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.

Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

Numerical simulation of inlet placement on sewage characteristics in the rounded square aquaculture tank with single inlet

To improve the self-cleaning ability of aquaculture tank and the efficiency of circulating water,physical and numerical experiments were conducted on the influence of inlet structure on sewage discharge in a rounded square aquaculture tank with a single inlet.Based on the physical model of the tank,analysis of how inlet structure adjustment affects sewage discharge efficiency and flow field characteristics was conducted to provide suitable flow field conditions for sinkable solid particle discharge.In addition,an internal flow field simulation was conducted using the RNG k-εturbulence model in hydraulic drive mode.Then a solid-fluid multiphase model was created to investigate how the inlet structure affects sewage collection in the rounded square aquaculture tank with single inlet and outlet.The finding revealed that the impact of inlet structure is considerably affecting sewage collection.The conditions of C/B=0.07-0.11(the ratio of horizontal distance between the center of the inlet pipe and the tank wall(C)to length of the tank(B))andα=25°(αis the angle between the direction of the jet and the tangential direction of the arc angle)resulted in optimal sewage collection,which is similar to the flow field experiment in the rounded square aquaculture tank with single inlet and outlet.An excellent correlation was revealed between sewage collection and fluid circulation stability in the aquaculture tank.The present study provided a reference for design and optimization of circulating aquaculture tanks in aquaculture industry.

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

Least Squares One-Class Support Tensor Machine

One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification problem for second-order tensor data. Traditional vector-based one-class classification methods such as one-class support vector machine (OCSVM) and least squares one-class support vector machine (LSOCSVM) have limitations when tensor is used as input data, so we propose a new tensor one-class classification method, LSOCSTM, which directly uses tensor as input data. On one hand, using tensor as input data not only enables to classify tensor data, but also for vector data, classifying it after high dimensionalizing it into tensor still improves the classification accuracy and overcomes the over-fitting problem. On the other hand, different from one-class support tensor machine (OCSTM), we use squared loss instead of the original loss function so that we solve a series of linear equations instead of quadratic programming problems. Therefore, we use the distance to the hyperplane as a metric for classification, and the proposed method is more accurate and faster compared to existing methods. The experimental results show the high efficiency of the proposed method compared with several state-of-the-art methods.

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.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

PSR-SQUARES:基于程序空间约简器的SQL逆向合成系统

针对SQUARES程序空间增长过快,导致程序合成效率偏低的问题,在SQUARES的基础上,增加了以深度神经网络为核心的程序空间约简器,将给定的<被查询表,查询结果>示例表示成二维张量,作为深度神经网络的输入,网络的输出是关于目标SQL语句合成规则的相关性标记向量。约简器根据神经网络的输出结果,采用末N位淘汰策略,删除与目标SQL语句相关性弱的合成规则,以减少候选SQL语句的生成和验证,提升系统合成效率。对约简器中深度神经网络的结构设计、训练样本集的生成方法和网络训练过程进行了详细描述。同时将PSR-SQUARES与当前有代表性SQL逆向合成系统进行实验对比,实验结果表明,PSR-SQUARES的综合性能不同程度地优于其他合成系统,平均合成时间由SQUARES的251 s降低至130 s,目标程序合成成功率由80%提升至89%。

BOOSTING SPARSE LEAST SQUARES SUPPORT VECTOR REGRESSION (BSLSSVR) AND ITS APPLICATION TO THRUST ESTIMATION

In order to realize direct thrust control instead of conventional sensors-based control for aero-engine, a thrust estimator with high accuracy is designed by using the boosting technique to improve the performance of least squares support vector regression （LSSVR）. There exist two distinct features compared with the conven- tional boosting technique： （1） Sampling without replacement is used to avoid numerical instability for modeling LSSVR. （2） To realize the sparseness of LSSVR and reduce the computational complexity, only a subset of the training samples is used to construct LSSVR. Thus, this boosting method for LSSVR is called the boosting sparse LSSVR （BSLSSVR）. Finally, simulation results show that BSLSSVR-based thrust estimator can satisfy the requirement of direct thrust control, i.e. , maximum absolute value of relative error of thrust estimation is not more than 5‰.

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。

Factor-square-full半模

作为factor-square-full模的真推广,引入了factor-square-full半模的概念.设S是半环,M是左S-半模.称M的真subtractive子半模X是d-square,若存在正规满同态f:M→(M/X)2;称M的真subtractive子半模X是quasi-d-square,若存在M的d-square子半模Y使得X≤Y;称M是factor-square-full,若M的任意真subtractive子半模是quasi-d-square.讨论了这些子半模类及factor-square-full半模的性质.

