%A Haopeng LIU, Yunpeng ZHU, Zhong LUO, Qingkai HAN %T PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems %0 Journal Article %D 2018 %J Front. Mech. Eng. %J Frontiers of Mechanical Engineering %@ 2095-0233 %R 10.1007/s11465-017-0459-5 %P 390-400 %V 13 %N 3 %U {https://journal.hep.com.cn/fme/EN/10.1007/s11465-017-0459-5 %8 2018-06-11 %X

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 PRESS-based 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.