Pseudospectral method for assessing stability robustness for linear time-periodic delayed dynamical systems

The article presents a pseudospectral approach to assess the stability robustness of linear time-periodic delay systems, where periodic functions potentially present discontinuities and the delays may also periodically vary in time. The considered systems are subject to linear real-valued time-periodic uncertainties affecting the coefficient matrices, and the presented method is able to fully exploit structure and potential interdependencies among the uncertainties. The assessment of robustness relies on the computation of the pseudospectral radius of the monodromy operator, namely, the largest Floquet multiplier that the system can attain within a given range of perturbations. Instrumental to the adopted novel approach, a solver for the computation of Floquet multipliers is introduced, which results into the solution of a generalized eigenvalue problem which is linear w.r.t. (samples of) the original system matrices. We provide numerical simulations for popular applications modeled by time-periodic delay systems, such as the inverted pendulum subject to an act-and-wait controller, a single-degree-of-freedom milling model and a turning operation with spindle speed variation.     

The Investigation of the Fractional-View Dynamics of Helmholtz Equations Within Caputo Operator

It is eminent that partial differential equations are extensively meaningful in physics, mathematics and engineering. Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior. In the present research, mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives. First, the Helmholtz equations are presented in Caputo’s fractional derivative. Then Natural transformation, along with the decomposition method, is used to attain the series form solutions of the suggested problems. For justification of the proposed technique, it is applied to several numerical examples. The graphical representation of the solutions shows that the suggested technique is an accurate and effective technique with a high convergence rate than other methods. The less calculation and higher rate of convergence have confirmed the present technique’s reliability and applicability to solve partial differential equations and their systems in a fractional framework.     

雷电通道水平电场影响因素分析

影响雷电通道产生的水平电场因素众多,分析其影响因素对电力系统的雷电防护具有重要意义。文中利用运动电荷电磁场方程求解得到闪电回击通道的水平电场和方位磁场,并结合C-R 算法,得到了有限电导率地面上方的水平电场。依据运动电荷电磁场方程的特征分析了不同回击速度、不同距离、不同电导率对雷击产生的水平电场的影响。得出以下结论:水平电场随回击速度增大而减小;水平电场波形呈双极性特征且水平距离越大或电导率越小负向偏移越明显。这些研究结论为输电线路雷电过电压计算打下良好的基础。与其他方法相比,本文方法可以避免远距离电磁场计算中的震荡问题和积分方程的奇异问题。     

A derivative UKF for tightly coupled INS/GPS integrated navigation

The tightly coupled INS/GPS integration introduces nonlinearity to the measurement equation of the Kalman filter due to the use of raw GPS pseudorange measurements. The extended Kalman filter (EKF) is a typical method to address the nonlinearity by linearizing the pseudorange measurements. However, the linearization may cause large modeling error or even degraded navigation solution. To solve this problem, this paper constructs a nonlinear measurement equation by including the second-order term in the Taylor series of the pseudorange measurements. Nevertheless, when using the unscented Kalman filter (UKF) to the INS/GPS integration for navigation estimation, it causes a great amount of redundant computation in the prediction process due to the linear feature of system state equation, especially for the case with system state vector in much higher dimension than measurement vector. To overcome this drawback in computational burden, this paper further develops a derivative UKF based on the constructed nonlinear measurement equation. The derivative UKF adopts the concise form of the original Kalman filter (KF) to the prediction process and employs the unscented transformation technique to the update process. Theoretical analysis and simulation results demonstrate that the derivative UKF can achieve higher accuracy with a much smaller computational cost in comparison with the traditional UKF.     

Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation

In this paper, novel computing approach using three different models of feed-forward artificial neural networks (ANNs) are presented for the solution of initial value problem (IVP) based on first Painlevé equation. These mathematical models of ANNs are developed in an unsupervised manner with capability to satisfy the initial conditions exactly using log-sigmoid, radial basis and tan-sigmoid transfer functions in hidden layers to approximate the solution of the problem. The training of design parameters in each model is performed with sequential quadratic programming technique. The accuracy, convergence and effectiveness of the proposed schemes are evaluated on the basis of the results of statistical analyses through sufficient large number of independent runs with different number of neurons in each model as well. The comparisons of these results of proposed schemes with standard numerical and analytical solutions validate the correctness of the design models.     

