Funding for this research was provided by:
National Natural Science Foundation of China (51805157, 51725502, 51490662)
Hunan Natural Science Foundation (2019JJ40015)
Article History
Received: 14 October 2019
Revised: 5 January 2020
Accepted: 14 January 2020
First Online: 13 February 2020
Compliance with ethical standards
:
: The authors declare that they have no conflict of interest.
: In order to facilitate the replication of results presented in this paper, the MATLAB code files of the steel column design in Sect. InternalRef removed are provided as the supplementary material, and brief descriptions are given to the function of each file, as shown in Table InternalRef removed. The results of the other examples can be reproduced conveniently, by modifying the characteristics of the problems such as objective function, probabilistic constraints, distribution type, dimensionality, etcThirteen Matlab code files are provided to perform the proposed sequential approximate method and double-loop method effectively. “MainProgram.m” is the main program of the proposed method, which consists of eight subprograms, namely, “GaussQuad.m”, “HermitePoly.m”, “UnivarQuad.m”, “GMFun.m”, “ReliabAsm.m”, “PdfFun.m”, “GNonlinear.m”, “ObjFun.m”. “DoubleLoop.m” is the main program of the double-loop method, which consists of one subprogram, namely “DLNonlinear.m”. “GMM_result.mat” is used in the programs of both methods to define the GMM characteristics and “MaxEnt_Newton” is the tool box to calculate the response PDF. The function of each subprogram is illustrated in Table InternalRef removed.