# Uncertainty Theory-Based Resilience Analysis for LEO Satellite Communication Systems
## 1 Introduction  
Due to short round-trip delays and wide-area coverage, the low-Earth-orbit satellite communication system (LEO-SCS) is becoming an important research topic. Iridium NEXT, OneWeb, and StarLink are typical examples. During system operation, disruptions may occur, causing satellite failure or signal interruption. The failure to quickly and effectively solve these problems may lead to huge economic losses. How to reasonably quantify and evaluate the impact of these failures is important to improve LEO-SCS operation and service stability. As an extension and expansion of reliability and risk, resilience is the ability of a system to withstand disruption and quickly return to a normal state. Resilience, which encompasses avoidance, robustness, reconstitution, and recovery, has become a key criterion in evaluating alternative space systems, including constellations [1; 2]. Researchers have already analyzed the resilience of constellation systems. [PERSON] [3] defined the resilience of a satellite network as the time-averaged network performance under an extreme-event situation and built an extreme event model to quantify the resilience of satellite communication systems. [PERSON] et al. [4] proposed a three-dimensional resilience evaluation matrix and analyzed the resilience of a communication constellation based on the coverage capacity and reconstruction energy index. [PERSON] and [PERSON] [5] used a Markov chain and semi-analytical approach to assess the resilience of both networking- and non-networking-capable constellation systems. Researchers have also proposed resilience assessment methods for other networked systems. [PERSON] et al. [6] defined resilience as theratio of the integral of the performance function to the recovery time. [PERSON] et al. [7] defined it as the ratio of the real performance integral to the target one during a year. [PERSON] et al. [8] defined resilience as the average performance within the maximum allowable recovery time. [PERSON] et al. [9] developed a resilience measure based on the polynomial chaos expansion method, which could characterize the resilience for a wide range of uncertainty distributions. It is important to analyze resilience during the design of a system, as it can guide resilience design and provide reasonable strategies. However, current resilience measures and modeling methods cannot be directly applied to the LEO-SCS design process for the following reasons:  
1. Generally, there are two types of uncertainties, aleatory and epistemic. Epistemic uncertainties can be reduced by collecting more data or refining models, and aleatory ones are natural randomness that cannot be reduced [10]. As a typical newly developing system, the LEO-SCS suffers from performance data insufficiency and performance data asymmetry [11], which limits knowledge on recognizing system performance and leads to epistemic uncertainty. Considering the aleatory uncertainty of the satellite failures [12] and the epistemic uncertainty of the system performance, the resilience of an LEO-SCS needs to be analyzed with both uncertainties. However, existing resilience assessment methods only individually focus on either aleatory uncertainty or epistemic uncertainty [3; 4; 5; 13], which will lead to inaccurate resilience assessment. In addition, the performance measures used in these resilience assessments vary widely and a unified measure is required for the resilience comparison among different systems. 2. To measure LEO-SCS resilience requires a system model to be built. Previous LEO-SCS modeling methods have only considered the dynamics of the network topology and the aleatory uncertainty of the performance parameters while neglecting their epistemic uncertainty. The uncertainty theory, founded by [PERSON] [14], defines uncertain measures to quantify events with epistemic uncertainty. Then, [PERSON] [15] extended the uncertain measure to chance measure for events with both aleatory and epistemic uncertainties.