Study On The Reliability Of A Repairable Solar Heat Collection System

A multi-component interconnected system is a special type of repairable system that is widely used in production and daily life.Such systems belong to complex systems and are an important research topic in reliability mathematics.To study and analyze this kind of complex repairable system,it is necessary to combine quantitative analysis and qualitative analysis to study the reliability of the system.Therefore,starting from the actual physical background of the system,this paper constructs a kind of repairable mathematical model of solar heat collection system and studies its reliability by using mathematical methods such as mathematical model and linear operator semigroup theory.The full text carries out research from the following six chapters:Chapter 1 is the introduction,which expounds the research background and status quo of repairable systems,summarizes the research content and research methods of this paper,and lists the relevant theorems and definitions.In chapter 2,a mathematical model of a repairable solar heat collection system is constructed,and an abstract Cauchy problem is obtained by using supplementary variable method and stochastic process theory.In chapter 3,the semigroup characteristics of the main operator of the system are discussed by means of the theory and method of linear operator semigroup,and the existence and uniqueness of the solution of the system model are obtained.In chapter 4,by using the theory and method of linear operator semigroup,the spectral characteristics and distribution law of the main operator of the system are studied,and the asymptotic stability of the system solution of the mathematical model of the repairable system is analyzed.Chapter 5 uses functional analysis method and ordinary differential equation theory to study the controllability and reliability of the system,obtain the corresponding reliability index,and operate Matlab software to carry out numerical simulation of the results.Chapter 6 summarizes the paper and discusses future research prospects.