Modified Harmony Methods for Slope Stability Problems - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 151

scatter point-NHS1
mean-NHS1
scatter point-NHS2
mean-NHS2

1.6

1.5

1.4

1.3

1.2

0 10 20 30 40 50

number of series of parameters

Fig. 9. Summary of the results for 50 series of parameters

NHS1
OHS
NHS2

30000

2

NHS1
OHS
NHS2

25000

1.8

20000

1.6

15000

1.4

10000

1.2

5000

1 0

20 30 40 50 60 20 30 40 50 60

number of slices number of slices

Fig. 10. Comparison of safety factor and NEOF for different number of control variables

If we assume the number of slice is equal to 20 (21 control variables) and four lev-
els are set for three parameters ( HMCR, PAR, λ ), we obtain orthogonal results given
in Table 2 (note that the parameter λ is not used in NHS2, so the number of total pa-
rameters is equal to 2).
Four levels for HMCR are (0.85, 0.9, 0.95, 1.0); (0.1, 0.15, 0.2, 0.25) for PAR ; and
(0.3, 0.4, 0.5, 0.6) for . The sensitivity of each parameter can be obtained through

16 tests. If the F value (Factorial Analysis of Variance [22]) of one parameter is larger
than the critical value F 0.05 and is smaller than F 0.01 , it implies that the calculated re-
sult is sensitive to this parameter. Otherwise, if the F value is smaller than F 0.05 , it
shows that the result is insensitive to this parameter. If the F value is larger than F 0.01 ,
the result is hyper-sensitive to this parameter.
For NHS1, from the result in the t 5 column in Table 2, the F values of the three
parameters can be obtained as 0.78, 0.90 and 0.92, while F 0.05 = 4.8 and F 0.01 = 9.8. It
can be concluded that the three parameters are insensitive to the analysis. Similarly,
the F values of the two parameters ( HMCR, PAR ) used in NHS2 can be calculated as
0.47 and 0.59, compared with the standard value F 0.05 = 3.9 and F 0.01 = 7.0 (different

λ