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...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.展开更多
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 rand...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.展开更多
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...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.展开更多
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 ...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.展开更多
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, ani...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.展开更多
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 Vecto...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.展开更多
During the electrochemical machining (ECM), the cathodes designed by the existing methods are mainly unitary cathodes, which can be only used to produce the workpieces with the same shapes. However, there are few rese...During the electrochemical machining (ECM), the cathodes designed by the existing methods are mainly unitary cathodes, which can be only used to produce the workpieces with the same shapes. However, there are few researches on designing cathodes for machining the different workpieces with the different surfaces. This paper presents the grid cathode composed of the square cells to produce the workpieces with different shapes. Three types of the square cells, 2.5 mm′2.5 mm, 3 mm′3 mm, and 4 mm′4 mm, are utilized to construct the plane, the slant, and the blade cathode. The material of the cathode and the anode is CrNi 18 Ti 9 , and the ingredient of electrolyte is 15% NaCl and 15% NaNO 3 . The machining equilibrium machining current and time are acquired and analyzed, the machining process and the workpiece quality are compared between using the grid cathode and the unitary cathode. Moreover, the machining errors on the workpiece surface are measured and analyzed, and the error reasons are traced and discussed to obtain the better surface quality of the workpiece. The experiment and analysis results show that the grid cathode can be used to manufacture the workpieces with complex shapes in certain range of the error. The workpiece quality improves with the size of the square cell being reduced, and if the square element is small enough, the workpiece quality is almost equal to the one machined by the unitary cathode. The proposed research realizes a single cathode machining the different workpieces with the different surfaces.展开更多
This article adopts Least Square Support Vector Machine (LSSVM) for prediction of Evaporation Losses (EL) in reservoirs. LSSVM is firmly based on the theory of statistical learning, uses regression technique. The inpu...This article adopts Least Square Support Vector Machine (LSSVM) for prediction of Evaporation Losses (EL) in reservoirs. LSSVM is firmly based on the theory of statistical learning, uses regression technique. The input of LSSVM model is Mean air temperature (T) (?C), Average wind speed (WS)(m/sec), Sunshine hours (SH)(hrs/day), and Mean relative humidity(RH)(%). LSSVM has been used to compute error barn of predicted data. An equation has been developed for the determination of EL. Sensitivity analysis has been also performed to investigate the importance of each of the input parameters. A comparative study has been presented between LSSVM and artificial neural network (ANN) models. This study shows that LSSVM is a powerful tool for determination EL in reservoirs.展开更多
This study used near-infrared(NIR)spectroscopy to predict mechanical properties of wood.NIR spectra were collected in wavelengths 900–1700 nm,and spectra averaged by radial and tangential surface spectra were used to...This study used near-infrared(NIR)spectroscopy to predict mechanical properties of wood.NIR spectra were collected in wavelengths 900–1700 nm,and spectra averaged by radial and tangential surface spectra were used to establish a partial least square(PLS)model based on correlation local embedding(CLE).Mongolian oak(Quercus mongolica Fisch.ex Ledeb.)was used to test the eff ectiveness of the model.The cross-validation method was used to verify the robustness of the CLE–PLS model.Ninety samples were tested as the calibration set and forty-fi ve as the validation set.The results show that the prediction coeffi cient of determination(R2 p)is 0.80 for MOR,and 0.78 for MOE.The ratio of performance to deviation is 2.23 for MOR and 2.15 for MOE.展开更多
Cerium contained conversion films were deposited on LC4 aluminum alloy usingsquare wave pulse (SWP) in a CeCl_3 solution with KMnO_4 as the oxidant. Energy dispersivespectroscopy (EDS) and scanning electron microscopy...Cerium contained conversion films were deposited on LC4 aluminum alloy usingsquare wave pulse (SWP) in a CeCl_3 solution with KMnO_4 as the oxidant. Energy dispersivespectroscopy (EDS) and scanning electron microscopy (SEM) were adopted to study the composition andthe morphology of the film. It is found that the film is composed of Al, Zn, Cu, and small amount ofcerium. The polarization curves of the specimens treated with SWP technique measured in 3.5% (massfraction) NaCl solution reveal that the film thus formed inhibits both the anodic and cathodicprocess of the corrosion of the specimen. The immersion tests of treated specimens in 3.5% NaClsolution indicate that the corrosion resistance of the SWP treated specimen is better than that ofthe untreated and is equivalent to or even better than that of the traditionally electro-chemicallytreated specimens.展开更多
In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived ...In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.展开更多
文摘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.
