Reliability Estimation And Optimization Incorporating Statistical Uncertainty For Multi-State Systems

Reliability is an important performance measure of large-scale energy systems (such as nuclear and coal-fired thermal power systems). Due to the randomness and diversity of component failure, these systems have an inherent multi-state property, and their reliability evaluation results are accompanied by statistical uncertainty. In reliability engineering, redundancy allocation based on reliability evaluation results is an important combinatorial optimization problem that aims to determine an optimal system structure with high reliability and low cost. Although this optimization problem has been well studied for traditional binary-state systems (BSSs), its exploration for multi-state systems (MSSs) is still limited. This doctoral dissertation focuses on addressing the following three fundamental issues that are essential for the optimization problem for multi-state systems.First, a novel hybrid algorithm based on particle swarm optimization and local search (PSO/LS) has been proposed to solve the basic formulation of the optimization problem for series-parallel and bridge MSSs with heterogeneous redundancy. The hybrid algorithm aims to select appropriate components and the levels of redundancy so that the. built system has a minimum cost while providing a desired level of reliability. Novel local search neighborhood strategies and a dynamic penalty scheme are proposed to enhance the performance of the hybrid algorithm. The common assumption appeared in the literature is adopted in this part of the work:true reliabilities of components are assumed to be precisely known. The universal generating function (UGF) method is applied to precisely calculate the system reliability. The effectiveness of the proposed hybrid algorithm is assessed by comparing it with existing best-known algorithms based on heuristics and meta-heuristics such as genetic algorithms (GAs), tabu search (TS), and ant colony optimization (ACO), reported in the literature. The comparisons have shown the merits of the proposed PSO/LS algorithm in terms of the improved solution quality.Second, realizing that component reliabilities have to be estimated based on experimental or historical operation data, this dissertation argues that the assumption that true component reliabilities are precisely known may not be applicable to many real-world applications. Statistical uncertainty arises at the component level due to limited experimental or operational data and propagates to the system level. In this dissertation, the perspective of the acquisition of system reliability based on component reliabilities and the structure function has been switched from precise calculation to statistical estimation. The reliability estimation problem for MSSs is addressed based on the theories in inferential statistics. The uncertainty propagation mechanism is mathematically explained through an iterative theoretical derivation. The unbiased estimators of system reliability and the associated variance are obtained. With the help of the derived estimators, a lower confidence bound is proposed and proved superior to two existing bounds in the literature. Three importance measures of individual components in an MSS are also proposed.Finally, the optimization problem formulation is revised to consider statistical uncertainty. The hybrid PSO/LS algorithm is revised accordingly to determine the system structure with a minimum cost while providing a desired level of reliability with 95%of confidence. The solution provides additional assurance about the optimized system structure. For the same reliability requirement, the revised solution generally costs more, but the system structure is enhanced, and the expected system reliability is improved. Furthermore, the solution of the revised optimization model provides at least 95%of assurance that the system structure will satisfy the required reliability standard, while the solution of the original optimization model is not able to provide such an implication.Throughout this dissertation, various numerical examples of MSSs appeared in the literature have been used to examine the effectiveness of the proposed hybrid PSO/LS optimization algorithm. Comparisons with existing research results have highlighted the merits of the proposed algorithm. Monte Carlo simulation has also been implemented as a helpful tool to validate the accuracy of the reliability estimation derivation. It has been shown that the proposed approach is in good agreement with the simulation results. A complete example system, the water/steam loop system of a 600MW electric power generation unit, is provided to facilitate understanding the application of the proposed algorithms, approaches, and models.