 This research proposes two new techniques for analyzing the reliability of multidimensional non-linear dynamic structures. The first technique uses an agotic time series to accurately estimate the system's failure probability. The second technique utilizes an extreme value prediction method to provide reliable estimates of system failure probabilities. These techniques can be combined to provide more accurate results than existing methods. This article was authored by Oleg Gaidi, Jin Xiangshu, Ping Yang, and others.