储油罐的变位识别与罐容表标定模型  

Model of the identification of oil tank’s position and the calibration of tank capacity table

作　　者：窦霁虹[1] 梅钰[1] 陈振勋[1] 王莉莉[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《纯粹数学与应用数学》2011年第6期829-840,共12页Pure and Applied Mathematics

基　　金：西北大学教学改革研究项目(kjg10042)

摘　　要：用数学建模方法试图研究解决储油罐变位识别与罐容表标定问题.首先精确推导了无变位以及纵向倾斜时罐内储油量与油位高度的函数关系,且设计了两种系统误差补偿方法.一种是基于等效思想的δ值法,另一种拟合法.其次,确定变位参数时依然使用补偿思想,将球冠体部分的储油体积和系统误差统一为整体拟合成油位高度h的三次多项式,并应用最小二乘原理建立了同时具有纵向倾斜和横向偏转变位参数的非线性优化模型.最后利用搜索算法得到由实际储油罐的实测数据确定的变位参数α=4.4,β=4.9,将其代入建立的罐容表标定模型,给定油位间隔10 cm,得到了所需罐容表标定值,并利用相关文献中的部分数据进行了检验.The identification of oil tank’s position and the calibration of tank capacity table were studied.First,the functions of the oil storage and the oil height were inferred when the oil tank position was not changed and was tilted,and two remedy methods of the error were devised.Second,by using remedy methods,the cubic polynomial of the oil height was fitted when the oil’s volume and the systematic error were seen as a whole,then the non-linear optimization model with tilt and deflection was found by using the least squares.Last,according to the real date,the parameters of tilt and deflection were obtained by using searching algorithm,those were α = 4.4,β = 4.9.The tank capacity table was given when the interval was 10 cm,and the part of data was examined.

关 键 词：罐容表 变位 系统误差 数据拟合 最小二乘法 

分 类 号：O29[理学—应用数学]