基于Taylor Series-LQR复合策略的双关节机械臂时滞补偿控制

为解决时滞导致的颤振问题,提出了一种基于Taylor Series-LQR(Linear Quadratic Regulator)复合策略的双关节机械臂时滞补偿控制方法。首先,利用两个一阶泰勒级数分别构建基于两机械臂当前理想控制力预测下一时滞时刻的理想控制力的预测方程;然后,利用这两个预测方程对描述双关节机械臂运动的状态方程进行扩展;最后,根据LQR控制策略设计时滞补偿预测控制器求取预测控制力。应用结果显示,随着时滞的变大,使用无补偿措施的LQR控制器的双关节机械臂的颤振逐渐增大,并最终走向运动发散,而使用Taylor Series-LQR时滞补偿预测控制器的双关节机械臂在较大时滞范围内均能稳定跟踪期望轨迹而不产生颤振,说明Taylor Series-LQR复合策略具有良好的双关节机械臂时滞补偿效果。

Evaluation of Generalized Error Function via Fast-Converging Power Series

A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders.

Comparative Studies between Picard’s and Taylor’s Methods of Numerical Solutions of First Ordinary Order Differential Equations Arising from Real-Life Problems

To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.

TAYLOR SERIES AND ORTHOGONALITY OF THE OCTONION ANALYTIC FUNCTIONS

The Taylor series of the Octonion analytic function is given. And the orthogonal formula for the Octonion analytic functions is also obtained.

SOME PROPERTIES OF MULTIPLE TAYLOR SERIES AND RANDOM TAYLOR SERIES

Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on any compact set properties of the series may also be studied. For some random multiple are some corresponding properties. Growth and other Taylor series there

SOME REMARKS ON HOLOMORPHIC FUNCTIONS AND TAYLOR SERIES IN C^n

Some previous results on convergence of Taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in C^n are constructed and the Taylor series expansion is deduced.

The Bivariate Normal Integral via Owen’s T Function as a Modified Euler’s Arctangent Series

The Owen’s T function is presented in four new ways, one of them as a series similar to the Euler’s arctangent series divided by 2π, which is its majorant series. All possibilities enable numerically stable and fast convergent computation of the bivariate normal integral with simple recursion. When tested computation on a random sample of one million parameter triplets with uniformly distributed components and using double precision arithmetic, the maximum absolute error was 3.45 × 10-16. In additional testing, focusing on cases with correlation coefficients close to one in absolute value, when the computation may be very sensitive to small rounding errors, the accuracy was retained. In rare potentially critical cases, a simple adjustment to the computation procedure was performed—one potentially critical computation was replaced with two equivalent non-critical ones. All new series are suitable for vector and high-precision computation, assuming they are supplemented with appropriate efficient and accurate computation of the arctangent and standard normal cumulative distribution functions. They are implemented by the R package Phi2rho, available on CRAN. Its functions allow vector arguments and are ready to work with the Rmpfr package, which enables the use of arbitrary precision instead of double precision numbers. A special test with up to 1024-bit precision computation is also presented.

MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method

This paper investigates the magnetohydrodynamic （MHD） boundary layer flow of an incompressible upper-convected Maxwell （UCM） fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear prob- lem is solved by using the successive Taylor series linearization method （STSLM）. The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.

Q estimation using multifrequency point average method based on the Taylor series expansion with a different order

The quality factor Q is an important parameter because it can refl ect the reservoir attenuated features and can be used for inverse-Q filtering to compensate for the seismic wave energy.The accuracy of the Q estimation is greatly significant for improving the precision of the reservoir prediction and the resolution of seismic data.In this paper,the Q estimation formulas of the single-frequency point are derived on the basis of a diff erent-order Taylor series expansion of the amplitude attenuated factor.Moreover,the multifrequency point average(MFPA)method is introduced to obtain a stable Q estimation.The model tests demonstrate that the MFPA method is less aff ected by the frequency band,travel time diff erence,time window width,and noise interference than the logical spectrum ratio(LSR)method and the energy ratio(ER)method and has a higher Q estimation accuracy.In addition,the proposed method can be applied to post-stack seismic data and obtain eff ective Q values of complex models.When the MFPA method was applied to real marine seismic data,the Q values estimated by the MFPA method with the 1st–4th order showed good consistency with each other.In contrast,the Q values obtained by the ER method were larger than those of the proposed method,while those estimated by the LSR method signifi cantly deviated from the average values.In conclusion,the MFPA method has superior stability and practicability for the Q estimation.

