A methodology for evaluating system-level uncertainty in the conceptual design of complex multidisciplinary systems

by Martin, Jay D.

Conceptual design is the early stage of system design, when little is precisely known about the physical description of a new system. One of the goals in conceptual design is to aggregate all current corporate knowledge about the new design and exhaustively search the feasible design space to find potential designs that best meet the design’s requirements and satisfies its constraints. In the conceptual design stage, simplified models are often created in preference to more complex models to permit the rapid assessment of many designs that cover the entire feasible design space. Uncertainty in the assessment of a potential design may result from uncertainty in the inputs to the design, such as sizes, weights, efficiencies, or costs. The use of simplified models may also introduce additional uncertainty, termed model uncertainty, due to the reduction in the number of parameters used to describe the system or due to incorrect relationships between parameters. A metamodel is a ”model of a model” and can be used as a computationally efficient approximation to a computer model such as a finite element analysis. Kriging models are a type of metamodel that can interpolate their observations and provide a probability distribution of the output that quantifies the model uncertainty. Kriging models are created as simplified models from observations of detailed subsystem models. A Monte Carlo simulation (MCS) based methodology is developed to permit the specification of arbitrary probability distributions of the inputs to the system design using a hierarchy of kriging models. Through the use of kriging models, the model uncertainty introduced can also be quantified along with the input uncertainties’ impact on the system performance measurements. This methodology is demonstrated on a satellite design problem composed of three subsystems. These results are compared to those found using original computer models in the MCS system uncertainty assessment. This methodology enables the computationally efficient use of MCS with simple random sampling to estimate the resulting uncertainty of the system’s performance parameters given the probability distribution of the system inputs and the uncertainty introduced by using approximations to the original deterministic computer models. iii