# Robust Design & Reliability

​​While tackling optimization within manufacturing process, engineers face uncertainty that needs to be quantified and handled to attain true product performance improvements.

In many engineering problems design parameters may be uncertain: tolerances, fluctuating operating conditions, etc. These uncertainties impact the design 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 of the optimal solution ( i.e. the stability of an optimization outcome against the variations in the input parameters). In these circumstances, traditional optimization techniques tend to "over-optimize", producing solutions that perform well at the design point, but have poor off-design characteristics.​

The modeFRONTIER approach dedicated to uncertainty management is based on Multi-Objective Robust Design Optimization (MORDO). By investigating the noise factors affecting a design sample, the deterministic model is replaced by an iterative stochastic model in a region of uncertainty represented as the probability distribution of the output variables. A multi-objective optimization algorithm then is used to optimize mean values while minimizing their variations.

Several sampling 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.

By 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.

WHAT'S NEW​

#### NEW efficient sampling technique > Adaptive Sparse Polynomial Chaos Expansion

Performing Robust Design Optimization is very expensive from the computational perspective. The new Adaptive Sparse Polynomial Chaos Expansion independently generates the most efficient model to be computed. After extracting only the terms affecting most the model, it combines them to build multiple models and then selects the one ensuring the best performance. Specific characteristics of the engineering problem are taken into account and designers can now benefit of the ability of the model in predicting the uncertainty with less computational effort.

INDUSTRY PERSPECTIVE