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 Functionally efficient

See Pareto optimal.

 Global approximation

A design function which is representative of the entire design space.

 Global Optimization

The mathematical procedure for finding the global optimum in the design space. E.g. Genetic Algorithm, Particle Swarm, etc.

 Global variable

A variable of which the scope spans across all the design disciplines or solvers. Used in the MDO context.

 Gradient vector

A vector consisting of the derivatives of a function f in terms of a number of variables x1 to xn. s = [df /dxi]. See Design Sensitivity.

 History

Response history containing two columns of (usually time) data generated by a simulation.

 Importance

See Weight.

 Infeasible Design

A design which does not comply with the constraint functions. An entire design space or region of interest can sometimes be infeasible.

 Iteration

A cycle involving an experimental design, function evaluations of the designs, approximation and optimization of the approximate problem.

 Kriging

A Metamodeling technique using Bayesian regression. (see e.g. [5,23]).

 Latin Hypercube Sampling

The use of a constrained random experimental design as a point selection scheme for response approximation.

 Least Squares Approximation

The determination of the coefficients in a mathematical expression so that it approximates certain experimental results by the minimization of the sum of the squares of the approximation errors. Used to determine response surfaces as well as calibrating analysis models.

 Local Approximation

See Gradient vector.

 Local variable

A variable of which the scope is limited to a particular discipline or disciplines. Used in the MDO context.

 Material identification

See parameter identification.

 MDO

Multidisciplinary design optimization.

 Metamodeling

The construction of surrogate design models such as polynomial response surfaces, Artificial Neural Networks or Kriging surfaces from simulations at a set of design points.

 Min-Max optimization problem

An optimization problem in which the maximum value considering several responses or functions is minimized.

 Model calibration

The optimal adjustment of parameters in a numerical model to simulate the physical model as closely as possible.

 Modeling error

See bias error.

 MP

Mathematical Programming. Mathematical optimization.

 MSE

Mean Squared Error. Used for system identification.

 Multi-objective

An objective function which is constituted of more than one objective. Symbolized by F. Multi-criteria. Refers to optimization problems in which several criteria are considered.

 Multidisciplinary design optimization (MDO)

The inclusion of multiple disciplines in the design optimization process. In general, only some design variables need to be shared between the disciplines to provide limited coupling in the optimization of a multidisciplinary target or objective.

 Neural network approximation

The use of trained feedforward neural networks to perform non-linear regression, thereby constructing a non-linear response surface.

 Noise

See random error.

 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.