Reliability estimation of balanced systems with multi-dimensional distributed units
Creators: name: Guo, Jingbo
Publisher: name: No Publisher Supplied
Year: 2022

description: Balanced systems with multi-dimensional distributed units are emerging in a diverse range of industries. This includes Unmanned Aerial Vehicles (UAV) with multi-level of rotary wings, Spherical Unmanned Vehicles (SUV), Spherical Phased Array Antenna (SPAA), etc. In this dissertation, we present the reliability estimation for such systems. In particular, we consider two configurations: 1) balanced systems with units distributed circularly on multi-level and 2) balanced systems with units distributed spherically. First, balanced systems with units distributed circularly on multi-level are generalized as (k₁, k₂)-out-of-(n, m) pairs: G balanced systems. We consider two scenarios: 1) all units perform the same function and 2) adjacent pairs perform complementary functions. For both scenarios, unbalanced system is considered as failed. When units fail and cause the system imbalance, we explore two approaches to rebalance the system: 1) forcing down units on other locations and 2) resuming units that are previously forced down (if any). When units in a system perform the same function, operational states are defined as balanced states with at least k₁ operating pairs and each operating pair has at least k₂ units on each side. The system reliability is obtained by enumerating all of the operational states and summing the probabilities of those states. For (k₁, k₂)-out-of-(n, m) pairs: G balanced systems with adjacent pairs performing complementary functions, in addition to maintaining system balance, the adjacent operating pairs are required to perform complementary functions. Thus, if a pair fails, one of the adjacent pairs is forced down. Similarly, the system reliability is obtained by enumerating all of the operational states. It becomes computational expensive when the number of units in each pair and/or the number of pairs are large. In that case, efficient algorithms are developed to obtain the reliability for such systems.The balanced system with units distributed spherically is generalized as a spherical k-n-i: G balanced system. We consider two balancing requirements: 1) rotational balance is maintained so that the system is not rotating w.r.t. roll, yaw and pitch axes and 2) symmetrical balance is essential in improving the systems’ stability. We present mathematical approaches to determine the balance status of a system. Similarly, the unbalanced system is rebalanced by 1) forcing down units on other locations and 2) resuming previously forced-down units. The system reliability is obtained by the enumeration of operational states and calculation of operational states’ probabilities. We develop an efficient algorithm for reliability estimation when the number of units in the system is large.Degradation models are developed for the (k₁, k₂)-out-of-(n, m) pairs: G balanced systems to further investigate the system reliability when degradation data are available. The degradation processes of units in the system are either stationary (inverse Gaussian process) or non-stationary (improved inverse Gaussian process). We propose a degradation balance mechanism in which the ‘most’ degraded units are forced down temporarily during the degradation process so that the system is less possible to fail due to imbalance. A closed-form lower bound reliability is presented when the balance mechanism is not applied. When it is applied, reliability is obtained by Monte Carlo simulation.From the reliability study of the both configurations, it is observed that the reliability of a balanced system with multi-dimensional distributed units depends not only on the system’s total number of units and the least number of operating units, but also on the system configurations and balance requirements. Systems with more units do not necessarily provide a higher reliability since they are more likely to fail due to imbalance. Thus, optimal system design is key to maximize the system reliability which is investigated through numerical examples in this dissertation.