Appendix A
The hysteresis curves corresponding to some other SSI systems when subjected to the NS component of the ground acceleration of the 1940 El Centro earthquake are presented here to further illustrate the effects of Fsv.
Figure A1.
Hysteresis curves of SSI systems with T = 0.5, R1 = 2, R2 = 0.01, S = 1, k = 300.
Figure A1.
Hysteresis curves of SSI systems with T = 0.5, R1 = 2, R2 = 0.01, S = 1, k = 300.
Figure A2.
Hysteresis curves of SSI systems with T = 0.5, R1 = 1, R2 = 0.2, S = 2, k = 300.
Figure A2.
Hysteresis curves of SSI systems with T = 0.5, R1 = 1, R2 = 0.2, S = 2, k = 300.
Figure A3.
Hysteresis curves of SSI systems with T = 0.5, R1 = 1, R2 = 0.2, S = 2, k = 300.
Figure A3.
Hysteresis curves of SSI systems with T = 0.5, R1 = 1, R2 = 0.2, S = 2, k = 300.
Table A1.
The parameters of the predictive formulae of Rf for S = 1, Fsv = 2.
Table A1.
The parameters of the predictive formulae of Rf for S = 1, Fsv = 2.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.150 | 0.650 | 0.349 | 1.168 | 1.145 | 1.183 | 1.144 | 1.103 |
b | −1.026 | −0.716 | −0.549 | −0.678 | −0.511 | −1.054 | −0.503 | −0.334 |
R2 | 0.986 | 0.979 | 0.995 | 0.978 | 0.975 | 0.979 | 0.974 | 0.973 |
RMSE | 0.036 | 0.026 | 0.006 | 0.047 | 0.045 | 0.048 | 0.045 | 0.037 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.136 | 0.379 | 0.215 | 1.153 | 1.148 | 1.179 | 1.138 | 1.095 |
b | −1.658 | −1.000 | −0.853 | −0.889 | −0.649 | −1.076 | −0.598 | −0.392 |
R2 | 0.977 | 0.992 | 0.940 | 0.989 | 0.983 | 0.989 | 0.984 | 0.986 |
RMSE | 0.043 | 0.009 | 0.014 | 0.034 | 0.040 | 0.034 | 0.038 | 0.028 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.112 | 0.278 | 0.149 | 1.146 | 1.152 | 1.169 | 1.121 | 1.087 |
b | −1.995 | −1.111 | −0.935 | −0.999 | −0.755 | −1.209 | −0.629 | −0.413 |
R2 | 0.956 | 0.993 | 0.972 | 0.992 | 0.986 | 0.993 | 0.989 | 0.989 |
RMSE | 0.056 | 0.006 | 0.007 | 0.028 | 0.038 | 0.028 | 0.031 | 0.025 |
Table A2.
The parameters of the predictive formulae of Rf for S = 1, Fsv = 3.
Table A2.
The parameters of the predictive formulae of Rf for S = 1, Fsv = 3.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.146 | 0.566 | 0.276 | 1.178 | 1.141 | 1.195 | 1.156 | 1.121 |
b | −1.246 | −0.918 | −0.689 | −0.687 | −0.501 | −0.859 | −0.458 | −0.302 |
R2 | 0.984 | 0.998 | 0.980 | 0.975 | 0.952 | 0.995 | 0.955 | 0.937 |
RMSE | 0.038 | 0.007 | 0.010 | 0.050 | 0.063 | 0.053 | 0.059 | 0.055 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.103 | 0.290 | 0.143 | 1.193 | 1.123 | 1.202 | 1.149 | 1.112 |
b | −1.887 | −1.134 | −0.917 | −0.897 | −0.714 | −1.064 | −0.534 | −0.356 |
R2 | 0.942 | 0.996 | 0.957 | 0.977 | 0.975 | 0.981 | 0.972 | 0.972 |
RMSE | 0.065 | 0.005 | 0.008 | 0.052 | 0.049 | 0.047 | 0.049 | 0.039 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.092 | 0.161 | 0.090 | 1.196 | 1.068 | 1.200 | 1.139 | 1.109 |
b | −2.256 | −1.013 | −0.816 | −1.022 | −0.816 | −1.134 | −0.560 | −0.384 |
R2 | 0.909 | 0.974 | 0.819 | 0.977 | 0.972 | 0.983 | 0.977 | 0.973 |
RMSE | 0.077 | 0.007 | 0.012 | 0.052 | 0.051 | 0.044 | 0.044 | 0.039 |
Table A3.
