基于贝叶斯神经网络的金属材料P-S-N曲线估计

doi:10.12141/j.issn.1000-565X.220649

摘要/Abstract

摘要：

疲劳破坏是机械结构的主要失效形式，而依据试验数据获取高精度的S-N曲线，是开展机械结构疲劳寿命预测的前提。但疲劳试验数据往往展示出较大的分散性，采用概率疲劳寿命（P-S-N）曲线进行应力循环关系的描述更为恰当。为了克服现有经典机器学习模型在材料疲劳数据分析中仅能给出疲劳寿命的确定值而无法定量其分散性的局限性，文中提出了一种基于贝叶斯神经网络（BNN）模型的金属材料P-S-N曲线估计方法。首先将传统神经网络模型的权重参数视为随机变量，采用贝叶斯参数估计方法，根据训练样本对权重参数的后验分布进行估计；然后，考虑到已有后验分布估计方法容易低估权重参数的不确定性程度，文中引入了一种基于α散度的黑盒（BB-α）算法，对权重参数进行后验估计；最后，采用BNN模型对2524-T3铝合金、2024-T4铝合金和S420MC钢的疲劳数据进行了分析。结果表明：BNN可以作为一个有效、稳健的模型，用于疲劳数据的拟合和不确定性量化；基于BB-α算法的BNN模型，可以更加准确地给出疲劳数据的不确定性量化结果。

关键词: 贝叶斯神经网络, 疲劳数据预测, P-S-N曲线, 不确定性分析

Abstract:

Fatigue failure is the main failure mode of mechanical structure, and the premise of the fatigue life prediction on mechanical structure is to obtain S-N curves of high precision based on test data. However, the fatigue test data often show large dispersion, so it is more appropriate to use probabilistic fatigue life curve (P-S-N) to describe the stress cycle relationship. To overcomes the limitations of the existing classical machine learning model which can only give the determined value of fatigue life but cannot quantify its dispersion in the analysis of material fatigue data, this study proposed a P-S-N curve estimation method for metal materials based on Bayesian neural network (BNN) model. Firstly, the weight parameters of the traditional neural network model were regarded as random variables, and the posterior distribution of the weight parameters was estimated by the BNN model according to the training samples. Then, considering that the existing posterior distribution estimation methods are easy to underestimate the uncertainty of weight parameters, this paper introduced a black-box alpha (BB-α) algorithm based on α divergence to estimate the posterior distribution of the weight parameters. Finally, the BNN model was used to analyze the fatigue data of 2524-T3 aluminum alloy, 2024-T4 aluminum alloy and S420MC steel. The results show that BNN can be used as an effective and robust model for fatigue data fitting and uncertainty quantification. Meanwhile, the BNN model based on BB-α algorithm can give a more accurate uncertainty quantification results of fatigue data.

Key words: Bayesian neural network, fatigue data prediction, P-S-N curve, uncertainty analysis

中图分类号:

O346.2

杨旭锋, 刘泽清, 张懿. 基于贝叶斯神经网络的金属材料P-S-N曲线估计[J]. 华南理工大学学报(自然科学版), 2023, 51(11): 82-92.

YANG Xufeng, LIU Zeqing, ZHANG Yi. Estimation of P-S-N Curve of Metal Materials Based on Bayesian Neural Network[J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(11): 82-92.

图/表 13

图1

表1

表2

2024-T4铝合金的疲劳寿命试验数据"

