基于机器学习原理的函数定阶法对乙醇偶合制备C4烯烃问题的分析

C4烯烃是工业生产中重要的化工原料,在探究不同催化剂组合对乙醇偶合制备C4烯烃的实验中往往需要用高阶函数对一段时间内的反应进行拟合。这个过程可以从机器学习的角度进行分析与建模,其核心方法是基于机器学习原理的函数定阶法。拟合过程及结果可应用python中numpy库的polyfit函数反馈在待拟合的散点图上,并测试其在不同阶数拟合条件下的均方误差以及决定系数,最终可以得到合适的拟合阶数,并最终确定样本拟合的通用函数模型。

无穷小量定阶法及其应用

确定无穷小量的阶是微积分中一类重要的问题．本文较为系统地归纳了确定无穷小量阶的基本方法及相应的推论，并介绍了这些方法在有关无穷小量阶的问题、求极限问题以及研究数项级数收敛性等问题中的应用．

基于预报误差最小的自回归模型定阶方法研究

以独立样本的平均绝对预报误差最小为依据，进行了自回归模型定阶方法的研究，简称MAPE方法（MeanAbsolutePredictionError）。应用MAPE方法及五种常用的定阶方法（FPE，AIC，BIC，L1和L2准则），对上海月平均温度序列（1873—1980年）进行定阶试验计算和预报检验。结果表明，MAPE方法是一种效果较好的自回归模型定阶方法，并且简单实用。

基于自动搜索定阶法的时间序列分析模型在桥梁索塔变形监测中的应用

针对桥梁索塔易发生变形的情况,探讨了一种基于自动搜索定阶的时间序列预测新方法。该方法首先利用spdiags函数对非平稳的桥梁GPS观测数据进行趋势项提取,之后对提取趋势项后的时间序列进行高阶差分,处理得到平稳的残差序列并对其进行时序建模,通过自动搜索定阶法确定模型的阶数,最后利用建立的ARMA模型完成对桥梁索塔变形的预报。该文以苏通大桥作为研究对象,通过该方法对2016年的大桥索塔GPS观测数据进行时序分析并建立相应的模型,通过此模型对苏通大桥索塔2017年前3个月的变形情况进行预报,并将预报结果与该时间段的索塔实测数据进行比较,发现预测值与实测值之间的差值都小于4mm,证明该方法的预测精度高,可以很好地应用于桥梁索塔变形监测的预报。

关于无穷小的若干比较方法及应用

函数的极限是极限理论的一个重要组成部分,无穷小的定义与计算则是函数极限的基础.无穷小的比较问题是微积分的重要内容,为了更系统地解决此类问题,文章从无穷小比较的定义、等价无穷小定阶法、比较定阶法、泰勒公式定阶法、求导定阶法这五种方法进行了讨论,并且分别给出了对应的实例分析.灵活使用这些方法,可以做到更加有效地解决无穷小的比较问题.

基于航天器复杂动力学模型的鲁棒H_∞振动抑制算法

现代大型航天器柔性越来越大,为了获得更好的姿态控制性能,需要主动振动抑制.鲁棒Η∞是一种正在走向工程应用的控制器设计方法,DGKF解析法,线形矩阵不等式LMI数值法,定阶Η∞范数优化法是3种重要的算法.本文对国际空间站俄罗斯舱的有限元模型提出了振动抑制的Η∞综合问题,分别用3种算法求解鲁棒Η∞控制器.基于DGKF法的全阶次优控制器,存在零极点对消,而基于LMI法的51控制器光滑,能有效抑制零极点对消,但LMI法不是一种优化算法,两种控制器降阶为2阶时,Η∞性能衰退大于80%.基于定阶法的2阶控制器和PI控制器具有与DGKF全阶控制器相近的Η∞性能,鲁棒性分析和扰动抑制的时域仿真验证了上述结论.

基于行列式比的阶次和参数同步递推辨识算法

针对输出误差模型,结合辅助模型的思想对原有阶次辨识和参数估计的方法进行融合和扩展,推导出基于辅助模型的行列式比定阶法,同时得出模型的阶次和参数,不仅减少了辨识过程的计算量,也节约了辨识时间。考虑到原有行列式比定阶法可能存在的不准确性,提出了一种系统模型的确认方法,增强了阶次辨识能力。仿真实验也充分表明,对行列式比定阶法的扩展不仅可以准确地辨识出系统的阶次,得出的参数估计值也有较高的精度。

自回归模型在井水埋深预测中的应用及改进

用时间序列分析方法建立井水埋深的预测模型时,首先采用差分的方法把季节性时间序列变成平稳时间序列,在此基础上,再用动态数据系统方法的传统F检验定阶法进行分析。由于样本的随机性可能过早地退出对模型的循环检验,从而不能找到合适的预测模型。笔者在用自回归模型建立井水预测模型的基础上,采用了一种改进的建模方法,提高了预测精度,并用实例进行了验证。

GPS坐标序列ARMA模型在桥梁索塔形变监测中的应用研究

针对运营期大跨径公路桥梁索塔易受承重、风力和太阳辐射等外界因素影响而发生变形的问题,研究了基于时间序列分析的桥梁索塔变形预测方法,将基于高阶差分的非平稳时间序列平稳化处理方法以及基于自动搜索定阶法的自回归ARMA模型阶数确定应用于桥梁索塔GPS坐标时间序列处理。以苏通长江公路大桥南塔2018年全年GPS监测数据作为研究对象进行试验,通过自动搜索定阶后的ARMA模型预测苏通大桥南塔2019年1—3月的索塔变形值,结果表明苏通大桥南塔预测值曲线起伏总体上与实测值的曲线起伏保持一致,且预测值与实测值的差异优于4 mm,但预测数据与实测数据之间的相关性随着预测天数的增加而逐渐减弱,此时可根据最新获得的监测数据重新建立模型对索塔进行变形预测。

Second-order difference scheme for a nonlinear model of wood drying process

A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result.

