Reliability analysis of the uncertain heat conduction model. (1st August 2022)

• Record Type: Journal Article
• Authors: Tian, Chenlei; Jin, Ting; Yang, Xiangfeng; Liu, Qinyu
• Is Part Of: Computers & mathematics with applications. Volume 119(2022)
• Page Start: 131
• Page End: 140
• Publication Date: 2022-08-01
• Subjects: Uncertain partial differential equation -- Belief reliability -- Heat conduction model -- First hitting time -- Distribution function; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.05.033
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Uncertainty theory has been demonstrated as a rigorous mathematical system to measure the reliability of products when there are few or no samples. Meanwhile, first hitting time, which is the first type of undetermined time appeared in history, has been extensively used in reliability analysis. Based upon it, this article mainly focuses on the reliability analysis of the uncertain heat equation through the first hitting time theorem and uncertain partial differential equation. First of all, first hitting time theorems of uncertain heat equation are provided via the inverse uncertainty distribution of the solution. Secondly, two novel belief reliability indexes (belief reliability function and belief reliable lifetime) are presented based on the proposed first hitting time theorem. Furthermore, analytic expressions and numerical calculations of belief reliability indexes are derived from uncertain heat conduction model with fixed heat source and periodic heat source, respectively. Lastly, numerical methods are designed, and some numerical examples are provided to demonstrate the rationality of the belief reliability indexes. Highlights: Provide first hitting time theorems for the uncertain heat equation. Present belief reliability function and belief reliable lifetime indexes of the uncertain heat equation. Formulate the belief reliability index of the uncertain heat conduction model with fixed heat source. Calculate the belief reliability index of the uncertain heat conduction model with periodic heat source.