Hector A. Jensen

A possibilistic decision support system for imprecise mathematical programming problems

Abstract An approach for decision support under uncertainty based on a nondeterministic possibilistic approach is considered. Problem uncertainties are defined by fuzzy numbers and characterized by membership functions. A method for the efficient numerical implementation of the proposed decision support system is presented. The method is basically an algebraic process which can be implemented for general decision making problems. A set of representative samples of the solution behavior can be obtained directly from the formulation. At the same time, information about the global effect of the problem uncertainties on the optimal solution can be evaluated immediately from the analysis. The effectiveness of the method is illustrated by the solution of a programming model that represents the logistics management of the sulfuric acid business in Chile. Numerical results show the usefulness and potential of the proposed possibilistic approach.

A global sensitivity analysis in structural mechanics

A methodology is developed to evaluate the response sensitivity of structural systems to variations in their design parameters. The sensitivity is evaluated by considering the global behavior of the system response when the parameters vary within a bounded region. The design parameters are characterized by means of baseline values plus fluctuating components, and the sensitivity of the system is measured in terms of the global variability of the response with respect to its baseline response. The methodology is then extended into the context of optimum redesign analysis of structural systems. Application of the method is made to a structural system defined by two-dimensional beam-column elements and to a system defined by plate elements. The numerical implementation of the global sensitivity approach is made by means of the finite element method. Several analyses are performed and the results are discussed. Finally, some extensions of the present work are presented.

Structural optimal design of systems with imprecise properties: a possibilistic approach

Abstract The optimization problem of structural systems with imprecise properties on the basis of a possibilistic approach is considered. System imprecisions are defined by fuzzy numbers and characterized by membership functions. A methodology for the efficient solution of the optimization process is presented. A two-step method is used to include the imprecision within the optimization, where high quality approximations are used for the evaluation of structural responses. The approximations are constructed using concepts of intermediate response quantities and intermediate variables. The approach is basically an algebraic process which can be implemented very efficiently for the optimal design of general structural systems with imprecise parameters. The method provides more information to the designer than is available using conventional design tools. The effectiveness of the methodology and the interpretation of the results are illustrated by the solution of two example problems.

Model-reduction techniques for reliability-based design problems of complex structural systems

This work presents a strategy for dealing with reliability-based design problems of a class of linear and nonlinear finite element models under stochastic excitation. In general, the solution of this class of problems is computationally very demanding due to the large number of finite element model analyses required during the design process. A model reduction technique combined with an appropriate optimization scheme is proposed to carry out the design process efficiently in a reduced space of generalized coordinates. In particular, a method based on component mode synthesis is implemented to define a reduced-order model for the structural system. The re-analyses of the component or substructure modes as well as the re-assembling of the reduced-order system matrices due to changes in the values of the design variables are avoided. The effectiveness of the proposed model reduction technique in the context of reliability-based design problems is demonstrated by two numerical examples.

Use of approximation concepts in fuzzy design problems

Abstract This paper presents a fuzzy formulation for design problems. Design variables, as well as problem parameters are modeled as fuzzy numbers characterized by membership functions. An optimization approach and a formulation based on functional requirements on performance parameters are presented. In both cases, numerically efficient algorithms are required to evaluate system responses and their membership functions. Approximation concepts are introduced to develop an efficient numerical methodology in order to define high quality approximations for response functions and membership functions of system responses. Example problems are presented to illustrate and validate the use of approximations in the context of fuzzy design problems. Numerical results show the usefulness and effectiveness of the proposed method.

Sensitivity estimation of failure probability applying line sampling

Abstract This contribution presents a framework for calculating a sensitivity measure for problems of computational stochastic mechanics. More specifically, the sensitivity measure considered is the derivative of the failure probability with respect to parameters of the probability distributions (e.g. mean value, standard deviation) associated with the random input quantities of a system’s model. The proposed framework is formulated as a post-processing step of Line Sampling, which is a simulation-based method for estimating small failure probabilities. In particular, the proposed framework comprises two different approaches for estimating the sought sensitivity. The application of the proposed framework and comparison of the two aforementioned approaches is discussed through a number of numerical examples. The results obtained indicate that both approaches allow estimating the sought sensitivity measure.

Implementation of an adaptive meta-model for Bayesian finite element model updating in time domain

This work explores the feasibility of integrating an adaptive meta-model into a finite element model updating formulation using dynamic response data. A Bayesian model updating approach based on a stochastic simulation method is considered in the present formulation. Such approach is combined with a surrogate technique and an efficient model reduction technique. In particular, an adaptive surrogate model based on kriging interpolants and a model reduction technique based on substructure coupling are implemented. The integration of these techniques into the updating process reduces the computational effort to manageable levels allowing the solution of complex problems. The effectiveness of the proposed strategy is demonstrated with three finite element model updating applications.

Reliability-based synthesis of non-linear stochastic dynamical systems: a global approximation approach

The paper presents an efficient methodology to carry out reliability-based structural optimisation of non-linear systems under stochastic loading. The optimisation problem is formulated as the minimisation of an objective function subject to multiple reliability constraints. The reliability constraints are given in terms of first excursion probabilities with large state-space dimensions. A sequential approximate optimisation scheme based on global approximations of the reliability constraints is implemented in the proposed formulation. The approximations of the first excursion probabilities in terms of the design variables are constructed by combining a global mixed linearisation approach with a reliability sensitivity analysis. The sensitivity of the first excursion probabilities are estimated by considering some statistics of an augmented reliability problem. The number of reliability estimations required during the optimal design process is generally very small. Two numerical examples are presented to illustrate the effectiveness of the method.

Optimal Design of Base-Isolated Systems Under Stochastic Earthquake Excitation

The development of a general framework for reliability-based design of base-isolated structural systems under uncertain conditions is presented. The uncertainties about the structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. Nonlinear elements composed by hysteretic devices are used for the isolation system. The optimal design problem is formulated as a constrained minimization problem which is solved by a sequential approximate optimization scheme. First excursion probabilities that account for the uncertainties in the system parameters as well as in the excitation are used to characterize the system reliability. The approach explicitly takes into account all non-linear characteristics of the combined structural system (superstructure-isolation system) during the design process. Numerical results highlight the beneficial effects of isolation systems in reducing the superstructure response.

Approximation Concepts For Fuzzy Structural Analysis

This contribution presents an approach for performing fuzzy structural analysis of linear structures subject to static loading where uncertainties are present in both material properties and loadings. The responses of interest are displacements of the structure. The proposed approach is based on a non-linear approximation of these responses. This non-linear approximation is constructed by taking into account the linearity of the displacements with respect to loading and by introducing intervening variables. In this manner, high quality approximations of the structural responses are obtained allowing to determine membership functions performing a single structural analysis.