Impact analysis of the multi-harmonic input splicing way based on the data-driven model
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Impact analysis of the multi-harmonic input splicing way based on the data-driven model Yue Qiu1,2 · Zhong Luo1,2,3 · Xiaobiao Ge1,2 · Yunpeng Zhu2,4 · Yi Gao1,2 Received: 13 August 2020 / Revised: 18 September 2020 / Accepted: 22 September 2020 / Published online: 9 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In response to the identification problem of nonlinear systems with harmonic input, this paper studies the identification effect of the different splicing way of the multi-harmonic input based model identification approach. In this method, the relationship between the input and output signals of the nonlinear system is represented by the Nonlinear Auto-Regressive model with exogenous inputs (NARX) model. Firstly, the modeling framework of the NARX model based on the multi-harmonic input method is introduced. Then the effect of the different splicing way contained sequence and period of splicing data on modeling results is researched and proved in theoretically. Finally, a case study is discussed to simultaneously validate that the different multi-harmonic signal splicing forms have no effect on the identification results. Keywords NARX model · Multi-harmonic excitation · Data driven model · Nonlinear system
1 Introduction In reality, almost every system we come into contact with can be described by mathematical model [1–3]. The mathematical modeling of the system is avail to analyze the operation mechanism of the system and design the system in line with the relevant requirements. Mathematical models can be divided into numerical models and physical models [4]. On account of physical models can clearly describe the relationship between parameters and output of its system through differential equations, physical models are preferred by researchers. However, for some complex systems such as rotor bearing [5], gas turbine system [6, 7], the physical models are difficult to obtain.
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Zhong Luo [email protected]
1
School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, People’s Republic of China
2
Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University, Shenyang 110819, People’s Republic of China
3
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, People’s Republic of China
4
Department of Automatic Control and System Engineering, University of Sheffield, Sheffield S13JD, UK
The above mentioned problems are expected to be addressed based on data driven models without an advanced knowledge of the system [8–11]. In practice, as a class of numerical models, the NARX model is usually used to depict the large number of nonlinear discrete systems [12–14], which was recommended in 1981 for the first time [15]. Numerous systems can be expressed by the NARX model for system analysis [16–18]. Some contents with respect to the recognition algorithm and the associated test criteria based on NARX model are widely stu
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