Scaling-law-based metamodels for the sizing of mechatronic systems

Abstract

This paper presents a new metamodel form and associated construction procedure adapted to the sizing tasks of mechatronics systems. This method of meta-modeling uses scaling laws to extract compact forms of design models from local numerical simulations (FEM). Compared to traditional metamodels (polynomial response surfaces, kriging radial basis function) the scaling-law-based metamodels have the advantage of a light, compact form and good predictive accuracy over a wide range of the design variables (several orders of magnitude). The general regression process is first explained and then illustrated on different examples: a purely numerical test function, a limited angle electromagnetic actuator and a flexible mechanical hinge.

Future Challenges in Mechatronics

“…This system-level design, distinct from component design, needs to represent in the mechatronic layer the key information of the specific domain layer with dedicated models [5][6][7]. Referred to as "estimation models" by Budinger et al [7], they enable the designer to readily take multiple design constraints into account.…”

“…This system-level design, distinct from component design, needs to represent in the mechatronic layer the key information of the specific domain layer with dedicated models [5][6][7]. Referred to as "estimation models" by Budinger et al [7], they enable the designer to readily take multiple design constraints into account. The models 2 Hierarchical design models (after Hehenberger et al [4]) 3 Future Challenges in Mechatronics directly and explicitly link a few primary characteristics, such as overall dimensions of components, to the secondary characteristics needed for the sizing [5] and optimization [1].…”

“…Despite a recent thrust of work on model order reduction, the computational cost of finite element models remains prohibitive in the preliminary design phase. The use of meta-modelling techniques [7,8] is thus interesting for this purpose. A challenge for mechatronic design is the development of meta-modelling techniques specifically dedicated to the selection of components of system from an integrator point of view.…”

“…A challenge for mechatronic design is the development of meta-modelling techniques specifically dedicated to the selection of components of system from an integrator point of view. A paper by Budinger et al [7] proposes a meta-modelling method based on scaling laws which extract simple, global expressions of estimation models from local numerical simulations (FEM).…”

Scaling laws based metamodels for the selection of the cooling strategy of electromechanical actuators in the early design stages

“…It supposes to generate a Design of Experiments (DoE) 1 on a particular case study for which the integration parameters are varied, and then fit a regression model on the obtained data. The problem of the regression models such as polynomial, Gaussian RBF or Kriging is their nonphysical basis which in some cases gives poor predictive capability outside the DoE used for their construction [17]. Nevertheless, a recent paper has shown that if a physical base is used for the regression, the fitting gives simple relations with acceptable predictive capability outside the DoE [17].…”