最小二乘法在流量计算中的应用
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摘要
超声波热量表是对热量进行检测的装置。在对管道内流量进行检测的过程中,得到的时差数据进行滤波需要转换成流速,因此转换误差的大小是衡量一个热量表精度的重要标准。通过实验将不同温度下测得的超声波热量表中的时差和流量数据进行绘制,用最小二乘法对测得的数据进行拟合。通过MATLAB仿真得到每个温度下时差和流量关系的曲线方程和温度、时差、流量关系曲面图。然后用两只热量表进行对比实验,一只热量表采用传统的时差流量拟合法,另一只用最小二乘法改进拟合时差和流量。实验对比发现,用传统时差流量拟合法的热量表满足二级表的要求,但是小流量点稳定性较差,误差上下浮动;用最小二乘法改进拟合时差和流量的热量表在大流量点和小流量点都比较稳定,改善了热量表流量测量中遇到的小流量点不稳定的问题。
Ultrasonic heat meters are devices that detect heat. In the detection process, after filtering the obtained time difference data, the magnitude of the error in the conversion into the flow rate becomes an important criterion for measuring the accuracy of a heat meter. The time difference and flow data in the ultrasonic flow meter measured at different temperatures are plotted,Fitting the measured data using least squares. Through MATLAB simulation, the curve equations of the relationship between time difference and flow rate at each temperature and temperature, time difference and flow relation curve are obtained. Then use two calorimeters for comparison experiments. One calorimeter uses the traditional time difference flow fitting method, and the other uses only the least squares method to improve the fitting time difference and flow rate. Through experimental comparison, it is found that the heat meter with traditional time difference flow fitting method meets the requirements of the secondary table, but the stability of the small flow point is poor, and the error is floating up and down. The heat table with improved least-squares method to improve the fitting time difference and flow rate is relatively stable at both large flow point and small flow point, improves the problem of instability of small flow points encountered in heat meter flow measurement.
Ultrasonic heat meters are devices that detect heat. In the detection process, after filtering the obtained time difference data, the magnitude of the error in the conversion into the flow rate becomes an important criterion for measuring the accuracy of a heat meter. The time difference and flow data in the ultrasonic flow meter measured at different temperatures are plotted,Fitting the measured data using least squares. Through MATLAB simulation, the curve equations of the relationship between time difference and flow rate at each temperature and temperature, time difference and flow relation curve are obtained. Then use two calorimeters for comparison experiments. One calorimeter uses the traditional time difference flow fitting method, and the other uses only the least squares method to improve the fitting time difference and flow rate. Through experimental comparison, it is found that the heat meter with traditional time difference flow fitting method meets the requirements of the secondary table, but the stability of the small flow point is poor, and the error is floating up and down. The heat table with improved least-squares method to improve the fitting time difference and flow rate is relatively stable at both large flow point and small flow point, improves the problem of instability of small flow points encountered in heat meter flow measurement.
引文
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[14] 陈良波, 郑亚青. 基于最小二乘法的曲线拟合研究[J]. 无锡职业技术学院学报, 2012, 11(5):52-55.
[15] 邹乐强.最小二乘法原理及其简单应用[J].科技信息,2010(23):282-283.
[2] 张贤雨.时差法超声波流量计产业化的关键技术研究[D].重庆:重庆理工大学,2014.
[3] 邵仙鹤, 鲁志成, 王翥,等. 基于最小二乘曲面拟合的流量计量温度补偿算法[J]. 传感技术学报, 2016, 29(6):897-902.
[4] 王乐洋,许才军.总体最小二乘研究进展[J].武汉大学学报(信息科学版),2013,38(7):850-856,878.
[5] 周春丽.超声波热量表非定常数值模拟及性能研究[D].济南:山东大学,2014.
[6] 石硕.水中杂质对超声波热量表测量精度影响规律的研究[D].济南:山东大学,2017.
[7] 郭银景, 任现勇, 郭登岭,等. 低功耗超声波热量表的设计与实现[J]. 自动化与仪表, 2012, 27(10):8-12.
[8] 鲁铁定. 总体最小二乘平差理论及其在测绘数据处理中的应用[J]. 测绘学报, 2013, 42(4):630-630.
[9] 王贤妮,孙丽华,宋财华.时差法超声波热量表测量流量的修正算法[J].现代制造工程,2013(6):101-104,131.
[10] 吴叶兰,赵瑾,黄亚楠,等.超声波热量表流量计算的新方法[J].仪表技术与传感器,2014(12):31-32,74.
[11] 田垅,刘宗田.最小二乘法分段直线拟合[J].计算机科学,2012,39(S1):482-484.
[12] 唐利民.非线性最小二乘的不适定性及算法研究[D].长沙:中南大学,2011.
[13] 丁克良,沈云中,欧吉坤.整体最小二乘法直线拟合[J].辽宁工程技术大学学报(自然科学版),2010,29(1):44-47.
[14] 陈良波, 郑亚青. 基于最小二乘法的曲线拟合研究[J]. 无锡职业技术学院学报, 2012, 11(5):52-55.
[15] 邹乐强.最小二乘法原理及其简单应用[J].科技信息,2010(23):282-283.