For that purpose, we introduce the necklace distance and tailor accordingly the trust-region constraints of the optimization problems.
In the first part, we focus on the development and adaptation of a DFO method to problems with continuous and mixed discrete variables exhibiting a cyclic-symmetry property. Another difficulty is that these problems involve heterogeneous nature variables: a varying number of components (integer variables), different materials (categorical variables, usually nonordered), the presence or not of some components (binary variables), and continuous variables describing dimensions/characteristics of the structure pieces.This thesis aims to develop and adapt Derivative-Free Optimization (DFO) methods for different types of applications, including the optimal design of aircraft engines. In these nonlinear optimization problems, derivatives of the objective function (and, possibly of the constraint functions) are not available and cannot be directly approximated. In recent years, there has been a considerable number of industrial applications that involve mixed variables and time-consuming simulators, e.g., at Safran Tech and IFPEN: optimal designs of aircraft engine turbine, of mooring lines of offshore wind turbines, of electric engine statorsn and rotors. At last, five examples involving nonlinearity problem, small failure probability problem and practical engineering problem are tested to verify the efficiency of the proposed AFBAM. The proposed AFBAM technically makes reliability evaluation phase independent of adaptive iterative process, which greatly improves the efficiency of model refinement phase. In order to ensure classification accuracy of the constructed Kriging model, a new stopping criterion is designed based on average misclassification probability and misclassification ratio. The number of experimental design samples is constantly updated by selecting informative samples with the proposed learning strategy.
Matlab latin hypercube sampling code full#
The proposed AFBAM makes full use of the binary classification feature of reliability analysis in the way that the failure boundary of the original model can be efficiently approximated.
For the purpose of reducing the computational cost in reliability analysis, this work develops an adaptive failure boundary approximation method (AFBAM) by combining Kriging and uniform sampling with a new adaptive learning strategy.
Matlab latin hypercube sampling code how to#
How to obtain an accurate reliability index with a fewer number of calls to original performance function in reliability analysis has become an important challenge. In practical engineering problems, accurate reliability assessment often is computationally expensive with time-consuming numerical models or simulation models.