序号	N
序号	S=313.8 MPa	S=333.8 MPa	S=353.8 MPa	S=371.7 MPa	S=411.7 MPa	S=451.7 MPa	S=490.3 MPa	S=530.3 MPa	S=550.3 MPa
1	481 100	477 000	282 100	213 100	131 800	78 400	51 100	31 700	27 200
2	628 100	517 600	284 200	218 900	133 900	79 200	53 200	32 400	27 600
3	1 355 700	562 600	291 400	222 500	136 700	79 800	53 500	33 200	28 900
4	1 428 000	587 800	311 700	234 000	137 100	82 300	54 200	33 700	29 300
5	2 407 100	658 900	315 900	241 500	139 300	85 800	55 000	35 500	29 900
6	2 489 300	710 700	317 600	246 800	140 100	86 000	57 000	35 700	30 100
7	3 963 400	763 200	331 300	248 600	140 400	86 600	57 000	35 900	30 600
8	3 969 900	785 000	335 300	251 200	145 700	88 100	57 200	36 000	30 700
9	4 301 900	875 200	391 600	251 300	145 900	88 500	57 700	36 500	30 800
10	5 896 300	984 900	405 900	252 700	146 000	88 700	58 400	36 800	30 900
11	6 092 200	1 039 500	411 500	255 600	146 900	89 300	58 500	37 000	30 900
12	6 684 500	1 166 800	418 800	261 600	148 600	90 300	59 200	37 000	31 000
13	8 618 400	1 283 600	445 000	261 600	148 600	90 800	59 300	37 200	31 200
14	8 961 900	1 359 800	447 700	262 400	148 800	92 200	59 800	37 500	31 200
15	9 695 300	1 614 900	455 100	262 900	149 400	92 500	59 800	37 500	31 700
16	9 716 800	1 699 600	457 800	265 300	152 500	93 200	60 900	37 600	31 800
17	10 296 100	1 704 300	457 900	265 700	153 600	93 400	61 400	37 600	31 900
18	12 000 000	1 851 200	472 200	268 700	154 200	93 700	61 400	37 900	32 100
19	12 000 000	2 087 100	501 100	274 000	155 000	94 100	61 600	38 200	32 400
20	12 000 000	2 177 800	533 600	280 500	155 800	95 300	62 500	38 600	32 400
21	12 000 000	2 305 800	587 200	282 100	156 200	95 500	62 900	39 400	34 900
22		2 469 600	594 800	284 800	156 700	95 600	63 000	39 600
23		2 628 900	647 900	287 900	157 100	96 300	63 100	40 300
24		2 746 800	670 900	289 300	159 200	96 600	63 300	40 500
25		3 386 300	708 900	306 200	160 900	96 700	63 400	40 700
26		3 399 800	739 600	310 100	161 000	99 200	63 600	40 800
27		3 555 900	880 600	323 600	163 900	99 500	63 900	40 900
28		4 336 400	927 800	326 200	164 300	107 500	66 700	41 000
29		4 915 400	933 500	340 200	168 400	107 700	67 700	41 300
30		5 291 200	1564 700	343 200	183 200	110 600	70 000	42 700

表2

表3

图2

图3

图4

图5

图6

图7

表4

图8

图9

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序号	lg N
序号	S=200 MPa	S=300 MPa	S=350 MPa	S=400 MPa
1	5.603	5.028	4.784	4.477
2	5.544	5.074	4.842	4.400
3	5.528	5.016	4.776	4.426
4	5.630	4.894	4.813	4.462
5	5.594	4.993	4.813	4.592
6	5.540	5.071	4.860	4.411
7	5.581	5.024	4.798	4.447
8	5.548	5.035	4.776	4.402
9	5.426	4.954	4.758	4.665
10	5.567	5.039	4.770	4.475
11	5.554	5.098	4.755	4.458
12	5.627	5.057	4.837	4.551
13	5.630	5.092	4.736	4.525
14	5.596	5.082	4.842	4.641
15	5.626	5.005	4.796

序号	S/MPa	N		S/MPa	N		S/MPa	N		S/MPa	N
1	204	946 200	18	229	690 600	35	248	698 500	52	271	313 000
2	207	1 851 500	19	229	730 500	36	250	313 700	53	271	346 100
3	210	1 281 700	20	229	1 009 600	37	250	256 900	54	286	61 600
4	211	1 215 000	21	229	1 555 800	38	250	238 800	55	286	119 400
5	214	628 100	22	229	1 358 000	39	250	323 500	56	286	81 600
6	214	1 307 600	23	229	1 447 200	40	250	213 700	57	286	132 000
7	214	1 316 000	24	232	488 400	41	250	389 000	58	286	130 000
8	214	1 410 600	25	232	380 500	42	267	199 400	59	286	104 300
9	214	851 900	26	232	567 000	43	267	194 000	60	286	97 400
10	214	1 566 600	27	232	701 800	44	267	224 800	61	286	175 600
11	214	959 900	28	232	553 000	45	268	120 800	62	286	136 500
12	214	1 159 400	29	232	630 000	46	268	139 800	63	295	136 800
13	219	1 095 800	30	248	286 700	47	268	159 100	64	295	129 900
14	219	1 499 200	31	248	376 900	48	268	187 100	65	295	151 400
15	221	1 926 800	32	248	488 300	49	268	219 600
16	224	1 999 500	33	248	650 100	50	268	238 600
17	224	997 600	34	248	585 900	51	271	259 500

方法	落入95%置信区间占比/%			训练时间/s
方法	算例1	算例2	算例3	算例1	算例2	算例3
MLE	93	91	89	0.016	0.078	0.016
BNN-BBP	95	74	71	422.940	613.600	591.870
PPgNN	93	95	97	19.480	87.390	21.080
BNN-BB-α	100	100	97	77.430	124.190	101.930