Inverse Engineering

Inverse problems are rapidly becoming a multi-disciplinary field with many practical engineering applications. The objective of this lecture is to present several such multi-disciplinary concepts and applications. In some examples, sophisticated regularization formulations were used. In other examples, different optimization algorithms were used as tools to solve

de facto

inverse problems. Due to the mathematical complexity of these multi-disciplinary and often multi-scale inverse problems, the most widely acceptable formulations eventually result in a need for minimization of a certain norm or a simultaneous extremization of several such norms. These single-objective and multiobjective minimization problems are then solved using appropriate robust evolutionary optimization algorithms. Specifically, we focus here on inverse problems of determining spatial distribution of a heat source for specified thermal boundary conditions, finding simultaneously thermal and stress/deformation boundary conditions on inaccessible boundaries, and determining chemical compositions of steel alloys for specified multiple properties.