CAJ | 학술논문

文章结合铁路坡段设计过程的数学属性，运用数理统计学常用的最小一乘法、最小二乘法，利用计算程序来解决既有铁路坡度拟合、新建铁路坡度设计问题。文章简要介绍了最小一乘法、最小二乘法数学原型，分析了2种方法的优劣和适用范围。阐述了既有铁路坡度拟合，新建铁路拉坡过程属于数理统计的线性收敛过程，建议使用最小二乘法计算相关系数检验坡段划分，使用最小一乘法或最小二乘法拟合最佳坡度。对黄石山南铁路一段既有线坡度进行了实例计算，利用大众工具EXCEL附带的散点图工具和规划求解工具分别计算线性相关系数和线性回归方程。运算的结果说明本文建议方法科学，计算过程快捷，计算结果准确，效率高。
문장결합철로파단설계과정적수학속성，운용수리통계학상용적최소일승법、최소이승법，이용계산정서래해결기유철로파도의합、신건철로파도설계문제。문장간요개소료최소일승법、최소이승법수학원형，분석료2충방법적우렬화괄용범위。천술료기유철로파도의합，신건철로랍파과정속우수리통계적선성수렴과정，건의사용최소이승법계산상관계수검험파단화분，사용최소일승법혹최소이승법의합최가파도。대황석산남철로일단기유선파도진행료실례계산，이용대음공구EXCEL부대적산점도공구화규화구해공구분별계산선성상관계수화선성회귀방정。운산적결과설명본문건의방법과학，계산과정쾌첩，계산결과준학，효솔고。
The author observed the mathematical properties of railway slope design process by the use of the widely ac-cepted statistic methods-least absolute deviation and least squares methods including the computer excel program to solve problems of existing railway slope fitting and newly build railway slope design . In the paper, the author briefly describes the method of least absolute deviation and least squares method, and analyzes suitable sphere of each method by analy-zing the advantages and disadvantages of them . Considering the linear convergence process of the railway slope design process of existing railway and newly build railway, the least squares method is recommended to calculate the linear cor-relation coefficient between that data sequence to test whether the slope segment is correctly divided, and least absolute deviation or least squares method is used to fit the railway slope through example of Huangshi Shannan railway. In that process, using solving tool and Scatter tool of Microsoft Excel to calculate the linear correlation coefficient and the linear regression equation. The result shows that the calculation is more efficient and accurate than the regular method used in practices.