Model 1: TSK0-2MF (gbellmf × 2 per input) ===================================== Initial rules: 32 ANFIS info: Number of nodes: 92 Number of linear parameters: 32 Number of nonlinear parameters: 30 Total number of parameters: 62 Number of training data pairs: 902 Number of checking data pairs: 301 Number of fuzzy rules: 32 Start training ANFIS ... 1 4.25643 4.51914 2 4.22775 4.48492 3 4.1994 4.45216 4 4.17142 4.42081 Step size increases to 0.011000 after epoch 5. 5 4.14386 4.39082 6 4.11676 4.36215 7 4.08753 4.33208 8 4.05896 4.3035 Step size increases to 0.012100 after epoch 9. 9 4.0311 4.27637 10 4.004 4.25063 11 3.97511 4.22389 12 3.94724 4.19874 Step size increases to 0.013310 after epoch 13. 13 3.92044 4.17515 14 3.89473 4.15306 15 3.86777 4.13049 16 3.84221 4.10967 Step size increases to 0.014641 after epoch 17. 17 3.81806 4.09058 18 3.79532 4.0732 19 3.77194 4.05604 20 3.75022 4.04091 Step size increases to 0.016105 after epoch 21. 21 3.73013 4.0278 22 3.7116 4.0167 23 3.69293 4.00682 24 3.67596 3.99934 Step size increases to 0.017716 after epoch 25. 25 3.66054 3.99425 26 3.64656 3.99151 27 3.63269 3.99118 28 3.62021 3.99352 Step size increases to 0.019487 after epoch 29. 29 3.60898 3.99839 30 3.59883 4.00557 31 3.58878 4.01587 32 3.57974 4.02819 Step size increases to 0.021436 after epoch 33. 33 3.57161 4.04196 34 3.56429 4.05654 35 3.55707 4.07282 36 3.55066 4.08823 Step size increases to 0.023579 after epoch 37. 37 3.54498 4.10185 38 3.53995 4.1129 39 3.53508 4.12181 40 3.53083 4.12685 Step size increases to 0.025937 after epoch 41. 41 3.5271 4.12846 42 3.52381 4.12733 43 3.5206 4.12391 44 3.51772 4.11867 Step size increases to 0.028531 after epoch 45. 45 3.51509 4.11214 46 3.51267 4.10466 47 3.51021 4.09579 48 3.50794 4.08656 Step size increases to 0.031384 after epoch 49. 49 3.50585 4.07728 50 3.50391 4.06815 51 3.50193 4.05832 52 3.50009 4.04887 Step size increases to 0.034523 after epoch 53. 53 3.49836 4.03931 54 3.4968 4.03148 55 3.49646 4.01735 56 3.49577 4.01706 Step size increases to 0.037975 after epoch 57. 57 3.49528 4.00918 58 3.4945 4.01098 59 3.4945 4.0023 60 3.49332 4.00347 61 3.49319 3.99792 62 3.49216 3.99805 Step size increases to 0.041772 after epoch 63. 63 3.49194 3.99353 64 3.49123 3.99357 65 3.49167 3.98955 66 3.49062 3.98891 67 3.49093 3.98663 Step size decreases to 0.037595 after epoch 68. 68 3.48995 3.98598 69 3.49029 3.98279 70 3.4883 3.98284 71 3.48954 3.98056 Step size decreases to 0.033836 after epoch 72. 72 3.48769 3.98048 73 3.48891 3.97664 74 3.48635 3.97757 75 3.4881 3.97462 Step size decreases to 0.030452 after epoch 76. 76 3.48584 3.97574 77 3.48749 3.9711 78 3.48473 3.97298 79 3.4867 3.96937 Step size decreases to 0.027407 after epoch 80. 80 3.48431 3.97148 81 3.48615 3.96648 82 3.48339 3.96895 83 3.48544 3.96508 Step size decreases to 0.024666 after epoch 84. 84 3.48307 3.96771 85 3.48498 3.96281 86 3.48233 3.96547 87 3.48437 3.96168 Step size decreases to 0.022200 after epoch 88. 