基金the financial support of the National Natural Science Foundation of China(Grant No.42074016,42104025,42274057and 41704007)Hunan Provincial Natural Science Foundation of China(Grant No.2021JJ30244)Scientific Research Fund of Hunan Provincial Education Department(Grant No.22B0496)。
文摘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.
基金supported by the Key Project of Gansu Provincial National Science Foundation(23JRRA1022)the National Natural Science Foundation of China(12071431)+1 种基金the Fundamental Research Funds for the Central Universities(lzujbky-2021-ey18)the Innovative Groups of Basic Research in Gansu Province(22JR5RA391).
文摘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.
文摘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.
文摘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.
文摘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.
基金supported by Aeronautics Science Foundation of China (Grant No. 2008ZE52049)National Natural Science Foundation of China (Grant No. 51005122)
文摘During the electrochemical machining (ECM), the cathodes designed by the existing methods are mainly unitary cathodes, which can be only used to produce the workpieces with the same shapes. However, there are few researches on designing cathodes for machining the different workpieces with the different surfaces. This paper presents the grid cathode composed of the square cells to produce the workpieces with different shapes. Three types of the square cells, 2.5 mm′2.5 mm, 3 mm′3 mm, and 4 mm′4 mm, are utilized to construct the plane, the slant, and the blade cathode. The material of the cathode and the anode is CrNi 18 Ti 9 , and the ingredient of electrolyte is 15% NaCl and 15% NaNO 3 . The machining equilibrium machining current and time are acquired and analyzed, the machining process and the workpiece quality are compared between using the grid cathode and the unitary cathode. Moreover, the machining errors on the workpiece surface are measured and analyzed, and the error reasons are traced and discussed to obtain the better surface quality of the workpiece. The experiment and analysis results show that the grid cathode can be used to manufacture the workpieces with complex shapes in certain range of the error. The workpiece quality improves with the size of the square cell being reduced, and if the square element is small enough, the workpiece quality is almost equal to the one machined by the unitary cathode. The proposed research realizes a single cathode machining the different workpieces with the different surfaces.
文摘This article adopts Least Square Support Vector Machine (LSSVM) for prediction of Evaporation Losses (EL) in reservoirs. LSSVM is firmly based on the theory of statistical learning, uses regression technique. The input of LSSVM model is Mean air temperature (T) (?C), Average wind speed (WS)(m/sec), Sunshine hours (SH)(hrs/day), and Mean relative humidity(RH)(%). LSSVM has been used to compute error barn of predicted data. An equation has been developed for the determination of EL. Sensitivity analysis has been also performed to investigate the importance of each of the input parameters. A comparative study has been presented between LSSVM and artificial neural network (ANN) models. This study shows that LSSVM is a powerful tool for determination EL in reservoirs.
基金financially supported by the China State Forestry Administration“948”projects(2015-4-52)Fundamental Research Funds for the Central Universities(2572017DB05)Heilongjiang Natural Science Foundation(C2017005)。
文摘This study used near-infrared(NIR)spectroscopy to predict mechanical properties of wood.NIR spectra were collected in wavelengths 900–1700 nm,and spectra averaged by radial and tangential surface spectra were used to establish a partial least square(PLS)model based on correlation local embedding(CLE).Mongolian oak(Quercus mongolica Fisch.ex Ledeb.)was used to test the eff ectiveness of the model.The cross-validation method was used to verify the robustness of the CLE–PLS model.Ninety samples were tested as the calibration set and forty-fi ve as the validation set.The results show that the prediction coeffi cient of determination(R2 p)is 0.80 for MOR,and 0.78 for MOE.The ratio of performance to deviation is 2.23 for MOR and 2.15 for MOE.
基金This work was financially supported by the National Natural Science Foundation of China (No. 59771067) and the National Key Laboratory of New Metal Materials.
文摘Cerium contained conversion films were deposited on LC4 aluminum alloy usingsquare wave pulse (SWP) in a CeCl_3 solution with KMnO_4 as the oxidant. Energy dispersivespectroscopy (EDS) and scanning electron microscopy (SEM) were adopted to study the composition andthe morphology of the film. It is found that the film is composed of Al, Zn, Cu, and small amount ofcerium. The polarization curves of the specimens treated with SWP technique measured in 3.5% (massfraction) NaCl solution reveal that the film thus formed inhibits both the anodic and cathodicprocess of the corrosion of the specimen. The immersion tests of treated specimens in 3.5% NaClsolution indicate that the corrosion resistance of the SWP treated specimen is better than that ofthe untreated and is equivalent to or even better than that of the traditionally electro-chemicallytreated specimens.
文摘In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.