Approximate dynamic similitude in energetic multi-domain systems: Quantification and use in multiobjective scaling

This paper examines the scaling of an energetic system to meet new design requirements while satisfying dynamic similitude. The literature defines such similitude discretely, in terms of whether the scaled design satisfies monomial scaling laws derived via the Pi Theorem (or its group-theoretic extensions). Previous work adds flexibility to this approach by using activity analysis to (i) assess the relative importance of scaling laws and (ii) neglect less important ones. Difficulties still arise when scaling laws deemed important cannot be followed exactly (e.g., due to design constraints), thus precluding exact similitude. To address these difficulties, this paper proposes the first continuous measure of approximate similitude, namely, the activity-weighted deviation of a system design from exact similitude. The paper then presents a multiobjective scaling framework that trades approximate similitude off versus other scaling requirements and constraints. Two examples, pertaining to quarter-car and fuel cell air supply scaling, demonstrate the proposed approach.