The HL-RF algorithm of the first-order reliability method (FORM) is a widely useful tool in structural reliability analysis. However, the iteration results of HL-RF algorithm may not converge due to periodic cycles for some highly nonlinear reliability problems. In this paper, an adaptive first-order reliability method (AFORM) is proposed to improve solution efficiency for some highly nonlinear reliability problems by introducing an adaptive factor. In AFORM, based on the two-parameter approximate first-order reliability method, the new iteration point and the previous iteration point are used to obtain the corresponding angle, and the result of convergence is judged by angle condition. According to the convergence degree of the results, two iteration parameters of the approximate reliability method are adjusted continuously by adaptive factor. Moreover, iteration step size is adjusted by changing the parameters to improve the efficiency and robustness of FORM. Finally, four numerical examples and one mechanical reliability analysis example are used to verify the proposed method. Compared with the different algorithms, the results show that AFORM has better efficiency and robustness for some highly nonlinear reliability problems.
In this paper, we study the traveling wave problem for a three species lattice competition system with monostable nonlinearity. We are interested in the linear or nonlinear determinacy of the minimal wave speed. Some conditions on the linear determinacy has been obtained in [J.-S. Guo, Y. Wang, C.-H. Wu and C.-C. Wu, The minimal speed of traveling wave solutions for a diffusive three species competition system, Taiwanese J. Math. 19 (2015) 1805–1829]. In this paper, we first provided some general conditions for the linear determinacy. Then, we derive some novel results on the nonlinear determinacy. Finally, some numerical simulations are carried out to illustrate our analytic results. To our knowledge, this may be the first investigation on the nonlinear determinacy of the three species competition system.
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