The parameters of the predictive formulae of Rf for S = 1, Fsv = 5.
Table A3.
The parameters of the predictive formulae of Rf for S = 1, Fsv = 5.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.131 | 0.329 | 0.160 | 1.118 | 0.900 | 1.208 | 1.157 | 1.107 |
b | −1.548 | −0.921 | −0.718 | −0.747 | −0.499 | −0.904 | −0.418 | −0.254 |
R2 | 0.967 | 0.986 | 0.954 | 0.968 | 0.946 | 0.971 | 0.949 | 0.943 |
RMSE | 0.052 | 0.011 | 0.009 | 0.056 | 0.052 | 0.059 | 0.061 | 0.046 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.087 | 0.162 | 0.066 | 1.181 | 0.675 | 1.219 | 1.170 | 1.119 |
b | −2.225 | −1.125 | −0.806 | −1.025 | −0.607 | −1.045 | −0.479 | −0.323 |
R2 | 0.886 | 0.988 | 0.936 | 0.987 | 0.964 | 0.971 | 0.948 | 0.953 |
RMSE | 0.088 | 0.005 | 0.005 | 0.037 | 0.034 | 0.060 | 0.066 | 0.049 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.065 | 0.106 | 0.042 | 1.085 | 0.616 | 1.226 | 1.174 | 1.125 |
b | −2.599 | −1.102 | −0.630 | −1.134 | −0.730 | −1.093 | −0.525 | −0.364 |
R2 | 0.861 | 0.928 | 0.611 | 0.985 | 0.934 | 0.968 | 0.953 | 0.958 |
RMSE | 0.091 | 0.008 | 0.009 | 0.037 | 0.045 | 0.064 | 0.065 | 0.050 |
Table A4.
The parameters of the predictive formulae of Rf for S = 1, Fsv = 10.
Table A4.
The parameters of the predictive formulae of Rf for S = 1, Fsv = 10.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.066 | 0.175 | 0.074 | 0.959 | 0.570 | 1.199 | 1.114 | 1.097 |
b | −1.965 | −0.991 | −0.734 | −0.785 | −0.391 | −0.931 | −0.387 | −0.275 |
R2 | 0.906 | 0.989 | 0.907 | 0.970 | 0.840 | 0.975 | 0.935 | 0.977 |
RMSE | 0.080 | 0.005 | 0.006 | 0.047 | 0.055 | 0.054 | 0.064 | 0.030 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 0.992 | 0.067 | 0.027 | 1.007 | 0.511 | 1.202 | 1.092 | 1.000 |
b | −2.672 | −0.950 | −0.601 | −1.109 | −0.594 | −1.066 | −0.501 | −0.388 |
R2 | 0.824 | 0.952 | 0.778 | 0.994 | 0.909 | 0.980 | 0.946 | 0.956 |
RMSE | 0.096 | 0.004 | 0.004 | 0.022 | 0.042 | 0.049 | 0.064 | 0.046 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 0.962 | 0.069 | 0.015 | 0.780 | 0.402 | 1.174 | 1.152 | 0.929 |
b | −2.993 | −1.340 | −0.367 | −1.003 | −0.619 | −1.113 | −0.609 | −0.454 |
R2 | 0.812 | 0.701 | 0.121 | 0.967 | 0.918 | 0.980 | 0.956 | 0.954 |
RMSE | 0.093 | 0.012 | 0.009 | 0.040 | 0.031 | 0.047 | 0.064 | 0.048 |
Table A5.
The parameters of the predictive formulae of Rf for S = 2, Fsv = 2.
Table A5.
