Comparative Study of Probabilistic and Least-Squares Methods for Developing Predictive Models

This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.

Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

APPLICATION OF LEAST MEDIAN OF SQUARED ORTHOGONAL DISTANCE (LMD) AND LMD BASED REWEIGHTED LEAST SQUARES (RLS) METHODS ON THE STOCK RECRUITMENT RELATIONSHIP

Analysis of stock recruitment (SR) data is most often done by fitting various SR relationship curves to the data. Fish population dynamics data often have stochastic variations and measurement errors, which usually result in a biased regression analysis. This paper presents a robust regression method, least median of squared orthogonal distance (LMD), which is insensitive to abnormal values in the dependent and independent variables in a regression analysis. Outliers that have significantly different variance from the rest of the data can be identified in a residual analysis. Then, the least squares (LS) method is applied to the SR data with defined outliers being down weighted. The application of LMD and LMD based Reweighted Least Squares (RLS) method to simulated and real fisheries SR data is explored.

采用改进遗传算法优化LS-SVM逆系统的外转子无铁心无轴承永磁同步发电机解耦控制

为了实现外转子无铁心无轴承永磁同步发电机(outer rotor coreless bearingless permanent magnet synchronous generator,ORC-BPMSG)的精确控制,提出一种基于改进遗传算法(improved genetic algorithm,IGA)优化最小二乘支持向量机(least square support vector machine,LS-SVM)逆系统的解耦控制策略。首先,基于ORC-BPMSG的结构及工作原理,推导其数学模型,并分析其可逆性。其次,建立LS-SVM回归方程,并采用IGA优化LS-SVM的性能参数,从而训练得到逆系统。然后,将逆系统与原系统串接,形成伪线性系统,实现了ORC-BPMSG的线性化和解耦。最后,将提出的控制方法与传统LS-SVM逆系统控制方法进行对比仿真和实验。仿真和实验结果表明:所提出的控制策略可以较好地实现ORC-BPMSG输出电压和悬浮力、以及悬浮力之间的解耦控制。

Preconditioned iterative methods for solving weighted linear least squares problems

A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.

基于FFRLS和ASR-UKF滤波算法的锂电池SOC估计

锂电池在工作过程中,其内部参数易受多种因素影响,为提高锂电池在复杂环境下荷电状态(SOC)估计精度,以二阶戴维宁(Thevenin)等效模型为基础,结合遗忘因子递推最小二乘法(FFRLS)对模型参数进行在线辨识。针对传统卡尔曼滤波算法高度非线性及系统噪声不确定性等缺点,提出了一种自适应平方根无迹卡尔曼滤波(ASR-UKF)算法,该算法利用平方根算法处理均值和协方差,确保了状态协方差的半正定性和稳定性,并引入自适应滤波算法对噪声进行实时修正,消除了系统时变噪声影响。结果表明,FFRLS能有效解决数据饱和及算法矩阵计算量大的问题,等效模型精度高达98%。在混合动力脉冲特性(HPPC)测试和北京公交动态测试工况(BBDST)下,ASR-UKF算法SOC估计最大误差分别为3.264%和0.572%,具备更好的跟踪效果,验证了改进算法良好的收敛性与自适应性。

美国户外休闲产业发展特征及预测模型构建研究——基于PLS和PLS-DA方法的分析

户外休闲产业是美国经济的支柱性产业,分析其发展特征和构建预测模型对于我国健身休闲产业健康、可持续发展有重要借鉴价值。研究收集了美国50个州2021年户外休闲产业相关数据,选取27个影响指标,运用PLS和PLS-DA方法,对美国户外休闲产业发展特征进行分析并构建预测模型。研究表明:(1)美国州域户外休闲产业可分为4种发展模式,即总量大占比小型、总量小占比大型、总量较大占比较小型、总量较小占比较大型,4种发展模式在空间上呈现一定集聚分布特征。(2)构建的预测模型有效且精度较高,并筛选出12个VIP指标,经济、人口和社会因素似乎更多地影响美国户外休闲产业发展,而自然环境因素的影响相对较弱。

ON THE BREAKDOWNS OF THE GALERKIN AND LEAST-SQUARES METHODS

The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.

基于PLS-SEM的航天器控制系统能力建模方法

为提升航天任务完成品质,航天器需根据任务及环境针对性调整自身能力,而对航天器控制系统高层次能力的定量刻画,即系统能力建模是实现上述调整的重要理论依据。针对一类航天器姿态控制系统,提出一种基于偏最小二乘-结构方程模型(partial least square structural equation model,PLS-SEM)的航天器控制系统能力建模方法,实现对包括控制能力、观测能力等抽象能力的定量描述。首先,根据航天器闭环控制系统的结构要素,综合设计能力建模所需的指标类型,生成建模数据样本。在此基础上,设计并构建SEM框架下的能力变量体系,进而通过PLS算法完成模型路径、载荷、权重等关键参数的确定,并对所得PLS-SEM能力模型的结构方程与测量方程的有效性、可信性等分别进行评估。最终,根据航天器PLS-SEM能力模型对控制系统的各抽象能力进行定量描述与分析,验证本文所提出建模方法的可行性。

