A trajectory‐based sampling strategy for sequentially refined metamodel management of metamodel‐based dynamic optimization in mechatronics

Abstract

Dynamic optimization problems based on computationally expensive models that embody the dynamics of a mechatronic system can result in prohibitively long optimization runs. When facing optimization problems with static models, reduction in the computational time and thus attaining convergence can be established by means of a metamodel placed within a metamodel management scheme. This paper proposes a metamodel management scheme with a dedicated sampling strategy when using computationally demanding dynamic models in a dynamic optimization problem context. The dedicated sampling strategy enables to attain dynamically feasible solutions where the metamodel is locally refined during the optimization process upon satisfying a feasibility-based stopping condition. The samples are distributed along the iterate trajectories of the sequential direct dynamic optimization procedure. Algorithmic implementation of the trajectory-based metamodel management is detailed and applied on two case studies involving dynamic optimization problems. These numerical experiments illustrate the benefits of the presented scheme and its sampling strategy on the convergence properties. It is shown that the acceleration of the solution time of the dynamic optimization problem can be achieved when evaluating the metamodel that is lower than 90% compared to the computationally expensive model. KEYWORDSmetamodel-based optimization, metamodel management, sequential dynamic optimization INTRODUCTIONA recurring task within the area of mechatronics is the identification of a set of time-dependent signals (ie, the optimal state trajectory and the corresponding optimal control [OC] policy) to achieve improved system behavior with respect to a well-defined task or objective. 1-3 Reduction in energy consumption, minimization of the execution time, increased safety of operation, and robust tracking are only a few examples of such tasks. A rigorous framework to formulate such dynamic optimization problems (DOPs) is provided by the OC framework, 1 which requires a dynamic model of the system. Having a high-fidelity dynamic model is key to assure close correspondence between optimized and actual system behavior. Dynamic models may incorporate multidomain physics and subsystem interaction, rendering simulation times that can be much slower than real time (see, eg, other works 4-9 ).

Adaptive Approximate Dynamic Optimization : a slider-crank case study

“…The latter is linear in function ofv, τ and f and hence we can solve for the couple {v, f } be it for the couple {τ , f }. This will either generate the so called forward,q(q,q, u), be it inverse, u(q,q,q), dynamic model representations 1 . Note that this only holds when dim(u) = dim(q) and when interaction term, w, is independent of f andv or τ , which we will assume for the remainder of this article, i.e.…”

“…The AADO algorithm was originally developed for application in the forward convention [1]. However, the framework does lend itself for application in an inverse setting as well.…”

“…In [1] we proposed a method to deal with this problem that is inspired on metamodel based optimization methods. We suggested to replace the HF model with an approximator that is fitted on sampled HF model evaluations.…”