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

WANG Lei; CHENG Liaoliao; HU Juxi; GU Kaixuan; LIU Yingliang

doi:10.21656/1000-0887.450152

Volume 46 Issue 8

Aug. 2025

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(8): 959-972

WANG Lei, CHENG Liaoliao, HU Juxi, GU Kaixuan, LIU Yingliang. A Long Short-Term Memory Networks Based Method for Force Reconstruction With Interval Uncertainties[J]. Applied Mathematics and Mechanics, 2025, 46(8): 959-972. doi: 10.21656/1000-0887.450152

Citation:

PDF( 5084 KB)

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

doi: 10.21656/1000-0887.450152

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

Received Date: 2024-05-22
Rev Recd Date: 2024-12-17

Available Online: 2025-09-10

Abstract

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

FullText(HTML)

References(40)

References

BARTLETT F D,FLANNELLY W G. Model verification of force determination for measuring vibratory loads[J].Journal of the American Helicopter Society, 1979, 24(2): 10-18.

[2]KREITINGER T J. Force identification from structural response[D]. University of New Mexico,1989.

[3]DEEN S,LUNDBERG B. Prediction of impact force by impulse response method[J].International Journal of Impact Engineering, 1991, 11(2): 149-158.

[4]DOYLE J F. A wavelet deconvolution method for impact force identification[J].Experimental Mechanics, 1997, 37(4): 403-408.

[5]MITRA M,GOPALAKRISHNAN S. Spectrally formulated wavelet finite element for wave propagation and impact force identification in connected 1-D waveguides[J].International Journal of Solids and Structures, 2005, 42(16/17): 4695-4721.

[6]DOYLE J F. Reconstructing dynamic events from time-limited spatially distributed data[J].International Journal for Numerical Methods in Engineering, 2002, 53(12): 2721-2734.

[7]GIANSANTE N,JONES R,CALAPODAS N J. Determination of in-flight helicopter loads[J].Journal of the American Helicopter Society, 1981,27(3): 58-64.

[8]CHAO M,FENG X. The identification of external forces for a nonlinear vibration system in frequency domain[J].Proceedings of the Institution of Mechanical Engineers （Part C）: Journal of Mechanical Engineering Science, 2014, 228(9): 1531-1539.

[9]LIU Y,SHEPARD W S. Dynamic force identification based on enhanced least squares and total least-squares schemes in the frequency domain[J].Journal of Sound and Vibration, 2005, 282(1/2): 37-60.

[10]HILLARY B,EWINS D J. The use of strain gauges in force determination and frequency response function measurements[C]//Proceedings of IMAC.1984.

[11]HOLZDEPPE D,RY H. Reconstruction of instationary wind load distribution on structures from measured structural response time histories[J].Journal of Wind Engineering and Industrial Aerodynamics, 1988, 28(1/2/3): 231-240.

[12]张方,朱德懋. 基于神经网络模型的动载荷识别[J]. 振动工程学报,1997, 10(2): 40-46. (ZHANG Fang,ZHU Demao. The dynamic load identification research based on neural network model[J].Journal of Vibration Engineering, 1997, 10(2): 40-46. (in Chinese))

[13]CAO X,SUGIYAMA Y,MITSUI Y. Application of artificial neural networks to load identification[J].Computers & Structures, 1998, 69(1): 63-78.

[14]李忠献,陈锋,王波. 基于BP神经网络的桥上移动荷载分阶段识别方法[J]. 工程力学,2008, 25(9): 85-92. (LI Zhongxian,CHEN Feng,WANG Bo. A BP neural network-based stage identification method for moving loads on bridges[J].Engineering Mechanics, 2008, 25(9): 85-92. (in Chinese))

[15]LIU Y,WANG L,GU K,et al. Artificial neural network (ANN)-Bayesian probability framework (BPF) based method of dynamic force reconstruction under multi-source uncertainties[J].Knowledge-Based Systems, 2022, 237: 107796.

[16]夏鹏,杨特,徐江,等. 利用时延神经网络的动载荷倒序识别[J]. 航空学报,2021, 42(7): 224452. (XIA Peng,YANG Te,XU Jiang,et al. Reversed time sequence dynamic load identification method using time delay neural network[J].Acta Aeronautica et Astronautica Sinica, 2021, 42(7): 224452. (in Chinese))

[17]YANG H,JIANG J,CHEN G,et al. Dynamic load identification based on deep convolution neural network[J].Mechanical Systems and Signal Processing, 2023, 185: 109757.

[18]张巧灵,高淑萍,何迪,等. 基于时间序列的混合神经网络数据融合算法[J]. 应用数学和力学,2021, 42(1): 82-91. (ZHANG Qiaoling,GAO Shuping,HE Di,et al. A hybrid neural network data fusion algorithm based on time series[J].Applied Mathematics and Mechanics, 2021, 42(1): 82-91. (in Chinese))

[19]WANG L,REN Q,MA Y,et al. Optimal maintenance design-oriented nonprobabilistic reliability methodology for existing structures under static and dynamic mixed uncertainties[J].IEEE Transactions on Reliability, 2019, 68(2): 496-513.

