Combining Mathematical Programming and SysML for Automated Component Sizing of Hydraulic Systems

Abstract

In this paper, we present a framework that improves a designer’s capability to determine near-optimal sizes of components for a given system architecture. Component sizing is a hard problem to solve because of competing objectives, requirements from multiple disciplines, and the need for finding a solution quickly for the architecture being considered. In current approaches, designers rely on heuristics and iterate over the multiple objectives and requirements until a satisfactory solution is found. To improve on this state of practice, we introduce advances in the following two areas: a) Formulating a component sizing problem in a manner that is convenient to designers and b) Solving the problem efficiently so that all of the imposed requirements are satisfied simultaneously and the solution obtained is mathematically optimal. An acausal, algebraic, equation-based, declarative modeling approach using mathematical programming (GAMS) is taken to solve these problems more efficiently. In addition the Systems Modeling Language (OMG SysML™) is used to formulate component sizing problems to facilitate problem formulation, model reuse and the automatic generation of low-level code that can be solved using GAMS and its solvers (BARON). This framework is demonstrated by applying it to an example of a hydraulic log splitter.