THE DISTRIBUTION OF VALUES OF TAYLOR SERIES

Clarify some classical results and their proofs on the distribution of values of simple Taylor series and extend them to multiple Taylor series.

On Random Taylor Series

This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive constant α. The convergence, growth, and value distribution of the series are investigated.

A Strong Stability Preserving Analysis for Explicit Multistage Two-Derivative Time-Stepping Schemes Based on Taylor Series Conditions

High-order strong stability preserving(SSP)time discretizations are often needed to ensure the nonlinear(and sometimes non-inner-product)strong stability properties of spatial discretizations specially designed for the solution of hyperbolic PDEs.Multi-derivative time-stepping methods have recently been increasingly used for evolving hyperbolic PDEs,and the strong stability properties of these methods are of interest.In our prior work we explored time discretizations that preserve the strong stability properties of spatial discretizations coupled with forward Euler and a second-derivative formulation.However,many spatial discretizations do not satisfy strong stability properties when coupled with this second-derivative formulation,but rather with a more natural Taylor series formulation.In this work we demonstrate sufficient conditions for an explicit two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and Taylor series formulation.We call these strong stability preserving Taylor series(SSP-TS)methods.We also prove that the maximal order of SSP-TS methods is p=6,and define an optimization procedure that allows us to find such SSP methods.Several types of these methods are presented and their efficiency compared.Finally,these methods are tested on several PDEs to demonstrate the benefit of SSP-TS methods,the need for the SSP property,and the sharpness of the SSP time-step in many cases.

基于1DCNN和D-S多信息融合的光伏系统直流母线串联电弧故障检测

直流母线是光伏系统输出能源的主干道,由于长期曝晒、风化等作用,电缆、连接器等组件劣化,光伏系统直流母线中发生电弧的可能性急剧上升,极易引发火灾、触电等事故。在光伏系统中,串联电弧故障将使回路电流下降,传统的过流保护无法识别。因此,本文提出基于深度学习和证据理论(D-S)的方法来识别串联电弧故障,该方法基于并联电容器电流和电压信号,采用一维卷积神经网络(1DCNN)对检测数据进行电弧识别;在此基础上将基于单个传感数据的识别结果作为证据,运用D-S多信息合成法则计算得到信度分配,最后利用决策规则判断是否发生串联电弧故障。搭建多参数可调模型获取数据进行测试,结果表明:使用1DCNN识别方法,基于并联电容器电流和电压信号的串联电弧识别准确率分别为97.19%和94.98%,而基于1DCNN和D-S多信息融合的光伏系统直流串联电弧故障检测的识别准确率可提升至99%以上。

Anomalies identification of Earth’s rotation rate time series (2012-2017) for possible correlation with strong earthquakes occurrence

The analysis of the Earth’s rotation rate time series,from January 1,2012 till December 31,2017,is performed using two different time series analysis methods,both based on signal decomposition joined with forecasting approach.Anomalies in the time series are detected making the comparison between the raw signal and the forecasting one at the 95% confidence interval.The two methods show consistent results and the best is selected according to the evaluation of the prediction uncertainty.Both methods highlight correlations between detected anomalies in the Earth’s rotation rate time series and the world’s earthquakes occurrence with magnitude≥7 and/or number of events≥150 per day,within a time interval of ±10 days from each earthquake event.This study brings an innovation in the analysis of such time series and helps to better understand the extent of this relationship.