The parameters of the predictive formulae of Rf for S = 2, Fsv = 2.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.141 | 0.982 | 0.704 | 1.121 | 1.102 | 1.140 | 1.102 | 1.074 |
b | −0.533 | −0.449 | −0.356 | −0.385 | −0.286 | −0.443 | −0.283 | −0.186 |
R2 | 0.979 | 0.977 | 0.963 | 0.969 | 0.960 | 0.972 | 0.960 | 0.951 |
RMSE | 0.038 | 0.035 | 0.028 | 0.043 | 0.041 | 0.044 | 0.041 | 0.033 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.153 | 0.719 | 0.325 | 1.150 | 1.109 | 1.180 | 1.119 | 1.077 |
b | −0.911 | −0.675 | −0.399 | −0.574 | −0.401 | −0.694 | −0.364 | −0.215 |
R2 | 0.984 | 0.990 | 0.964 | 0.972 | 0.963 | 0.974 | 0.966 | 0.969 |
RMSE | 0.039 | 0.019 | 0.014 | 0.050 | 0.048 | 0.052 | 0.044 | 0.029 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.153 | 0.564 | 0.259 | 1.154 | 1.098 | 1.190 | 1.123 | 1.081 |
b | −1.138 | −0.769 | −0.530 | −0.667 | −0.464 | −0.799 | −0.397 | −0.230 |
R2 | 0.984 | 0.981 | 0.986 | 0.972 | 0.968 | 0.973 | 0.967 | 0.970 |
RMSE | 0.038 | 0.021 | 0.007 | 0.053 | 0.047 | 0.055 | 0.045 | 0.030 |
Table A6.
The parameters of the predictive formulae of Rf for S = 2, Fsv = 3.
Table A6.
The parameters of the predictive formulae of Rf for S = 2, Fsv = 3.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.148 | 0.882 | 0.491 | 1.130 | 1.093 | 1.154 | 1.116 | 1.074 |
b | −0.669 | −0.553 | −0.360 | −0.439 | −0.311 | −0.531 | −0.301 | −0.173 |
R2 | 0.984 | 0.992 | 0.949 | 0.974 | 0.949 | 0.974 | 0.949 | 0.942 |
RMSE | 0.036 | 0.020 | 0.024 | 0.042 | 0.049 | 0.047 | 0.048 | 0.034 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.148 | 0.586 | 0.249 | 1.146 | 1.071 | 1.192 | 1.128 | 1.084 |
b | −1.100 | −0.789 | −0.504 | −0.612 | −0.436 | −0.764 | −0.359 | −0.202 |
R2 | 0.982 | 0.983 | 0.982 | 0.971 | 0.965 | 0.973 | 0.954 | 0.953 |
RMSE | 0.040 | 0.021 | 0.008 | 0.051 | 0.047 | 0.055 | 0.051 | 0.035 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.141 | 0.423 | 0.209 | 1.145 | 1.006 | 1.202 | 1.130 | 1.084 |
b | −1.359 | −0.863 | −0.604 | −0.686 | −0.484 | −0.857 | −0.378 | −0.215 |
R2 | 0.974 | 0.985 | 0.946 | 0.972 | 0.961 | 0.973 | 0.957 | 0.954 |
RMSE | 0.047 | 0.014 | 0.013 | 0.053 | 0.049 | 0.057 | 0.052 | 0.035 |
Table A7.
The parameters of the predictive formulae of Rf for S = 2, Fsv = 5.
Table A7.
The parameters of the predictive formulae of Rf for S = 2, Fsv = 5.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.149 | 0.632 | 0.297 | 1.156 | 1.003 | 1.178 | 1.116 | 1.074 |
b | −0.865 | −0.604 | −0.386 | −0.517 | −0.342 | −0.644 | −0.301 | −0.173 |
R2 | 0.985 | 0.968 | 0.969 | 0.969 | 0.959 | 0.973 | 0.949 | 0.942 |
RMSE | 0.036 | 0.030 | 0.011 | 0.051 | 0.042 | 0.052 | 0.048 | 0.034 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.135 | 0.386 | 0.174 | 1.097 | 1.071 | 1.208 | 1.128 | 1.084 |
b | −1.375 | −0.878 | −0.654 | −0.653 | −0.436 | −0.841 | −0.359 | −0.202 |
R2 | 0.969 | 0.992 | 0.913 | 0.967 | 0.965 | 0.968 | 0.954 | 0.953 |
RMSE | 0.052 | 0.009 | 0.014 | 0.054 | 0.047 | 0.062 | 0.051 | 0.035 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.109 | 0.266 | 0.133 | 1.083 | 0.796 | 1.215 | 1.130 | 1.084 |
b | −1.649 | −0.897 | −0.768 | −0.743 | −0.485 | −0.924 | −0.378 | −0.215 |
R2 | 0.944 | 0.941 | 0.954 | 0.986 | 0.965 | 0.969 | 0.957 | 0.954 |
RMSE | 0.066 | 0.018 | 0.008 | 0.036 | 0.036 | 0.061 | 0.052 | 0.035 |
Table A8.
