Optimal zone

Optimization. Zone travel rate, sample geometry and orientation, zone length and spacing, stirring in the zone, and the number of zone passes can all be controlled. These variables can be optimized either with respect to purification or to the purification rate. 

TABLE 6.4 Optimal Zone Temperatures for Consecutive Reactions... 

Figure 3.4 Radar plot to demonstrate the physicochemical characteristics of Lipitor. The simple plot demonstrates that two parameters fall within the optimal zone (logP and PSA), while three others slightly exceed the boundaries molecular weight, water solubility and number of rotatable bonds.

In a second step, a simplex centroid design was realized with seven design points and six check points. Two responses were optimized consistency and whiteness. Using the second-order equations from this matrix, it is possible to obtain isoresponse graphs. The contour plots are given in Figs. S and 6. The optimal gel must correspond to a gel similar to petrolatum. This optimal zone is reported in Fig. 7 where contour plots of the two responses are superimposed. 

Figure 2. Increment factor g of the bending strength of the bipartite beam as a function of the position of the flexible adhesive layer in the beam cross section. The optimal zone of h2/h for the greatest strengthening effect is shown as shaded zone.

For Nz = 3, the theoretical analysis is also confirmed. In this case, the configuration with all zones as close as possible to the reactor inlet is optimal for Da< 1/2. At Da=1/2, La detaches and up to Da=3/2 the optimal configuration has two active zones as close as possible to the reactor inlet and the third at a distance L2 from the inlet. When Da=3/2, Li detaches and for all values Da >3/2 the optimal configuration consists of three separate active zones the first zone at the reactor inlet, the second at a distance Li, and the third at a distance L2 from the first zone. As Da —> 00, the three distances tend to L/3 and in the limit the optimal zone configuration again is one with equal distances between the zones. Again, at all values of Da, L < Z/2 < Z/3. 

Optimal Zone Strategy of Large Margin Search... 

The purpose of industrial optimization is to improve the production process by optimal control, that is to achieve good product quality, high rate of recovery, low energy and raw materials consumption, low pollution and low production cost, etc. Since these targets are usually determined by many factors simultaneously, multivariate analysis has to be used to make mathematic modeling of an optimal zone in hyperspace spanned by operation parameters. 

One of the purposes of fault diagnosis is also to find an optimal zone in the high-dimensional space spanned by operation parameters in order to avoid the occurrence of fault. This is also usually a multivariate problem. 

So we have two methods to find the optimal zone from operation data records. These methods can be illustrated in Fig. 14.3 and Fig. 14.4. 

Fig. 14.3 Strategy for searching optimal zone by support vector classification.

We call these methods strategy of large margin search for optimal zone modeling. As we will see in the following paragraphs, these strategies are rather useful for industrial optimization or fault analysis in production. 

In many cases of industrial optimization, it is required to control the target value of optimization to be maximized value (for yield of recovery, product quality, productivity, etc.) or minimized value (for energy consumption, pollution, production cost, etc.). In order to find the mathematical model of optimal zone for these purposes, the large margin search strategy, mentioned above for fault diagnosis, is also useful. 

If we assign the samples with target values smaller than 30 as class 1 , and the rest of the sample points as class 2 . By SVM computation, it can be found that the samples of number 17, 18, 19, 20, 22 and 24 are located in the region of good samples far away from the optimal hyperplane. And these sample points are located in an optimal zone defmed by the following inequalities in the hyperspace spanned by the four features listed in Table 14.3 ... 

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