次多项式插值法将地形图中的等高线分段来求曲线的表达式,然后对每段上的表达式采取曲率最大值法,得出等高线弯曲变化的特征点,来提取地形图中的山谷线和山脊线,并选取了某一地区的地形等高线图进行了实验,以验证该方法的正确性。     

基于排列熵的泵站压力管道运行状态监测

为实现泵站管道工作状态的在线监测,保障其安全稳定运行,提出一种基于排列熵算法(permutation entropy,简称PE)的泵站压力管道监测方法。该方法充分发挥排列熵算法计算简单和敏感度高等优点,适宜于处理非线性、非平稳信号,通过在关键部位设置传感器获取泵站管道的振动信号,利用信号子序列熵值的变化判断泵站管道振动状况。将该方法应用于景电工程二期七泵站管道的运行监测,通过设置不同的运行工况进行实例验证。结果表明,在开关机组瞬间,振动信号子序列熵值的最大幅差达到0.37,机组稳定运行期间子序列熵值的最大幅差仅为0.07,根据其熵值的变化可快速方便地识别出泵站管道的运行状态,具有较高的精度与可靠度。该方法为泵站管道运行状况的在线监测提供了新思路,为结构下一步安全诊断工作提供基础,具有较好的工程实用性和推广价值。     

基于VMD的故障特征信号提取方法

变模式分解(variational mode decomposition,简称VMD)能够将多分量信号一次性分解成多个单分量调幅调频信号(variational intrinsic mode function,简称VIMF),但对噪声比较敏感。利用VMD对噪声的敏感特性,提出了一种基于VMD的降噪方法。利用排列熵定量确定VMD分解后各分量的含噪程度,对高噪分量直接剔除,对低噪分量进行Savitzky-Golay平滑处理,然后重构信号。运用该方法降噪后,对重构信号进行变模式分解,能够有效提取故障特征信号。仿真和实例分析表明,基于VMD的降噪方法的降噪效果优于小波变换降噪方法,VMD能有效提取故障特征信号。     

Rejewski’s equations: Solving for the entry permutation

In 1932, Marian Rejewski, who was a young mathematician working at the Polish Cipher Bureau, brilliantly recovered the internal wiring of the military Enigma. His initial efforts were unsuccessful because he assumed that the entry permutation was the same as in the commercial machine. Luckily he tried the identity permutation as an alternative and that proved to be correct. This note describes how Rejewski’s equations may be used to deduce the entry permutation without any guesswork, a technique that was later rediscovered by Alan Turing and by Lieutenant Andrew Gleason.     

Robust non-fragile power system stabilizer

This paper presents a step towards the design of robust non-fragile power system stabilizers (PSSs) for single-machine infinite-bus systems. To ensure resiliency of a robust PSS, the proposed approach presents a characterization of all stabilizers that can guarantee robust stability (RS) over wide range of operating conditions. A three-term controller (x₁ + x₂s)/(1 + x₃s) is considered to accomplish the design. Necessary and sufficient stability constraints for existing of such controller at certain operating point are derived via Routh–Hurwitz criterion. Continuous variation in the operating point is tackled by an interval plant model where RS problem is reduced to simultaneous stabilization of finite number of plants according to Kharitonov theorem. Controller triplets that can robustly stabilize vertex plants are characterized in a similar manner. The most resilient controller is computed at the center of maximum-area inscribed rectangle. Simulation results confirm robustness and resiliency of the proposed stabilizer.     

A new image encryption algorithm based on non-adjacent coupled map lattices

We propose a new image encryption algorithm which is based on the spatiotemporal non-adjacent coupled map lattices. The system of non-adjacent coupled map lattices has more outstanding cryptography features in dynamics than the logistic map or coupled map lattices does. In the proposed image encryption, we employ a bit-level pixel permutation strategy which enables bit planes of pixels permute mutually without any extra storage space. Simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed algorithm.