The parameters of the predictive formulae of Rf for S = 2, Fsv = 10.
Table A8.
The parameters of the predictive formulae of Rf for S = 2, Fsv = 10.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.124 | 0.421 | 0.224 | 1.058 | 0.868 | 1.189 | 1.127 | 1.079 |
b | −0.825 | −0.736 | −0.646 | −0.565 | −0.367 | −0.764 | −0.324 | −0.179 |
R2 | 0.987 | 0.984 | 0.955 | 0.968 | 0.947 | 0.973 | 0.939 | 0.934 |
RMSE | 0.033 | 0.015 | 0.012 | 0.049 | 0.043 | 0.054 | 0.056 | 0.038 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.076 | 0.209 | 0.085 | 1.025 | 0.674 | 1.199 | 1.115 | 1.082 |
b | −1.310 | −0.909 | −0.651 | −0.756 | −0.444 | −0.904 | −0.378 | −0.254 |
R2 | 0.970 | 0.983 | 0.937 | 0.970 | 0.940 | 0.974 | 0.954 | 0.950 |
RMSE | 0.049 | 0.008 | 0.006 | 0.049 | 0.039 | 0.055 | 0.052 | 0.041 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.034 | 0.139 | 0.055 | 0.984 | 0.546 | 1.195 | 1.135 | 1.042 |
b | −1.583 | −0.896 | −0.639 | −0.847 | −0.435 | −0.944 | −0.433 | −0.287 |
R2 | 0.944 | 0.935 | 0.839 | 0.989 | 0.955 | 0.981 | 0.944 | 0.965 |
RMSE | 0.062 | 0.010 | 0.007 | 0.028 | 0.027 | 0.047 | 0.063 | 0.036 |
Table A9.
The parameters of the predictive formulae of Rf for S = 3, Fsv = 2.
Table A9.
The parameters of the predictive formulae of Rf for S = 3, Fsv = 2.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.109 | 1.052 | 0.874 | 1.084 | 1.075 | 1.104 | 1.075 | 1.062 |
b | −0.329 | −0.302 | −0.247 | −0.262 | −0.208 | −0.287 | −0.208 | −0.152 |
R2 | 0.973 | 0.974 | 0.967 | 0.962 | 0.954 | 0.965 | 0.954 | 0.940 |
RMSE | 0.034 | 0.032 | 0.026 | 0.037 | 0.034 | 0.038 | 0.034 | 0.031 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.148 | 0.863 | 0.580 | 1.107 | 1.091 | 1.151 | 1.097 | 1.069 |
b | −0.624 | −0.481 | −0.367 | −0.434 | −0.314 | −0.509 | −0.303 | −0.185 |
R2 | 0.982 | 0.977 | 0.968 | 0.972 | 0.960 | 0.973 | 0.957 | 0.951 |
RMSE | 0.038 | 0.031 | 0.022 | 0.043 | 0.043 | 0.047 | 0.044 | 0.032 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.152 | 0.797 | 0.416 | 1.115 | 1.091 | 1.172 | 1.101 | 1.069 |
b | −0.792 | −0.623 | −0.392 | −0.517 | −0.368 | −0.623 | −0.337 | −0.199 |
R2 | 0.982 | 0.982 | 0.953 | 0.972 | 0.965 | 0.974 | 0.963 | 0.958 |
RMSE | 0.040 | 0.028 | 0.020 | 0.047 | 0.044 | 0.050 | 0.048 | 0.032 |
Table A10.
