目的通过一组单线性梯度洗脱实验获取线性溶剂强度模型的参数值,为色谱图的预测提供所必须的参数值。方法首先,在实验中固定流动相组成的起始和结束值,通过改变梯度洗脱的时间,从而改变梯度的斜率(B)。测定溶质在这些梯度条件下的保留时...目的通过一组单线性梯度洗脱实验获取线性溶剂强度模型的参数值,为色谱图的预测提供所必须的参数值。方法首先,在实验中固定流动相组成的起始和结束值,通过改变梯度洗脱的时间,从而改变梯度的斜率(B)。测定溶质在这些梯度条件下的保留时间,计算其流出色谱柱时所对应的流动相组成(φR)。然后,将描述φR与B之间关系的数学公式对实验数据进行非线性拟合,从而获取线性溶剂强度模型的参数值。拟合基于Levenberg-Marquardt算法,通过Excel中的Visual Basic for Applications(VBA)语言编程实现。结果计算机程序的可靠性通过实验进行验证。以12种芳环化合物为分离的对象,以C18柱为固定相,含1%乙酸的甲醇-水溶液为流动相,应用所编写的程序对单线性梯度洗脱实验数据进行处理,获取溶剂强度模型的参数值。然后,根据所得到的参数值预测多线性梯度洗脱条件下的色谱图,得到的理论色谱图与实验色谱图吻合。结论所建立的方法可快速准确地获取线性溶剂强度模型的参数值,具有良好的实用价值。展开更多
<p> <span style="font-family:Verdana;">To address the drawbacks of the traditional Parker test in multivariate linear</span><span style="font-family:;" "=""> ...<p> <span style="font-family:Verdana;">To address the drawbacks of the traditional Parker test in multivariate linear</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">models:</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">the process is cumbersome and computationally intensive,</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">we propose a new heteroscedasticity test.</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">A new heteroskedasticity test is proposed using the fitted values of the samples as new explanatory variables, reconstructing the regression model, and giving a new heteroskedasticity test based on the significance test of the coefficients, it is also compared with the existing Parker test which is improved using the principal component idea. Numerical simulations and empirical analyses show that the improved Parker test with the fitted values of the samples proposed in this paper is superior.</span> </p>展开更多
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and repr...Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.展开更多
Estimation of unknown parameters in exponential models by linear and nonlinear fitting methods is discussed. Based on the extreme value theorem and Taylor series expansion, it is proved theoretically that the paramete...Estimation of unknown parameters in exponential models by linear and nonlinear fitting methods is discussed. Based on the extreme value theorem and Taylor series expansion, it is proved theoretically that the parameters estimated by the linear fitting method alone cannot minimize the sum of the squared residual errors in the measurement data when measurement noise is involved in the data. Numerical simulation is performed to compare the performance of the linear and nonlinear fitting methods. Simulation results show that the linear method can obtain only a suboptimal estimate of the unknown parameters and that the nonlinear method gives more accurate results. Application of the fitting methods is demonstrated where the water spectral attenuation coefficient is estimated from underwater images and imaging distances, which supports the improvement in the accuracy of parameter estimation by the nonlinear fitting method.展开更多
文摘目的通过一组单线性梯度洗脱实验获取线性溶剂强度模型的参数值,为色谱图的预测提供所必须的参数值。方法首先,在实验中固定流动相组成的起始和结束值,通过改变梯度洗脱的时间,从而改变梯度的斜率(B)。测定溶质在这些梯度条件下的保留时间,计算其流出色谱柱时所对应的流动相组成(φR)。然后,将描述φR与B之间关系的数学公式对实验数据进行非线性拟合,从而获取线性溶剂强度模型的参数值。拟合基于Levenberg-Marquardt算法,通过Excel中的Visual Basic for Applications(VBA)语言编程实现。结果计算机程序的可靠性通过实验进行验证。以12种芳环化合物为分离的对象,以C18柱为固定相,含1%乙酸的甲醇-水溶液为流动相,应用所编写的程序对单线性梯度洗脱实验数据进行处理,获取溶剂强度模型的参数值。然后,根据所得到的参数值预测多线性梯度洗脱条件下的色谱图,得到的理论色谱图与实验色谱图吻合。结论所建立的方法可快速准确地获取线性溶剂强度模型的参数值,具有良好的实用价值。
文摘<p> <span style="font-family:Verdana;">To address the drawbacks of the traditional Parker test in multivariate linear</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">models:</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">the process is cumbersome and computationally intensive,</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">we propose a new heteroscedasticity test.</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">A new heteroskedasticity test is proposed using the fitted values of the samples as new explanatory variables, reconstructing the regression model, and giving a new heteroskedasticity test based on the significance test of the coefficients, it is also compared with the existing Parker test which is improved using the principal component idea. Numerical simulations and empirical analyses show that the improved Parker test with the fitted values of the samples proposed in this paper is superior.</span> </p>
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
文摘Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.
基金Project supported by the National Natural Science Foundation of China(Nos.61605038 and 11304278)the National High-Tech R&D Program(863)of China(No.2014AA093400)the Open Fund of State Key Laboratory of Satellite Ocean Environment Dynamics(No.SOED1606)
文摘Estimation of unknown parameters in exponential models by linear and nonlinear fitting methods is discussed. Based on the extreme value theorem and Taylor series expansion, it is proved theoretically that the parameters estimated by the linear fitting method alone cannot minimize the sum of the squared residual errors in the measurement data when measurement noise is involved in the data. Numerical simulation is performed to compare the performance of the linear and nonlinear fitting methods. Simulation results show that the linear method can obtain only a suboptimal estimate of the unknown parameters and that the nonlinear method gives more accurate results. Application of the fitting methods is demonstrated where the water spectral attenuation coefficient is estimated from underwater images and imaging distances, which supports the improvement in the accuracy of parameter estimation by the nonlinear fitting method.
