Explaining language change: an evolutionary approach

Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach

Using a quantified measure for non-probab ilistic reliability based on the multi-ellipsoid convex model, the topology optimization of continuum structures in presence of uncertain-but-bounded parameters is investigated. The problem is formulated as a double-loop optimization one. The inner loop handles evaluation of the non-probabilistic reliability index, and the outer loop treats the optimum material distribution using the results from the inner loop for checking feasibility of the reliability constraints. For circumventing the numerical difficulties arising from its nested nature, the topology optimization problem with reliability constraints is reformulated into an equivalent one with constraints on the concerned performance. In this context, the adjoint variable schemes for sensitivity analysis with respect to uncertain variables as well as design variables are discussed. The structural optimization problem is then solved by a gradient-based algorithm using the obtained sensitivity. In the present formulation, the uncertain-but bounded uncertain variations of material properties, geometrical dimensions and loading conditions can be realistically accounted for. Numerical investigations illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques. The computational results also reveal that non-probabilistic reliability-based topology optimization may yield more reasonable material layouts than conventional deterministic approaches. The proposed method can be regarded as an attractive supplement to the stochastic reliability-based topology optimization.

Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model

Uncertainties in design variables and problem parameters are often inevitable and must be considered in an optimization task if reliable optimal solutions are sought. Besides a number of sampling techniques, there exist several mathematical approximations of a solution's reliability. These techniques are coupled in various ways with optimization in the classical reliability-based optimization field. This paper demonstrates how classical reliability-based concepts can be borrowed and modified and, with integrated single and multiobjective evolutionary algorithms, used to enhance their scope in handling uncertainties involved among decision variables and problem parameters. Three different optimization tasks are discussed in which classical reliability-based optimization procedures usually have difficulties, namely (1) reliability-based optimization problems having multiple local optima, (2) finding and revealing reliable solutions for different reliability indices simultaneously by means of a bi-criterion optimization approach, and (3) multiobjective optimization with uncertainty and specified system or component reliability values. Each of these optimization tasks is illustrated by solving a number of test problems and a well-studied automobile design problem. Results are also compared with a classical reliability-based methodology.

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Reliability-Based Optimization Using Evolutionary Algorithms

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Interval Monte Carlo methods for structural reliability

A new methodology for seismic design is proposed based on structural optimization with performance-based constraints. Performance-based criteria are introduced for the seismic design of new buildings. These criteria are derived from the National Guidelines for Seismic Rehabilitation of Buildings (Reference [19], Federal Emergency Management Agency (FEMA), ‘NHERP Guidelines for seismic rehabilitation of buildings’, Report Nos 273 and 274, Washington, DC, 1997) for retrofitting existing structures. The proposed design methodology takes into account the non-linear behaviour of the structure. The goal is to incorporate in the design the actual performance levels of the structure, i.e. how much reserve capacity the structure has in an earthquake of a given magnitude. The optimal design of the structure minimizes the structural cost subjected to performance constraints on plastic rotations of beams and columns, as well as behavioural constraints for reinforced concrete frames. Uncertainties in the structural period and in the earthquake excitation are taken into account using convex models. The optimization routine incorporates a non-linear analysis program and the procedure is automated. The proposed methodology leads to a structural design for which the levels of reliability (performance levels) are assumed to be quantifiable. Furthermore, the entire behaviour of the structure well into the non-linear range is investigated in the design process. Copyright © 2000 John Wiley & Sons, Ltd.

Performance‐based design using structural optimization

The optimal design of trusses subjected to loads considered to be uncertain in both magnitude and direction is investigated. A non-probabilistic ellipsoidal convex model is established for considering the uncertainties using three different criteria. The convex model is described as a set of constraints on the upper and lower limits of the load magnitudes and directions. The optimal design of the trusses is performed using two different optimization objectives. The first objective function to be minimized is the structural volume; constraints are imposed on the stresses and buckling loads of the members and on the joint displacements. Another objective function to be minimized is a selected displacement; constraints are implemented on the stresses and buckling loads of the members and on the structural volume. The presented method yields optimal designs that violate stress, displacement, and buckling constraints with less frequency than the assumed worst load condition. This method offers an alternative t...

Design of Trusses under Uncertain Loads Using Convex Models

Optimum structural design via convex model superposition

This paper is concerned with the optimal design of structures that are affected by uncertainties present in the loads applied to the structure, and by uncertainties affecting the internal resistance of the structural members. The magnitude of the applied loads and the modulus of elasticity of the structural members are assumed to vary within deterministic bounds. These uncertainties are idealized using a nonprobabilistic method, the convex model. The two types of uncertainties are considered simultaneously by employing the Cartesian product of convex sets. Two different convex models are examined to account for the uncertainties: the ellipsoidal convex model, and the uniform bound convex model. The optimum designs of a truss using the two convex models are compared to a worst case scenario optimum design in order to evaluate their performance. It is shown that it is not possible to identify a single worst case scenario that would be able to account for all possible combinations of uncertainties. However, both the ellipsoidal and the uniform bound convex model designs are found to be superior to the worst case scenario design in terms of constraint violations.

Sara Ganzerli

Papers

Performance‐based design using structural optimization

Design of Trusses under Uncertain Loads Using Convex Models

Optimum structural design via convex model superposition

Load and resistance convex models for optimum design

Comparison of fuzzy set and convex model theories in structural design