BP Neural Netwok Constitutive Model Based on Optimization with Genetic Algorithm for SMA

doi:10.11900/0412.1961.2016.00218

Acta Metall Sin

2017, Vol. 53

Issue (2): 248-256 DOI: 10.11900/0412.1961.2016.00218

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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

Cite this article:

Binshan YU,Sheliang WANG,Tao YANG,Yujiang FAN. BP Neural Netwok Constitutive Model Based on Optimization with Genetic Algorithm for SMA. Acta Metall Sin, 2017, 53(2): 248-256.

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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 words: SMA genetic algorithm BP neural network dynamic constitutive model

Received: 06 June 2016

Fund: Supported by Nation Natural Science Foundation of China (No.51678480), Co-ordinator Innovation Projects Foundation of Shaanxi Province (No.2013SZS01-S02), and Industry-Foundation Research Project of Shaanxi Province (No.2014K06-34)

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	Binshan YU
	Sheliang WANG
	Tao YANG
	Yujiang FAN

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https://www.ams.org.cn/EN/10.11900/0412.1961.2016.00218 OR https://www.ams.org.cn/EN/Y2017/V53/I2/248

Table 1 Test conditions used for measuring SMA superelastic properties

Fig.1 Simplified four-line constitutive curve and feature points (a, b, c, d—feature points; E, E^’— elastic modulus)

Fig.2 Effects of diameter on stress-strain curve of SMA wire

Table 2 Mechanical properties of SMA wire with different diameters

Fig.3 Effects of strain amplitude on stress-strain of SMA wire

Table 3 Mechanical properties of SMA wires with different strain amplitudes

Fig.4 Effects of loading rate on stress-strain of SMA wire

Table 4 Mechanical properties of SMA wires with different loading rates

Fig.5 Effects of loading/unloading cycle number n on mechanical properties
(a) stress-strain (b) feature point stress (c) dissipated energy ΔW (d) equivalent damping ratio ξ

Table 5 Mechanical property parameters of SMA wires with different loading/unloading cyclic numbers

Fig.6 Flow chart of BP network optimized by genetic algorithm

Fig.7 BP network topology for austenite SMA constitutive relationship

Fig.8 Topology of BP network constitutive model

Fig.9 Training process

Fig.10 Variation curves of objective function of genetic algorithm changed with hereditary algebra

Fig.11 Comparisons between test curves and BP network constitutive curves without optimization

Fig.12 Comparisons between SMA test curves and pre-optimized /post-optimized BP network predicted curves under the loading rates of 10 mm/min (a), 30 mm/min (b), 60 mm/min (c) and 90 mm/min (d)

