Optimisation
Glossary Of Terms

Curve fitting is the process of constructing a mathematical function that has the best fit for a set of data points. The curve fitting process uses methods such as interpolation for exact fitting or smoothing for approximate fitting.

Design Of Experiments (DOE) is a technique used to scientifically determine the location of a number of sampling points to obtain a good insight into the response of a system. In general, those sampling points are a number of input variables, bounded by a maximum and minimum value. When multiple input variables are considered, the number of possible combinations can rapidly become too large. With DOE the large number of sampling points is reduced to a more manageable level. Results of analyses based on DOE are often presented in a response surface to predict the behaviour of a system without the need for performing additional analyses.

see Design Of Experiments

With parametric optimisation a number of input parameters, such as geometry, material properties, loads, etc. are varied to examine the response of a structure. Techniques as DOE and response surfaces are used in combination with parametric optimisation to avoid the need of executing a different analysis for every possible value of an input variable.

A response surface is a best-fit curve of a set of data points of multiple variables. A response surface predicts or approximates an output variable as a function of two or more input variables, based on a limited number of calculated or measured data points.

A typical analysis assumes input parameters (material, geometry, loads, etc.) to have a fixed value. To eliminate the uncertainty around these fixed values, a safety factor is often used. This approach is called deterministic.
Designing for Six Sigma provides for a mechanism that takes a statistical deviation of those input variables into account. The output of a Six Sigma analysis is a statistical distribution of the response of the system. This approach is called probabilistic. A product has Six Sigma quality if only 3.4 per 1 million parts fail.

Topology optimisation is a mathematical method that optimises the layout of a material within a given design space, for a given set of loads, constraints and boundary conditions. The goal of a topology optimisation is to maximise the performance of a system.
Contrary to parametric optimisation, topology optimisation can result in any possible shape within the design space. These organic shapes, typical for topology optimisation, are often difficult to manufacture with traditional production methods and are therefore more suitable for additive manufacturing or advanced cast techniques.

Various what-if scenarios quantify the influence of a number of design variables on the performance of a product or process. See also Parametric Optimisation.