Noisy functions Subject

Finally, the use of real economics means the MVC objective function is a real measure of process profitability. This can then be used to assess the value of the application. While the minute-to-minute value is probably too noisy and subject to change if the objective coefficients are changed, it can be used offline. For example, the average C4 content of propane before implementation might have been 4.1 %. With the MVC in place it was increased to 4.5 % and so the improvement is 0.4 %. We repeat this calculation for the other hmiting constraints such as the C3 content of bottoms and the reboiler steam flow. 

Based on the above expressions, it is obvious that by this approach one needs to estimate numerically the time derivatives of Xv, S and P as a function of time. This can be accomplished by following the same steps as described in Section 7.1.1. Namely, we must first smooth the data by a polynomial fitting and then estimate the derivatives. However, cell culture data are often very noisy and hence, the numerical estimation of time derivatives may be subject to large estimation errors. 

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