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A full dual mean square error criterion for the equivalent linearization

In this paper a special case of the weighted full dual mean square error criterion is introduced and investigated in detail. Numerical results are carried out to show that this special full dual mean square error criterion can give more accurate approximate solutions for both deterministic and random nonlinear systems. | Journal of Science and Technology 54 (4) (2016) 557-562 DOI: 10.15625/0866-708X/54/4/8103 A FULL DUAL MEAN SQUARE ERROR CRITERION FOR THE EQUIVALENT LINEARIZATION Nguyen Dong Anh*, Nguyen Minh Triet University of Engineering and Technology, Vietnam National University, 144 Xuan Thuy Str., Cau Giay Dist., Vietnam * Email: ndanh10000@yahoo.com Received: 3 June 2015; Accepted for publication: 19 April 2016 ABSTRACT Among approximate methods, the method of equivalent linearization proposed by N. Krylov and N. Bogoliubov and extended by Caughey has remained an effective tool for both deterministic and stochastic problems. The idea of the method is based on the replacement of a nonlinear oscillator by a linear one under the same excitation. The standard way of implementing this method is that the coefficients of linearization are to be found from a criterion of equivalence. When the difference between the nonlinear function and equivalent linear one is significant the replacement leads to unaccepted errors. In order to reduce the errors one may apply the dual approach. One of significant advantages of the dual conception is its consideration of two different aspects of a problem in question allowing the investigation to be more appropriate. In this paper a special case of the weighted full dual mean square error criterion is introduced and investigated in detail. Numerical results are carried out to show that this special full dual mean square error criterion can give more accurate approximate solutions for both deterministic and random nonlinear systems. Keywords: weighted, full dual approach, equivalent linearization, extended Duffing system. 1. INTRODUCTION Nonlinear oscillator models have been widely used in many areas of physics and engineering and are of significant importance in mechanical and structural problems for the comprehensive understanding and accurate prediction of motion. The study of nonlinear systems is of interest to many researchers and various .