Optimal Control for Problem of Restricted Response

Besides the optimal problems mentioned above, there is another type of problems of industrial optimization the problems of restricted response. In these problems, it is necessary to control the target values within certain narrow range. Both the samples having too high or too low target values are considered as bad samples. For example, in steel production the chemical compositions (such as carbon content) of steel product must be controlled within some narrow range. In some machine part production, the surface hardness should not be kept too low. Too high 

1 SVM applied to optimization of ML values in butadiene rubber production 

ML value is an index of the mechanical property of synthetic rubber. It is related to the averaged molecular weight of synthetic rubber products. In butadiene rubber production, the ML value should be controlled within 43 to 47. Too high ML values correspond to insufficiency of elasticity, while too low ML values correspond to low tensile strength of products. Table 14.4 illustrates some data of production records about the factors affecting ML values in production. It has been found that there are five chief factors influencing the ML values in production X (feed rate of butadiene monomer), X2 (feed rate of solvent oil), Xj (feed rate of catalyst), X4 (temperature of feed), X5 (temperature of the lower part of the first reactor). 

Although the result of the example mentioned above is rather satisfactory, the PCA projection method, as a linear projection method, cannot be used for the problems having significant nonlinearity. The following section will consider an example of such kind. 

2 SVM applied to modeling for the carbon content control in steel making 

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