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金属学报  2017, Vol. 53 Issue (2): 248-256    DOI: 10.11900/0412.1961.2016.00218
  本期目录 | 过刊浏览 |
基于遗传算法优化的SMABP神经网络本构模型
余滨杉1,王社良1(),杨涛1,樊禹江2
1 西安建筑科技大学土木工程学院 西安 710055
2 长安大学建筑学院 西安 710061
BP Neural Netwok Constitutive Model Based on Optimization with Genetic Algorithm for SMA
Binshan YU1,Sheliang WANG1(),Tao YANG1,Yujiang FAN2
1 School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China
2 School of Architecture, Chang'an University, Xi'an 710061, China
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摘要: 

系统研究了形状记忆合金丝(SMA)应力-应变曲线、特征点应力、耗能能力及等效阻尼比随材料直径、应变幅值、加载速率、加载循环次数的变化规律;由于SMA唯象Brinson等常见本构模型无法以数学模型方式精确描述SMA各影响因素对其力学性能的影响程度,基于SMA实验结果,本工作采用BP神经网络智能算法(一种利用误差反向传播训练的神经网络算法)对其进行非线性建模,同时利用遗传算法对神经元的初始权值和阈值进行优化,进而获得了一种基于遗传算法优化的SMA BP神经网络本构模型。利用该模型对SMA实验结果进行模拟,所得结果平均误差仅为1.13%,优于未优化的SMA BP神经网络模型。结果表明,基于遗传算法优化的SMA BP神经网络本构模型,能够精确地预测SMA在反复荷载作用下的超弹性性能,避免由于初始权/阈值取值不当引起的BP网络振荡而产生不收敛的问题,同时也充分考虑了加/卸载速率的动态影响,是一种良好的速率相关型动力本构模型。

关键词 形状记忆合金(SMA)遗传算法BP神经网络动力本构模型    
Abstract

Systematic study was conducted on the variation regularity of stress-strain curve, feature point stress, dissipated energy and equivalent damping ratio of shape memory alloy (SMA) wires changed with wire diameter, strain amplitude, loading rate and loading cyclic number. By nonlinearly modeling experimental results for SMA using the neural network intelligent algorithm (a neural network algorithm with back-propagation training) and optimizing the initial weight and threshold value of neurons using genetic algorithm, a new BP neural network constitutive model for SMA optimized with genetic algorithm is established. This model successfully overcomes the shortcomings of other mathematical models such as the phenomenological Brinson, by which the various influence factors to mechanical properties in an experiment for SMA are hardly simulated exactly. In fact, the average error between experimental and simulated results is only 1.13% by using this model, much better than conventional BP neural network models. The results show that the BP neural networks constitutive model optimized with genetic algorithm can not only predict accurately the superelastic performance of SMA under cyclic loading, but also avoid the no convergence problem caused by concussion of BP network due to the improper initial weight and threshold value set up. Furthermore, this model would be a better model than others because of fully considering the dynamic influence of loading/unloading rate on SMA experiments.

Key wordsSMA    genetic algorithm    BP neural network    dynamic constitutive model
收稿日期: 2016-06-06      出版日期: 2016-11-16
基金资助:国家自然科学基金项目No.51678480, 陕西省科技统筹创新计划项目No.2013SZS01-S02及陕西省工业攻关项目No.2014K06-34

引用本文:

余滨杉,王社良,杨涛,樊禹江. 基于遗传算法优化的SMABP神经网络本构模型[J]. 金属学报, 2017, 53(2): 248-256.
Binshan YU,Sheliang WANG,Tao YANG,Yujiang FAN. BP Neural Netwok Constitutive Model Based on Optimization with Genetic Algorithm for SMA. Acta Metall, 2017, 53(2): 248-256.

链接本文:

http://www.ams.org.cn/CN/10.11900/0412.1961.2016.00218      或      http://www.ams.org.cn/CN/Y2017/V53/I2/248

Test No. Diameter
mm
Loading rate mmmin-1 Strain amplitude
%
1 0.5 10 3
2 0.5 10 6
3 0.5 10 8
4 0.5 30 3
5 0.5 30 6
6 0.5 30 8
7 0.5 60 3
8 0.5 60 6
9 0.5 60 8
10 0.5 90 3
11 0.5 90 6
12 0.5 90 8
13~24 0.8 Same as the conditions with diameter 0.5 mm
25~36 1.0
37~48 1.2
表1  SMA丝超弹性性能实验工况
图1  四折线SMA简化本构曲线及特征点
图2  材料直径对SMA丝应力-应变性能的影响
Diameter / mm σa / MPa σb / MPa σc / MPa σd / MPa ΔW / (MJm-3) ξ / %
0.5 483.83 585.69 331.04 203.72 12.43 6.49
0.8 447.62 527.20 358.10 139.26 12.22 6.01
1.0 420.17 502.93 331.94 118.23 10.52 5.34
1.2 349.26 464.20 247.57 70.74 9.63 5.00
表2  材料直径对应的SMA丝力学性能
图3  应变幅值对SMA丝应力-应变的影响
Strain amplitude / % σa / MPa σb / MPa σc / MPa σd / MPa ΔW / (MJm-3) ξ / %
3 426.90 496.56 260.65 120.96 4.46 4.18
6 420.17 509.30 254.65 101.86 12.70 6.09
8 432.90 515.66 254.65 70.03 20.76 6.60
表3  不同应变幅值对应的SMA丝力学性能
图4  加载速率对SMA丝应力-应变的影响
Loading rate mmmin-1 σa / MPa σb / MPa σc / MPa σd / MPa ΔW / (MJm-3) ξ / %
10 420.17 509.30 254.65 101.86 12.70 6.09
30 426.54 515.36 280.11 107.59 12.31 6.25
60 420.17 502.93 326.04 109.86 11.93 6.15
90 420.17 502.93 331.94 118.23 10.52 5.34
表4  不同加载速率对应的SMA丝力学性能
图5  加载/卸载循环次数对SMA丝力学性能的影响
n / cyc σa / MPa σb / MPa σc / MPa σd / MPa ΔW / (MJm-3) ξ / %
1 604.79 604.79 273.75 178.25 6.843 6.11
2 560.23 572.96 254.65 171.89 6.190 5.81
3 541.13 560.23 241.92 171.89 5.796 5.44
5 515.66 541.13 241.92 165.52 5.481 5.18
10 483.83 509.30 222.82 159.15 5.035 4.76
15 440.73 496.56 222.82 159.15 4.769 4.48
20 439.27 483.83 216.45 152.79 4.603 4.37
25 432.90 477.46 216.45 152.79 4.461 4.18
30 432.90 477.46 216.45 152.79 4.438 4.16
表5  不同加载/卸载循环次数对应的SMA丝力学性能
图6  遗传算法优化BP网络流程图
图7  奥氏体SMA本构的BP网络拓扑结构
图8  BP网络本构模型拓扑结构
图9  训练过程
图10  遗传算法目标函数随代数的变化
图11  未优化的BP网络本构曲线与实验曲线比较
图12  不同加载速率下SMA实验曲线与优化前后BP网络预测曲线的比较
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