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利用結合糾偏百分位思想的Bootstrap方法對疲勞分散系數(shù)進行置信區(qū)間分析的可信性已經(jīng)在上節(jié)中得到了驗證，下面對文獻[1]中選取的GC4、30CrMnSiNi2A鋼合金的5種狀態(tài)共140個試件的疲勞壽命試驗數(shù)據(jù)和LY12、LC4、LC9鋁合金的10種狀態(tài)共295個試件的疲勞壽命試驗數(shù)據(jù)進行疲勞分散系數(shù)置信區(qū)間分析。為了研究使用載荷譜中的高中低載荷對試驗數(shù)據(jù)標準差及疲勞分散系數(shù)的影響，文獻[1]在數(shù)據(jù)處理時，每組標準差
數(shù)據(jù)除
和
的試驗數(shù)據(jù)單獨統(tǒng)計外，其他二者間的試驗數(shù)據(jù)按
各數(shù)據(jù)取平均值。由于置信區(qū)間不能像點估計那樣取平均值，因此表9 4和表9 5中列出了不同應力水平下的標準差
的置信區(qū)間的詳細結果。
表9 4 140個鋼合金試件的標準差
和疲勞分散系數(shù)
置信區(qū)間計算表
|
材料 |
|
試件
個數(shù) |
原始樣本
Si估計值 |
原始樣本
Lf估計值 |
S糾偏Boot
置信區(qū)間 |
Lf糾偏Boot
置信區(qū)間 |
||
|
GC-4 |
~0.60 |
6 |
0.0941 |
|
2.1 |
[0.0390, 0.1278] |
|
[1.4, 2.8] |
|
Kt=1 |
~0.45 |
9 |
0.2504 |
7.2 |
12.5 |
[0.1455, 0.3417] |
[3.2, 15.0] |
|
|
11 |
0.3691 |
18.0 |
[0.2591, 0.4576] |
[7.6, 35.9] |
||||
|
R=-1 |
~0.30 |
10 |
0.3673 |
|
18.0 |
[0.3233, 0.4200] |
|
[12.7, 27.2] |
|
30CrMnSiNi2A |
~0.60 |
4 |
0.1148 |
|
2.6 |
[0.0313, 0.1482] |
|
[1.3, 3.5] |
|
Kt=2.9 |
~0.45 |
4 |
0.1069 |
2.5 |
2.3 |
[0.0448, 0.1348] |
[1.5, 3.1] |
|
|
5 |
0.0920 |
2.1 |
[0.0789, 0.1029] |
[1.9, 2.3] |
||||
|
R=0.1 |
~0.30 |
6 |
0.1485 |
|
3.3 |
[0.0971, 0.1946] |
|
[2.2, 4.9] |
|
材*2 |
~0.60 |
3 |
0.0224 |
|
1.2 |
[0.0229, 0.0256] |
|
[1.2, 1.2] |
|
Kt=2.9 |
~0.45 |
3 |
0.0460 |
1.5 |
3.2 |
[0.0385, 0.0508] |
[1.4, 1.6] |
|
|
6 |
0.2028 |
5.2 |
[0.1365, 0.3001] |
[3.0, 11.5] |
||||
|
6 |
0.1358 |
3.0 |
[0.1153, 0.1729] |
[2.6, 4.1] |
||||
|
R=0.5 |
~0.30 |
4 |
0.1332 |
|
3.1 |
[0.0083, 0.1564] |
|
[1.1, 3.7] |
|
材*2 |
~0.60 |
3 |
0.0643 |
|
1.7 |
[0.0630, 0.0655] |
|
[1.7, 1.8] |
|
Kt=4.1 |
~0.45 |
4 |
0.1172 |
2.7 |
2.4 |
[0.0261, 0.1482] |
[1.2, 3.5] |
|
|
3 |
0.0838 |
2.1 |
[0.0575, 0.0962] |
[1.6, 2.3] |
||||
|
4 |
0.1065 |
2.4 |
[0.0417, 0.1372] |
[1.4, 3.2] |
||||
|
R=0.5 |
~0.30 |
4 |
0.1981 |
|
5.3 |
[0.1096, 0.2607] |
|
[2.5, 9.0] |
|
材*2 |
~0.60 |
6 |
0.0487 |
|
1.5 |
[0.0140, 0.0665] |
|
[1.1, 1.7] |
|
Kt=3 |
~0.45 |
11 |
0.1113 |
2.4 |
2.2 |
[0.0353, 0.1448] |
[1.3, 3.1] |
|
|
10 |
0.1041 |
