To establish an appreciation for the role of optimisation within modern (science and) engineering practice and to provide evidence that optimisation is just one component of an integrated tool kit (that includes analytical, simulation, and statistical methods met at earlier FHEQs) for addressing, evaluating, and improving multiple solutions to science and engineering-based problems.
Outline Syllabus
MODELLING
Building empirical models through linear regression analysis; design of engineering experiments; introduction to response surface methodology;
Designed experiments and empirical transfer functions, including least squares fitting.
Specific designs including two-level fractional factorials, Central Composite, custom designs for special situations.
Statistical models for hardware data; analysis of residuals
Success criteria for a prediction equation; selecting terms in a polynomial model
Dealing with background variation.
Using a prediction equation with noise factors, including Monte Carlo methods
Planning and managing an experiment in practice
OPTIMISATION
Formulation: translating descriptive (semantic) engineering design problems into mathematical optimisation problems, design variables, objective function, linear/nonlinear mathematical programming, constrained and unconstrained problems, formulating constraints imposed on engineering system behaviour.
Global/local optima.
Kuhn-Tucker optimality conditions.Classification of optimisation problems.
Numerical optimisation: iterative techniques (local/global 1D, unconstrained multi-parameter, general constrained).
Penalty function methods, random search, bio-inspired techniques.