排列互比法角度偏差检定序列的可辨识性

Identifiability of partial combinational permutation intercomparison in checking angular bias

摘要:

为了解决棱体-多齿分度台排列互比法的部分序列组合,检定它们的偏差的可辨识性问题,分别针对素数面棱体和合数面棱体的检定序列的选定方法进行了研究． 首先研究了素数面棱体检定的序列问题,得出了素数面棱体检定的任意两个或两个以上的序列组合都能检定出齿盘偏差与棱体偏差的结论． 其次对于合数面棱体,研究了序列组合时偏差向量的可辨识问题,得出了两个序列号的差值为棱体面数的公因子或公因子的倍数时,偏差向量是不可辨识的． 然后选择多个序列进行组合的选定原则进行了研究． 针对正23、24面棱体的实测数据,对检定精度的评估问题进行了研究,并通过理论计算和实测数据计算了辨识的偏差的标准差,实验表明实际统计计算标准差时,量测的数量应大于辨识的偏差数量的4倍以上,统计计算的标准差才有效．

Abstract:

To solve the identifiability of partial combinational permutation intercomparison in checking angular bias of the regular polygon and the angle dividing table, aiming at prime-sided polygon and composite-sided polygon respectively, the checking series selecting was studied. At first, the prime-sided polygon checking series was studied, the conclusion was drawn that arbitrary two or above series combinatory measurement could identify the angular biases of the regular polygon and the angle dividing table. While aiming at composite-sided polygon, if the difference between the numbers of the two checking series is the factor( or integer times of the factor) of the side number of the polygon, the biases are not identifiable. The multi-series selecting problem was also researched. According to the practical measurement data about 23-sided and 24-sided polygon, checking accuracy appraisal of identified biases was studied. The theoretical standard deviation and the practical calculated standard deviation were given. The results show that only the number of measurement data should be four times greater than the number of the identified bias, the statistic standard deviation will be effective.