基于扩展移相的ISOP-DAB变换器混合优化控制方法

输入串联输出并联-双有源电桥(ISOP-DAB)变换器多应用于大功率高电压场合,为降低ISOP-DAB变换器的电流应力并提高系统的动态性能,本文提出一种基于扩展移相调制混合优化控制方法。首先分析在扩展移相下变换器的工作模式和功率模型,通过拉格朗日优化算法获取电流应力最优的相移组合,并结合虚拟电压均衡控制方案,以应对负载突变或输入电压扰动状态,同时结合变换器的结构特征使用输入电压均值完成模块间功率的动态平衡。最后,将混合优化控制方法、基于单移相的虚拟功率控制和传统的扩展移相优化控制进行对比实验。实验结果证明了混合优化控制在功率均分的同时可以实现电流应力优化,提高能量传输效率,同时也显著地改善了变换器在扰动情况下的动态特性。

Probabilistic analysis of tunnel face seismic stability in layered rock masses using Polynomial Chaos Kriging metamodel

Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines the Upper bound Limit analysis of Tunnel face stability,the Polynomial Chaos Kriging,the Monte-Carlo Simulation and Analysis of Covariance method(ULT-PCK-MA),is proposed to investigate the seismic stability of tunnel faces.A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis.An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects.Ten input parameters,including geological strength indices,uniaxial compressive strengths and constants for three rock formations,and the horizontal seismic coefficients,are treated as random variables.The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed.In addition,the effects of weak layer position,the middle layer thickness and quality,the tunnel diameter,the parameters correlation,and the seismic loadings are investigated,respectively.The results show that the layer distributions significantly influence the tunnel face probabilistic stability,particularly when the weak rock is present in the bottom layer.The efficiency of the proposed ULT-PCK-MA is validated,which is expected to facilitate the engineering design and construction.

Diophantine equations and Fermat's last theorem for multivariate(skew-)polynomials

Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.

Improving Video Watermarking through Galois Field GF(2^(4)) Multiplication Tables with Diverse Irreducible Polynomials and Adaptive Techniques

Video watermarking plays a crucial role in protecting intellectual property rights and ensuring content authenticity.This study delves into the integration of Galois Field(GF)multiplication tables,especially GF(2^(4)),and their interaction with distinct irreducible polynomials.The primary aim is to enhance watermarking techniques for achieving imperceptibility,robustness,and efficient execution time.The research employs scene selection and adaptive thresholding techniques to streamline the watermarking process.Scene selection is used strategically to embed watermarks in the most vital frames of the video,while adaptive thresholding methods ensure that the watermarking process adheres to imperceptibility criteria,maintaining the video's visual quality.Concurrently,careful consideration is given to execution time,crucial in real-world scenarios,to balance efficiency and efficacy.The Peak Signal-to-Noise Ratio(PSNR)serves as a pivotal metric to gauge the watermark's imperceptibility and video quality.The study explores various irreducible polynomials,navigating the trade-offs between computational efficiency and watermark imperceptibility.In parallel,the study pays careful attention to the execution time,a paramount consideration in real-world scenarios,to strike a balance between efficiency and efficacy.This comprehensive analysis provides valuable insights into the interplay of GF multiplication tables,diverse irreducible polynomials,scene selection,adaptive thresholding,imperceptibility,and execution time.The evaluation of the proposed algorithm's robustness was conducted using PSNR and NC metrics,and it was subjected to assessment under the impact of five distinct attack scenarios.These findings contribute to the development of watermarking strategies that balance imperceptibility,robustness,and processing efficiency,enhancing the field's practicality and effectiveness.

A Collocation Technique via Pell-Lucas Polynomials to Solve Fractional Differential EquationModel for HIV/AIDS with Treatment Compartment

In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct.

Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments

In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.