Supramolecular Assembly on Coordination of Azopolymer Complexes: A Review

This review gives an account of the coordination chemistry of supramolecular azopolymer complexes. The syntheses and structures of azomonomers and their azopolymer complexes were described. Spectral techniques such as (IR, ¹H-NMR, ESR) and thermal analysis were investigated. Supramolecular architectures assembled were exhibited through weak interaction including hydrogen bonding and π–π stacking. The spectral data indicate geometry of azopolymer complexes and the orbital reduction factors. ESR spectral data provided information about their structures on the basis of Hamiltonian parameters and degree of covalency. All the azopolymer complexes are ESR active due to the presence of an unpaired electron. The force constant F_U–O(mdyn/Å) and the bond length R_U–O (Å) of the U–O bond were calculated from the IR data and related to the electronic properties of the substituents. Wilson's method, the matrix method, Badger's formula, and the Jones and El-Sonbati equations were used to calculate the U–O bond distances from the values of the stretching and interaction force constants. The most probable correlations between U–O force constant to U–O bond distance were satisfactorily discussed in terms of Badger's rule, and the Jones and El-Sonbati equations. The thermal stability was investigated using thermogravimetric analysis. The results showed that the azopolymer complexes are mostly more stable than the homopolymer. The stability of the proton ligand/metal ligand constants in the monomeric and polymeric forms was studied carefully using potentiometery. Based on the thermodynamic functions, the dissociation process is nonspontaneous, endothermic and entropically unfavorable. The metal complexes that were formed exhibited spontaneous, endothermic and entropically favorable behavior.     

Questioning numerical integration methods for microsphere (and microplane) constitutive equations

In the last few years, more and more complex microsphere models have been proposed to predict the mechanical response of various polymers. Similarly than for microplane models, they consist in deriving a one-dimensional force vs. stretch equation and to integrate it over the unit sphere to obtain a three-dimensional constitutive equation. In this context, the focus of authors is laid on the physics of the one-dimensional relationship, but in most of the case the influence of the integration method on the prediction is not investigated.Here we compare three numerical integration schemes: a classical Gaussian scheme, a method based on a regular geometric meshing of the sphere, and an approach based on spherical harmonics. Depending on the method, the number of integration points may vary from 4 to 983,040! Considering simple quantities, i.e. principal (large) strain invariants, it is shown that the integration method must be carefully chosen. Depending on the quantities retained to described the one-dimensional equation and the required error, the performances of the three methods are discussed. Consequences on stress–strain prediction are illustrated with a directional version of the classical Mooney–Rivlin hyperelastic model. Finally, the paper closes with some advices for the development of new microsphere constitutive equations.     

SiC单晶片切割力建模与自适应控制

Si C单晶因优良的物理和机械性能而大量用于大功率器件和IC行业。但由于材料的高硬度和高脆性,使其加工过程变得很困难。为此,分析了Si C单晶片切割过程,建立切割过程模型,通过F检验法进行系统阶次辨识,采用遗忘因子递推最小二乘算法在线估计模型参数,建立进给量与切割力的差分方程,设计基于最小方差自校正的切割力控制器,并进行实验验证。结果表明:控制器能够很好的跟踪不同信号,具有良好的鲁棒性,提高了Si C单晶片的加工效率和表面质量。     

Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems

Nonlinear equations systems (NESs) are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots. Evolutionary algorithms (EAs) are one of the methods for solving NESs, given their global search capabilities and ability to locate multiple roots of a NES simultaneously within one run. Currently, the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs. By contrast, problem domain knowledge of NESs is investigated in this study, where we propose the incorporation of a variable reduction strategy (VRS) into EAs to solve NESs. The VRS makes full use of the systems of expressing a NES and uses some variables (i.e., core variable) to represent other variables (i.e., reduced variables) through variable relationships that exist in the equation systems. It enables the reduction of partial variables and equations and shrinks the decision space, thereby reducing the complexity of the problem and improving the search efficiency of the EAs. To test the effectiveness of VRS in dealing with NESs, this paper mainly integrates the VRS into two existing state-of-the-art EA methods (i.e., MONES and DR-JADE) according to the integration framework of the VRS and EA, respectively. Experimental results show that, with the assistance of the VRS, the EA methods can produce better results than the original methods and other compared methods. Furthermore, extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance.