By Jim T Criswell; Oklahoma Cooperative Extension Service
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If the new MSE error is not reduced, then increase µk and go back to step 3. The algorithm terminates when i) the norm of gradient is less than some predetermined value or, ii) MSE error has been reduced to some error goal or, iii) µk is too large to be increased practically or, iv) a predefined maximum number of iterations has been reached. Data generated from the five different feed rate profiles were divided in three groups: the training data set, the validation data set and the testing data set.
3. Plots of simulation data for five different feed rates. 46 4 On-line Softsensor Development be in the range [-1,1]. A post-processing procedure has to be performed in order to convert the output back to its original unit. 3) i=1 where, N is the number of training data pairs; Xia is the target (actual) value ˆ i is the corresponding estimated value preduced by the neural of biomass; X softsensors. The Levenberg-Marquardt backpropagation (LMBP) training algorithm is adopted to train the neural networks due to its faster convergence and memory efficiency [34, 93].
The prediction starts from an arbitrary initial point. As can be seen from the figure, the softsensor is able to converge within a very short time and can predict the trend of the growth of biomass. 3580. 35, which has been previously reported in the literature by using Knowledge Based Modular networks [99]. As can be seen in the plot, a fluctuation appears in the prediction trajectory. 7%. 5. As discussed in the simulation study, the main reason for the fluctuation could be that the historical input values are not presented to the network.