This work proposes an inverse design approach by using Rough Sets to establish mapping from the performance space to the design space and can identify multiple subregions in a design space, within which all of the design points are expected to have a performance value equal to or less than desired level. Discretized decision system/table and extracted rules act as transparent metamodel establishing relationship between performance space and design variable space. Thus our method can identify multiple global optima in contrast to single optimum identified by traditional global optimizers. Latinized Nearly Orthogonal Hammersley Sequence Sampling (LNOHSS) is proposed to generate information/decision system to ensure a modest number of total expensive function evaluations to identify attractive spaces even for complex high dimensional problems. The proposed idea is evaluated for the conceptual design of a solid fueled expendable Multistage Space Launch Vehicle.

Inverse Design Optimization of a Multistage Space Launch Vehicle Using Rough Sets

Design engineers prefer to have multiple performing solutions, rather than a single optimum. This set of design alternatives gives desired flexibility to engineers. The motivation of current research effort stems from the question that "Can the design process be reversed?" Every design endeavor has a specific set of stringent performance requirements to meet. So, if we "reverse" the classical design process and start from those performance requirements, we should obtain a design point meeting such requirements. The traditional inverse engineering methods depends greatly on specific domain knowledge and usually, can effectively facilitate the inversion for a specific application problem. However, it is very difficult to apply them into diverse design scenarios where any of the presumed conditions is violated. Development of a more generic and robust approach is deemed necessary to achieve reliable design results in various design endeavors.This work also aims to answer the question, How to find sufficient design alternatives sufficing a given performance level? In doing so, we also intend to keep check on the computational budget (reduce the total number of function evaluations) even for high dimensional problems. This work addresses these needs by proposing a methodical approach to identify the feasible region(s), of the large design space of complex problems, containing design points meeting the same or little-less desired performance level. In this way, continuous and/or discontinuous segments of design space can also be identified. Such regions are anticipated to meet acceptable performance levels. The proposed approach can be cast as a rough set based design methodology. The procedure identifies the design spaces corresponding to the required objective function value, by extracting rules from input-output information system, instead of an approximation of the objective function. The discretized decision system/table and extracted rules act as transparent metamodel establishing relationship between performance space and design variable space. Thus the proposed method can identify multiple global optima in contrast to a single optimum identified by traditional global optimizers. Latinized Hypercube Sampling is employed to generate information/decision system to identify attractive spaces even for complex high dimensional problems, thus, limiting total function evaluations to a modest number.The performance of the proposed procedure has been tested and, thus, validated by the trajectory modelling problem. The inverse design approach based on rough sets is intended for initial conceptual design purposes, thus, providing an immediate insight on the performance prior to the detailed design phase.

Reversing The Design Process To Aid In Complex Engineering Problems

Efficient Sampling and Support Vector Regression for Multidisciplinary Design Optimization of Multistage Space Launch Vehicle

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Efficient Sampling and Support Vector Regression for Multidisciplinary Design Optimization of Multistage Space Launch Vehicle