[20]WANG L,LIU Y. A novel method of distributed dynamic load identification for aircraft structure considering multi-source uncertainties[J].Structural and Multidisciplinary Optimization, 2020, 61(5): 1929-1952.

[21]AVEN T,BARALDI P, FLAGE R,et al.Uncertainty in Risk Assessment: the Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods[M]. West Sussex,United Kingdom: John Wiley & Sons, 2014.

[22]QIU Z,WANG X. Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach[J].International Journal of Solids and Structures, 2003, 40(20): 5423-5439.

[23]MOENS D,VANDEPITTE D. A survey of non-probabilistic uncertainty treatment in finite element analysis[J].Computer Methods in Applied Mechanics and Engineering, 2005, 194(12/13/14/15/16): 1527-1555.

[24]SHEN Y,LIN W. Collocation method for the natural boundary integral equation[J].Applied Mathematics Letters, 2006, 19(11): 1278-1285.

[25]WANG L,CHENG L,XU H,et al. Multi-source uncertainty-oriented dynamic force reconstruction framework based on adaptive fitting precise integration and optimized wavelet denoising[J].Structural and Multidisciplinary Optimization, 2024, 67(3): 28.

[26]WANG L,LIU Y,LIU Y. An inverse method for distributed dynamic load identification of structures with interval uncertainties[J].Advances in Engineering Software, 2019, 131: 77-89.

[27]LIU J,HAN X,JIANG C,et al. Dynamic load identification for uncertain structures based on interval analysis and regularization method[J].International Journal of Computational Methods, 2011, 8(4): 667-683.

[28]LIU J,SUN X,MENG X,et al. A novel shape function approach of dynamic load identification for the structures with interval uncertainty[J].International Journal of Mechanics and Materials in Design, 2016, 12(3): 375-386.

[29]XU M,DU J,WANG C,et al. Hybrid uncertainty propagation in structural-acoustic systems based on the polynomial chaos expansion and dimension-wise analysis[J].Computer Methods in Applied Mechanics and Engineering, 2017, 320: 198-217.

[30]陈保家,陈学力,沈保明,等. CNN-LSTM深度神经网络在滚动轴承故障诊断中的应用[J]. 西安交通大学学报,2021, 55(6): 28-36. (CHEN Baojia,CHEN Xueli,SHEN Baoming,et al. An application of convolution neural network and long short-term memory in rolling bearing fault diagnosis[J].Journal of Xi’an Jiaotong University, 2021, 55(6): 28-36. (in Chinese))

[31]柏万宽. RNN神经网络在股票指数价格预测模型的研究与应用[D]. 重庆: 重庆大学,2018. (BAI Wankuan. Research and application of recurrent neural network in stock index forecasting model[D]. Chongqing: Chongqing University,2018. (in Chinese))

[32]LECUN Y,BENGIO Y,HINTON G. Deep learning[J].Nature, 2015, 521(7553): 436-444.

[33]齐传凯. 基于模型无关元学习的材料数据预测算法研究[D]. 沈阳: 辽宁大学,2021. （QI Chuankai. Research on material data prediction algorithm based on model-agnostic meta-learning[D]. Shenyang: Liaoning University,2021. （in Chinese））

[34]WANG L,XIONG C,WANG X,et al. A dimension-wise method and its improvement for multidisciplinary interval uncertainty analysis[J].Applied Mathematical Modelling, 2018, 59: 680-695.

[35]RUSSELL R D,SHAMPINE L F. A collocation method for boundary value problems[J].Numerische Mathematik, 1972, 19(1): 1-28.

[36]MA X,HUANG C. Numerical solution of fractional integro-differential equations by a hybrid collocation method[J].Applied Mathematics and Computation, 2013, 219(12): 6750-6760.

[37]ABRAMOWITZ M, STEGUN I A.Handbook of Mathematical Functions With Formulas,Graphs, and Mathematical Tables[M]. Washington: U S Government Printing Office, 1967.

[38]WU J,LUO Z,ZHENG J,et al. Incremental modeling of a new high-order polynomial surrogate model[J].Applied Mathematical Modelling, 2016, 40(7/8): 4681-4699.

[39]WU J,ZHANG Y,CHEN L,et al. A Chebyshev interval method for nonlinear dynamic systems under uncertainty[J].Applied Mathematical Modelling, 2013, 37(6): 4578-4591.

[40]QIU Z,WANG X. Vertex solution theorem for the upper and lower bounds on the dynamic response of structures with uncertain-but-bounded parameters[J].Acta Mechanica Sinica, 2009, 25(3): 367-379.

Relative Articles

Supplements(0)

Cited By

Proportional views