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PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

Frontiers of Mechanical Engineering 2018年第3期13卷 390-400页

作者： Haopeng LIU Yunpeng ZHU Zhong LUO Qingkai HAN School of Mechanical Engineering and Automation Northeaste University Shenyang 110819 China Key Laboratory of Vibration and Control of Aero-Propulsion Systems (Ministry of Education) Northeastern University Shenyang 110819 China Departrnent of Automatic Control and System Engineering Sheffield University Sheffield S13JD UK School of Mechanical Engineering Dalian University of Technology Dalian 116023 China

In response to the identification problem concerning multi-degree of freedom （MDOF） nonlinear systems, this study presents the extended forward orthogonal regression （EFOR） based on predicted residual sums of squares （PRESS） to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs （NARX） model and aims to explicitly reveal the physical design parameters of the system. The PRESSbased EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio （AERR）-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5- DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.

关键词： MDOF dynamic parametrical model NARX model PRESS-based EFOR cantilever beam

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