Large-scale reliability-based structural optimization

In this paper a robust and efficient methodology is presented for treating largescale reliability-based, structural optimization problems. The optimization part is performed with evolution strategies, while the reliability analysis is carried out with the Monte Carlo simulation method incorporating the importance sampling technique for the reduction of the sample size. Efficient hybrid methods are implemented for the solution of the reanalysis type of problems that arise in optimization and reliability analysis phases of the proposed method. The hybrid solution methods are based on the preconditioned conjugate gradient algorithm using efficient preconditioning schemes. The numerical tests presented demonstrate the computational advantages of the proposed methods, which become more pronounced for large-scale optimization problems.

Progress in Structural Engineering, 1991

A brief retrospective of the past eight years of research efforts at the University of Colorado, Boulder, in reliability-based structural optimization (RBSO) is presented. This includes research related to (a) new formulations of both multi-limit state and multi-objective RBSO of steel and reinforced concrete structures, (b) use of interactive graphics in RBSO, (c) sensitivity of RBSO solutions to change in problem parameters, (d) RBSO of special structures such as large frames and bridges, (e) damage-tolerant RBSO, and (f) new probabilistic finite element formulations for nonlinear concrete structures.

2012

Solution of structural reliability problems by the First Order method require optimization algorithms to find the smallest distance between a limit state function and the origin of standard Gaussian space. The Hassofer-Lind-Rackwitz-Fiessler (HLRF) algorithm, developed specifically for this purpose, has been shown to be efficient but not robust, as it fails to converge for a significant number of problems. On the other hand, recent developments in general (augmented Lagrangian) optimization techniques have not been tested in aplication to structural reliability problems. In the present article, three new optimization algorithms for structural reliability analysis are presented. One algorithm is based on the HLRF, but uses a new differentiable merit function with Wolfe conditions to select step length in linear search. It is shown in the article that, under certain assumptions, the proposed algorithm generates a sequence that converges to the local minimizer of the problem. Two new augmented Lagrangian methods are also presented, which use quadratic penalties to solve nonlinear problems with equality constraints. Performance and robustness of the new algorithms is compared to the classic augmented Lagrangian method, to HLRF and to the improved HLRF (iHLRF) algorithms, in the solution of 25 benchmark problems from the literature. The new proposed HLRF algorithm is shown to be more robust than HLRF or iHLRF, and as efficient as the iHLRF algorithm. The two augmented Lagrangian methods proposed herein are shown to be more robust and more efficient than the classical augmented Lagrangian method.

Proceedings of the Ninth International Conference on Computational Structures Technology

Reliability-based optimization (RBO) is a powerful tool for design, as it allows to determine an optimal structural configuration while explicitly taking into account the effects of uncertainty (loading, geometry, structural parameters, etc.) on the structural performance. Nonetheless, the practical application of RBO to problems of engineering interest may be rather involved, due to the necessity of repeatedly computing the structural response for different sets of the uncertain parameters and design variables. This contribution proposes a framework for performing reliability-based optimization efficiently. The proposed approach, based on a decoupling approach and sequential approximations, introduces two new techniques: a line search strategy and weighted approximations. An application example involving a non linear structure under dynamic loading is presented, showing the advantages and efficiency of the proposed framework.

Volume 2: 29th Design Automation Conference, Parts A and B, 2003

The use of probabilistic optimization in structural design applications is hindered by the huge computational cost associated with evaluating probabilistic characteristics, where the computationally expensive finite element method (FEM) is often used for simulating design performance. In this paper, a Sequential Optimization and Reliability Assessment (SORA) method with analytical derivatives is applied to improve the efficiency of probabilistic structural optimization. With the SORA method, a single loop strategy that decouples the optimization and the reliability assessment is used to significantly reduce the computational demand of probabilistic optimization. Analytical sensitivities of displacement and stress functionals derived from finite element formulations are incorporated into the probability analysis without recurring excessive cost. The benefits of our proposed methods are demonstrated through two truss design problems by comparing the results with using conventional app...

