A Note on the Optimality of Generalized Cross-validation Bandwidth Selection in Partially Linear Models with Kernel Smoothing Estimator

The issue of selection of bandwidth in kernel smoothing method is considered within the context of partially linear models, hi this paper, we study the asymptotic behavior of the bandwidth choice based on generalized cross-validation （CCV） approach and prove that this bandwidth choice is asymptotically optimal. Numerical simulation are also conducted to investigate the empirical performance of generalized cross-valldation.     

半参数空间变系数回归模型的Back-Fitting估计

针对半参数空间变系数回归模型给出了一种估计方法-后向拟合估计,该方法可得到模型中常值系数估计量的精确解析表达式,广泛的数值模拟表明所提出的估计方法对估计常值系数具有满意的精度和稳定性,最后,利用该方法分析了一个实际的例子.     

Convergence rates for unconstrained bandwidth matrix selectors in multivariate kernel density estimation

Progress in selection of smoothing parameters for kernel density estimation has been much slower in the multivariate than univariate setting. Within the context of multivariate density estimation attention has focused on diagonal bandwidth matrices. However, there is evidence to suggest that the use of full (or unconstrained) bandwidth matrices can be beneficial. This paper presents some results in the asymptotic analysis of data-driven selectors of full bandwidth matrices. In particular, we give relative rates of convergence for plug-in selectors and a biased cross-validation selector.     

Criteria for selection of response variables and the asymptotic properties in a multivariate calibration

Summary Let a set ofp responsesy=(y ₁,...y _p )′ has a multivariate linear regression on a set ofq explanatory variablesx=(x ₁,...x _q )′. Our aim is to select the most informative subset of responses for making inferences about an unknownx from an observedy. Under normality ony, two selection methods, based on the asymptotic mean squared error and on the Akaike's information criterion, are proposed by Fujikoshi and Nishii (1986,Hiroshima Math. J.,16, 269–277). In this paper, under a mild condition we will derive the cross-validation criterion and obtain the asymptotic properties of the three procedures.     

多元素LIBS分析的标准化交叉验证及其优化

交叉验证是用于验证模型性能的一种统计分析方法,可避免由训练集与测试集重合引起的过拟合。进行交叉验证时通常使用交叉验证均方根误差(RMSECV)的均值来表征多元素的分析准确度。但对于激光诱导击穿光谱(LIBS)用于多元素分析的情况,发现各元素的RMSECV与其在样品中的浓度范围可近似用线性关系表述,由于不同元素在样品集中的浓度范围差异很大,不同元素之间的RMSECV差异较大,实验中C与Cr在样品集中的浓度范围差异为28.11倍,其RMSECV差异达到8.96倍。发现RMSECV均值对于个别元素过于灵敏,在数据优化过程中,可能导致其不能反映大多数元素的分析准确度变化趋势。为减小RMSECV均值对不同元素的灵敏度差异,更全面地表征多元素的分析准确度,提出了多元素的RMSECV标准化方法,即将各元素的RMSECV与该元素在样品集中的浓度范围相除,并引入标准化交叉验证均方根误差(SRMSECV)的概念。LIBS检测受测量条件波动(如激光脉冲能量、振动等)等不确定因素的影响,会引入异常光谱,并对分析准确度产生负面影响。为通过滤除异常光谱来提高多元素分析准确度,利用光谱面积筛选对光谱数据进行预处理,以同一样品下各张光谱的面积中位数为中心,选定某一光谱面积区间,舍弃该区间之外的光谱,并使用余下光谱用作定量分析。在此基础上,通过对0.5 Pa真空环境下的10块Ni基合金中的14种元素成分进行的多谱线内标法定量分析展开实验验证。标准化后各元素RMSECV的相对标准差(RSD)由68.7%减小至48.9%,元素间的RMSECV的最大差异由8.96倍降低至3.93倍,表明SRMSECV均值能够较全面表征多元素的分析准确度,从而有利于实现定标曲线的全自动优化。在优化面积筛选跨度下,各元素定标模型的决定系数(R2)均值与SRMSECV均值都得到一定程度的改善,证明光谱面积筛选对于提高多元素分析准确度的价值。     

Rolling Bearing Fault Diagnosis Based on WOA-VMD-MPE and MPSO-LSSVM

In order to further improve the accuracy of fault identification of rolling bearings, a fault diagnosis method based on the modified particle swarm optimization (MPSO) algorithm optimized least square support vector machine (LSSVM), combining parameter optimization variational mode decomposition (VMD) and multi-scale permutation entropy (MPE), was proposed. Firstly, to solve the problem of insufficient decomposition and mode mixing caused by the improper selection of mode component K and penalty factor α in VMD algorithm, the whale optimization algorithm (WOA) was used to optimize the penalty factor and mode component number in the VMD algorithm, and the optimal parameter combination (K, α) was obtained. Secondly, the optimal parameter combination (K, α) was used for the VMD of the rolling bearing vibration signal to obtain several intrinsic mode functions (IMFs). According to the Pearson correlation coefficient (PCC) criterion, the optimal IMF component was selected, and its optimal multi-scale permutation entropy was calculated to form the feature set. Finally, K-fold cross-validation was used to train the MPSO-LSSVM model, and the test set was input into the trained model for identification. The experimental results show that compared with PSO-SVM, LSSVM, and PSO-LSSVM, the MPSO-LSSVM fault diagnosis model has higher recognition accuracy. At the same time, compared with VMD-SE, VMD-MPE, and PSO-VMD-MPE, WOA-VMD-MPE can extract more accurate features.     

Ultrasonic-assisted catalytic transfer hydrogenation for upgrading pyrolysis-oil

Recent interest in biomass-based fuel blendstocks and chemical compounds has stimulated research efforts on conversion and upgrading pathways, which are considered as critical commercialization drivers. Existing pre-/post-conversion pathways are energy intense (e.g., pyrolysis and hydrogenation) and economically unsustainable, thus, more efficient process solutions can result in supporting the renewable fuels and green chemicals industry. This study proposes a process, including biomass conversion and bio-oil upgrading, using mixed fast and slow pyrolysis conversion pathway, as well as sono-catalytic transfer hydrogenation (SCTH) treatment process. The proposed SCTH treatment employs ammonium formate as a hydrogen transfer additive and palladium supported on carbon as the catalyst. Utilizing SCTH, bio-oil molecular bonds were broken and restructured via the phenomena of cavitation, rarefaction, and hydrogenation, with the resulting product composition, investigated using ultimate analysis and spectroscopy. Additionally, an in-line characterization approach is proposed, using near-infrared spectroscopy, calibrated by multivariate analysis and modeling. The results indicate the potentiality of ultrasonic cavitation, catalytic transfer hydrogenation, and SCTH for incorporating hydrogen into the organic phase of bio-oil. It is concluded that the integration of pyrolysis with SCTH can improve bio-oil for enabling the production of fuel blendstocks and chemical compounds from lignocellulosic biomass.     

Numerical solutions of inverse spatial Lotka-Volterra systems

A numerical marching scheme is introduced for the recovery of the solutions and gradient distributions in a one-dimensional nonlinear system of parabolic partial differential equations with space dependent coefficients. In this inverse problem, only Cauchy noisy data at the active boundary is given and no information about the amount and/or character of the noise in the data is assumed. The error analysis for the algorithm is discussed and several numerical examples are presented.