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Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (3): 435-443    DOI: 10.3785/j.issn.1008-973X.2019.03.004
Mechanical Engineering     
Sparse hybrid uncertain variable optimization method and application
Peng ZHANG(),Xiao-jian LIU*(),Shu-you ZHANG,Le-miao QIU,Guo-dong YI
State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
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Abstract  

Sparse hybrid uncertainties in the distribution of random variables brings the problem of hard border detection and calculation results distortion in complex product design. A sparse hybrid uncertain variable optimization method based on Chebyshev approximation was proposed. Firstly, the maximum likelihood estimation was utilized to construct the probability density function of a sparse hybrid uncertain variable under a given distribution, and its distribution parameter corresponding to the given distribution was preliminarily determined. Secondly, based on the Bayesian information criterion, the information loss of the corresponding distribution was calculated, and the most suitable distribution and parameters of the sparse mixed uncertain variables were further determined. Thirdly, in order to solve the computational distortion caused by interval expansion of the traditional interval analysis method, Chebyshev approximation was used to optimize the objective function and the improved HL-RF algorithm was used to obtain the reliability index and the failure probability value; while meeting the design requirements, the design goal of light weight and rigidity retention was effectively realized. Finally, the effectiveness of the proposed method is verified by numerical examples and the optimization design of a high-speed press slider.



Key wordssparse hybrid uncertainty      optimization design      Bayesian information criterion      distribution parameters      Chebyshev approximation     
Received: 09 February 2018      Published: 04 March 2019
CLC:  TH 122  
Corresponding Authors: Xiao-jian LIU     E-mail: absent1353@163.com;liuxj@zju.edu.cn
Cite this article:

Peng ZHANG,Xiao-jian LIU,Shu-you ZHANG,Le-miao QIU,Guo-dong YI. Sparse hybrid uncertain variable optimization method and application. Journal of ZheJiang University (Engineering Science), 2019, 53(3): 435-443.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.03.004     OR     http://www.zjujournals.com/eng/Y2019/V53/I3/435


稀疏混合不确定变量优化方法及应用

针对复杂产品设计中稀疏混合不确定变量导致的设计边界识别困难、计算结果失真等问题,提出一种基于Chebyshev逼近的稀疏混合不确定变量优化方法. 首先采用极大似然估计方法构造稀疏混合不确定变量在给定分布下的概率密度函数,初步确定其在给定分布下对应的分布参数;其次基于贝叶斯信息准则计算对应分布的信息损失,进一步确定稀疏混合不确定变量的最合适的分布及分布参数. 再次,为解决传统区间分析方法中区间扩张导致的计算失真问题,采用Chebyshev逼近优化目标函数并利用改进的HL-RF算法求解,获取可靠性指标及失效概率,在满足设计需求的同时,有效实现产品轻量化、刚度保持的设计目标. 最后,以数值算例及高速压力机滑块的优化设计验证了所提方法的有效性.


关键词: 稀疏混合不确定,  优化设计,  贝叶斯信息准则,  分布参数,  Chebyshev逼近 
Fig.1 Error comparison between interval analysis method and Chebyshev approximation
对比方法 β Pf δ/%
区间分析方法 ?0.65 0.742 2 1.41
本文方法 ?0.676 4 0.750 6 0.29
Rosenbrock精确解 ?0.683 0.752 8
Tab.1 Comparison of reliability analysis for numerical examples
Fig.2 Digital prototype of wide table top ultra-precision high speed press machine and slider
分布 参数1 参数2 BIC值
θ1:正态分布 600 5 29.34
θ2:均匀分布 520 687 35.45
θ3:极值I型分布 622 9 38.36
θ4:对数正态分布 6.42 2.48 33.82
θ5:F分布 5 2 42.23
θ6:威布尔分布 590 85 27.25
θ7:指数分布 600 38.56
θ8:伽马分布 600 1.58 36.85
Tab.2 Distribution types and optimal distribution parameters
Fig.3 Probability density distribution of variable x3 under Weibull conditions
最优设计变量 β Pf 设计目标
区间分析
方法
x1=412 mm 1.982 0.023
x2=266 mm m=1 287 kg,
Pmax=53.48 MPa
x3=572 mm
E=1.45×105 MPa
v=0.25
本文方法 x1=366 mm 2.10 0.018
x2=272 mm m=1 201 kg,
Pmax=53.44 MPa
x3=564 mm
E=1.44×105 MPa
v=0.24
Tab.3 Optimization and comparison of slider design for wide countertop ultra-precision high-speed stress machine
Fig.5 Schematic of load path and constraint
Fig.4 Iterative process for reliability analysis using Chebyshev approximation and interval analysis method
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