BSN:Photometric Light Curve Analysis of Two Contact Binary Systems LS Del and V997 Cyg

The light curve analyses and orbital period variations for two contact binary stars,LS Del and V997 Cyg,are presented in this work which was conducted in the frame of the Binary Systems of South and North project Ground-based photometric observations were performed at two observatories in France.We used the Transiting Exoplanet Survey Satellite(TESS)data for extracting times of minima and light curve analysis of the targe systems.The O-C diagram for both systems displays a parabolic trend.LS Del and V997 Cyg’s orbital periods are increasing at rates of dP/dt=7.20×10^(-08)days yr^(-1)and dP/dt=2.54×10^(-08)days yr^(-1),respectively Therefore,it can be concluded that mass is being transferred from the less massive star to the more massive component with a rate of dM/dt=-1.96×10^(-7)M_(⊙)yr^(-1)for the LS Del system,and dM/dt=-3.83×10^(-7)M_(⊙)yr-1for V997 Cyg.The parameters of a third possible object in the system are also considered.The PHysics Of Eclipsing BinariEs Python code was used to analyze the light curves.The light curve solutions needed a cold starspot due to the asymmetry in the LS Del system’s light curve maxima.The mass ratio fill-out factor,and star temperature all indicate that both systems are contact binary types in this investigation.Two methods were applied to estimate the absolute parameters of the systems:one method relied on the parallax of Gaia DR3,and the other used a P-M relationship.The positions of the systems are also depicted on the M-L,M-R q-L_(ratio),and logM_(tot)-logJ_(0)diagrams.We recommend that further observations and investigations be done on the existence of a fourth body in this system.

NEGATIVE NORM LEAST-SQUARES METHODS FOR THE INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS

The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.

Distributed Least-Squares Iterative Methods in Large-Scale Networks:A Survey

Many science and engineering applications involve solvinga linear least-squares system formed from some field measurements. In the distributed cyber-physical systems(CPS),each sensor node used for measurement often only knowspartial independent rows of the least-squares system. To solve the least-squares all the measurements must be gathered at a centralized location and then perform the computa-tion. Such data collection and computation are inefficient because of bandwidth and time constraints and sometimes areinfeasible because of data privacy concerns. Iterative methods are natural candidates for solving the aforementionedproblem and there are many studies regarding this. However,most of the proposed solutions are related to centralized/parallel computations while only a few have the potential to beapplied in distributed networks. Thus distributed computations are strongly preferred or demanded in many of the realworld applications, e.g. smart-grid, target tracking, etc. Thispaper surveys the representative iterative methods for distributed least-squares in networks.

基于DFFRLS的PMSM自校正PI速度控制策略研究

基于惯量辨识的永磁同步电机自校正PI速度控制具有良好的抗负载扰动性能,但受到惯量辨识过程存在抖动的影响转速响应会产生高频振荡。为抑制高频振荡,提出一种基于动态遗忘因子递推最小二乘法惯量辨识的自校正PI控制策略。首先,构造指数函数形式的动态遗忘因子,分析其跟随辨识误差变化的规律并用于转动惯量辨识。然后,采用“振荡指标法”设计PI参数整定公式,并结合DFFRLS惯量辨识过程进行自校正PI控制。仿真和实验结果表明:改进的DFFRLS有效减小了辨识惯量的抖动幅度;所提ST-PIC调速控制策略在保证转速高性能响应的同时有效抑制了高频振荡。

MAFFRLS算法辨识锂离子电池模型参数

建模方法和模型参数辨识方法会影响锂离子电池状态的准确估计,特别是在动态工况下,因此在线辨识电池模型参数的方法很重要。提出一种改进的自适应遗忘因子递推最小二乘(MAFFRLS)法,优点是在不同误差范围内可以自适应地更新遗忘因子最优值。选用二阶RC等效电路模型,在动态工况下对该算法进行验证。将所提出的算法与递推最小二乘(RLS)法和遗忘因子递推最小二乘(FFRLS)法进行对比。在动态应力测试(DST)工况下,使用RLS、FFRLS和MAFFRLS算法估计电压,平均绝对误差分别为0.0102 V、0.0099 V和0.0046 V,均方根误差分别为0.0155 V、0.0150 V和0.0068 V。MAFFRLS算法的平均绝对误差和均方根误差更小,准确性更高。

基于Bootstrap方法和LSSVM模型的滑坡位移区间预测

针对滑坡预测中的不确定性和传统点位移预测无法对预测结果的可靠程度进行有效描述这一问题,本文提出了一种区间预测方法,通过Bootstrap方法和最小二乘支持向量机来构建滑坡位移预测模型。并以三峡库区秭归县树坪滑坡为例,选取ZG85监测点在2007年1月—2012年12月期间的位移、降水量及库水位数据进行研究。研究结果表明,滑坡位移区间预测模型相比于传统的确定性点预测模型,能够同时兼顾准确性和可靠性,为滑坡灾害预测提供了一种新思路。

基于非线性摩擦力模型和WLS-CS算法的机器人动力学参数辨识

为了实现对工业机器人的高精度控制,需要一个高精度的动力学模型,因此要对动力学参数进行精准辨识。提出一种基于非线性摩擦力模型和加权最小二乘法与布谷鸟算法(WLS-CS)结合的动力学参数辨识方法。首先通过Newton-Euler法进行机器人的动力学建模,结合非线性摩擦力模型,完成机器人全动力学模型的建模。设计5阶有限项傅里叶级数作为激励轨迹,并优化激励轨迹参数。使用加权最小二乘法对动力学参数进行初步辨识。辨识结果作为布谷鸟算法的初始解范围,结合Levy飞行与巢穴的优胜劣汰机制,寻找到动力学参数辨识的全局最优解。更换轨迹对机器人全动力学模型进行验证,计算机器人的仿真力矩,并与实验力矩反馈值进行对比。结果表明上述方法辨识的动力学参数辨识精度的残差方根(RMS)值下降8.6%,可以建立精确度较高的动力学模型。

基于改进灰狼算法优化WLSSVM的短期风功率预测

为提高风功率短期预测的准确率,提出一种基于改进灰狼算法优化加权最小二乘支持向量机(Weighted Least Squares Support Vector Machine,WLSSVM)的短期风功率预测方法。采用C-C法对风功率时间序列的嵌入维数进行了计算,根据计算结果确定短期风速预测输入量与输出量的关系。利用Tent映射和参数非线性调整策略对灰狼算法进行改进,得到了优化性能更强的改进灰狼优化(Improved Grey Wolf Optimization,IGWO)算法,并利用测试函数验证了IGWO算法能够加快迭代收敛,提高计算精度。采用IGWO算法对WLSSVM的惩罚系数和核参数进行优化,建立基于IGWO-WLSSVM的短期风功率预测模型。采用某风电场春夏两个不同季节的风功率数据进行算例分析,结果表明,所提短期风功率预测结果的平均相对误差、均方根误差和最大相对误差更小,风功率预测精度和预测结果的稳定性均优于其他方法,验证了所提方法的有效性和实用性。

基于LSSVM的火力发电厂燃煤发电机组碳排放测算方法

为解决燃煤发电机组在投产使用后存在的碳排放过大等问题,降低机组运行对大气环境的负面影响,作者以某火力发电厂为例,引入最小二乘支持向量机(LSSVM),开展燃煤发电机组碳排放测算方法的设计研究。以LSSVM中的径向基(RBF)函数核,构建燃煤发电机组碳排放相关数据样本集合,根据样本集合容量,进行数据的非线性映射,实现对发电机组碳排放相关数据的筛查;建立火力发电厂碳排放强度计算模型,对火力发电厂燃煤发电机组在运行过程中煤耗综合情况进行系统化分析。考虑到火力发电厂燃煤发电机组在投产使用后会不可避免地存在损耗,在碳排放强度已知的情况下,对考虑网损的发电机组碳排放进行测算。实验结果表明:设计的测算方法应用效果良好,规范使用该方法进行火力发电厂燃煤发电机组碳排放测算,测算结果更加贴合实际。

Least-Squares及Galerkin谱元方法求解环形区域内的泊松方程

为研究基于Least-Squares变分及Galerkin变分两种形式的谱元方法的求解特性,推导了极坐标系中采用两种变分方法求解环形区域内Poisson方程时对应的弱解形式,采用Chebyshev多项式构造插值基函数进行空间离散,得到两种谱元方法对应的代数方程组,由此分析了系数矩阵结构的特点。数值计算结果显示:Least-Squares谱元方法为实现方程的降阶而引入新的求解变量,使得代数方程组形式更为复杂,但边界条件的处理比Galerkin谱元方法更为简单;两种谱元方法均能求解极坐标系中的Poisson方程且能获得高精度的数值解,二者绝对误差分布基本一致;固定单元内的插值阶数时,增加单元数可减小数值误差,且表现出代数精度的特点,误差降低速度较慢,而固定单元数时,在一定范围内数值误差随插值阶数的增加而减小的速度更快,表现出谱精度的特点;单元内插值阶数较高时,代数方程组系数矩阵的条件数急剧增多,方程组呈现病态,数值误差增大,这一特点限制了单元内插值阶数的取值。研究内容对深入了解两种谱元方法在极坐标系中求解Poisson方程时的特点、进一步采用相关分裂算法求解实际流动问题具有参考价值。

用于损伤状态识别的极值延拓EMD和LS-SVM算法

针对机电系统损伤状态识别问题,提出一种基于极值延拓经验模态分解(EMD)和最小二乘支持向量机(LS-SVM)算法。首先,分析EMD算法的基本原理,针对端点效应利用多项式拟合极值延拓的算法改进设计方案,并利用标准化处理的特征向量设计程式;其次,考虑到机电系统损伤状态数据归属小样本特征,利用LS-SVM算法给出了状态识别的设计程式;最后,开展仿真验证实验。实验结果表明,采用所提算法的损伤状态识别方案,可以确保损伤状态识别的正确率超过96%,满足机电系统工程应用要求。