数据探测法中的粗差误判分析

Separability Analysis for Baarda Data Snooping Method

摘要:

重点讨论了数据探测法中系统发生误警、漏检和误判的原因.探讨了3类错误与检验量间相关系数的函数关系，给出了在多个备选假设下3类错误发生概率的估计公式.以2个备选假设为例，通过仿真模拟计算了3类错误发生概率随统计量间相关系数的变化趋势，并证明当观测值统计量间强相关时，数据探测法发生误警的概率显著增加，从而导致最小可探测粗差理论值与实际值不符，降低了数据探测法的可信度及系统的可靠性.最后利用2个不同网形的算例验证了结论.

Abstract:

The Baarda’ data snooping method detects the outlier by making decision between the null and alternative hypotheses. Based on this method, usually only the false alert and missed detection were considered and the possibilities were defined for the minimal detectable bias (MDB). Nevertheless, in practical application, there are always multiple alternative hypotheses. Therefore, a third type error  wrong exclusion  occurs, which was caused by the correlation between two test statistics. The probabilities of false alert, missed detection, wrong exclusion can be considered as functions of the correlation coefficient. Monte Carlo methods were used to calculate the possibilities of these three types of errors with different correlation coefficients for two alternative hypotheses. It has proved that when the correlation is high the probability of committing wrong exclusion increases exponentially. As a result, the discrepancy between the theoretical and realistic MDB values enlarges, and accordingly the confidence level and the system reliability decrease. Finally, numerical experiments were conducted to analyze and compare the performance of two examples with different geometry conditions.