The parameters of the predictive formulae of Rf for S = 3, Fsv = 3.
Table A10.
The parameters of the predictive formulae of Rf for S = 3, Fsv = 3.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.126 | 0.991 | 0.773 | 1.105 | 1.088 | 1.123 | 1.090 | 1.066 |
b | −0.431 | −0.369 | −0.321 | −0.325 | −0.240 | −0.367 | −0.238 | −0.152 |
R2 | 0.978 | 0.956 | 0.980 | 0.961 | 0.956 | 0.970 | 0.951 | 0.934 |
RMSE | 0.036 | 0.045 | 0.021 | 0.044 | 0.038 | 0.041 | 0.040 | 0.033 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.149 | 0.754 | 0.412 | 1.130 | 1.081 | 1.166 | 1.115 | 1.073 |
b | −0.767 | −0.585 | −0.396 | −0.490 | −0.351 | −0.595 | −0.319 | −0.177 |
R2 | 0.984 | 0.990 | 0.966 | 0.973 | 0.953 | 0.974 | 0.947 | 0.939 |
RMSE | 0.038 | 0.019 | 0.017 | 0.045 | 0.049 | 0.049 | 0.051 | 0.035 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.150 | 0.669 | 0.294 | 1.129 | 1.073 | 1.185 | 1.121 | 1.071 |
b | −0.969 | −0.729 | −0.446 | −0.568 | −0.402 | −0.704 | −0.344 | −0.184 |
R2 | 0.984 | 0.990 | 0.983 | 0.972 | 0.957 | 0.972 | 0.944 | 0.950 |
RMSE | 0.038 | 0.018 | 0.009 | 0.049 | 0.050 | 0.053 | 0.055 | 0.033 |
Table A11.
The parameters of the predictive formulae of Rf for S = 3, Fsv = 5.
Table A11.
The parameters of the predictive formulae of Rf for S = 3, Fsv = 5.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.141 | 0.843 | 0.501 | 1.117 | 1.069 | 1.144 | 1.112 | 1.067 |
b | −0.584 | −0.463 | −0.322 | −0.393 | −0.284 | −0.477 | −0.271 | −0.148 |
R2 | 0.984 | 0.983 | 0.962 | 0.969 | 0.943 | 0.974 | 0.937 | 0.924 |
RMSE | 0.035 | 0.026 | 0.019 | 0.044 | 0.047 | 0.044 | 0.051 | 0.035 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.148 | 0.611 | 0.277 | 1.130 | 1.037 | 1.188 | 1.123 | 1.070 |
b | −0.987 | −0.716 | −0.475 | −0.558 | −0.382 | −0.705 | −0.322 | −0.167 |
R2 | 0.985 | 0.984 | 0.992 | 0.971 | 0.955 | 0.972 | 0.939 | 0.948 |
RMSE | 0.037 | 0.021 | 0.006 | 0.049 | 0.048 | 0.054 | 0.056 | 0.031 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.145 | 0.424 | 0.216 | 1.143 | 0.946 | 1.201 | 1.127 | 1.072 |
b | −1.224 | −0.732 | −0.568 | −0.633 | −0.430 | −0.798 | −0.346 | −0.179 |
R2 | 0.979 | 0.970 | 0.971 | 0.971 | 0.965 | 0.970 | 0.939 | 0.950 |
RMSE | 0.043 | 0.020 | 0.009 | 0.052 | 0.041 | 0.059 | 0.059 | 0.032 |
Table A12.
The parameters of the predictive formulae of Rf for S = 3, Fsv = 10.
Table A12.