Optimization of Routing Considering Uncertainties

A route optimization methodology in the frame of an onboard decision support/guidance system for the ship＇s master has been developed and is presented in this paper. The method aims at the minimization of the fuel voyage cost and the risks related to the ship＇s seakeeping performance expected to be within acceptable limits of voyage duration. Parts of this methodology were implemented by interfacing alternative probability assessment methods, such as Monte Carlo, first order reliability method （FORM） and second order reliability method （SORM）, and a 3-D seakeeping code, including a software tool for the calculation of the added resistance in waves of NTUA-SDL. The entire system was integrated within the probabilistic analysis software PROBAN. Two of the main modules for the calculation of added resistance and the probabilistic assessment for the considered seakeeping hazards with respect to exceedance levels of predefined threshold values are herein elaborated and validation studies proved their efficiency in view of their implementation into an on-board optimization system.

A Two-Stage Method for an Approximate Calculation of Statically Indeterminate Trusses

The paper presents the principles of a method, which in two simple stages makes possible to carry out the statically calculation of values of forces acting in the fiat static indeterminate trusses. In each stage, it is considered the static determinate truss, scheme of which is obtained after remove the suitable number of members from the basic static indeterminate truss. The both intermediate statically determinate trusses are of the same clear span and they are loaded by forces of half values applied to the corresponding truss nodes. The method applies one of the typical procedures of calculation of the statically determinate trusses and then it is applied in an appropriate way the rule of superposition for obtaining the final values of forces acting in particular members of the basic truss. The values of forces calculated in this way are of a very close approximation to the force values determined in the special and complex ways being considered as the exact calculation methods. The proposed method can be useful mostly but not only for the initial structural design of such systems. The simplicity of the two-stage method justifies an assumption that it can be relatively easy and worthy to adjust to the requirements of the computer aided technology of statically calculation of the complex forms of trusses.

AR 模型识别及其参数的高阶Yule-Walker估计

一、引言自回归谱估计在许多领域获得了广泛的应用,随着科学技术的不断发展,对谱估计分辨力的要求越来越高.高阶 Yule-Walker 谱估计就是具有较高分辨力的一种估计(见[1]).为了进一步研究这种估计首先必须研究自回归模型阶的识别及其参数的高阶Yule-Walker 估计.通常使用的自回归定阶方法与参数的矩估计方法使用了样本自协方差函数(或样本自相关函数)在零点的值(?)(0)(或(?)(0))。而(?)(0)(或(?)(0))就是影响自回归谱估计分辨力的一个重要因素.实际上。

Assessment of alternative scale-providing variables in a Reynolds-stress model using high-order methods

This paper is set in the high-order finite-difference discretization of the Reynolds-averaged Navier-Stokes(RANS)equations,which are coupled with the turbulence model equations.Three alternative scale-providing variables for the specific dissipation rate(o)are implemented in the framework of the Reynolds stress model(RSM)for improving its robustness.Specifically,g(=1/√ω)has natural boundary conditions and reduced spatial gradients,and a new numerical constraint is imposed on itω(=lnω)can preserve positivity and also has reduced spatial gradients;the eddy viscosity v,also has natural boundary conditions and its equation is improved in this work.The solution polynomials of the mean-flow and turbulence-model equations are both reconstructed by the weighted compact nonlinear scheme(WCNS).Moreover,several numerical techniques are introduced to improve the numerical stability of the equation system.A range of canonical as well as industrial turbulent flows are simulated to assess the accuracy and robustness of the scale-transformed models.Numerical results show that the scale-transformed models have significantly improved robustness compared to the w model and still keep the characteristics of RSM.Therefore,the high-order discretization of the RANS and RSM equations,which number 12 in total,can be successfully achieved.

Simultaneous determination of brilliant blue and indigotine by derivative fluorescence spectrometry combined with WT-RBFNN

The mixed solutions of brilliant blue and indigotine are prepared and the fluorescence spectra of them are experimentally measured. The serious overlapping spectra of brilliant blue and indigotine are solved by means of the first-derivative fluorescence spectrometry. The wavelet coefficients, obtained by compressing the spectral data using wavelet transformation （WT）, are taken as inputs to establish the radial basis function neural network （RBFNN）. The neural network model can realize simultaneous determination of brilliant bFue and indigotine, and the mean relative errors of both compounds are 1.84% and 1.26%, respectively

A Novel Approach with Time-Splitting Spectral Technique for the Coupled Schrdinger–Boussinesq Equations Involving Riesz Fractional Derivative

In the present paper the Riesz fractional coupled Schr6dinger-Boussinesq （S-B） equations have been solved by the time-splitting Fourier spectral （TSFS） method. This proposed technique is utilized for discretizing the Schrodinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here.