We predict the quality parameters by fetching direct copies of the missing components of the best-matching unit in the SOM. The best-matching unit is searched with regard to the known components only. In this case, we are interested in predicting the quality parameter values with given incoming raw material and process parameter settings. We thus map vectors with known components to the Self-Organizing Map and fetch the values of quality parameters from the best-matching unit of the input vector.

The choice of the missing components are up to the user. No committment to which components are inputs and which are outputs is made.

To validate the model, we removed a random sample of 500 vectors from the input data to form an independent testing set. This set was not used during training. For these vectors, the quality parameters were known.The quality parameters were omitted from the testing set vectors and the SOM was used to predict the values of the quality parameters by fetching direct copies of the quality parameters of the best-matching unit with regard to the known components. The predicted values for the quality parameter values can be compared with the corresponding known values.

**Figure 5.6:** The real values versus the predicted values of the quality parameter

The points in Figure 5.6 are the pairs of real values and predicted values. Ideally, these should be on a line where both are equal. It can be seen that the predicted values lie around this line and are most accurate in the middle of the quality parameter range.

**Figure 5.7:** The predicted values and the sorted, real values

The Figure 5.7 shows the sorted real values of the quality parameter as points, and the predicted values of the respective quality parameters as a connected line. This shows that the predicted values for small values of the quality parameter are consistently above the real value. Predictions for the large values of the quality parameter are consistently below the right value.

The Figures above show that this method, despite its relative simplicity, can produce predictions with good accuracy. This method predicts well on average. The expected value of the prediction error is 0.6 and the standard deviation for the prediction error is 19 MPa.

Fri Mar 8 13:44:32 EET 1996