The parameters of the predictive formulae of Rf for S = 3, Fsv = 10.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.124 | 0.656 | 0.308 | 1.134 | 1.009 | 1.157 | 1.124 | 1.063 |
b | −0.825 | −0.619 | −0.392 | −0.496 | −0.329 | −0.621 | −0.299 | −0.146 |
R2 | 0.987 | 0.992 | 0.968 | 0.966 | 0.959 | 0.977 | 0.935 | 0.942 |
RMSE | 0.033 | 0.016 | 0.012 | 0.051 | 0.041 | 0.047 | 0.056 | 0.029 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.076 | 0.397 | 0.180 | 1.085 | 0.892 | 1.184 | 1.127 | 1.061 |
b | −1.310 | −0.860 | −0.643 | −0.632 | −0.459 | −0.813 | −0.347 | −0.181 |
R2 | 0.970 | 0.993 | 0.985 | 0.971 | 0.967 | 0.971 | 0.951 | 0.972 |
RMSE | 0.049 | 0.009 | 0.006 | 0.050 | 0.038 | 0.057 | 0.052 | 0.024 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.034 | 0.264 | 0.120 | 1.057 | 0.767 | 1.181 | 1.132 | 1.063 |
b | −1.583 | −0.894 | −0.664 | −0.731 | −0.495 | −0.887 | −0.393 | −0.235 |
R2 | 0.944 | 0.988 | 0.924 | 0.974 | 0.929 | 0.977 | 0.954 | 0.973 |
RMSE | 0.062 | 0.008 | 0.006 | 0.047 | 0.050 | 0.051 | 0.054 | 0.028 |
Table A13.
The parameters of the predictive formulae of Rf for S = 4, Fsv = 2.
Table A13.
The parameters of the predictive formulae of Rf for S = 4, Fsv = 2.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.084 | 1.042 | 0.952 | 1.055 | 1.050 | 1.082 | 1.050 | 1.042 |
b | −0.219 | −0.203 | −0.188 | −0.185 | −0.157 | −0.201 | −0.157 | −0.123 |
R2 | 0.963 | 0.957 | 0.953 | 0.955 | 0.952 | 0.956 | 0.952 | 0.952 |
RMSE | 0.030 | 0.032 | 0.029 | 0.031 | 0.028 | 0.033 | 0.028 | 0.022 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.130 | 0.984 | 0.778 | 1.065 | 1.066 | 1.124 | 1.068 | 1.057 |
b | −0.456 | −0.395 | −0.335 | −0.332 | −0.251 | −0.385 | −0.252 | −0.167 |
R2 | 0.978 | 0.972 | 0.982 | 0.966 | 0.957 | 0.973 | 0.956 | 0.937 |
RMSE | 0.036 | 0.036 | 0.021 | 0.039 | 0.038 | 0.040 | 0.038 | 0.034 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.147 | 0.839 | 0.593 | 1.067 | 1.062 | 1.148 | 1.072 | 1.055 |
b | −0.604 | −0.458 | −0.363 | −0.415 | −0.301 | −0.494 | −0.292 | −0.177 |
R2 | 0.982 | 0.972 | 0.970 | 0.972 | 0.961 | 0.973 | 0.956 | 0.945 |
RMSE | 0.038 | 0.033 | 0.022 | 0.040 | 0.040 | 0.046 | 0.042 | 0.033 |
Table A14.
The parameters of the predictive formulae of Rf for S = 4, Fsv = 3.
Table A14.
The parameters of the predictive formulae of Rf for S = 4, Fsv = 3.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.103 | 1.044 | 0.856 | 1.077 | 1.065 | 1.102 | 1.065 | 1.055 |
b | −0.299 | −0.282 | −0.227 | −0.245 | −0.188 | −0.268 | −0.188 | −0.134 |
R2 | 0.970 | 0.966 | 0.965 | 0.958 | 0.952 | 0.961 | 0.952 | 0.936 |
RMSE | 0.033 | 0.035 | 0.025 | 0.037 | 0.032 | 0.038 | 0.032 | 0.029 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.143 | 0.838 | 0.570 | 1.088 | 1.077 | 1.144 | 1.090 | 1.064 |
b | −0.579 | −0.440 | −0.343 | −0.393 | −0.292 | −0.473 | −0.278 | −0.165 |
R2 | 0.983 | 0.966 | 0.959 | 0.969 | 0.958 | 0.974 | 0.949 | 0.929 |
RMSE | 0.036 | 0.036 | 0.024 | 0.042 | 0.042 | 0.044 | 0.045 | 0.036 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.148 | 0.753 | 0.425 | 1.097 | 1.076 | 1.163 | 1.098 | 1.062 |
b | −0.744 | −0.565 | −0.397 | −0.475 | −0.347 | −0.581 | −0.309 | −0.173 |
R2 | 0.984 | 0.986 | 0.976 | 0.974 | 0.948 | 0.975 | 0.946 | 0.943 |
RMSE | 0.037 | 0.022 | 0.015 | 0.043 | 0.051 | 0.048 | 0.050 | 0.033 |
Table A15.
