Robust Multi-Disciplinary Optimization of Unmanned Entry Capsules

Abstract

Uncertainties in design variables and environmental factors are common in many engineering problems, and they must be taken into account when searching for robust optimal solutions. In robust multi-objective optimization it is common practice to optimize the average performance instead of the nominal objective functions. To compute average performance, and to determine the compliance of the solutions to the constraints, sampling is needed in a neighborhood of each individual and the performance of each sample point must be evaluated. This drives the computational cost of robust optimization up. In this paper we present a repository-based approach that reduces the number of evaluations needed during robust optimization. Unlike most of the approaches available to date, we introduce methods to keep the joint probability density function of the input variables intact when pre-existing points from the repository shall be used. This allows for cheap robustoptimization also in the presence of non-uniform uncertain-variable distributions. The robust optimization of unmanned entry capsules, considering continuous shape-variation models, aerothermodynamics, flight mechanics, and thermal protection system models at the same time is a valuable test-bed for the method presented here. In this paper we discuss the results of minimizing the mass of the capsules while maximizing the internal volume and the re-usability. We demonstrate that using a double-repository archive maintenance scheme it is possible to obtain accurate results and a reduction of the computational cost that is close to 70%, if compared to classical sampling-based methods for robust optimization. The analysis of robust-optimal entry capsules demonstrates that there are design conditions for which small and fully reusable capsules for unmanned entry from low Earth orbits perform as well as capsules with ablative materials, also under uncertainties.

Thermal Protection System Design of a Reusable Launch Vehicle Using Integral Soft Objects

“…where n blob is the total number of blobs present on the B-grid. Figures 2(a) and 2 (b) show the strength field of a twodimensional stick primitive obtained using n blob = 6 and 20, respectively, computed with equation (6). By increasing the number of blobs on a stick, the strength of F is still bounded to a maximum unit value.…”

“…Effectiveness and flexibility of these distributions have been increased by also allowing tapered and steerable sticks. (ii) A surrogate representation of a skeleton-based stick is simply obtained by distributing a finite number of one-point skeleton primitives (circular blobs), mixing each other with the MAX blending operator outlined by equation (6). As mentioned earlier, the rationale of this choice is that the field function of the assembled stick primitive still remains limited, and at the same time, only a small number of circular blobs (slightly more than a dozen) are required to obtain a satisfactory envelope of the finite support without bulges because of the low intrinsic resolution of the grid combined with the actual ranges assigned to the finite supports of primitives.…”

“…However, antithetical requirements between room for the payload, weight, and vehicle operability demand a trade-off between vehicle shape and TPS sizing. In preliminary design practice, thousands of design configurations are typically evaluated by an optimization algorithm to find the best fit [5][6][7][8][9][10]. As a consequence, a preliminary appraisal of vehicle performances is commonly performed using high-efficiency, low-order fidelity methods that give support to a multidisci-plinary analysis performed with a computational effort which fit the typical timeline of the conceptual design phase [11].…”

“…The above simplifying assumptions are considered reasonable for a conceptual design phase and determine a conservative overestimation of the TPS mass. A one-dimensional model of the TPS thickness [6] is used to determine TPS interior wall temperatures T w1 exploiting the exterior TPS surface T w2 temperature. Radiative equilibrium is assumed on wall w 2 [5]:…”

Parametric Integral Soft Objects-based Procedure for Thermal Protection System Modeling of Reusable Launch Vehicle

“…This requirement may conflict with the adoption of a fully reusable TPS, either limiting the choice of material category or penalizing the total mass. In preliminary design practice, thousands of design configurations are typically evaluated by an optimization algorithm to find the best fit [5][6][7][8][9][10][11]. Therefore, a preliminary appraisal of vehicle performances is commonly performed using high-efficiency, low-order fidelity methods that give a support to a multidisciplinary analysis performed with a computational effort which fit the typical timeline of the conceptual design phase [11].…”