Classification of Short Time Series in Early Parkinson’s Disease With Deep Learning of Fuzzy Recurrence Plots

There are many techniques using sensors and wearable devices for detecting and monitoring patients with Parkinson’s disease(PD).A recent development is the utilization of human interaction with computer keyboards for analyzing and identifying motor signs in the early stages of the disease.Current designs for classification of time series of computer-key hold durations recorded from healthy control and PD subjects require the time series of length to be considerably long.With an attempt to avoid discomfort to participants in performing long physical tasks for data recording,this paper introduces the use of fuzzy recurrence plots of very short time series as input data for the machine training and classification with long short-term memory(LSTM)neural networks.Being an original approach that is able to both significantly increase the feature dimensions and provides the property of deterministic dynamical systems of very short time series for information processing carried out by an LSTM layer architecture,fuzzy recurrence plots provide promising results and outperform the direct input of the time series for the classification of healthy control and early PD subjects.

APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES

Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.

Accelerating spectral digital image correlation computation with Taylor series image reconstruction

In this paper,we introduce an accelerating algorithm based on the Taylor series for reconstructing target images in the spectral digital image correlation method(SDIC).The Taylor series image reconstruction method is employed instead of the previous direct Fourier transform(DFT)image reconstruction method,which consumes the majority of the computational time for target image reconstruction.The partial derivatives in the Taylor series are computed using the fast Fourier transform(FFT)of the entire image,following the principles of Fourier transform theory.To examine the impact of different orders of Taylor series expansion on accuracy and efficiency,we employ third-and fourth-order Taylor series image reconstruction methods and compare them with the DFT image reconstruction method through simulated experiments.As a result of these enhancements,the computational efficiency using the third-and fourth-order Taylor series improves by factors of 57 and 46,respectively,compared to the previous method.In terms of analysis accuracy,within a strain range of 0–0.1 and without the addition of image noise,the accuracy of the proposed method increases with higher expansion orders,surpassing that of the DFT image reconstruction method when the fourth order is utilized.However,when different levels of Gaussian noise are applied to simulated images individually,the accuracy of the third-or fourth-order Taylor series expansion method is superior to that of the DFT reconstruction method.Finally,we present the analyzed experimental results of a silicone rubber plate specimen with bilateral cracks under uniaxial tension.

ON THE CONDITIONAL VERSION OFKOLMOGOROV'S THREE-SERIES THEOREM

This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the conditional version also provide necessary conditions for convergence in dependent cases. Furthermore, some new sufficient conditions are obtained.

Extended Wiener Measure by Nonstandard Analysis for Financial Time Series

We propose a new approach to construct an extended Wiener measure using nonstandard analysis by E. Nelson. For the new definition we construct non-standardized convolution of probability measure for independent random variables. As an application, we consider a simple calculation of financial time series.

Design of a Multifrequency Signal Parameter Estimation Method for the Distribution Network Based on HIpST

The application of traditional synchronous measurement methods is limited by frequent fluctuations of electrical signals and complex frequency components in distribution networks.Therefore,it is critical to find solutions to the issues of multifrequency parameter estimation and synchronous measurement estimation accuracy in the complex environment of distribution networks.By utilizing the multifrequency sensing capabilities of discrete Fourier transform signals and Taylor series for dynamic signal processing,a multifrequency signal estimation approach based on HT-IpDFT-STWLS(HIpST)for distribution networks is provided.First,by introducing the Hilbert transform(HT),the influence of noise on the estimation algorithm is reduced.Second,signal frequency components are obtained on the basis of the calculated signal envelope spectrum,and the interpolated discrete Fourier transform(IpDFT)frequency coarse estimation results are used as the initial values of symmetric Taylor weighted least squares(STWLS)to achieve high-precision parameter estimation under the dynamic changes of the signal,and the method increases the number of discrete Fourier.Third,the accuracy of this proposed method is verified by simulation analysis.Data show that this proposed method can accurately achieve the parameter estimation of multifrequency signals in distribution networks.This approach provides a solution for the application of phasor measurement units in distribution networks.