2.3 |
[0.0743, 0.1407] |
[1.8, 3.0] |
|
|||
|
6 |
0.0766 |
1.9 |
[0.0491, 0.0993] |
[1.5, 2.2] |
|
|||
|
R=0.445 |
~0.30 |
12 |
0.1359 |
|
2.9 |
[0.0942, 0.1972] |
|
[2.1, 4.6] |
|
平均 |
~0.60 |
|
|
|
1.8 |
|
|
|
|
~0.45 |
|
|
|
4.5 |
|
|
|
|
|
~0.30 |
|
|
|
6.5 |
|
|
|
|
|
|
|
140 |
23.3 |
|
|
|
|
|
表9 5 295個鋁合金試件的標準差
和疲勞分散系數(shù)
置信區(qū)間計算表
|
材料 |
|
試件
個數(shù) |
原始樣本
Si估計值 |
原始樣本
Lf估計值 |
Si糾偏Boot
置信區(qū)間 |
Lf糾偏Boot
置信區(qū)間 |
||
|
LY12CZ |
~0.60 |
11 |
0.1362 |
|
2.9 |
[0.1030, 0.1788] |
|
[2.2, 4.1] |
|
Kt=1 |
~0.45 |
10 |
0.1475 |
3.2 |
2.9 |
[0.0836, 0.2098] |
[1.9, 5.2] |
|
|
12 |
0.1157 |
2.5 |
[0.0769, 0.1635] |
[1.8, 3.6] |
||||
|
R=0.02 |
~0.30 |
11 |
0.2089 |
|
5.1 |
[0.1567, 0.2801] |
|
[3.4, 8.9] |
|
LY12B |
~0.60 |
3 |
0.0329 |
|
1.3 |
[0.0233, 0.0376] |
|
[1.2, 1.4] |
|
Kt=3 |
~0.45 |
4 |
0.1418 |
|
3.4 |
[0.0204, 0.1733] |
|
[1.2, 4.3] |
|
R=0.1 |
~0.30 |
7 |
0.1893 |
|
4.6 |
[0.1365, 0.2540] |
|
[3.0, 7.7] |
|
LY12B |
~0.60 |
3 |
0.0320 |
|
1.3 |
[0.0114, 0.0359] |
|
[1.1, 1.4] |
|
Kt=1 |
~0.45 |
5 |
0.0523 |
1.5 |
1.9 |
[0.0444, 0.0632] |
[1.4, 1.7] |
|
|
3 |
0.0956 |
2.3 |
[0.0252, 0.1057] |
[1.2, 2.5] |
||||
|
R=0.5 |
~0.30 |
3 |
0.2391 |
|
7.9 |
[0.2060, 0.2622] |
|
[5.9, 9.6] |
|
LY12B |
~0.60 |
7 |
0.0717 |
|
1.8 |
[0.0617, 0.0863] |
|
[1.6, 2.0] |
|
Kt=5 |
~0.45 |
7 |
0.0942 |
|
2.1 |
[0.0745, 0.1222] |
|
[1.8, 2.7] |
|
R=0.5 |
~0.30 |
8 |
0.2003 |
|
4.9 |
[0.1530, 0.2728] |
|
[3.4, 8.8] |
|
LY12B |
~0.60 |
8 |
0.0659 |
|
1.7 |
[0.0485, 0.0812] |
|
[1.5, 1.9] |
|
Kt=3 |
~0.45 |
10 |
0.0810 |
|
1.9 |
[0.0555, 0.1063] |
|
[1.5, 2.3] |
|
R=0.1人工 |
~0.30 |
14 |
0.3447 |
|
14.3 |
[0.2753, 0.4381] |
|
[8.4, 29.5] |
|
LY12CZ |
~0.60 |
10 |
0.0579 |
|
1.6 |
[0.0456, 0.0737] |
|
[1.4, 1.8] |
|
Kt=1 |
~0.45 |
10 |
0.1259 |
2.7 |
2.8 |
[0.0888, 0.1645] |
[2.0, 3.6] |
|
|
10 |
0.1373 |
2.9 |
[0.1169, 0.1644] |
[2.5, 3.6] |
||||
|
|
~0.30 |
10 |
0.2406 |
|
6.6 |
[0.1954, 0.2954] |
|
[4.7, 10.2] |
|
LY12CZ |
~0.60 |
10 |
0.0630 |
|
1.6 |
[0.0465, 0.0815] |
|
[1.4, 1.9] |
|
Kt=2.5 |
~0.45 |
10 |
