解析１の結果 - materialsintegration/optimization_by_sipmi GitHub Wiki

解析１の条件のうち、以下を除いた項目での結果を記す。

JMatProで力学特性を計算してみる。
最適化は、bayes推定により大局解をもとめ、それをDakotaの初期値として使用した。
Dakotaの最適化は制約付き最小化共役勾配最適化法(conmin_frcg)を使用した。

計算の結果

最終結果

解析1の一番良い結果を以下の表に示す。

平衡種別	Al	Ti	BTR	γ’の体積率
オルソ平衡	3.53641000	3.4635900000	2.3227100000e+02	0.334620
パラ平衡	4.02475400	2.975246	2.2386500000e+02	0.339880

３候補

BTRが最小の時のパラメータを３つ選択する。

平衡種別	Al	Ti	BTR	γ’体積率
オルソ平衡１	3.53641000	3.46359000	232.271000	0.334620
オルソ平衡２	3.53638539	3.46361461	232.272000	0.334620
オルソ平衡３	3.52585126	3.47414874	232.431000	0.334470
パラ平衡１	4.02475373	2.97524627	223.865000	0.339880
パラ平衡２	3.99500154	3.00499846	224.184000	0.339640
パラ平衡３	4.00686439	2.99313561	224.243000	0.339740

詳細

計算結果の抜粋を記す。

オルソ平衡の場合

bayes部分の最適化（最大を目指すので、-1.0倍してあります）

|   iter    |  target   |    ti     |
-------------------------------------
|  1        | -235.0    |  3.112    |
|  2        | -235.8    |  3.284    |
|  3        | -235.3    |  3.098    |
|  4        | -238.3    |  3.184    |
|  5        | -236.1    |  3.337    |
|  6        | -237.1    |  3.035    |
|  7        | -236.8    |  3.409    |
|  8        | -233.3    |  3.54     |
|  9        | -233.0    |  3.522    |
|  10       | -232.8    |  3.497    |
|  11       | -232.5    |  3.477    |
|  12       | -232.3    |  3.464    |
|  13       | -232.3    |  3.454    |

Dakotaの記録

 ITER =    3     OBJ =   0.23227E+03     NO CHANGE IN OBJ

     DECISION VARIABLES (X-VECTOR)
       1)    0.34636E+01
1



    FINAL OPTIMIZATION INFORMATION

     OBJ =   0.232271E+03

     DECISION VARIABLES (X-VECTOR)
       1)    0.34636E+01

     THERE ARE    0 ACTIVE SIDE CONSTRAINTS

     TERMINATION CRITERION
          ABS(1-OBJ(I-1)/OBJ(I)) LESS THAN DELFUN FOR  3 ITERATIONS
          ABS(OBJ(I)-OBJ(I-1))   LESS THAN DABFUN FOR  3 ITERATIONS

     NUMBER OF ITERATIONS =    3

     OBJECTIVE FUNCTION WAS EVALUATED           10  TIMES

     GRADIENT OF OBJECTIVE WAS CALCULATED        3  TIMES
<<<<< Function evaluation summary: 16 total (9 new, 7 duplicate)
<<<<< Best parameters          =
                      3.4635900000e+00 wt_ti
<<<<< Best objective function  =
                      2.3227100000e+02
<<<<< Best data captured at function evaluation 1


<<<<< Iterator conmin_frcg completed.
<<<<< Environment execution completed.
DAKOTA execution time in seconds:
  Total CPU        =       0.03 [parent =   0.030753, child =  -0.000753]
  Total wall clock =    3130.64

