Power of Global Test in Deformation Analysis

摘要

There are two kinds of global test procedures in deformation analysis; χ~2-test (CT) and F-test (FT). This study discusses their power functions. The CT is more powerful than the other one in an analytical point of view. However, it requires an accurate knowledge on the a priori variance of unit weight. Therefore, in practice, the FT is mostly chosen. Despite its common usage, a χ~2-power function is considered in the sensitivity design of deformation networks. It is claimed in this study that the F-distribution's power function should be taken into account, if, in reality, the FT will be applied. Thereby, some boundary values deduced from the noncentral F-distribution to be used in sensitivity analysis are computed and tabulated. Furthermore, a simulation for a monitoring network is designed, and it is shown that the mean success rates of the two testing procedures are identical with their own powers known beforehand. This numerical experiment depicts that one should consider the related power function in the design stage, and that each power function gives a realistic probability of how the corresponding test procedure is successful.