0.1147 |
2.5 |
2.4 |
[0.0862, 0.1469] |
[2.0, 3.2] |
|
|
10 |
0.0916 |
2.1 |
[0.0561, 0.1218] |
[1.6, 2.6] |
|
|||
|
10 |
0.1241 |
2.7 |
[0.0817, 0.1717] |
[1.9, 3.9] |
|
|||
|
|
~0.30 |
10 |
0.1784 |
|
4.1 |
[0.0660, 0.2630] |
|
[1.7, 7.9] |
|
LC9 |
~0.60 |
5 |
0.0544 |
|
1.6 |
[0.0403, 0.0684] |
|
[1.4, 1.8] |
|
Kt=1 |
~0.45 |
5 |
0.0411 |
|
1.4 |
[0.0290, 0.0579] |
|
[1.3, 1.6] |
|
R=0.1 |
~0.30 |
7 |
0.1373 |
|
3.0 |
[0.0933, 0.1818] |
|
[2.1, 4.3] |
|
LC4 |
~0.60 |
5 |
0.0537 |
|
1.6 |
[0.0402, 0.0675] |
|
[1.4, 1.7] |
|
Kt=1 |
~0.45 |
6 |
0.0364 |
1.3 |
2.0 |
[0.0212, 0.0521] |
[1.2, 1.5] |
|
|
6 |
0.0520 |
1.5 |
[0.0312, 0.0698] |
[1.3, 1.8] |
||||
|
5 |
0.1524 |
3.5 |
[0.1015, 0.2323] |
[2.3, 6.8] |
||||
|
4 |
0.0836 |
2.0 |
[0.0797, 0.0952] |
[2.0, 2.2] |
||||
|
4 |
0.0844 |
2.0 |
[0.0409, 0.1035] |
[1.4, 2.4] |
||||
|
4 |
0.0587 |
1.6 |
[0.0275, 0.0716] |
[1.3, 1.8] |
||||
|
|
~0.30 |
4 |
0.1169 |
|
2.7 |
[0.0167, 0.1443] |
|
[1.2, 3.4] |
|
LC4 |
~0.60 |
3 |
0.0707 |
|
1.8 |
[0.0456, 0.0815] |
|
[1.5, 2.0] |
|
Kt=1 |
~0.45 |
3 |
0.0596 |
1.7 |
2.3 |
[0.0596, 0.0596] |
[1.7, 1.7] |
|
|
4 |
0.1091 |
2.5 |
[0.0270, 0.1329] |
[1.3, 3.1] |
||||
|
3 |
0.0708 |
1.8 |
[0.0620, 0.0771] |
[1.7, 1.9] |
||||
|
5 |
0.1457 |
3.3 |
[0.0611, 0.1998] |
[1.7, 5.2] |
||||
|
|
~0.30 |
6 |
0.1252 |
|
2.8 |
[0.0684, 0.1653] |
|
[1.7, 3.8] |
|
平均 |
~0.60 |
|
|
|
1.7 |
|
|
|
|
~0.45 |
|
|
|
2.3 |
|
|
|
|
|
~0.30 |
|
|
|
5.6 |
|
|
|
|
|
|
|
295 |
43 |
|
|
|
|
|
由表9 4和表9 5的結果可以看出，載荷高低對疲勞分散系數(shù)置信上下限有影響。采用文中所述的方法得到的疲勞分散系數(shù)的置信區(qū)間隨載荷高低的變化規(guī)律同文獻[1]相同，即在其它條件不變的情況下，疲勞分散系數(shù)隨應力的提高而降低。這進一步說明采用本文方法對疲勞分散系數(shù)進行置信區(qū)間分析的思路是可行的，也是更可信的。而且通過該方法所得的分散系數(shù)的置信上限來估算飛機的安全疲勞壽命能夠得到更偏安全的結果，更適用于工程應用。
本章針對疲勞壽命小子樣統(tǒng)計分析問題，首先采用Bootstrap方法模擬母體標準差的抽樣分布，然后結合糾偏的百分位法估算母體標準差的置信區(qū)間，進而對疲勞分散系數(shù)進行置信區(qū)間分析。通過對140個鋼合金試件和295個鋁合金試件的疲勞試驗數(shù)據(jù)進行疲勞分散系數(shù)置信區(qū)間分析發(fā)現(xiàn)，疲勞分散系數(shù)置信限隨應力的提高而降低，由疲勞安全壽命分散系數(shù)置信上限可以得到更偏安全的飛機安全疲勞壽命。為疲勞壽命試驗數(shù)據(jù)的工程應用提供了依據(jù)，同時也探索了一種試驗數(shù)據(jù)分析的參考方法。
公司地址：廣東省東莞市寮步鎮(zhèn)嶺安街2號