bayseとdakotaの最適化の記録

Al = 3.88805011 / Ti = 3.11194989 diff = 234.981000 gamma prime Volume fruction = 0.338670
Al = 3.71552080 / Ti = 3.28447920 diff = 235.779000 gamma prime Volume fruction = 0.336870
Al = 3.90222296 / Ti = 3.09777704 diff = 235.300000 gamma prime Volume fruction = 0.338810
Al = 3.81598984 / Ti = 3.18401016 diff = 238.329000 gamma prime Volume fruction = 0.337960
Al = 3.66273899 / Ti = 3.33726101 diff = 236.097000 gamma prime Volume fruction = 0.336250
Al = 3.96513545 / Ti = 3.03486455 diff = 237.053000 gamma prime Volume fruction = 0.339380
Al = 3.59144967 / Ti = 3.40855033 diff = 236.835000 gamma prime Volume fruction = 0.335350
Al = 3.46000000 / Ti = 3.54000000 diff = 233.328000 gamma prime Volume fruction = 0.333530
Al = 3.47783574 / Ti = 3.52216426 diff = 233.009000 gamma prime Volume fruction = 0.333790
Al = 3.50260624 / Ti = 3.49739376 diff = 232.750000 gamma prime Volume fruction = 0.334150
Al = 3.52296814 / Ti = 3.47703186 diff = 232.531000 gamma prime Volume fruction = 0.334430
Al = 3.53641010 / Ti = 3.46358990 diff = 232.271000 gamma prime Volume fruction = 0.334620
Al = 3.54648103 / Ti = 3.45351897 diff = 232.272000 gamma prime Volume fruction = 0.334760
Al = 3.53641000 / Ti = 3.46359000 diff = 232.271000 gamma prime Volume fruction = 0.334620
Al = 3.50177410 / Ti = 3.49822590 diff = 232.750000 gamma prime Volume fruction = 0.334140
Al = 3.57104590 / Ti = 3.42895410 diff = 236.894000 gamma prime Volume fruction = 0.335090
Al = 3.46000000 / Ti = 3.54000000 diff = 233.328000 gamma prime Volume fruction = 0.333530
Al = 3.50538029 / Ti = 3.49461971 diff = 232.691000 gamma prime Volume fruction = 0.334190
Al = 3.52585126 / Ti = 3.47414874 diff = 232.431000 gamma prime Volume fruction = 0.334470
Al = 3.53602173 / Ti = 3.46397827 diff = 232.431000 gamma prime Volume fruction = 0.334610
Al = 3.53638539 / Ti = 3.46361461 diff = 232.272000 gamma prime Volume fruction = 0.334620
Al = 3.53640286 / Ti = 3.46359714 diff = 232.272000 gamma prime Volume fruction = 0.334620

パラ平衡の場合

bayesの最適化（最大を目指すので、-1.0倍してある。）

|   iter    |  target   |    ti     |
-------------------------------------
|  1        | -230.4    |  3.056    |
|  2        | -227.7    |  3.475    |
|  3        | -229.9    |  3.085    |
|  4        | -226.7    |  3.41     |
|  5        | -225.9    |  3.341    |
|  6        | -230.1    |  3.271    |
|  7        | -226.3    |  3.369    |
|  8        | -226.0    |  3.352    |
|  9        | -225.2    |  2.9      |
|  10       | -224.9    |  2.929    |
|  11       | -224.7    |  2.955    |
|  12       | -223.9    |  2.975    |
|  13       | -224.3    |  2.99     |

Dakotaの記録

     ITER =    3     OBJ =   0.22387E+03     NO CHANGE IN OBJ

     DECISION VARIABLES (X-VECTOR)
       1)    0.29752E+01
1



    FINAL OPTIMIZATION INFORMATION

     OBJ =   0.223865E+03

     DECISION VARIABLES (X-VECTOR)
       1)    0.29752E+01

     THERE ARE    0 ACTIVE SIDE CONSTRAINTS

     TERMINATION CRITERION
          ABS(1-OBJ(I-1)/OBJ(I)) LESS THAN DELFUN FOR  3 ITERATIONS
          ABS(OBJ(I)-OBJ(I-1))   LESS THAN DABFUN FOR  3 ITERATIONS