88 3.4821 3.96443 89 3.484 3.95987 90 3.48151 3.96249 91 3.4835 3.95894 Step size decreases to 0.019980 after epoch 92. 92 3.48135 3.96161 93 3.48319 3.95745 94 3.4809 3.95993 95 3.48275 3.95666 Step size decreases to 0.017982 after epoch 96. 96 3.48078 3.95917 97 3.48248 3.95537 98 3.48043 3.9577 99 3.48207 3.95468 Step size decreases to 0.016184 after epoch 100. 100 3.48033 3.95705 Designated epoch number reached. ANFIS training completed at epoch 100. Minimal training RMSE = 3.48033 Minimal checking RMSE = 3.95468 MSE : 16.9264 RMSE: 4.11417 R2 : 0.664677 NMSE: 0.335323 NDEI: 0.57907 Model 2: TSK0-3MF (gbellmf × 3 per input) ===================================== Initial rules: 243 ANFIS info: Number of nodes: 524 Number of linear parameters: 243 Number of nonlinear parameters: 45 Total number of parameters: 288 Number of training data pairs: 902 Number of checking data pairs: 301 Number of fuzzy rules: 243 Start training ANFIS ... 1 3.48949 6.18916 2 3.45915 6.06247 3 3.41872 5.91346 4 3.38236 5.73296 Step size increases to 0.011000 after epoch 5. 5 3.353 5.57846 6 3.32197 5.47698 7 3.28593 5.3751 8 3.2483 5.26731 Step size increases to 0.012100 after epoch 9. 9 3.20873 5.1596 10 3.16709 5.06056 11 3.11912 4.97062 12 3.07004 4.90448 Step size increases to 0.013310 after epoch 13. 13 3.02187 4.86429 14 2.97737 4.85458 15 2.93582 4.88936 16 2.90427 4.98087 Step size increases to 0.014641 after epoch 17. 17 2.88219 5.12211 18 2.86471 5.26311 19 2.84624 5.36588 20 2.82829 5.46658 Step size increases to 0.016105 after epoch 21. 21 2.81115 5.55392 22 2.79487 5.67287 23 2.77853 5.64686 24 2.76872 6.11556 25 2.77206 5.14558 26 2.75702 6.19896 27 2.7602 5.14994 Step size decreases to 0.014495 after epoch 28. 28 2.74638 6.24052 29 2.75098 5.11992 30 2.73409 6.17768 31 2.74283 5.10258 Step size decreases to 0.013045 after epoch 32. 32 2.72821 6.17703 33 2.73726 5.07044 34 2.7204 6.07671 35 2.73153 5.05552 Step size decreases to 0.011741 after epoch 36. 36 2.7168 6.06383 37 2.7272 5.03036 38 2.71115 5.95635 39 2.72224 5.02069 Step size decreases to 0.010567 after epoch 40. 40 2.70844 5.94394 41 2.71842 5.00057 42 2.70399 5.83984 43 2.71392 4.99542 Step size decreases to 0.009510 after epoch 44. 44 2.70177 5.83091 45 2.71053 4.9791 46 2.69812 5.73434 47 2.70652 4.97696 Step size decreases to 0.008559 after epoch 48. 48 2.69623 5.72879 49 2.70354 4.96362 50 2.69316 5.64101 51 2.70004 4.96338 Step size decreases to 0.007703 after epoch 52. 52 2.69153 5.63813 53 2.69744 4.95251 54 2.68891 5.55924 55 2.69442 4.9536 Step size decreases to 0.006933 after epoch 56. 56 2.68746 5.55841 57 2.69215 4.94479 58 2.6852 5.48794 59 2.68954 4.94684 Step size decreases to 0.006239 after epoch 60. 60 2.68391 5.48866 61 2.68755 4.93971 62 2.68193 5.42588 63 2.68528 4.94243 Step size decreases to 0.005616 after epoch 64. 64 2.68076 5.42767 65 2.68353 4.93659 66 2.67901 5.37175 67 2.68155 4.93972 Step size decreases to 0.005054 after epoch 68. 