结合Cokriging模型和单目标函数的随机模型修正

彭珍瑞; 张雪萍; 张亚峰

doi:10.13433/j.cnki.1003-8728.20220191

结合Cokriging模型和单目标函数的随机模型修正

doi: 10.13433/j.cnki.1003-8728.20220191

兰州交通大学机电工程学院, 兰州 730070

基金项目:

国家自然科学基金项目 51768035

详细信息

作者简介:
彭珍瑞, 教授, 博士生导师, pzrui@163.com

中图分类号: TB123; TH113.1
计量
- 文章访问数: 153
- HTML全文浏览量: 49
- PDF下载量: 61
- 被引次数: 0
出版历程
- 收稿日期: 2021-02-17
- 刊出日期: 2024-01-25

Stochastic Model Updating Combining Cokriging Model and Single Objective Function

School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

摘要

摘要: 将Cokriging代理模型技术和单目标函数进行结合，提出了一种随机模型修正方法。该方法将不确定性模型修正问题转化为较简单的待修正参数统计特征的修正问题，能够在保证模型修正精度的同时，有效缓解模型修正中由于分步修正和多目标修正造成的计算成本高的问题。首先，假设待修正参数和响应均服从高斯分布，采用拉丁超立方抽样获取训练集样本，构造满足精度要求的Cokriging模型以替代复杂的有限元模型参与迭代计算。然后，建立有限元模型计算响应统计特征与试验响应统计特征的加权残差目标函数，引入土狼优化算法最小化该单目标函数来得到待修正参数的统计特征。最后，通过二维和三维桁架结构验证了所提方法的可行性。
- 不确定性 /
- 模型修正 /
- 单目标函数 /
- 全局优化 /
- Cokriging模型
Abstract: A stochastic model updating method is proposed by combining the Cokriging surrogate model technique with the single objective function. The method transforms the uncertainty model updating problem into a simple updating problem of the statistical characteristics of the parameters to be updated, which can effectively alleviate the high computational cost problem caused by the stepwise and multi-objective updating while ensuring the updating accuracy. Firstly, assuming that the parameters to be updated and the corresponding responses obey Gaussian distribution, the Latin hypercube sampling is used to obtain the training set samples, and the Cokriging model satisfying the accuracy requirement is constructed to replace the complex finite element model in the iterative calculation. Then, the weighted residual objective function between the statistical characteristics of the finite element model calculated responses and the statistical characteristics of the test responses is established, and the coyote optimization algorithm is introduced to minimize the single objective function to obtain the statistical characteristics of the parameters to be updated. Finally, the feasibility of the proposed method is verified by the two-dimensional and the three-dimensional truss structures.
- uncertainty /
- model updating /
- single objective function /
- global optimization /
- Cokriging model

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图 1 模型修正流程图

Figure 1. Flow chart of model updating

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图 2 二维桁架模型

Figure 2. Two dimensional truss structure

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图 3 频率的预测值和真实值

Figure 3. Predicted value and true value of frequencies

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图 4 振型的预测值和真实值

Figure 4. Predicted value and true value of shapes

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图 5 频率对比图

Figure 5. Comparison of frequencies

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图 6 振型对比图

Figure 6. Comparison of shapes

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图 7 修正后频率的概率密度函数曲线

Figure 7. Updated frequency probability density function curve

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图 8 修正后参数响应的分布及置信椭圆

Figure 8. The distribution and confidence ellipse of the updated parameter response

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图 9 三维桁架模型

Figure 9. Three dimensional truss model

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图 10 第1阶频率的预测值和真实值

Figure 10. Predicted value and true value of first order frequencies

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图 11 频率对比图

Figure 11. Comparison of frequencies

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图 12 振型对比图

Figure 12. Comparison of shapes

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图 13 修正后频率的概率密度函数曲线

Figure 13. Updated frequency probability density function curve

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图 14 修正后参数响应的分布及置信椭圆

Figure 14. The distribution and confidence ellipse of the updated parameter response

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表 1 修正前后结构参数均值与标准差(二维桁架)

Table 1. The mean and standard deviation of structural parameters before and after updating(2D truss)

修正参数	试验值	有限元值	修正前误差/%	多目标修正结果		单目标修正结果
修正参数	试验值	有限元值	修正前误差/%	修正值	相对误差/%	修正值	相对误差/%
E₁均值/GPa	190	209	10	190.006	3.16×10^-3	190.099	5.21×10^-2
E₂均值/GPa	210	231	10	209.988	5.71×10^-3	209.817	8.71×10^-2
d均值/(kg·m^-3)	7 800	7 020	-10	7 799.936	8.21×10^-4	7 801.184	1.52×10^-2
E₁标准差	2.5	-	-	2.622	4.88	2.581	3.24
E₂标准差	2.2	-	-	2.103	4.41	2.225	1.14
d标准差	25.0	-	-	24.855	0.58	25.828	3.31

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表 2 三维桁架模型属性

Table 2. Properties of 3D truss model

总重	节长	跨长	主桁中心距	跨高比	桁高	泊松比	杆单元	节点
54 kg	0.4 m	2.8 m	0.36 m	10	0.27 m	0.3	94个	28个

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表 3 修正前后结构参数均值与标准差(三维桁架)

Table 3. The mean and standard deviation of structural parameters before and after updating(3D truss)

修正参数	试验值	有限元值	修正前误差/%	多目标优化		单目标优化
修正参数	试验值	有限元值	修正前误差/%	修正值	相对误差/%	修正值	相对误差/%
E₁均值/GPa	230	253	10	229.406	0.258	229.638	0.157
E₂均值/GPa	210	189	-10	210.910	0.433	210.320	0.152
d均值/(kg·m^-3)	7 300	8 030	10	7 305.604	7.68×10^-2	7 300.361	4.95×10^-3
E₁标准差	3.0	-	-	2.949	1.70	2.904	3.20
E₂标准差	2.0	-	-	2.089	4.45	2.003	0.15
d标准差	20.0	-	-	20.400	2.00	20.473	2.36

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