Anomaly Detection and Reliability Analysis of Groundwater by Crude Monte Carlo and Importance Sampling Approaches

In this paper, Crude Monte Carlo method and importance sampling are utilized to determine the reliability of long-term changes in groundwater level. Furthermore, different data analysis methods are used to determine the abnormal patterns and to investigate the cause of spatial variations of failure probability. For this purpose, three methods including robust covariance, one-class SVM, and Isolation Forest are applied to define the decision function. In the preliminary detection of the outliers, DFFITS and COOK measures are used to confirm the existence of abnormal plains in a two-dimensional space. The validity of prediction results is verified through the developed method of uncertain monitoring by selecting the most significant outlier points. In addition, the abnormal pattern detection methods are compared using non-random pattern discovery decision functions. The reliability analysis of groundwater is conducted during the two periods from 1994 to 2007 and 2008 to 2021. In the second period, parts of the eastern part of the northwest, central parts of the desert of Iran, and areas from west-southwest and east-south-east to other regions exposed to a lower probability of passing through the critical conditions. In contrast, the outcomes confirm the occurrence of drought with probability more than 80% for most of the plains. Eventually, the importance sampling method showed the closest relation in the correct distribution of the decision function. In contrast, due to the cluster shape and density of the outliers, the upper part of the decision function was determined with high certainty in the discovery of abnormal plains.