Response surface models with central composite designs

This model is capable of estimating both linear and non-linear effects observed experimentally. Hence, it can also be used for optimization of the desired response with respect to the variables of the system. Two popular response surface designs are central composite designs and Box-Behnken designs. Box-Behnken designs were not employed in the experimental research described here and will therefore not be discussed further, but more information on Box-Behnken designs can be obtained from reference [15]. 

Based on the obtained response surface, a second roimd of optimization follows, using the steepest ascent method where the direction of the steepest slope indicates the position of the optimum. Alternatively, a quadratic model can be fitted around a region known to contain the optimum somewhere in the middle. This so-called central composite design contains an imbedded factorial design with centre... 

Now if each of the design points in the central composite design is replicated five times, so that the complete design has 75 runs, then at each design point we can calculate the average response and the standard deviation of the response. The analysis techniques associated with response surface methodology can then be applied to fit separate models to... 

Full second-order polynomial models used with central composite experimental designs are very powerful tools for approximating the true behavior of many systems. However, the interpretation of the large number of estimated parameters in multifactor systems is not always straightforward. As an example, the parameter estimates of the coded and uncoded models in the previous section are quite different, even though the two models describe essentially the same response surface (see Equations 12.63 and 12.64). It is difficult to see this similarity by simple inspection of the two equations. Fortunately, canonical analysis is a mathematical technique that can be applied to full second-order polynomial models to reveal the essential features of the response surface and allow a simpler understanding of the factor effects and their interactions. 

The latest DoE was focussing on the axial and swirl stream temperature (Tswiri) the rotation speed (n) in a face-centred central composite (CCF) response surface design with those three factors (/=3) on three levels. Levels were set linearly as mentioned in section Improved Experimental Setup so that N = 2 +2/+1 = 15 experiments were required for this model. The centre point was repeated five times to ensure reproducibility and reasonable model validity. Particle size, span, particle shape, surface roughness, flowabDity and BET surface area were chosen as responses to evaluate the significant effects of the factors on these particle properties [34, 35]. 

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