Belief reliability analysis of the complex uncertain single pendulum system
ZHAO Yunpeng
LIU Liying
Abstract：Belief reliability theory has proven to be an effective tool for analyzing the reliability of systems with small sample data.This paper investigates uncertain pendulum systems and introduces two belief reliability metrics:belief reliability function and belief reliability lifetime.Two models are studied:the logarithmic utility uncertain time-varying pendulum model and the linear time-shift uncertain time-varying pendulum model.Firstly,based on the logarithmic utility function,the logarithmic utility uncertain time-varying pendulum model is constructed,and an analytical expression for its belief reliability function is derived.The computational formulas and numerical algorithms for the belief reliability lifetime are also provided.Second,the noise in the pendulum system is modeled as linear time-shift noise,and the linear time-shift uncertain time-varying pendulum model is proposed.The computational formula for its certainty reliability function is derived,and a numerical solution method is introduced.Numerical examples demon-strate that these two certainty reliability metrics effectively measure the reliability of uncertain pendulum systems.This study provides new theoretical foundations and computational tools for reliability analysis of uncertain systems with small sample data.
Keywords：uncertain differential equationbelief reliabilityuncertain single pendulum equationinverse uncertainty distribution
Publication Date：2025-10-25
Online Publishing Date：2026-08-28(First online date of this platform, not the publication date of the document)
Pages：10( 654-662,678 )