基于长短期记忆网络的区间不确定性动态载荷识别方法

王磊; 程辽辽; 胡举喜; 顾凯旋; 刘英良

doi:10.21656/1000-0887.450152

基于长短期记忆网络的区间不确定性动态载荷识别方法

doi: 10.21656/1000-0887.450152

1.
北京航空航天大学航空科学与工程学院固体力学研究所, 北京 100191
2.
上海交通大学船舶海洋与建筑工程学院, 上海 200240
3.
航空工业航宇救生装备有限公司试验部, 湖北襄阳 441003
4.
中国船舶及海洋工程设计研究院, 上海 200011

基金项目:

国防基础科研计划项目 JCKY2019205A006

详细信息

通讯作者:
王磊(1987—)，男，副教授，博士，博士生导师(通讯作者. E-mail: leiwang_beijing@buaa.edu.cn)

中图分类号: O342
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- 文章访问数: 41
- HTML全文浏览量: 7
- PDF下载量: 7
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-22
- 修回日期: 2024-12-17
- 刊出日期: 2025-08-01

A Long Short-Term Memory Networks Based Method for Force Reconstruction With Interval Uncertainties

1.
Institute of Solid Mechanics, School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, P. R. China
2.
School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
3.
Aviation Key Laboratory of Science and Technology on Life-Support Technology, Xiangyang, Hubei 441003, P. R. China
4.
Marine Design & Research Institute of China, Shanghai 200011, P. R. China

摘要

摘要: 针对传统神经网络在处理时间依赖性动态过程和含噪数据时的不稳定性问题，提出了一种基于长短期记忆网络动态力重构方法. 测量响应信号经噪声污染后，被归一化为输入变量；而归一化的动态载荷则作为输出变量. 长短期记忆网络的实现方法被采用. 为了提高网络的泛化能力，不同类型的动力响应和原始载荷被定义为每个时刻的样本结构. 考虑区间不确定性，在传统配点法的基础上调整配点策略得到逐维法，在研究某一维度不确定性变量时固定其他维度，可以高精度地解决区间变量相互独立的不确定性载荷识别问题. 最后，采用数值算例与传统神经网络(BP神经网络)对比，表征长短期记忆网络在含噪数据的处理上更为稳定，设计试验证实了对于时间依赖性的数据，该方法的有效性和可行性.
- 长短期记忆网络 /
- 逐维法 /
- 载荷识别 /
- 区间不确定性
Abstract: In response to the instability issues of traditional neural networks in handling time-dependent dynamic processes and noisy data, a dynamic force reconstruction method based on long short-term memory (LSTM) networks was proposed. The measured response signals, contaminated by noise, were normalized as input variables, while the normalized dynamic loads as output variables. The implementation approach of LSTM networks was adopted. To enhance the network's generalization ability, various types of dynamic responses and original loads were defined as sample structures at each time step. In view of interval uncertainty, the point distribution strategy results were adjusted to build the dimension-wise method (DWM) based on the traditional point distribution methods, to get precise resolution of uncertainty load identification with independent interval variables in the investigation of uncertainty variables in a specific dimension through fixation of others. Finally, by numerical examples and a comparison with traditional neural networks (back-propagation neural networks), the LSTM neural network was proved to be more stable in handling noisy data. An experimental design validates the effectiveness and feasibility of this method for time-dependent data.
- long short-term memory /
- dimension-wise method /
- force reconstruction /
- interval uncertainty

HTML全文

图 1 LSTM神经网络

Figure 1. The LSTM neural network

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图 2 DWM配点方案

Figure 2. The matching points layout of the dimension-wise method

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图 3 基于DWM的载荷识别流程图

Figure 3. The flowchart of load identification based on the dimension-wise method

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图 4 悬臂板传感器分布

Figure 4. The distribution of cantilever plate structure sensors

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图 5 悬臂板边界条件

Figure 5. Boundary conditions of the cantilever plate structure

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图 6 不同传感器布局下的力重构结果

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 6. Results of force reconstruction under different sensor layouts

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图 7 训练集的载荷样本

Figure 7. Load samples for the training set

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图 8 初始样本训练过程收敛曲线

Figure 8. Convergence curves of the initial data training process

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图 9 噪声影响下训练集的响应样本

Figure 9. Response samples of the training set under the influence of noise

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图 10 含噪样本训练过程收敛曲线

Figure 10. Convergence curves of the noise affected data training process

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图 11 不同噪声条件下利用LSTM网络和BP神经网络进行力重构的结果

Figure 11. Results of force reconstruction by LSTM and BP under noisy conditions

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图 12 利用DWM进行不确定性传播分析的重构载荷边界

Figure 12. Results of force boundaries with the dimension-wise method for uncertainty propagation

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图 13 动态载荷实验模型

Figure 13. The dynamic load experimental model

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图 14 悬臂板传感器布置

Figure 14. The cantilever plate structure sensor arrangement

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图 15 不同工况下的动态载荷识别

Figure 15. Identification of dynamic forces under different operating conditions

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表 1 悬臂板材料参数

Table 1. Cantilever plate structure material parameters

material property	symbol	specific value
Young’s modulus	E/GPa	210
Poisson’s ratio	ν	0.3
density	ρ/(kg/m³)	7 800

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表 2 神经网络训练集与测试集载荷

Table 2. The expressions of actual dynamic forces of training sets and test sets

	condition	actual dynamic force expression
training set	sample 1	F=100sin(20πt)+50sin(10πt)
	sample 2	F=300sin(40πt²)
	sample 3	F=300e^－4tsin(20πt)
	sample 4	F=350e^－6tsin(50πt²)
	sample 5	F=250e^－10t
test set	-	F=200sin(20πt)

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表 3 不同传感器布局下力重构的总相对误差

Table 3. Relative errors of force reconstruction with different sensor layouts

sensor selection	relative error/%
1, 2, 3, 4, 5, 6	8.79
1, 2, 3, 4	7.89
1, 2, 3	13.75
1, 4, 6, 9	8.05
1, 3, 6, 7	9.12
1, 6, 7, 9	8.92

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表 4 初始样本和含噪样本回归的LSTM架构概要

Table 4. Summary of the LSTM architecture for initial and noise affected data regression

layer(type)	number of parameters (original data)	number of parameters (noise affected data)
sequence input layer	20	60
Bi-LSTM layer	100(hidden layer unit)	128(hidden layer unit)
fully connected layer	300	300
dropout layer	0.2(probability)	0.8(probability)
fully connected layer	1(response)	1(response)
regression layer	-	-

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表 5 不同噪声条件下利用LSTM网络和BP神经网络进行力重构的相对误差

Table 5. Relative errors of force reconstruction by LSTM and BP under noisy conditions

SNR of additive noise	LSTM/%	BP/%
20	8.78	26.29
20, 30	18.00	41.43
20, 30, 40	18.31	41.39

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表 6 不同工况下的动态载荷识别总相对误差

Table 6. Total relative errors of dynamic load recognition under different operating conditions

state	temperature/℃	frequency/Hz	relative error/%
post-impact	60	3	3.98
pre-impact	100	5	4.44
post-impact	150	1	4.72

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