# Glossary

Numerical sensitivity
A derivative of a function computed by using finite differences.
Objective
A function of the design variables that the designer wishes to minimize or maximize. If there exists more than one objective, the objectives have to be combined mathematically into a single objective. Symbolized by Φ.
Optimal design
The methodology of using mathematical optimization tools to improve a design iteratively with the objective of finding the ‘best’ design in terms of predetermined criteria.
Parameter identification
See System identification.
Pareto optimal
A multi-objective design is Pareto-optimal if none of the objectives can be improved without at least one objective being affected adversely. Also referred to as functionally efficient.
Point selection scheme
Same as experimental design.
Preference function
A function of objectives used to combine several objectives into a single one suitable for the standard MP formulation.
Preprocessor
A graphical tool used to prepare the input for a solver.
Process
A series of analysis stages (or steps) designed to produce a result. Multistage process.
Example: metal forming analysis which consists of several stages, e.g. gravity loading, stamping,
springback, trimming, etc.
Process simulation
The use of computer programming, computer vision, and feedback to simulate manufacturing techniques.
Random error
The total error – the difference between the exact and computed response - is composed of a random and a bias component. The random component is, as the name implies, a random deviation from the nominal value of the exact response, often assumed to be normally distributed around the nominal value. (See also bias error).
RBDO
Reliability-based Design optimization.
Reasonable design space
A subregion of the design space within the region of interest. It is bounded by lower and upper bounds of the response values.
Region of interest
A sub-region of the design space. Usually defined by a mid-point design and a range of each design variable. Usually dynamic.
Reliability-based design optimization (RBDO)
The performing of design optimization while considering reliability-based failure criteria in the constraints of the design optimization formulation. This implies the inclusion of random variables in the generation of responses and then extracting the standard deviation of the responses about their mean values due to the random variance and including the standard deviation in the constraint(s) calculation.
Residual
The difference between the computed response (using simulation) and the predicted response (using a response surface).
Response
A numerical indicator of the performance of the design. A function of the design variables approximated using a metamodel which can be used for optimization. Symbolized by f. Collected over all design iterations for plotting. (See also history).
Response quantity
See response.
Response Surface
A mathematical expression which relates the response variables to the design parameters. Typically computed using statistical methods.
Result
A numerical indicator of the performance of the design. A result is not associated with a metamodel, but is typically used for intermediate calculations in metamodel-based analysis.
RSM
Response Surface Methodology.
Sampling
In the context of the GUI a Sampling is the same as a Case. It is based on a unique subset of variables.
In general, Sampling is synonymous with Point Selection or Experimental Design.
Saturated design
An experimental design in which the number of points equals the number of unknown coefficients of the approximation. For a saturated design no test can be made for the lack of fit.
Scale factor
A factor which is specified as a divisor of a response in order to normalize the response.
Sensitivity
See Design sensitivity.
Sequential Random Search
An iterative method in which the best design is selected from all the simulation results of each iteration. A Monte Carlo based point selection scheme is typically applied to generate a set of design points.
Simulation
The analysis of a physical process or entity in order to compute useful responses. See Function evaluation.
Slack constraint
A constraint with a slack variable. The violation of this constraint can be minimized.
Slack variable
The variable which is minimized to find a feasible solution to an optimization problem, e.g. e in: min e subject to g j ( x) ≤ e; e ≥ 0. See Strictness.
Solver
A computational tool used to analyze a structure or fluid using a mathematical model. See Discipline.