Computer Methods in Applied Mechanics and Engineering, 2002

This paper examines the application of neural networks (NN) to reliability-based structural optimization of largescale structural systems. The failure of the structural system is associated with the plastic collapse. The optimization part is performed with evolution strategies, while the reliability analysis is carried out with the Monte Carlo simulation (MCS) method incorporating the importance sampling technique for the reduction of the sample size. In this study two methodologies are examined. In the first one an NN is trained to perform both the deterministic and probabilistic constraints check. In the second one only the elasto-plastic analysis phase, required by the MCS, is replaced by a neural network prediction of the structural behaviour up to collapse. The use of NN is motivated by the approximate concepts inherent in reliability analysis and the time consuming repeated analyses required by MCS. Ó

The real world behavior and the sensitiveness of structures are continuously gaining interest in structural design. This is a direct result of improvements due to advances made in modern computational mechanics. By that, the demands on structural optimization models representing an abstract and rational basis for computer-aided design also increase. To map reality, in particular, probabilistic phenomena are becoming essential and have to be taken into account. Within this contribution, two approaches are presented that allow for a realistic but simultaneously efficient reproduction of the probabilistic nature associated with structural design problems. First, a semi-deterministic approach is elucidated by which the random nature of geometric imperfections induced into a structural system can be caught. Second, a probabilistic approach is presented considering loads and stresses as random processes that lead to design quantities described by probability density functions.

Structural and Multidisciplinary Optimization, 2010

Reliability-based Optimization is a most appropriate and advantageous methodology for structural design. Its main feature is that it allows determining the best design solution (with respect to prescribed criteria) while explicitly considering the unavoidable effects of uncertainty. In general, the application of this methodology is numerically involved, as it implies the simultaneous solution of an optimization problem and also the use of specialized algorithms for quantifying the effects of uncertainties. In view of this fact, several approaches

Doboku Gakkai Ronbunshu, 1987

This paper presents an optimization approach for the reliability analysis of large-scaled skeletal structures by using the revised PNET method. In order to evaluate the collapse probability of the structural system, it is needed to consider all possible collapse modes and the effects of their mutual correlations. However, it is considerablly difficult to find all possible collapse modes for the highly redundant systems. To overcome this problem, an optimization technique for the PNET method is initially developed to find the approximate collapse probability of the structure, which is defined as the sum of the collapse probabilities of the representative modes classified by the extent of correlation. In order to confirm the validity of this approach, the computational results are compared with the values found by the Monte Carlo simulation using the collapse load analysis. Two fairly large framed structures are numerically analyzed to illustrate the features and scopes of this approach.

Applied Mathematics, 2013

In order to take into account the uncertainties linked to the variables in the evaluation of the statistical properties of structural response, a reliability approach with probabilistic aspect was considered. This is called the Probabilistic Transformation Method (PTM). This method is readily applicable when the function between the input and the output of the system is explicit. However, the situation is much more involved when it is necessary to perform the evaluation of implicit function between the input and the output of the system through numerical models. In this work, we propose a technique that combines Finite Element Analysis (FEA) and Probabilistic Transformation Method (PTM) to evaluate the Probability Density Function (PDF) of response where the function between the input and the output of the system is implicit. This technique is based on the numerical simulations of the Finite Element Analysis (FEA) and the Probabilistic Transformation Method (PTM) using an interface between Finite Element software and Matlab. Some problems of structures are treated in order to prove the applicability of the proposed technique. Moreover, the obtained results are compared to those obtained by the reference method of Monte Carlo. A second aim of this work is to develop an algorithm of global optimization using the local method SQP, because of its effectiveness and its rapidity of convergence. For this reason, we have combined the method SQP with the Multi start method. This developed algorithm is tested on test functions comparing with other methods such as the method of Particle Swarm Optimization (PSO). In order to test the applicability of the proposed approach, a structure is optimized under reliability constraints.