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In this paper the development of statistical metamodels and statistical fast running models is presented first. They are utilized for propagating uncertainties in a multi-discipline design optimization process. Two main types of uncertainty can be considered in this manner: uncertainty due to variability in design variables or in random parameters; uncertainty due to the utilization of metamodels instead of the actual simulation models during the optimization process. The value of the new developments and their engagement in multi-discipline design optimization is demonstrated through a case study. An underwater vehicle is designed under four different disciplines, namely, noise radiation, self-noise due to TBL excitation, dynamic response due to propulsion impact loads, and response to an underwater detonation.

The Energy Boundary Element Analysis (EBEA) has been utilized in the past for computing the exterior acoustic field at high frequencies (above ∼400Hz) around vehicle structures and numerical results have been compared successfully to test data [1, 2 and 3]. The Energy Finite Element Analysis (EFEA) has been developed for computing the structural vibration of complex structures at high frequencies and validations have been presented in previous publications [4, 5]. In this paper the EBEA is utilized for computing the acoustic field around a vehicle structure due to external acoustic noise sources. The computed exterior acoustic field comprises the excitation for the EFEA analysis. Appropriate loading functions have been developed for representing the exterior acoustic loading in the EFEA simulations, and a formulation has been developed for considering the acoustic treatment applied on the interior side of structural panels.

The Energy Finite Element Analysis (EFEA) has been developed for computing the structural vibration and the interior noise level of complex structural-acoustic systems by solving governing differential equations with energy densities as primary variables. A finite element approach is employed for the numerical solution of the governing differential equations. Results from EFEA simulations have been compared successfully with test results for Naval, automotive, and aircraft structures. The Energy Boundary Element Analysis (EBEA) has been developed for conducting exterior acoustic simulations using the acoustic energy density as primary variable in the formulation. EBEA results have been compared successfully to the test results in the past for predicting the exterior acoustic field around a vehicle structure due to external noise sources. In this paper, the EBEA and EFEA methods are combined for predicting the interior noise levels in a vehicle due to exterior acoustic sources.

The Energy Finite Element Analysis (EFEA) has been developed for evaluating the vibro-acoustic behavior of complex systems. In the past EFEA results have been compared successfully to measured data for Naval, automotive, and aircraft systems. The main objective of this paper is to present information about the process of developing EFEA models for two configurations of a business jet, performing analysis for computing the vibration and the interior noise induced from exterior turbulent boundary layer excitation, and discussing the correlation between test data and simulation results. The structural EFEA model is generated from an existing finite element model used for stress analysis during the aircraft design process. Structural elements used in the finite element model for representing the complete complex aircraft structure become part of the EFEA structural model.

A multi-disciplinary optimization under uncertainty (MDO-U) capability has been developed in order to solve optimization problems with multiple sets of objectives and constraints originating from different design disciplines while simultaneously accounting for uncertainty during the optimization process. Uncertainties are introduced in the optimization process by considering the constraints which depend on any random variables and any random parameters as probabilistic. Satisfying the probabilistic constraints in the presence of uncertainty introduces sufficient conservatism in the solution and eliminates the need for further application of safety factors. The MDO-U capability is applied for performing design optimization for the TPS of an Apollo type vehicle. The Traj and FIAT codes of NASA Ames are employed during this design process for trajectory and for thermal analyses, respectively.

A multi-disciplinary optimization analysis is a highly iterative process that requires a large number of function evaluations for computing the objective functions and the constraints. Metamodels (i.e. response surface methodologies) can be constructed before starting the optimization for each one of the objective functions and the constraint functions. The metamodels can be employed in the multi-discipline optimization instead of high fidelity simulations resulting in significant computational savings. A multi-discipline design optimization of an aircraft wing under aerodynamic and structural analysis considerations is performed in this manner. Design variables associated with the shape of the wing are considered in the CFD simulations, while sizing structural design variables are considered in the structural discipline. At the top system level, a cost type metric is defined for driving the overall design optimization process.