Optimisation.

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Presentation transcript:

Optimisation

Optimisation Simplex Steepest ascent

Response surface for an experimental system Optimum U1 U2 At the outset of an experimental study the location of the optimum is not known.

Optimisation by Simplex search I Optimum U1 U2 1 3 2 4 Starting simplex and the first move from the poor conditions

Optimisation by Simplex search II Optimum U1 U2 1 3 2 4 5 6 7 9 11 10 8 12 Progression of the simplex towards the optimum conditions.

First order response surface and path of steepest ascent. Region of fitted first order response surface

Response Surface Modelling (RSM)

Central Composite Design Three parts: 1. Factorial or reduced factorial design Estimate of main effects and interactions 2. At least one center point experiment Possible to reveal curvature and estimate the experimental error 3. Experiments  on the variable axes Possible to estimate quadratic terms

Central composite rotatable design for two variables

Central composite rotatable design for three variables Number of experiments: 23 + 4 + 6 = 18