Three-dimensional pseudo-dynamic reliability analysis of seismic shield tunnel faces combined with sparse polynomial chaos expansion

To address the seismic face stability challenges encountered in urban and subsea tunnel construction,an efficient probabilistic analysis framework for shield tunnel faces under seismic conditions is proposed.Based on the upper-bound theory of limit analysis,an improved three-dimensional discrete deterministic mechanism,accounting for the heterogeneous nature of soil media,is formulated to evaluate seismic face stability.The metamodel of failure probabilistic assessments for seismic tunnel faces is constructed by integrating the sparse polynomial chaos expansion method(SPCE)with the modified pseudo-dynamic approach(MPD).The improved deterministic model is validated by comparing with published literature and numerical simulations results,and the SPCE-MPD metamodel is examined with the traditional MCS method.Based on the SPCE-MPD metamodels,the seismic effects on face failure probability and reliability index are presented and the global sensitivity analysis(GSA)is involved to reflect the influence order of seismic action parameters.Finally,the proposed approach is tested to be effective by a engineering case of the Chengdu outer ring tunnel.The results show that higher uncertainty of seismic response on face stability should be noticed in areas with intense earthquakes and variation of seismic wave velocity has the most profound influence on tunnel face stability.

The Study of Root Subspace Decomposition between Characteristic Polynomials and Minimum Polynomial

Let Abe the linear transformation on the linear space V in the field P, Vλibe the root subspace corresponding to the characteristic polynomial of the eigenvalue λi, and Wλibe the root subspace corresponding to the minimum polynomial of λi. Consider the problem of whether Vλiand Wλiare equal under the condition that the characteristic polynomial of Ahas the same eigenvalue as the minimum polynomial (see Theorem 1, 2). This article uses the method of mutual inclusion to prove that Vλi=Wλi. Compared to previous studies and proofs, the results of this research can be directly cited in related works. For instance, they can be directly cited in Daoji Meng’s book “Introduction to Differential Geometry.”

A coupled Legendre-Laguerre polynomial method with analytical integration for the Rayleigh waves in a quasicrystal layered half-space with an imperfect interface

The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.

Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring

This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.

Solving Some Problems and Elimination in Systems of Polynomial Equations

In a factorial ring, we can define the p.g.c.d. of two elements (defined to the nearest unit) and the notion of prime elements between them. More generally, Bezout’s identity characterizes two prime elements in a main ring. A ring that satisfies the property of the theorem is called a Bezout ring. We have given some geometry theorems that can be proved algebraically, although the methods of geometry and, in particular, of projective geometry are by far the most beautiful. Most geometric problems actually involve polynomial equations and can be translated into the language of polynomial ideals. We have given a few examples of a different nature without pretending to make a general theory.

Linear Functional Equations and Twisted Polynomials

A certain variety of non-switched polynomials provides a uni-figure representation for a wide range of linear functional equations. This is properly adapted for the calculations. We reinterpret from this point of view a number of algorithms.

含ISOP-DAB变换器的中低压直流配电系统阻抗建模及稳定性分析

“双碳”目标下,高比例可再生能源和高比例电力电子设备成为中低压直流配电系统的主要特征,使得系统因其低惯量、弱阻尼的特性所引起的稳定性问题尤为突出。为此,针对含输入串联输出并联型双有源桥(ISOP-DAB)变换器的中低压直流配电系统进行阻抗建模并提出一种适用于中低压直流配电系统的稳定性分析方法。首先,建立了ISOP-DAB变换器的二端口阻抗模型以及其他单元的阻抗模型。在此基础上根据系统内各单元的端口特性将中低压直流配电系统等效为2个单母线直流子系统,并得到整个系统在中、低压侧的等效阻抗比,当且仅当该等效阻抗比满足奈奎斯特判据时,系统可稳定运行。最后,基于PSCAD/EMTDC平台搭建了含ISOP-DAB变换器的中低压直流配电系统的时域仿真模型,通过仿真实验以及理论计算对比分析了恒功率负载及线路参数对系统稳定性的影响。仿真结果验证了ISOP-DAB变换器的小信号模型以及所提稳定性分析方法的准确性和有效性。

