Multi-fidelity optimization via surrogate modelling

This paper demonstrates the application of correlated Gaussian process based approximations to optimization where multiple levels of analysis are available, using an extension to the geostatistical method of co-kriging. An exchange algorithm is used to choose which points of the search space to sample within each level of analysis. The derivation of the co-kriging equations is presented in an intuitive manner, along with a new variance estimator to account for varying degrees of computational ‘noise’ in the multiple levels of analysis. A multi-fidelity wing optimization is used to demonstrate the methodology

A global-local optimization method for problems in structural dynamics

The optimization of complex structures involving many design variables and constraints can be performed using a multi-level approach: a structure consisting of several components is optimized as a whole (global) and on the component level (local). Earlier work [1], [2], [3], described a multilevel technique developed for the optimization the Airbus A380 vertical tail plane. In this application, a global model is used to calculate the loads on each of the components. These components are then optimized using the prescribed loads, followed by a new global calculation to update the loads. The component optimization strategy is based on Neural Networks (NN) and Genetic Algorithms (GA). This paper describes a strategy that makes this global-local optimization method possible for problems in structural dynamics. It is established that a parametrization of the component interactions (e.g. component loads) is problematic due to frequency dependence. Hence, a modified method is proposed in which the speed of Component Mode Synthesis (CMS) is used to avoid this parametrization. The effectiveness of this method is demonstrated in a test case concerning the placement of sensor and actuator locations in Active Structural Acoustic Control (ASAC). Special attention is paid to the behavior of the optimization strategy

Uncertainty propagation in multi-agent systems for multidisciplinary optimization problems

International audienceBecause of uncertainties on models and variables, deterministic multidisciplinary optimization may achieve under-sizing (without design margins) or over-sizing (with arbitrary design margins). Thus, it is necessary to implement multidisciplinary optimization methods that take into account the uncertainties in order to design systems that are both robust and reliable. Probabilistic methods such as reliability-based design optimization (RBDO) or robust design methods, provide designers with powerful decision-making tools but may involve very time-consuming calculations. New optimization approaches have been developed to deal with such complex problems. Auto-adaptive Multi-Agent Systems (AMAS) is a new approach developed recently, allowing to take into account the various aspects of a multidisciplinary optimization problem (multi-level, computation burden etc.). This approach was suggested for solving complex deterministic optimization problem. Now, the question of the integration of uncertainties in this multi-agent based optimization arises. The aim of this paper is to propose a new methodology for integrating the treatment of uncertainties in an adaptive multi-agent system for sequential optimization. The developed method employs a single loop process in which cycles of deterministic optimization alternate with evaluations of the system reliability. For each cycle, the optimization and the reliability analysis are decoupled from each other. The reliability analysis is carried out at agent level and only after the resolution of the deterministic optimization, to verify the feasibility of the constraints under uncertainties. Following the probabilistic study, the constraints violated (with low reliability) are shifted to the area of feasibility by integrating adaptive safety coeficients whose calculations are based on the agent-level reliability information. The method developed is applied to a conceptual aircraft design problem

Multi-Level Optimal Design Using Game Theory with Model Updating By Low Discrepancy Sampling

The Design of Experiment (DOE) based response surface methodology (RSM) is a commonly used technique for solving optimization problems. The traditional DOE method has some shortcomings when used to update the RSM model. This thesis aims to develop a new DOE technique to solve the model updating problems in design optimization. Toward this end, a new DOE based RSM method is proposed to solve this problem by using low-discrepancy sequence method to generate the additional data points needed to update the model to replace the traditional factor and level based DOE method. Tested on a couple of numerical example problems, the low-discrepancy sequence method is seen to be effective not only in solving the model updating problem, but also more effective and convenient compared to the traditional DOE method. The second part of this thesis deals with using game theory for solving multi-level design optimization problems. Based on three basic game modes, the Nash game (which is also considered as non-cooperative game), cooperative game, and Stackelberg game (a game between leaders and followers), two solution approaches for Stackelberg game with multiple leaders and followers are proposed: The Decentralized mode and the Hierarchical mode. During the research on these two game systems, solution approaches for a third system namely the Decentralized-Hierarchical model is also addressed in this thesis. It is seen that the low discrepancy sampling based approaches proposed in this thesis are quite effective in solving multi-level optimization problems

Dynamic multiscale topology optimization for multi-regional micro-structured cellular composites

© 2018 Elsevier Ltd In this paper, a new dynamic multiscale topology optimization method for cellular composites with multi-regional material microstructures is proposed to improve the structural performance. Firstly, a free-material distribution optimization method (FMDO) is developed to generate the overall configuration for the discrete element densities distributed within a multi-regional pattern. The macrostructure is divided into several sub regions, and each of them consists of a number of elements but with the same densities. Secondly, a dynamic topology optimization formulation is developed to perform the concurrent design of the macrostructure and material microstructures, subject to the multi-regional distributed element densities. A parametric level set method is employed to optimize the topologies of the macrostructure and material microstructures, with the effective macroscopic properties evaluated by the homogenization. In the numerical implementation, the quasi-static Ritz vector (QSRV) method is incorporated into the finite element analysis so as to reduce the computational cost in numerical analysis, and some kinematical connectors are introduced to make sure the connectivity between adjacent material microstructures. Finally, 2D and 3D numerical examples are tested to demonstrate the effectiveness of the proposed dynamic multiscale topology optimization method for the material-structural composites

Pareto Ranking Bisection Algorithm for EM-Driven Multi-Objective Design of Antennas in Highly-Dimensional Parameter Spaces

A deterministic technique for fast surrogate-assisted multi-objective design optimization of antennas in highly-dimensional parameters spaces has been discussed. In this two-stage approach, the initial approximation of the Pareto set representing the best compromise between conflicting objectives is obtained using a bisection algorithm which finds new Pareto-optimal designs by dividing the line segments interconnecting previously found optimal points, and executing poll-type search that involves Pareto ranking. The initial Pareto front is generated at the level of the coarsely-discretized EM model of the antenna. In the second stage of the algorithm, the high-fidelity Pareto designs are obtained through optimization of corrected local-approximation models. The considered optimization method is verified using a 17-variable uniplanar antenna operating in ultra-wideband frequency range. The method is compared to three state-of-the-art surrogate-assisted multi-objective optimization algorithms