68 2.67793 5.37416 69 2.68 4.93481 70 2.67637 5.32424 71 2.67826 4.93813 Step size decreases to 0.004549 after epoch 72. 72 2.67537 5.32691 73 2.67687 4.93383 74 2.67396 5.28218 75 2.67533 4.93716 Step size decreases to 0.004094 after epoch 76. 76 2.67302 5.28479 77 2.67407 4.93317 78 2.67174 5.24452 79 2.6727 4.93637 Step size decreases to 0.003684 after epoch 80. 80 2.67084 5.24682 81 2.67156 4.93247 82 2.66967 5.21037 83 2.67031 4.93543 Step size decreases to 0.003316 after epoch 84. 84 2.66881 5.21218 85 2.66927 4.93142 86 2.66772 5.17901 87 2.66813 4.93412 Step size decreases to 0.002984 after epoch 88. 88 2.66689 5.1802 89 2.66716 4.92983 90 2.66588 5.14986 91 2.66611 4.93226 Step size decreases to 0.002686 after epoch 92. 92 2.66507 5.15035 93 2.6652 4.92758 94 2.66412 5.12247 95 2.66422 4.92977 Step size decreases to 0.002417 after epoch 96. 96 2.66333 5.1222 97 2.66335 4.92461 98 2.66244 5.09648 99 2.66243 4.92661 100 2.66165 5.09539 Designated epoch number reached. ANFIS training completed at epoch 100. Minimal training RMSE = 2.66165 Minimal checking RMSE = 4.85458 MSE : 17.1406 RMSE: 4.14012 R2 : 0.660434 NMSE: 0.339566 NDEI: 0.582723 Model 3: TSK1-2MF (gbellmf × 2 per input) ===================================== Initial rules: 32 ANFIS info: Number of nodes: 92 Number of linear parameters: 192 Number of nonlinear parameters: 30 Total number of parameters: 222 Number of training data pairs: 902 Number of checking data pairs: 301 Number of fuzzy rules: 32 Start training ANFIS ... 1 2.85009 4.69235 2 2.83691 4.61659 3 2.82381 4.5385 4 2.81077 4.45873 Step size increases to 0.011000 after epoch 5. 5 2.79775 4.37785 6 2.78474 4.29631 7 2.7704 4.2064 8 2.756 4.11658 Step size increases to 0.012100 after epoch 9. 9 2.7415 4.02712 10 2.72683 3.93818 11 2.71042 3.84107 12 2.69361 3.74462 Step size increases to 0.013310 after epoch 13. 13 2.67624 3.64883 14 2.65807 3.5539 15 2.63684 3.45151 16 2.6138 3.35379 Step size increases to 0.014641 after epoch 17. 17 2.5883 3.2663 18 2.55954 3.19899 19 2.52297 3.16663 20 2.47983 3.20424 Step size increases to 0.016105 after epoch 21. 21 2.42917 3.3412 22 2.37416 3.59905 23 2.34422 3.89625 24 2.36179 3.60671 25 2.33613 3.94345 26 2.3545 3.59925 Step size decreases to 0.014495 after epoch 27. 27 2.32932 3.98109 28 2.34864 3.58976 29 2.31899 4.00715 30 2.34073 3.59264 Step size decreases to 0.013045 after epoch 31. 31 2.3134 4.05635 32 2.33536 3.58825 33 2.30527 4.05997 34 2.32785 3.59718 Step size decreases to 0.011741 after epoch 35. 35 2.30083 4.10646 36 2.32309 3.59599 37 2.29443 4.0886 38 2.31615 3.60889 Step size decreases to 0.010567 after epoch 39. 39 2.29086 4.12772 40 2.31186 3.61014 41 2.2857 4.09768 42 2.30547 3.62593 Step size decreases to 0.009510 after epoch 43. 43 2.28273 4.13163 44 2.30157 3.62894 45 2.27844 4.09721 46 2.29579 3.64627 Step size decreases to 0.008559 after epoch 47. 