Modeling of Flight Delay State-Space Model - Advanced Research on Computer Education, Simulation and Modeling - page 30

∑

m

∑

m

Step3. Calculate the mixed delay time interval [a,b]: a= α a = α b ;

ii ii

i=1 i=1

Step4. On the test set, calculate the proportion of the values fall interval [a,b];

In the tests, two intervals were set as P=90, [p 1 ,p 2 ]=[0.05,0.95] and P=80,
[p 1 ,p 2 ]=[0.1,0.9]. Results from all four tests on these models are listed in Table 1. For
the case study, the normal mixture model with two components has the best fitness.

Table 1. Results of the model tests

P%

m

90% 80%

2 90.29% 85.32%

3 87.67% 79.48%

4 83.05% 75.33%

3.3 Performance Validation of the Genetic EM Algorithm

On the same stop criteria, log likelihood values produced in all iterations from the two
EM algorithms with m=3 were collected and shown in Fig. 3. It can be concluded
that, in each step, the genetic EM algorithm achieves better log likelihood value,
which represents higher effectiveness.

3870

3850

3830

3810

EM
Genetic EM

3790

3770

2000

500 1500

0 1000

Iteration Steps

Fig. 3. The log likelihood values of genetic EM and EM

4 Conclusions and Further Work

In this paper, we demonstrated the modeling process of flight delay state-space
model. The genetic EM algorithm was used to find the global optimal estimates of the
parameters in the normal mixture model. Case study shows that the model has an
excellent fit to the real data in both mixture density distribution calculation and the
probability interval tests. In conclusion, the traditional EM algorithm can be opti-
mized and become more efficient by introducing GA methods in finding the global
optimum. Most importantly, the flight delay state-space model proposed in this paper
would make it possible to apply the dynamic data-driven prediction into the air trans-
portation industry in the near future.