数据拟合函数的加权最小二乘积分法

数据拟合的方法很多,每种方法各有特点.探讨了积分准则下的数据加权拟合函数的方法,称为加权最小二乘积分法,并给出了三个常用拟合函数具体形式.     

A spectral/hp least‐squares finite element analysis of the Carreau–Yasuda fluids

A least‐squares finite element model with spectral/hp approximations was developed for steady, two‐dimensional flows of non‐Newtonian fluids obeying the Carreau–Yasuda constitutive model. The finite element model consists of velocity, pressure, and stress fields as independent variables (hence, called a mixed model). Least‐squares models offer an alternative variational setting to the conventional weak‐form Galerkin models for the Navier–Stokes equations, and no compatibility conditions on the approximation spaces used for the velocity, pressure, and stress fields are necessary when the polynomial order (p) used is sufficiently high (say, p > 3, as determined numerically). Also, the use of the spectral/hp elements in conjunction with the least‐squares formulation with high p alleviates various forms of locking, which often appear in low‐order least‐squares finite element models for incompressible viscous fluids, and accurate results can be obtained with exponential convergence. To verify and validate, benchmark problems of Kovasznay flow, backward‐facing step flow, and lid‐driven square cavity flow are used. Then the effect of different parameters of the Carreau–Yasuda constitutive model on the flow characteristics is studied parametrically. Copyright © 2016 John Wiley & Sons, Ltd.     

Regression models based on new local strategies for near infrared spectroscopic data

In this work, a comparative study of two novel algorithms to perform sample selection in local regression based on Partial Least Squares Regression (PLS) is presented. These methodologies were applied for Near Infrared Spectroscopy (NIRS) quantification of five major constituents in corn seeds and are compared and contrasted with global PLS calibrations. Validation results show a significant improvement in the prediction quality when local models implemented by the proposed algorithms are applied to large data bases.     

Fusion method for infrared and visible images by using non-negative sparse representation

In this paper, an interesting fusion method, named as NNSP, is developed for infrared and visible image fusion, where non-negative sparse representation is used to extract the features of source images. The characteristics of non-negative sparse representation coefficients are described according to their activity levels and sparseness levels. Multiple methods are developed to detect the salient features of the source images, which include the target and contour features in the infrared images and the texture features in the visible images. The regional consistency rule is proposed to obtain the fusion guide vector for determining the fused image automatically, where the features of the source images are seamlessly integrated into the fused image. Compared with the classical and state-of-the-art methods, our experimental results have indicated that our NNSP method has better fusion performance in both noiseless and noisy situations.     

Quantitative determination and evaluation of Paris polyphylla var. yunnanensis with different harvesting times using UPLC‐UV‐MS and FT‐IR spectroscopy in combination with partial least squares discriminant analysis

A rapid method was developed and validated by ultra‐performance liquid chromatography–triple quadrupole mass spectroscopy with ultraviolet detection (UPLC‐UV‐MS) for simultaneous determination of paris saponin I, paris saponin II, paris saponin VI and paris saponin VII. Partial least squares discriminant analysis (PLS‐DA) based on UPLC and Fourier transform infrared (FT‐IR) spectroscopy was employed to evaluate Paris polyphylla var. yunnanensis (PPY) at different harvesting times. Quantitative determination implied that the various contents of bioactive compounds with different harvesting times may lead to different pharmacological effects; the average content of total saponins for PPY harvested at 8 years was higher than that from other samples. The PLS‐DA of FT‐IR spectra had a better performance than that of UPLC for discrimination of PPY from different harvesting times.     

A Comparative Study of Pentafluorophenyl and Octadecylsilane Columns in High‐throughput Profiling of Biological Fluids

In high‐throughput metabolomic profiling, chromatographic separation is crucial because a well‐performed chromatographic separation may reduce signal suppression from complex biological matrices and improve the discoverability of low‐abundance metabolites. We compared the performance of pentafluorophenyl (PFP )‐ and octadecylsilane (ODS )‐based columns in profiling biological fluids. Peak resolutions and consistencies were acquired using several reversed‐phase columns and were evaluated. Total and extracted ion chromatograms demonstrated that the PFP column achieved better analyte separations than the ODS column. Low relative standard deviations on peak areas and retention times (<10.2 and <0.9%, respectively) acquired using the PFP column evidenced the high reproducibility and consistency of this column. In our study, a PFP column was used for profiling metabolomes extracted from urine and serum samples. Metabolomic study revealed a metabolome difference in normal and overweight participants. In total, 26 lipid species were significantly perturbed and further identified. Choline‐containing lipids were the most abundant perturbed lipidome in overweight participants, followed by sphingolipids and various phospholipids. We recommend the use of PFP columns in high‐throughput metabolomic analysis to promote the development of basic biological and clinical research in the future.     

Direct determination of organic acids in wine and wine-derived products by Fourier transform infrared (FT-IR) spectroscopy and chemometric techniques

FT-IR with partial least squares (PLS) was used to establish a full calibration model for tartaric acid, malic acid, lactic acid, succinic acid, citric acid and acetic acid in wines, vinegars and spirits. Sample pre-treatment was not required except for filtering.     

Matlab语言在物理实验数据处理中的应用

以单摆测量重力加速度实验的数据处理为例,探讨了用Matlab语言对物理实验数据进行最小二乘法的处理。与传统的实验数据处理方法相比,用Matlab处理物理实验数据准确快捷,能有效避免手工处理带来的误差,Matlab的可视化功能也可以更加直观地反映实验结果,适合在实验教学中应用。     

多体系统Euler-Lagrange方程的最小二乘法与违约修正

针对受完整约束的多体系统动力学Euler-Lagrange方程,在其传统的直接增广算法和零空间方法基础上提出了当系统存在冗余约束情形下的最小二乘法.同时,对应于最小二乘法提出了改进的约束违约修正方法.本文还针对Euler-Lagrange方程的计算过程给出了相应Jacobi矩阵的QR分解和零空间连续正交基的算法.最后,以平行五连杆机构给出了数值结果并与部分现有方法进行比较.     

一种中低精度捷联惯测装置的不开箱标定方法研究

针对中低精度捷联惯测装置提出了一种实用的不开箱条件下的标定方法．该方法所需测试设备简单，用一套精度较高的惯测装置来标定低精度的惯测装置。文中给出了一套六位置测试方法，理论分析表明，该方法通过最小二乘法能有效的分离了陀螺和加速度计的各项误差。