Information Technology Reference
In-Depth Information
The step width for the DoS values has been set to 0.1 for each cycle. The step
width for the terms has been set to 5% in the first cycle, which was increased by 5%
in later cycles. The maximum and average deviations were observed after completion
of each cycle. The cycle, for which the deviation values are less, was selected as the
final FLM. The process was run for both weekday and weekend models. After the
training phase, the MBFs and the DoS values were determined as shown in Table 4
and Figure 5. It can be seen from the Figure 5 that the initial 85
th
percentile speed
terms were set uniformly over the variable's range [Figure 5(a)]. The base value for
high 85th percentile speed is 77.9 km/hr (indicated by black arrow). The training al-
gorithm examines the effect of introducing a pre-specified shift to the term's base
value (+5% in this case). If the base shift results in a reduction in the deviation, a new
base is identified [71.5 in this case as shown with black arrow in Figure 5(b) for
weekday model].
Fig. 5.
Membership function of '85
th
percentile speed' (a) before and (b) after neuro-fuzzy
training
4
Model Validation and Result Analysis
After completing the training phase, the 85
th
percentile speeds were estimated (for
both weekday and weekend) with the same set of input data which were used to de-
velop the models. As the notion of fuzzy sets are completely non statistical in nature
[23], the residual values (Figure 6) were used to compare both weekday and weekend
