Spacecraft Reliability-Based Design Optimization Under Uncertainty Including Discrete Variables

Abstract

High reliability is a primary design goal in commercial communication satellite systems because they require large capital investment and are inaccessible after launch. Spacecraft system reliability is typically computed using standard parallel-series combination techniques based upon component and subsystem failure rates provided by suppliers. Component failure rates are empirically determined and, as such, are nondeterministic parameters. Treating these failure rates as uncertain parameters in spacecraft design may avoid unnecessary high redundancy. However, probabilistic methods in reliability evaluation are often ignored because handling uncertain parameters associated with discrete or categorical design variables, such as technology choices and redundancy levels, requires computationally expensive sampling techniques. The computational cost of optimization approaches becomes prohibitive when considering discrete technology and redundancy choices as variables. This work presents a genetic algorithm with Monte Carlo sampling for probabilistic reliability-based design optimization of satellite systems. In this approach, confidence-level constraints ensure that system reliability requirements are met with high probability. The genetic algorithm-Monte Carlo sampling approach is compared to a deterministic margin-based approach that enforces margins or safety factors on the reliability of individual components. The comparison shows that the genetic algorithm-Monte Carlo sampling approach produces satellite designs that have low launch mass (a surrogate for cost) while achieving reliability requirements at specified high confidence levels, while the genetic algorithmdeterministic margin-based approach produces heavy satellite designs with excessive redundancy. Based on this work, extensions of a genetic algorithm-based approach for discrete optimization under uncertainty that may require less computational effort appear possible. Nomenclature c = penalty multiplier E = expected value of f = fitness function G = uncertain inequality constraint g = inequality constraint M = mass N samples = number of samples P = probability of R = reliability x = design vector = failure rate = mean = uncertain parameters vector = standard deviation = Gaussian probability density function = objective function

Robust Multi-Disciplinary Optimization of Unmanned Entry Capsules

“…It is also common that multi-objective algorithms are developed for robust design, where one of the objectives is the expected value and the other is the variance of the performance. 5,6 In these cases the underlying problem is not multi-objective, and the interest of the designers is to capture the trade-off between robustness and optimality. With true multi-objective problems the approach of optimizing for both the expected value and the variance of each objective will become computationally expensive even with only few objectives, and the final Pareto front would be difficult to interpret.…”

Reliability Based Design Optimization of a CubeSat De-Orbiting Mechanism

“…The required reliability index is chosen as 3.5 for both probabilistic constraints, that choice leads to a probability of failure value as 0.00023, which obviously means only 23 of 100000 samples can violate performance functions defined for membrane mass and stress on spiral spring. The definition of multi-objective RBDO problem is given in (13) to (19) while the maximum allowable limits for mass and stress are specified as 0.19 kg and 1.0 GPa in the formulation. The system is expected to be lighter and safer since the maximum limits are less than the values in initial design.…”

“…A probabilistic analysis with Monte Carlo Simulation (MCS) for minimizing launch mass by defining 5% of maximum failure limit was performed by Hassan. 13 Mutyalarao et al 14 estimated re-enrty time of a satellite with response surface methodology by considering uncertainties in eccentricity and ballistic coefficient. Williams 15 presented a method for deployment optimization of tethered satellites by defining minimum tension as a design constraint.…”

Low Carbon-Oriented Optimal Reliability Design with Interval Product Failure Analysis and Grey Correlation Analysis

“…For many engineering problems, such as observation distortion, resource limitations, system complexity, and so on, it is difficult to collect sufficient information at the early design phase which tends to cause uncertainty in modeling real industrial products. Therefore, product designers often need to manage the treatment of all kinds of uncertainties in reliability optimal design [28][29][30][31]. Bayesian models and fuzzy theories are basic approaches for handling uncertainties [32][33][34].…”