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Kaj Madsen - DTU Informatics•Head of Department


Space Mapping Technology

The space mapping approach to engineering model enhancement and design optimization intelligently links companion "coarse" (ideal or low-fidelity) and "fine" (practical or high-fidelity) models of different complexities. Examples include full-wave electromagnetic (fine) simulations with empirical circuit-theory based (coarse or surrogate) simulations, or an engineering device under test coupled with a suitable simulation surrogate.

Our methodology has been adopted for diverse design applications: electronic components, magnetic systems, civil and mechanical engineering structures including automotive crashworthiness design. Space mapping facilitates efficient optimization while avoiding direct optimization of the fine model. It is a simple CAD methodology, which closely follows the traditional experience and intuition of engineers, yet is amenable to rigorous mathematical treatment.

Following the original concept of Bandler in 1993, algorithms have utilized Broyden updates, trust regions, and artificial neural networks. New developments include implicit space mapping, in which we allow preassigned parameters not used in the optimization process to change in the coarse model, and output space mapping, where a transformation is applied to the response of the model.

The space mapping interpolating surrogate (SMIS) framework locally matches the surrogate with the fine model. In a handful of fine model evaluations, it delivers the accuracy expected from classical direct optimization algorithms using sequential linear programming, such as the Hald-Madsen minimax algorithm.

We have invented the "cheese-cutting" and other simple illustrations of space mapping.

Our work is applied in the areas of radio frequency (RF), wireless and microwave circuit design, integrating electromagnetic simulations.

The SMF System

In 2005 we announced SMF, the world's first friendly system for engineering modeling, optimization and statistical analysis based on Space Mapping.  Matlab based, SMF drives the commercial solvers MEFiSTo, Sonnet em, ADS, and FEKO.  SMF also features interactive Space Mapping.


Diverse Implementations of Space Mapping

Space Mapping Application to SAAB 9-3 Sport Sedan (Redhe et al., 2001-, Sweden)

In crashworthiness finite element simulations, each evaluation is expensive. Space Mapping reduces the total computing time to optimize the vehicle structure up to 50% compared to traditional optimization. Space Mapping has been applied to the complete FE model of the new Saab 9-3 Sport Sedan. Intrusion into the passenger compartment area after the impact was reduced by 32% with no reduction in other crashworthiness responses.

See: Space mapping optimization of the new Saab 9-3 Sport Sedan exposed to impact load (M. Redhe and L. Nilsson).

See also: Optimisation improves car crashworthiness

Used in the microwave industry for optimization of dielectric resonator filters and multiplexers (Com Dev, Cambridge, Ontario, 2003-)

Used for development of new library models for wireless components (Philips, The Netherlands, 2001-)


Knowledge Based Modeling

We have forged links between space mapping technology and artificial neural network (ANN) technology for device modeling and circuit optimization. This is related to the knowledge based neural network (KBNN) methodology developed at Carleton University by Dr. Q.J. Zhang and his group.


Historical Notes on Space Mapping

Space Mapping (Bandler, Biernacki and Chen)
Space Mapping Based Neuromodeling