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 squa...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.展开更多
基金Acknowledgements This work was supported by the National Science Foundation of China （Grant No. 11572082）, the Excellent Talents Support Program in Institutions of Higher Learning in Liaoning Province, China （Grant No. LJQ2015038）, the Fundamental Research Funds for the Central Universities of China （Grant Nos. N150304004 and N140301001）, and the Key Laboratory for Precision and Non-traditional Machining of the Ministry of Education, Dalian University of Technology （Grant No. JMTZ201602）.
文摘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.
