Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 260

variable. Several performance indices (RMSE and MAE), and the correlation
coefficient between the measured and the model predicted tensile stress were used
to evaluate the performance of the fuzzy models developed. Property prediction
results for different types of steel are summarized below.
6.8.1.1 Property Prediction for C-Mn Steels
Using the proposed input selection paradigm, five inputs (the carbon, silicon,
manganese, nitrogen contents and the ferrite grain size D -1/2 (mm -1/2 ), were
selected from the 15 possible input variables. Three hundred and fifty-eight
industrial data were used, with 50% of them for training and the remaining 50% for
model testing. After partition validation and parameter learning, the final fuzzy
models of the Mamdani type consisting of six rules were obtained. The rule-based
fuzzy model was represented by six fuzzy rules . From the fuzzy model generated,
Chen et al. (2001) used linguistic hedges to derive the corresponding linguistic
model.
The fuzzy model with linguistic hedges finally generated used six Mamdani-
type fuzzy rules, such as one described below:
Rule-1 : IF Carbon is large and Silicon is medium and Manganese is large and
Nitrogen is medium and D - 1/2 is more or less medium, THEN Tensile
Stress is large
Using the above model, Chen et al. (2001) obtained good prediction results that
gave RMSE = 12.44 and 16.85 and MAE = 9.46 and 13.15 for model training and
testing respectively.
According to their simulation result, the out-of-10% error-band prediction
patterns for the testing data is 2.2%. It was claimed that the fuzzy model generated
gave good prediction and generalization capability.
6.8.1.2 Property Prediction for C-Mn-Nb Steels
In another experiment of Chen et al. (2001), for property prediction for C-Mn-Nb
steels, more than 600 measured data, including the previously used 358 C-Mn data,
were used to build the fuzzy model. Three hundred and fifteen data were selected
for training and the remaining 314 data were used for testing. Using their proposed
fuzzy modelling approach, six out of 15 variables were selected as the inputs (C,
Si, Mn, N, Nb, D -1/2 ) with tensile stress as output. A six-rule fuzzy model was
developed after structure identification and parameter training. The property
prediction resulted in RMSE = 15.48 and 19.74 and MAE = 12.11 and 14.46 for
training and testing, respectively. Furthermore, the out-of-10% error-band patterns
for the testing data were found to be only 3%.
6.8.2 Correction of Pyrometer Reading
As a second engineering application, we describe here the prediction capability of
a self-constructing neural-fuzzy inference network (SONFIN) proposed by Lai
and Lin (1999) for pyrometer reading correction in wafer temperature
measurement, based on emissivity changes. The motivation for this was that,