基于PLSR和LSSVM模型的土壤水分高光谱反演

为对地下采矿扰动区表层土壤水分进行反演,以大柳塔煤矿52501工作面为例,利用无人机搭载成像光谱仪获取高光谱影像,对获取的光谱数据进行对数、倒数对数、一阶和包络线去除变换,结合地面采集的128个土壤水分数据,基于偏最小二乘回归(PLSR)和最小二乘支持向量机(LSSVM)构建土壤水分预测模型并验证其预测精度。结果表明,基于一阶变换的PLSR模型和LSSVM模型预测精度相对较好,一阶变换的PLSR模型建模集R^(2)_(c)和预测集R^(2)_(p)分别为0.7021和0.6405,均方根误差RMSE_(c)和RMSE_(p)分别为1.6384%和1.1034%,相对分析误差RPD_(p)为1.7263;一阶变换的LSSVM模型建模集R^(2)_(c)和预测集R^(2)_(p)分别为0.8125和0.5979,均方根误差RMSE_(c)和RMSE_(p)分别为1.2755%和1.3459%,相对分析误差RPD_(P)为1.6323。最终基于PLSR和LSSVM模型完成了土壤水分的制图,实现了土壤水分的空间预测,为该研究区植被引导修复中土壤水分精准提升提供了空间数据支持。

基于ISSA-HKLSSVM的浮选精矿品位预测方法

针对浮选过程变量滞后、耦合特征及建模样本数量少所导致精矿品位难以准确预测的问题,提出了一种基于改进麻雀搜索算法(Improved Sparrow Search Algorithm,ISSA)优化混核最小二乘支持向量机(Hybrid Kernel Least Squares Support Vector Machine,HKLSSVM)的浮选过程精矿品位预测方法.首先采集浮选现场载流X荧光品位分析仪数据作为建模变量并进行预处理,建立基于最小二乘支持向量机(Least Squares Support Vector Machine,LSSVM)的预测模型,以此构建新型混合核函数,将输入空间映射至高维特征空间,再引入改进麻雀搜索算法对模型参数进行优化,提出基于ISSA-HKLSSVM方法实现精矿品位预测,最后开发基于LabVIEW的浮选精矿品位预测系统对本文提出方法实际验证.实验结果表明,本文提出方法对于浮选过程小样本建模具有良好拟合能力,相比现有方法提高了预测准确率,可实现精矿品位的准确在线预测,为浮选过程的智能调控提供实时可靠的精矿品位反馈信息.

基于OPLS-DA模型分析不同养殖方式下宁都黄鸡肌肉关键挥发性风味物质

为研究不同养殖方式下宁都黄鸡肌肉关键挥发性风味物质,将试验鸡随机分为笼养组和平养组,饲喂同一日粮。试验鸡达上市日龄时对鸡肉进行感官品尝评价和挥发性风味物质检测,并采用正交偏最小二乘-判别分析(orthogonal partial least squares-discriminant analysis,OPLS-DA)方法筛选与不同养殖方式相关的差异性风味物质。结果表明:平养组和笼养组共有的挥发性风味物质27种,主要为酚类、醇类和烃类。挥发性风味物质中,己醛、1-辛烯-3-醇、E-2-壬烯醛、正己醇、壬醛、2,3-戊二酮、癸醛、2,3-辛二酮、E-2-辛烯醛为具有显著性差异的挥发性风味物质。综上,这一研究可为地方鸡肉品质基于风味物质的评价提供科学依据。

基于TLS的改进子空间投影算法

针对经典MUSIC算法在信源相干、低信噪比、小快拍数等非理想环境下性能失效的问题,提出了一种改进的基于TLS的加权子空间投影算法。首先对阵列接收的数据协方差矩阵进行重构处理,以达到解相干目的;其次充分利用子空间信息,基于总体最小二乘拟合方法对特征值进行拟合修正,基于修正MUSIC算法思想,利用校正后的噪声特征值和信号特征值分别对噪声子空间和信号子空间进行加权处理,得到改进后的噪声子空间和信号子空间,并将两者结合得到新的空间谱函数;最后进行谱峰搜索,完成信号源的波达方向估计。仿真结果表明,改进后的算法既适用于相干信号环境,在低信噪比、小快拍数及信号入射角度间隔较小的情况下,又能有效估计出信源的波达方向。

