Sparse identification of time-space coupled distributed dynamic load


Distributed dynamic loads are common in practical engineering. As an input of vibrating structures, they play a critical role in numerous specific applications such as vibration control, structural design, and noise reduction. Unfortunately, despite the convenience and accuracy in measuring structural dynamic responses, the accurate and direct measurement of the distributed spatial loads has remained a significant challenge. This can be attributed to limited measurement techniques and adverse service environments. To this end, developing effective reverse methods for determining the distributed dynamic loads from measured structural response has drawn significant research attention as an effective approach for overcoming the inherent measurement challenges.

Dynamic load identification has undergone rapid development in the past few decades focusing on the three types of dynamic loads: concentrated, distributed and moving dynamic loads. However, the involved dynamic loads present in most literary works have been regarded as the first and third types of concentrated and moving dynamic loads. Numerous identification methods mostly based on time and frequency domains have been developed. Despite the good progress, identifying the second type of distributed dynamic loads is challenging due to the limited measured responses, time and space coupling of the distributed loads, and large amounts of unknown variables in both the time and space domains. Previous research revealed that effective identification of distributed dynamics loads is possible through the iterative reverse of spatial distribution and time history. Unfortunately, this approach is confronted by a non-uniqueness problem, which is scarcely explored in the literature.

To address the above challenges, Professor Jie Liu from Hunan University and Dr. Kun Li from Changsha University proposed a novel identification method to achieve reverse calculation with a few measurements, to enhance the calculation accuracy and efficiency of the identification processes, and to overcome the non-uniqueness problem. The main objective was to identify the time-space coupled dynamic distributed loads. Their research work is currently published in the journal, Mechanical Systems and Signals Processing.

In their approach, the proposed method was based on two key conditions: linear elastic and time-invariant structures and the availability of few structural measurements. Overall, the method was based on blind source separation (BSS) and orthogonal matching pursuit (OMP). Through proper orthogonal decomposition (POD), the time-space coupled distributed dynamic load was represented as a series of sub-distributed dynamic loads decoupled with independent time history and spatial distribution functions. Next, the non-uniqueness problem of the dynamic loads was analyzed in the modal domain. The BSS technique retrieved the time history functions to permit sparse identification of the distribution functions via OMP.

Results showed that the proposed method successfully decomposed the time-space coupled distributed dynamic load into a series of independent spatial distribution and time history functions. Consequently, the unique optimal solutions for the history and distribution functions of the dynamic loads were obtained by also considering the independence and sparsity constraint. The capability of the method to deal with time-space coupled distributed dynamic loads of complicated structures was validated. It also exhibited the ability to achieve time history reconstruction and spatial distribution representation separately.

In summary, a novel method for equivalent identification and sparse representation of coupled distributed dynamic loads was reported. The non-uniqueness problem was analyzed and proved in detail. The contributions of the proposed method include effective BSS and OMP integration for signal processing, identification and description of the dynamic loads from the perspective of time and space domains, and a thorough exploration of the multi-solution nature of the distributed loads. In a statement to Advances in Engineering, Professor Jie Liu said the study insights would effectively analyze distributed loads in practical engineering problems.

Sparse identification of time-space coupled distributed dynamic load - Advances in Engineering

About the author

Jie Liu is a full professor as well as a doctoral supervisor in State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body and College of Mechanical and Vehicle Engineering, Hunan University, Changsha, China.

Dr. Liu has over twenty years of teaching and research experience in the fields of the advanced structural design theory and methods. Dr. Liu’s major research interests are in computational inverse techniques, uncertain inverse problem theory, numerical simulation-based design, uncertainty quantification, reliability design, dynamic load identification, uncertain optimization design, vehicle structure design and optimization.

Dr. Liu has authored two books and published more than 100 research papers in technical journals. His book Numerical Simulation-based Design Theory and Methods was published by Springer Press in 2020 and has been well received in the research community.

About the author

Kun Li is currently a lecturer in the School of Mechatronics Engineering, Changsha University. He received his BS from Hunan Engineering institute in 2012 and PhD from Hunan University (HNU) in 2018. He began his post-doctoral research in the College of Mechanical and Vehicle Engineering, HNU in 2019. He is mainly engaged in the research of computational inverse techniques, uncertain inverse problem theory and dynamic load identification, and has authored or coauthored more than 15 peer-reviewed journal papers, applied 4 invention patents. His research program is funded by the National Natural Science Foundation of China and Natural Science Foundation of Hunan Province.


Liu, J., & Li, K. (2021). Sparse identification of time-space coupled distributed dynamic loadMechanical Systems and Signal Processing, 148, 107177.

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