The parameters of the predictive formulae of Rf for S = 4, Fsv = 5.
Table A15.
The parameters of the predictive formulae of Rf for S = 4, Fsv = 5.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.124 | 0.970 | 0.728 | 1.099 | 1.071 | 1.123 | 1.086 | 1.063 |
b | −0.423 | −0.369 | −0.314 | −0.318 | 0.230 | −0.365 | −0.231 | −0.141 |
R2 | 0.979 | 0.965 | 0.975 | 0.959 | 0.958 | 0.969 | 0.949 | 0.926 |
RMSE | 0.035 | 0.039 | 0.022 | 0.044 | 0.035 | 0.042 | 0.040 | 0.033 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.144 | 0.741 | 0.386 | 1.119 | 1.077 | 1.164 | 1.11 | 1.062 |
b | −0.756 | −0.591 | −0.387 | −0.478 | −0.342 | −0.588 | −0.300 | −0.158 |
R2 | 0.985 | 0.989 | 0.937 | 0.972 | 0.947 | 0.975 | 0.939 | 0.945 |
RMSE | 0.036 | 0.020 | 0.021 | 0.045 | 0.052 | 0.048 | 0.053 | 0.030 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.149 | 0.625 | 0.278 | 1.111 | 1.035 | 1.186 | 1.113 | 1.064 |
b | −0.959 | −0.716 | 0.447 | −0.550 | −0.390 | −0.694 | −0.319 | −0.170 |
R2 | 0.986 | 0.992 | 0.987 | 0.973 | 0.96 | 0.973 | 0.938 | 0.952 |
RMSE | 0.036 | 0.014 | 0.007 | 0.047 | 0.046 | 0.054 | 0.056 | 0.030 |
Table A16.
The parameters of the predictive formulae of Rf for S = 4, Fsv = 10.
Table A16.
The parameters of the predictive formulae of Rf for S = 4, Fsv = 10.
k = 100 |
---|
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.111 | 0.794 | 0.465 | 1.122 | 1.087 | 1.127 | 1.114 | 1.063 |
b | −0.620 | −0.503 | −0.372 | −0.416 | −0.316 | −0.503 | −0.277 | −0.144 |
R2 | 0.986 | 0.986 | 0.985 | 0.971 | 0.961 | 0.977 | 0.935 | 0.932 |
RMSE | 0.032 | 0.023 | 0.012 | 0.043 | 0.042 | 0.042 | 0.053 | 0.032 |
k = 300 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.062 | 0.794 | 0.241 | 1.128 | 1.006 | 1.154 | 1.124 | 1.068 |
b | −1.029 | −0.503 | −0.526 | −0.579 | −0.41 | −0.718 | −0.324 | −0.172 |
R2 | 0.977 | 0.986 | 0.950 | 0.968 | 0.963 | 0.974 | 0.934 | 0.945 |
RMSE | 0.042 | 0.023 | 0.013 | 0.053 | 0.044 | 0.051 | 0.059 | 0.033 |
k = 500 |
R1 | R1R2 ≤ 1 | 0.5 | 1 | 2 |
R2 | 3 | 6 | 3 | 6 | 1 | 3 | 6 |
a | 1.020 | 0.386 | 0.29 | 1.072 | 0.855 | 1.159 | 1.116 | 1.077 |
b | −1.249 | −0.794 | −1.044 | −0.652 | −0.439 | −0.802 | −0.344 | −0.201 |
R2 | 0.971 | 0.977 | 0.878 | 0.969 | 0.967 | 0.972 | 0.944 | 0.916 |
RMSE | 0.045 | 0.016 | 0.027 | 0.05 | 0.036 | 0.055 | 0.055 | 0.046 |