## 1 Introduction
Internationally, aviation criteria ARP 4754 (A) [29; 30] recommended by the American Society of Automotive Engineers defines safety as a state where the risk is lower than the border risk. The domestic GJB 900A defines safety as the ability of a product not to cause personal injury or death, system damage, major property damage, or damage human health and the environment. For the measurement of risk, risk model of probability and severity is the most widely used, such as the civil aviation standard ARP 4761 [31], the US military standard MIL-STD-882E [32], the national military standard GJB 900A, etc., FTA, FMEA, ETA, and other reliability and safety analysis methods all use the models to evaluate risks. However, with the further understanding of the concept of risk, people have more research and cognition of the elements involved in risk. [PERSON]. [33] developed a relationship for the probability of wire failure as a function of influencing factors in an aircraft environment in order to analyze wire failure in aircraft. [PERSON]. [34] presented a method for quantifying the probability of fatalities resulting from an uncontrolled descent of an unmanned aircraft conducting a beyond visual line-of-sight (BVLOS) flight so as to solve the major challenges to make a realistic and effective risk assessment of conducting operation of BVLOS. [PERSON]. [35] proposed a new risk assessment method based on the cloud model, aiming to make an effective risk assessment method for subway operation by considering five aspects. [PERSON] [36] proposed an integrated risk index model based on hierarchical fuzzy logic for underground risk assessment to avoid occurrence of accidents due to underground facilities. [PERSON] [37] presented a novel network security risk assessment approach by combining subjective and objective weights under uncertainty to effectively evaluate computer network security. Most of the above risk assessment methods focus on the analysis of accident probability and severity, and lack of multi-dimensional safety risk assessment methods by taking time factor related fault into consideration. In view of the above considerations, this paper proposes a novel risk assessment and analysis method for correlation in complex system based on multi-dimensional theory, aiming at analyzing and evaluating the risk of complex system considering the coupling correlation, so as to identify the critical risk elements. Firstly, the formal description and coupling correlation analysis method of the hierarchical structure of complex systems based on the typical task-function-resource model is proposed, aiming to achieve a formal description of the coupling correlation between components within complex systems, providing the foundation for and analysis and evaluation of risk. Moreover, considering the three safety risk factors of propagation probability, potential severity, and propagation time, a multi-dimensional safety risk theory is proposed, in order to evaluate the risk of each element in the system effecting on the overall system from multiple perspectives. Furthermore, critical safety elements are identified based on Pareto rules, ALARP principles, and safety risk entropy to support the preventive measures. The remainder of the paper is organized as follows. Section 2 describes the hierarchical model of complex systems and coupling correlation between elements in system. In Section 3, multi-dimensional safety risk theory and assessment are proposed. Section 4 introduces an application of avionics system. Section 5 presents the conclusions.