Many physical processes have nonlinear behavior which can be well represented by a polynomial NARX or NARMAX model. The identification of such models has been widely explored in literature. The majority of these appro...Many physical processes have nonlinear behavior which can be well represented by a polynomial NARX or NARMAX model. The identification of such models has been widely explored in literature. The majority of these approaches are for the open-loop identification. However, for reasons such as safety and production restrictions, open-loop identification cannot always be done. In such cases, closed-loop identification is necessary. This paper presents a two-step approach to closed-loop identification of the polynomial NARX/NARMAX systems with variable structure control （VSC）. First, a genetic algorithm （GA） is used to maximize the similarity of VSC signal to white noise by tuning the switching function parameters. Second, the system is simulated again and its parameters are estimated by an algorithm of the least square （LS） family. Finally, simulation examples are given to show the validity of the proposed approach.展开更多
Building collapses during recent earthquakes have brought up the need for research on factors pertaining to collapse and the safety of structures.This requires response replication of structures that account for uncer...Building collapses during recent earthquakes have brought up the need for research on factors pertaining to collapse and the safety of structures.This requires response replication of structures that account for uncertainties from ground motions and structural properties.Structural collapse often implies that the structural system is no longer capable of maintaining its gravity load-carrying capacity,which often points to factors involving strength and stiffness degradation.In this study,the polynomial chaos nonlinear autoregressive with exogenous input form(PC-NARX)model is explored for dynamic response replication of a nonlinear single-degree-of-freedom(SDOF)structure.The generalized hysteretic Bouc-Wen model is applied to emulate stiffness and strength degradation for an SDOF structure close to collapse.A stochastic ground motion model is used to represent the uncertainties in seismic excitation.The PC-NARX model is employed and further evaluated for response replication of an SDOF system with inherent uncertain structural properties.A generic algorithm(GA)is used to select the terms for structural dynamics,and polynomial chaos expansion(PCE)is used to incorporate uncertain parameters into NARX model coefficients.It is demonstrated that the PC-NARX model provides good accuracy to account for both ground motion and structural uncertainties into response replication of SDOF structures with significant strength and stiffness degradation.The PC-NARX model thus presents a promising technique for collapse safety analysis of structures.展开更多
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
文摘Many physical processes have nonlinear behavior which can be well represented by a polynomial NARX or NARMAX model. The identification of such models has been widely explored in literature. The majority of these approaches are for the open-loop identification. However, for reasons such as safety and production restrictions, open-loop identification cannot always be done. In such cases, closed-loop identification is necessary. This paper presents a two-step approach to closed-loop identification of the polynomial NARX/NARMAX systems with variable structure control （VSC）. First, a genetic algorithm （GA） is used to maximize the similarity of VSC signal to white noise by tuning the switching function parameters. Second, the system is simulated again and its parameters are estimated by an algorithm of the least square （LS） family. Finally, simulation examples are given to show the validity of the proposed approach.
基金National Natural Science Foundation of China under Grant No.51878390。
文摘Building collapses during recent earthquakes have brought up the need for research on factors pertaining to collapse and the safety of structures.This requires response replication of structures that account for uncertainties from ground motions and structural properties.Structural collapse often implies that the structural system is no longer capable of maintaining its gravity load-carrying capacity,which often points to factors involving strength and stiffness degradation.In this study,the polynomial chaos nonlinear autoregressive with exogenous input form(PC-NARX)model is explored for dynamic response replication of a nonlinear single-degree-of-freedom(SDOF)structure.The generalized hysteretic Bouc-Wen model is applied to emulate stiffness and strength degradation for an SDOF structure close to collapse.A stochastic ground motion model is used to represent the uncertainties in seismic excitation.The PC-NARX model is employed and further evaluated for response replication of an SDOF system with inherent uncertain structural properties.A generic algorithm(GA)is used to select the terms for structural dynamics,and polynomial chaos expansion(PCE)is used to incorporate uncertain parameters into NARX model coefficients.It is demonstrated that the PC-NARX model provides good accuracy to account for both ground motion and structural uncertainties into response replication of SDOF structures with significant strength and stiffness degradation.The PC-NARX model thus presents a promising technique for collapse safety analysis of structures.
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.