[1]	Muller I.A model for a body with shape memory[J]. Arch. Rat. Mech. Anal., 1979, 70: 61
[2]	Ren W J.Seismic response control of structures using superelastic shape memory alloy wires[D] [D]. Dalian: Dalian University of Technology, 2008
[2]	(任文杰. 超弹性形状记忆合金丝对结构减震控制的研究 [D]. 大连: 大连理工大学, 2008)
[3]	Brinson L C.One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable[J]. J. Intell. Mater. Syst. Struct., 1993, 4: 229
[4]	Tanaka K, Sato Y.Phenomenological description of the mechanical behavior of shape memory alloys[J]. Trans. JSME, 1987, 53: 1368
[5]	Liang C.The constitutive modeling of shape memory alloys [D]. Virginia: Department of Mechanical Engineering,[D] Virginia Polytechnic Institute and State University, 1990
[6]	Peng X, Yang Y, Huang S.A comprehensive description for shape memory alloys with a two-phase constitutive model[J]. Int. J. Solids Struct., 2001, 38: 6925
[7]	Brocca M, Brinson L C, Ba?ant Z P.Three-dimensional constitutive model for shape memory alloys based on microplane model[J]. J. Mech. Phys. Solids, 2002, 50: 1051
[8]	Zhou B, Wang Z Q, Liang W Y.A micromechanical constitutive model of shape memory alloys[J]. Acta Metall. Sin., 2006, 42: 919
[8]	(周博, 王振清, 梁文彦. 形状记忆合金的细观力学本构模型[J]. 金属学报, 2006, 42: 919)
[9]	Wang Z Q, Zhou B, Liang W Y.The constitutive relationship of shape memory alloy[J]. Acta Metall. Sin., 2007, 43: 1211
[9]	(王振清, 周博, 梁文彦. 形状记忆合金的本构关系[J]. 金属学报, 2007, 43: 1211)
[10]	Qu D.Prediction of shape memory alloy recovery stress based on BP neural networks [D].[D] Chongqing: Chongqing Jiaotong University, 2010
[10]	(曲冬. 基于BP神经网络的形状记忆合金回复力预测研究 [D][D]. 重庆: 重庆交通大学, 2010)
[11]	Cui D, Li H N, Song G B.A constitutive model for superelasticity of shape memory alloy based on neural network[J]. J. Vib. Eng., 2006, 19: 109
[11]	(崔迪, 李宏男, 宋钢兵. 形状记忆合金超弹性本构关系的神经网络模型[J]. 振动工程学报, 2006, 19: 109)
[12]	Ren W J, Li H N, Song G B.A new constitutive model of superelastic shape memory alloy[J]. J. Dalian Univ. Technol., 2006, 46: S157
[12]	(任文杰, 李宏男, 宋刚兵. 一种新的超弹性形状记忆合金本构模型[J]. 大连理工大学学报, 2006, 46: S157)
[13]	Ren W J, Li H N, Wang L Q.Cyclic model for superelastic shape memory alloy based on neural network[J]. Rare Met. Mater. Eng., 2012, 41(S2): 243
[13]	(任文杰, 李宏男, 王利强. 基于神经网络的超弹性形状记忆合金循环本构模型[J]. 稀有金属材料与工程, 2012, 41(S2): 243)
[14]	Li S, Liu L J, Xie Y L.Chaotic prediction for short-term traffic flow of optimized BP neural network based on genetic algorithma[J]. Contl. Decis., 2011, 26: 1581
[14]	(李松, 刘力军, 解永乐. 遗传算法优化BP神经网络的短时交通流混沌预测[J]. 控制与决策, 2011, 26: 1581)
[15]	Li S.Identified deformation of shape memory alloys based on neural network [D].[D] Wuhan: Wuhan University of Technology, 2007
[15]	(李爽. 基于神经网络的形状记忆合金形变识别研究 [D][D]. 武汉: 武汉理工大学, 2007)
[16]	Wang W.The constitutive model and expermental study on shape memory alloys [D].[D] Dalian: Dalian University of Technology, 2012
[16]	(王伟. 形状记忆合金的本构模型及试验研究 [D][D]. 大连: 大连理工大学, 2012)
[17]	Wu Y Z.Mechanical properties and constitutive model of shape memory alloys [D].[D] Guangzhou: South China University of Technology, 2012
[17]	(吴昀泽. 形状记忆合金的力学性能与本构模型研究 [D][D]. 广州: 华南理工大学, 2012)
[18]	Cong S.Neural Network Theory and Applications with MATLAB Toolboxes [M]. 3rd Ed.,Hefei: University of Science and Technology of China Press, 2010: 151
[18]	(丛爽. 面向MATLAB工具箱的神经网络理论与应用[M]. 第3版,合肥: 中国科学技术大学出版社, 2010: 151)
[19]	Chen M.MATLAB Neural Network Theory and Examples of Fine Solution [M]. Beijing: Tsinghua University Press, 2013: 52
[19]	(陈明. MATLAB神经网络原理与实例精解 [M]. 北京: 清华大学出版社, 2013: 52)
[20]	Xue M Y.Application of neural network and genetic algorithms in structural damage identification [D].[D] Dalian: Dalian University of Technology, 2010
[20]	(薛明玉. 遗传算法和神经网络在结构损伤识别中的应用 [D][D]. 大连: 大连理工大学, 2010)
[21]	Bani-Hani K, Ghaboussi J.Neural networks for structural control of a benchmark problem, active tendon system[J]. Earthq. Eng. Struct. Dyn., 1998, 27: 1225
[22]	Yun C B, Yi J H, Bahng E Y.Joint damage assessment of framed structures using a neural networks technique[J]. Eng. Struct., 2001, 23: 425
[23]	Lei Y J, Zhang S W, Li X W, et al.MATLAB Genetic Algorithm Toolbox and Application[D][M]. Xi'an: Xi'an University of Electronic Science and Technology, 2005: 78
[23]	(雷英杰, 张善文, 李旭武等. MATLAB遗传算法工具箱及应用[D][M]. 西安: 西安电子科技大学, 2005: 78)
[24]	Zhou X D, Peng X M.Study on optimal damper of building structures using real coded genetic algorithms[J]. Chin. J. Comput. Mech., 2005, 22: 780
[24]	(周星德, 彭宣茂. 基于遗传算法的建筑结构最优阻尼研究[J]. 计算力学学报, 2005, 22: 780)
[25]	Meng H.Research on the seismic monitoring of spatial structure in application of shape memory alloy [D]. Xi'an: Xi'an University of Architecture and[D] Technology, 2010
[25]	(孟和. 应用形状记忆合金进行空间结构抗震监控的理论和方法研究 [D][D]. 西安: 西安建筑科技大学, 2010)

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