Langmuir方程参数线性回归与非线性回归的比较
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摘要
Langmuir方程是常用的吸附等温线方程之一,Langmuir方程参数估计有线性回归和非线性回归2种方法。以实测数据为依据,采用IBM SPSS Statistics 24.0软件进行Langmuir方程参数线性回归与非线性回归的对比分析。结果表明:线性回归方法不满足相应曲线因变量的残差平方和最小,线性回归方法中对变量由无理数到有限小数的数值修约是引起舍入误差的原因。基于非线性回归方法对实测数据具有残差平方和较小的特点,在应用Langmuir方程求参数时建议采用非线性回归方法。
Langmuir equation is one of the commonly used adsorption isotherm equations, there are two methods of Langmuir equation parameters estimation: linear regression method and nonlinear regression method. Based on the measured data, this paper using the IBM SPSS Statistics 24.0 software to compare the linear regression method and nonlinear regression method of Langmuir equation parameters. The results show that the linear regression method does not satisfy the minimum of the residual sum of squares of the dependent variables of Langmuir equation, rounding off for values from the irrational number to finite decimal is the cause of round-off error in the linear regression method. Because the nonlinear regression method has the characteristics of smaller residual sum of squares of the measured data, the nonlinear regression method is recommended in the Langmuir equation.
Langmuir equation is one of the commonly used adsorption isotherm equations, there are two methods of Langmuir equation parameters estimation: linear regression method and nonlinear regression method. Based on the measured data, this paper using the IBM SPSS Statistics 24.0 software to compare the linear regression method and nonlinear regression method of Langmuir equation parameters. The results show that the linear regression method does not satisfy the minimum of the residual sum of squares of the dependent variables of Langmuir equation, rounding off for values from the irrational number to finite decimal is the cause of round-off error in the linear regression method. Because the nonlinear regression method has the characteristics of smaller residual sum of squares of the measured data, the nonlinear regression method is recommended in the Langmuir equation.
引文
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[4] GB/T 19560—2008煤的高压等温吸附试验方法[S].
[5] MT/T 752—1997煤的甲烷吸附量测定方法(高压容量法)[S].
[6] SY/T 6132—2013煤岩中甲烷等温吸附量测定(干燥基容量法)[S].
[7]何晓群,刘文卿.应用回归分析[M].北京:中国人民大学出版社,2015.
[8]谢政,李建平,陈挚.非线性最优化理论与方法[M].北京:高等教育出版社,2010.
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[10]徐海飞.河南省中高煤级构造煤吸附/解吸特征研究[D].焦作:河南理工大学,2015.
[11]王亚军.相关系数与决定系数辨析[C]∥长江流域暨西北地区科技期刊协作网2008年学术年会论文集.北京:中国科学技术期刊编辑学会,2008.
[12] GB/T 8170—2008数值修约规则与极限数值的表示和判定[S].
[13]李庆扬,王能超,易大义.数值分析[M].4版.武汉:华中科技大学出版社,2006.
[14]珍唐.舍入误差分析引论[M].上海:上海科学技术出版社,1987.
[15]石必明.Langmuir方程中ab常数的优化拟合[J].西安科技大学学报,1997(3):221-224.
[16]陈元千,郭二鹏,齐亚东.关于确定兰氏体积和兰氏压力的方法[J].断块油气田,2015,22(1):67-69.
[17]苏现波,林晓英.煤层气地质学[M].北京:煤炭工业出版社,2009.
[2] Clarkson C R, Bustin R M. Binary gas adsorption/desorption isotherms:effect of moisture and coal composition upon carbon dioxide selectivity over methane[J].International Journal of Coal Geology, 2000, 42(4):241-271.
[3]赵志根,唐修义.对煤吸附甲烷的Langmuir方程的讨论[J].河南理工大学学报(自然科学版),2002,21(1):1-4.
[4] GB/T 19560—2008煤的高压等温吸附试验方法[S].
[5] MT/T 752—1997煤的甲烷吸附量测定方法(高压容量法)[S].
[6] SY/T 6132—2013煤岩中甲烷等温吸附量测定(干燥基容量法)[S].
[7]何晓群,刘文卿.应用回归分析[M].北京:中国人民大学出版社,2015.
[8]谢政,李建平,陈挚.非线性最优化理论与方法[M].北京:高等教育出版社,2010.
[9]赵艳青.不同变质变形形煤的孔隙结构与吸附特征研究[D].焦作:河南理工大学,2013.
[10]徐海飞.河南省中高煤级构造煤吸附/解吸特征研究[D].焦作:河南理工大学,2015.
[11]王亚军.相关系数与决定系数辨析[C]∥长江流域暨西北地区科技期刊协作网2008年学术年会论文集.北京:中国科学技术期刊编辑学会,2008.
[12] GB/T 8170—2008数值修约规则与极限数值的表示和判定[S].
[13]李庆扬,王能超,易大义.数值分析[M].4版.武汉:华中科技大学出版社,2006.
[14]珍唐.舍入误差分析引论[M].上海:上海科学技术出版社,1987.
[15]石必明.Langmuir方程中ab常数的优化拟合[J].西安科技大学学报,1997(3):221-224.
[16]陈元千,郭二鹏,齐亚东.关于确定兰氏体积和兰氏压力的方法[J].断块油气田,2015,22(1):67-69.
[17]苏现波,林晓英.煤层气地质学[M].北京:煤炭工业出版社,2009.