     NUMBER OF ITERATIONS =    3

     OBJECTIVE FUNCTION WAS EVALUATED           10  TIMES

     GRADIENT OF OBJECTIVE WAS CALCULATED        3  TIMES
<<<<< Function evaluation summary: 16 total (14 new, 2 duplicate)
<<<<< Best parameters          =
                      2.9752460000e+00 wt_ti
<<<<< Best objective function  =
                      2.2386500000e+02
<<<<< Best data not found in evaluation cache


<<<<< Iterator conmin_frcg completed.
<<<<< Environment execution completed.
DAKOTA execution time in seconds:
  Total CPU        =       0.05 [parent =   0.036387, child =   0.013613]
  Total wall clock =    4618.72

bayseとdakotaの最適化の記録

Al = 3.94407019 / Ti = 3.05592981 / btr = 230.441000 / gamma prime Volume fruction = 0.339190
Al = 3.52542661 / Ti = 3.47457339 / btr = 227.691000 / gamma prime Volume fruction = 0.334470
Al = 3.91486419 / Ti = 3.08513581 / btr = 229.922000 / gamma prime Volume fruction = 0.338920
Al = 3.58997254 / Ti = 3.41002746 / btr = 226.734000 / gamma prime Volume fruction = 0.335330
Al = 3.65888810 / Ti = 3.34111190 / btr = 225.938000 / gamma prime Volume fruction = 0.336200
Al = 3.72949950 / Ti = 3.27050050 / btr = 230.141000 / gamma prime Volume fruction = 0.337030
Al = 3.63148476 / Ti = 3.36851524 / btr = 226.256000 / gamma prime Volume fruction = 0.335860
Al = 3.64774545 / Ti = 3.35225455 / btr = 226.038000 / gamma prime Volume fruction = 0.336060
Al = 4.10000000 / Ti = 2.90000000 / btr = 225.240000 / gamma prime Volume fruction = 0.340480
Al = 4.07144237 / Ti = 2.92855763 / btr = 224.922000 / gamma prime Volume fruction = 0.340260
Al = 4.04471161 / Ti = 2.95528839 / btr = 224.662000 / gamma prime Volume fruction = 0.340050
Al = 4.02475373 / Ti = 2.97524627 / btr = 223.865000 / gamma prime Volume fruction = 0.339880
Al = 4.00992889 / Ti = 2.99007111 / btr = 224.343000 / gamma prime Volume fruction = 0.339760
Al = 4.02475400 / Ti = 2.97524600 / btr = 223.865000 / gamma prime Volume fruction = 0.339880
Al = 3.99500154 / Ti = 3.00499846 / btr = 224.184000 / gamma prime Volume fruction = 0.339640
Al = 4.05450646 / Ti = 2.94549354 / btr = 224.762000 / gamma prime Volume fruction = 0.340130
Al = 3.72722940 / Ti = 3.27277060 / btr = 230.140000 / gamma prime Volume fruction = 0.337000
Al = 3.97784478 / Ti = 3.02215522 / btr = 226.415000 / gamma prime Volume fruction = 0.339490
Al = 4.02167808 / Ti = 2.97832192 / btr = 224.503000 / gamma prime Volume fruction = 0.339860
Al = 3.87599170 / Ti = 3.12400830 / btr = 228.428000 / gamma prime Volume fruction = 0.338560
Al = 4.00686439 / Ti = 2.99313561 / btr = 224.243000 / gamma prime Volume fruction = 0.339740
Al = 4.02217011 / Ti = 2.97782989 / btr = 224.503000 / gamma prime Volume fruction = 0.339860
Al = 3.99500154 / Ti = 3.00499846 / btr = 224.184000 / gamma prime Volume fruction = 0.339640
Al = 4.05450646 / Ti = 2.94549354 / btr = 224.762000 / gamma prime Volume fruction = 0.340130
Al = 4.02244932 / Ti = 2.97755068 / btr = 224.503000 / gamma prime Volume fruction = 0.339870
Al = 4.02471494 / Ti = 2.97528506 / btr = 223.866000 / gamma prime Volume fruction = 0.339880
Al = 4.02474869 / Ti = 2.97525131 / btr = 224.503000 / gamma prime Volume fruction = 0.339880