直流高压ISOP型多电平逆变拓扑控制及对比分析

在输入直流电压较高的场合,考虑到逆变器的功率开关管耐压能力有限,采用了一种输入串联输出并联(ISOP)逆变器拓扑,由两个单相全桥逆变器模块组成,在输入均压控制下可以均分输入直流电压,使功率开关管只承受输入直流电压的1/2,并在载波移相正弦脉宽调制(SPWM)方式下输出电平数增加,从而可以降低输出电压的THD。此外,在谐波、扩展性等方面对比ISOP逆变器和有源中点钳位(ANPC)三电平逆变器,指出ISOP逆变器的优越性。最后进行了仿真验证。

THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH EXPONENTIAL POLYNOMIALS AS ITS COEFFICIENTS

By looking at the situation when the coefficients Pj(z)(j=1,2,…,n-1)(or most of them) are exponential polynomials,we investigate the fact that all nontrivial solutions to higher order differential equations f((n))+Pn-1(z)f((n-1))+…+P0(z)f=0 are of infinite order.An exponential polynomial coefficient plays a key role in these results.

A Robust Indoor Localization Algorithm Based on Polynomial Fitting and Gaussian Mixed Model

Wireless sensor network(WSN)positioning has a good effect on indoor positioning,so it has received extensive attention in the field of positioning.Non-line-of sight(NLOS)is a primary challenge in indoor complex environment.In this paper,a robust localization algorithm based on Gaussian mixture model and fitting polynomial is proposed to solve the problem of NLOS error.Firstly,fitting polynomials are used to predict the measured values.The residuals of predicted and measured values are clustered by Gaussian mixture model(GMM).The LOS probability and NLOS probability are calculated according to the clustering centers.The measured values are filtered by Kalman filter(KF),variable parameter unscented Kalman filter(VPUKF)and variable parameter particle filter(VPPF)in turn.The distance value processed by KF and VPUKF and the distance value processed by KF,VPUKF and VPPF are combined according to probability.Finally,the maximum likelihood method is used to calculate the position coordinate estimation.Through simulation comparison,the proposed algorithm has better positioning accuracy than several comparison algorithms in this paper.And it shows strong robustness in strong NLOS environment.

Optimizing Polynomial-Time Solutions to a Network Weighted Vertex Cover Game

Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks.We first model the WVC problem as a general game on weighted networks.Under the framework of a game,we newly define several cover states to describe the WVC problem.Moreover,we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums(SNEs)of the game.Then,we propose a game-based asynchronous algorithm(GAA),which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time.Subsequently,we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms,termed the improved game-based asynchronous algorithm(IGAA),in which we prove that it can obtain a better solution to the WVC problem than using a the GAA.Finally,numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.

A Note on Bell-Based Bernoulli and Euler Polynomials of Complex Variable

In this article,we construct the generating functions for new families of special polynomials including two parametric kinds of Bell-based Bernoulli and Euler polynomials.Some fundamental properties of these functions are given.By using these generating functions and some identities,relations among trigonometric functions and two parametric kinds of Bell-based Bernoulli and Euler polynomials,Stirling numbers are presented.Computational formulae for these polynomials are obtained.Applying a partial derivative operator to these generating functions,some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained.In addition,some remarks and observations on these polynomials are given.

AN ALGEBRAIC APPROACH TO DEGENERATE APPELL POLYNOMIALS AND THEIR HYBRID FORMS VIA DETERMINANTS

It is remarkable that studying degenerate versions of polynomials from algebraic point of view is not limited to only special polynomials but can also be extended to their hybrid polynomials.Indeed for the first time,a closed determinant expression for the degenerate Appell polynomials is derived.The determinant forms for the degenerate Bernoulli and Euler polynomials are also investigated.A new class of the degenerate Hermite-Appell polynomials is investigated and some novel identities for these polynomials are established.The degenerate Hermite-Bernoulli and degenerate Hermite-Euler polynomials are considered as special cases of the degenerate Hermite-Appell polynomials.Further,by using Mathematica,we draw graphs of degenerate Hermite-Bernoulli polynomials for different values of indices.The zeros of these polynomials are also explored and their distribution is presented.

Duality between Bessel Functions and Chebyshev Polynomials in Expansions of Functions

In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found.