While tackling optimization within manufacturing process, engineers face uncertainty with regards to design variables and problem parameters from various sources.
These uncertainties impact the optimization process both in terms of reliability (i.e. the probability that a certain design will not fail to meet a predefined criterion or performance function) and in terms of robustness ( i.e. the stability of an optimization outcome against the variations in the input parameters).
The modeFRONTIER® approach of dealing with uncertainties is based on Multi-Objective Robust Design Optimization (MORDO). This consists of investigating the noise factors in the neighbourhood of a sample design with a given probability distribution through a multi-objective optimization algorithm aimed at optimizing mean values while minimizing their variations.
Several techniques are available within the platform, such as Monte Carlo, Latin Hypercube Sampling, and Polynomial Chaos. The latter is capable of providing accurate estimates whilst requiring a small number of function evaluations, thus reducing drammatically computational time.
Using Polynomial Chaos Techniques within modeFRONTIER® it is possible to perform a Reliability Analysis, considering, for example, that a certain percentage of designs satisfy given constraints. This method consists of highlighting the failure probability of a certain distribution by means of a Percentile study. With the definition of a percentile on a constraint, it is possible to minimize the failure probability with respect to that constraint, so that the percentile can be seen as the measure of reliability, carefully using computational resources or third-party simulation software.