47 2.27589 4.1275 48 2.29224 3.65042 49 2.27223 4.09275 50 2.2871 3.6682 Step size decreases to 0.007703 after epoch 51. 51 2.27 4.11992 52 2.28389 3.67307 53 2.26682 4.08658 54 2.27936 3.69061 Step size decreases to 0.006933 after epoch 55. 55 2.26483 4.11089 56 2.27645 3.6959 57 2.26204 4.07957 58 2.27247 3.7128 Step size decreases to 0.006239 after epoch 59. 59 2.26024 4.10119 60 2.26983 3.71823 61 2.25776 4.07206 62 2.26633 3.73423 Step size decreases to 0.005616 after epoch 63. 63 2.25611 4.09117 64 2.26395 3.73959 65 2.25389 4.06416 66 2.26087 3.75453 Step size decreases to 0.005054 after epoch 67. 67 2.25236 4.08094 68 2.25871 3.75961 69 2.25036 4.0559 70 2.25599 3.77339 Step size decreases to 0.004549 after epoch 71. 71 2.24893 4.07052 72 2.25403 3.77802 73 2.24711 4.04729 74 2.25162 3.7906 Step size decreases to 0.004094 after epoch 75. 75 2.24576 4.05991 76 2.24983 3.79463 77 2.24409 4.03828 78 2.24767 3.806 Step size decreases to 0.003684 after epoch 79. 79 2.2428 4.04906 80 2.24604 3.80931 81 2.24127 4.02885 82 2.2441 3.81953 Step size decreases to 0.003316 after epoch 83. 83 2.24002 4.03794 84 2.2426 3.82204 85 2.2386 4.019 86 2.24084 3.83118 Step size decreases to 0.002984 after epoch 87. 87 2.2374 4.02654 88 2.23945 3.83283 89 2.23608 4.00874 90 2.23783 3.84101 Step size decreases to 0.002686 after epoch 91. 91 2.23491 4.01486 92 2.23654 3.84179 93 2.23367 3.99812 94 2.23504 3.84916 Step size decreases to 0.002417 after epoch 95. 95 2.23253 4.00297 96 2.23383 3.84907 97 2.23136 3.98724 98 2.23243 3.8558 Step size decreases to 0.002176 after epoch 99. 99 2.23025 3.99091 100 2.23128 3.85487 Designated epoch number reached. ANFIS training completed at epoch 100. Minimal training RMSE = 2.23025 Minimal checking RMSE = 3.16663 MSE : 12.8953 RMSE: 3.591 R2 : 0.744537 NMSE: 0.255463 NDEI: 0.505433 Model 4: TSK1-3MF (gbellmf × 3 per input) ===================================== Initial rules: 243 ANFIS info: Number of nodes: 524 Number of linear parameters: 1458 Number of nonlinear parameters: 45 Total number of parameters: 1503 Number of training data pairs: 902 Number of checking data pairs: 301 Number of fuzzy rules: 243 Warning: Number of training data is smaller than number of modifiable parameters. > In anfis>trainFIS (line 203) In anfis>anfisWithOptionObject (line 109) In anfis (line 68) In scenario1 (line 66) Start training ANFIS ... 1 2.18266 13.9384 2 2.16266 14.302 3 2.14218 14.771 4 2.12092 15.3612 Step size increases to 0.011000 after epoch 5. 5 2.0985 16.0849 6 2.07446 16.9408 7 2.04563 17.9967 8 2.01387 19.1103 Step size increases to 0.012100 after epoch 9. 9 1.97901 20.1856 10 1.94113 21.1309 11 1.89631 21.9439 12 1.84864 22.4876 Step size increases to 0.013310 after epoch 13. 13 1.79858 22.7812 14 1.74656 22.8849 15 1.68767 22.8664 16 1.62771 22.7684 Step size increases to 0.014641 after epoch 17. 17 1.56748 22.5829 18 1.50801 22.2279 19 1.44544 21.5009 20 1.38899 20.2966 Step size increases to 0.016105 after epoch 21. 