基于DBN和BES-LSSVM的矿用压风机异常状态识别方法

针对矿用压风机这类分布式系统的异常类别复杂、识别精度低等问题,提出了一种基于深度置信网络(DBN)和最小二乘支持向量机(LSSVM)的异常状态识别方法。首先,分析压风机组成系统及其运行机理,确定常见的异常状态类型;其次,采用DBN无监督学习方式充分挖掘监测数据中异常特征并快速提取;然后,利用秃鹰搜索算法(BES)优化LSSVM的超参数,构建最优的BES-LSSVM分类模型;最后,将DBN提取的异常特征作为BES-LSSVM模型的输入,对矿用压风机异常状态进行识别。试验验证与对比分析结果表明,相较于GA,PSO,GWO算法,BES算法的求解精度和收敛速度均有所提高,同时DBN-BES-LSSVM模型在测试集上平均识别精度达到94.65%,较PCA-LSSVM模型、DBN模型和DBN-LSSVM模型的识别精度分别提高了10.53%,5.84%和3.76%,验证了DBN-BES-LSSVM模型在矿用压风机异常特征提取以及特征识别方面的优越性。

硫酮衍生物LS对天然胶乳保存效果的研究

天然胶乳很容易腐败变质,而当前的高氨保存体系存在严重的污染问题。本研究采用硫酮衍生物LS保存天然胶乳,研究保存剂LS对天然胶乳的保存效果。结果表明:LS保存的鲜胶乳挥发脂肪酸值(VFA No.)和黏度值均比较低,当LS用量为0.1%时,对鲜胶乳的保存效果优于0.25%氨;采用LS-氨复合保存制备低氨浓缩胶乳,当LS用量为0.01%~0.05%时可稳定保存浓缩胶乳达180d之久;所保存的低氨浓缩胶乳挥发脂肪酸值(VFANo.)较低,稳定性良好,各项指标均满足当前生产应用需求。此外,LS-氨复合保存低氨浓缩胶乳具有优异的理化性能和成膜性能,硫化胶膜的拉伸强度和撕裂强度普遍优于当前高氨保存浓缩胶乳。通过红外吸收光谱分析,LS-氨复合保存的低氨浓缩胶乳硫化胶膜的结构无明显变化;热分析结果表明,硫化胶膜热稳定性与高氨浓缩胶乳胶膜基本一致。此外,安全性分析结果表明,LS-氨复合保存低氨浓缩胶乳干胶膜不具有潜在毒性影响;同时无皮肤刺激性反应,安全性良好。硫酮衍生物LS对天然胶乳具有优异的保存效果,复合保存制备低氨浓缩胶乳性能良好,可用于多种纯胶制品的生产,同时使用成本低廉,具有广阔的应用前景。

Experimental Study of Submergence Ratio on Local Scour Around a Square Pile in Steady Flow

Scour around a submerged square pile was realized experimentally in a steady flow to study the effects of flow depth on local scour.Flow depth to pile height ratios ranging from 1.5 to 5 in uniform sand and 2 to 5 in non-uniform sand were tested in the approaching flow velocity to critical velocity(larger than which the sediment particle is motivated)ratios of 0.56 and 1.03,respectively.The influences of flow depth were investigated on the basis of analysis of the three-dimensional topography,temporal maximum scour depth,bed profile development,and equilibrium scour depth.Results showed that the maximum scour depth was at the upstream corners of the pile other than at the stagnation point.The evolutions of the maximum scour depth data in non-uniform sand were well fitted with a recent exponential function,which characterized the initial,developing,and equilibrium stages of scour depth.The scour hole slopes upstream of the pile were found to be parallel to each other in the process of each test and were mainly governed by the sediment repose underwater.The equilibrium scour depth varied slightly with flow depth when the submergence ratio was larger than 1 in uniform sand while it was 2 in non-uniform sand.The armoring effects of coarse sediment particles markedly reduced the sediment transport in non-uniform sand despite the 0.34 increment in non-uniformity.

基于WRLS-ARMAX系统辨识的新能源电力系统惯量评估

随着高比例新能源机组并入电网,电力系统低惯量特性愈加显著,严重影响了系统运行稳定性。为了准确估计新能源电网实际运行状态下的惯量大小,提出了一种基于加权递推最小二乘(WRLS)-受控自回归滑动平均(ARMAX)系统辨识的新能源电力系统等效惯量评估方法。首先,以发电机为对象,建立不同扰动情况下发电机功频响应特性的通用惯量解析模型;其次,以发电机并网母线有功功率和频率扰动作为输入和输出,建立ARMAX模型,考虑到实际电网运行过程中受大、小扰动共同影响,实际测量数据具有异方差性,采用WRLS求解模型中的待辨识参数;然后,提取辨识模型中包含惯量响应的传递函数模型,利用阶跃响应计算惯量源的惯性时间常数,进而计算得到系统等效惯量大小;最后,通过Matlab/Simulink仿真算例验证了所提方法的准确性和实用性。

Robust least squares projection twin SVM and its sparse solution

Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.