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
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。
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.
