Design optimization is based on the idea of exploiting the power of computer simulations and optimization in the engineering design process.
An optimization algorithm interacts with a computational model of a physical system in order to find the particular shape or material arrangement of an object that will lead to the most favorable systems performance. Presently, we focus particularly on situations where the measure of performance involves wave propagation effects or fluid forces. Other problems that from a methodological perspective are closely related to design optimization are also of interest, for example inverse problems, that is, the problem of determining properties of a system from data observations, and off-line optimal control problems.
Our core competence lies within the Scientific Computing aspects of design optimization. However, we wish to understand and make contribution to the whole chain of activities needed for a successful design: mathematical modeling of the physical system, analysis of the mathematical problem, discretization of the mathematical problem, construction of suitable numerical algorithms, and efficient implementations of the algorithms. We have recently also started some efforts in the second step of the design process, namely experimental assessment of the optimized designs on manufactured prototypes.
Below, we show examples of previous and ongoing projects in which members of the group have participated.
The design of the individual components in a loudspeaker system has a large impact on the quality of the sound reproduction. Horns are used in public-address systems both to improve the acoustic efﬁciency and to direct the sound towards the audience. We use design optimization to improve the performance of acoustic horns with respect to their efficiency and directivity properties. The horn on the top left is 50 cm long, and 30 cm wide. An optimization algorithm is invoked to distribute material, pixel by pixel, inside the horn in order to obtain perfect transmission efficiency in the frequency range 400-500 Hz.
It is difficult to design a horn to possess both high transmission efficiency and even far-field directivity properties. To create the lower-left device, we optimized the flare shape of the horn simultaneously with the placement of material in a region in front of the horn. The final acoustic horn/lens combination shows high efficiency and a beamwidth above 100° throughout the two-octave-wide frequency range 250--1000 Hz.
Material distribution problems (such as the horn optimization problems above) are typically cast as large scale nonlinear optimization problems over the coefficients in a partial differential equation. An important step toward solving complicated large scale problems of this kind is the development of efficient parallel algorithms and implementations tailored for these problems. The image on the right illustrates the solution of an optimization problem with over 4 million decision variables. (Each of the 4 million pixels is subject to optimization.) We utilize the power of a graphics processing unit (GPU) to solve the problem of finding the distribution of two materials with different heat conduction properties to obtain a temperature distribution that is as even as possible.
In a project illustrated by the pictures above, the aim was to optimize the shape of airfoils and aircraft wings in order to reduce the aerodynamic drag without destroying other crucial properties, such as the lift and twist forces on the wing. The pictures show the pressure field on the surface of a wing at Mach 0.84, before and after shape optimization. The project was carried out as a Ph.D. project at Uppsala University, and the graduated researcher, Olivier Amoignon (firstname.lastname@example.org), continues the development and application of aerodynamic shape optimization at FOI, the Swedish Defence Research Agency.
The picture shows an acoustic wave guide and a horn (diameter around 30 cm) manufactured by a rapid prototyping technique. The horn flare is designed by shape optimization, in which the acoustic pressure field is computed by finite-element solutions of the governing Helmholtz equations. The optimized horn shows almost perfect transmission properties in the frequency range 1.6 - 9 kHz. Preliminary results from ongoing acoustic measurements verifies indeed that the horn is highly transmission efficient.