2.3.   Data Preprocessing

Data preprocessing can be used for systematically modifying the raw signals of the device with the hope that the altered signals provide more useful input to the calibration method. Unfortunately, no general guidelines exist to determine the appropriate data preprocessing technique and thus the different preprocessing techniques are controversially discussed in literature [7],[8].

In this work, the input variables are preprocessed by autoscaling according to:

(2)

With  as response of the i^th sample at the j^th variable, as the mean of the j^th variable and  as the standard deviation of the j^th variable. Autoscaling involves a mean-centering of the data and a division by the standard deviation of all responses of a particular input variable resulting in a mean of zero and a unit standard deviation of each variable. For some calibration methods autoscaling can improve the calibration as autoscaling allows all variables to influence equally the calibration especially if different variables show different magnitudes of variation.

The dependent variables were range-scaled between -0.9 to 0.9, which is essential for calibration by neural networks with hyperbolic tangent activation functions, according to:

(3)

For the calculation of the prediction errors and the true-predicted plots, the range-scaling was reversed.