21 1.34211 18.5912 22 1.30602 16.488 23 1.27558 14.1361 24 1.25531 13.5366 Step size increases to 0.017716 after epoch 25. 25 1.22833 11.9472 26 1.20732 11.145 27 1.17735 9.2776 28 1.15854 8.56663 Step size increases to 0.019487 after epoch 29. 29 1.12679 6.41978 30 1.12503 6.60586 31 1.09297 4.9284 32 1.10129 5.326 33 1.06957 4.68211 34 1.08124 4.74092 Step size decreases to 0.017538 after epoch 35. 35 1.05297 4.99736 36 1.0659 4.73721 37 1.03553 5.54205 38 1.04981 5.0522 Step size decreases to 0.015785 after epoch 39. 39 1.02529 6.28831 40 1.03688 5.44902 41 1.009 7.02564 42 1.02048 5.91912 Step size decreases to 0.014206 after epoch 43. 43 0.998267 8.03611 44 1.00675 6.31568 45 0.981053 8.87018 46 0.992248 6.70868 Step size decreases to 0.012786 after epoch 47. 47 0.973147 9.9055 48 0.983062 6.97916 49 0.958957 10.505 50 0.973683 7.26996 Step size decreases to 0.011507 after epoch 51. 51 0.954367 11.3465 52 0.967501 7.4856 53 0.942356 11.7345 54 0.960308 7.75761 Step size decreases to 0.010356 after epoch 55. 55 0.939278 12.4896 56 0.955315 7.97285 57 0.928728 12.7622 58 0.948976 8.26813 Step size decreases to 0.009321 after epoch 59. 59 0.926441 13.4981 60 0.944515 8.50717 61 0.91711 13.7127 62 0.938576 8.84703 Step size decreases to 0.008389 after epoch 63. 63 0.915346 14.4517 64 0.934437 9.12183 65 0.907143 14.6391 66 0.928786 9.51736 Step size decreases to 0.007550 after epoch 67. 67 0.905787 15.3775 68 0.924938 9.83222 69 0.898656 15.5517 70 0.919613 10.2861 Step size decreases to 0.006795 after epoch 71. 71 0.89764 16.2705 72 0.916096 10.6381 73 0.891518 16.4343 74 0.911178 11.1444 Step size decreases to 0.006115 after epoch 75. 75 0.890784 17.1082 76 0.908033 11.5239 77 0.885587 17.2586 78 0.903579 12.0686 Step size decreases to 0.005504 after epoch 79. 79 0.885076 17.8654 80 0.90081 12.4607 81 0.8807 17.9986 82 0.896814 13.0247 Step size decreases to 0.004953 after epoch 83. 83 0.880351 18.5253 84 0.894379 13.4131 85 0.876676 18.6391 86 0.890789 13.9761 Step size decreases to 0.004458 after epoch 87. 87 0.876438 19.0838 88 0.888624 14.3467 89 0.873343 19.1782 90 0.885379 14.8903 Step size decreases to 0.004012 after epoch 91. 91 0.873172 19.5467 92 0.883427 15.2336 93 0.870543 19.6236 94 0.880489 15.7433 Step size decreases to 0.003611 after epoch 95. 95 0.870406 19.9261 96 0.878716 16.0547 97 0.868147 19.9882 98 0.876081 16.5202 Step size decreases to 0.003250 after epoch 99. 99 0.868021 20.2362 100 0.874473 16.7991 Designated epoch number reached. ANFIS training completed at epoch 100. Minimal training RMSE = 0.868021 Minimal checking RMSE = 4.68211 MSE : 30.4753 RMSE: 5.52045 R2 : 0.396266 NMSE: 0.603734 NDEI: 0.777003 Metrics Model_1 Model_2 Model_3 Model_4 _______ _______ _______ _______ _______ MSE 16.926 17.141 12.895 30.475 RMSE 4.1142 4.1401 3.591 5.5204 R2 0.66468 0.66043 0.74454 0.39627 NMSE 0.33532 0.33957 0.25546 0.60373 NDEI 0.57907 0.58272 0.50543 0.777