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This study aims to propose an efficient method for solving reliability-based design optimization (RBDO) problems.

In the proposed algorithm, genetic algorithm (GA) is employed to search the global optimal solution of design parameters satisfying the reliability and deterministic constraints. The Kriging model based on U learning function is used as a classification tool to accurately and efficiently judge whether an individual solution in GA belongs to feasible region.

Compared with existing methods, the proposed method has two major advantages. The first one is that the GA is employed to construct the optimization framework, which is helpful to search the global optimum solutions of the RBDO problems. The other one is that the use of Kriging model is helpful to improve the computational efficiency in solving the RBDO problems.

Since the boundaries are concerned in two Kriging models, the size of the training set for constructing the convergent Kriging model is small, and the corresponding efficiency is high.

The purpose of this study is to improve the computational efficiency and accuracy of fatigue reliability analysis.

By absorbing the advantages of Markov chain and active Kriging model into the hierarchical collaborative strategy, an enhanced active Kriging-based hierarchical collaborative model (DCEAK) is proposed.

The analysis results show that the proposed DCEAK method holds high accuracy and efficiency in dealing with fatigue reliability analysis with high nonlinearity and small failure probability.

The effectiveness of the presented method in more complex reliability analysis problems (i.e. noisy problems, high-dimensional issues etc.) should be further validated.

The current efforts can provide a feasible way to analyze the reliability performance and identify the sensitive variables in aeroengine mechanisms.

To improve the computational efficiency and accuracy of fatigue reliability analysis, an enhanced active DCEAK is proposed and the corresponding fatigue reliability framework is established for the first time.

This study aims to optimize the structural design of reinforced concrete columns with variable hollow circular sections.

The columns were optimized according to the criteria of instability (buckling) and mechanical strength (compression and/or tensile strength). To perform the optimizations, routines are developed in Python using the penalty and sequential linearization programming (SLP) function methods to optimize the elements satisfying the buckling and stress criteria.

At the end of the optimization process, the optimal section is obtained for the example of a circular column with a variable section, this section has an average radius of 5% smaller than that initially defined.

The theoretical basis for column optimization and the structuring of an algorithm in Python language for the computational resolution of these problems are presented in a didactic way, as well as the comparative efficiency of the methods.