An extreme value prediction method based on clustering algorithm

Extreme value prediction has been widely applied in many safety-critical scenarios. Due to the influence of mixed types of events, the random variables oftentimes do not comply with the independence and identical distributions. Neglecting the mixed distribution characteristics of these variables may lead to inaccurate extreme value prediction. To solve this problem, this study proposes a novel clustering algorithm based on the generalized extreme value mixture model (GEVMM). The algorithm adaptively classifies the block maximum data into different clusters and synthesizes the clusters according to their weights in the population, thus forming a GEVMM that can predict the maximum values in a given return period. The elbow method combined with root mean squared error (RMSE) and coefficient of determination (R-squared) is used to select the optimal number of clusters to prevent over- and under-fitting the model. Through theoretical examples, the proposed method shows strong applicability to promote the accurate extrapolation of extreme values regardless of overlap among the original mixture components. To demonstrate the practical application of the proposed approach, traffic load effects on bridges based on weight-in-motion data are used to extrapolate extreme values during a specific return period. The process and results show that the developed approach is more reliable for estimating extreme values with mixed probability distribution as compared with existing methods. It also provides a powerful tool for extreme value analysis of mixed distribution data in other fields.