Robust fuzzy structural safety assessment using mathematical programming approach

Structural reliability analysis with fuzzy random variables using error principle

This paper aims to develop a suitable restoration method by a joint usage of an Expert system (ES) and a Mathematical Programming (MP) approach. Under this devise, the optimal target system for storation is formulated as an MP problem and solved efficiently by the decomposition-coordination strategy; that is a whole problem is decomposed into subproblems according to the generic knowledge of experts. The introduction of a new concept ?>restorative operation cost ?> that reflects the various restoration strategies has decreased the number of rules in the knowledge-base to one third that of typical existing ES's. The validity and effectiveness of the combined method have been demonstrated by applying it to a practical size restoration problem.

In structural reliability calculation, there are fuzzy uncertainties in the distribution parameters of random variables, which bring the problem of large computation and poor precision. In order to improve accuracy and efficiency of structural reliability, a novel structural reliability calculation method with fuzzy random variables is proposed from the perspective of perturbation principle. First, the fuzzy characteristic parameters of the structural fuzzy random variables are expressed as the sums of their true values and fuzzy perturbations. At the same time, the perturbations are equivalently selected. Second, the probability density function and the performance function are decomposed into a series of intervals under different level cut sets, and the Taylor series is expanded on the upper and lower limits of the intervals. Finally, according to the definition of structural reliability, based on the direct integration method, the sigmoid function is introduced into the reliability function to approximate the step function, and the fuzzy reliability is obtained. The simulation results show the effectiveness and accuracy of the proposed method, and it provides a feasible way for structural reliability analysis with fuzzy variables or fuzzy random variables.

This paper proposes a new mathematical programming approach to represent the dimensions of the discriminant space for the multiple-group classification problem. Few papers have investigated generalizations of two-group mathematical programming approaches for the classification of multiple groups. While several papers have proposed mathematical programming models for separating groups of observations, the issue of considering the classification problem by finding discriminant linear functions to describe the groups in fewer dimensions has not been addressed. The new mathematical programming approach proposed in this paper first solves the multiple-group problem using a single discriminant function, which essentially represents the separation of the groups in one dimension. Then the multiple-group problem is successively solved using single discriminant functions with the requirement that successive linear discriminant functions have a sample covariance equal to zero. An algorithm is proposed to classify observations from multiple groups using the linear discriminant functions from the mathematical programming approach in a reduced number of dimensions.

Fuzzy stochastic finite element method for the hybrid uncertain temperature field prediction

The main subjects of this chapter are the variational formulations for the computation of a safety factor in shakedown analysis, the numerical procedures available to implement this analysis, and an overview on the wide field of applications and conceptual extensions.In structural engineering and solid mechanics, the wordshakedown, introduced in the 1940s by W. Prager, became, since then, synonymous with elastic adaptation in the presence of variable loadings, a safe stabilized phenomenon, often due to some limited plastic deformation (or equivalently, due to the residual stress distribution associated with inelastic strains).Concerning the failure analysis of ductile structures, the termsalternating plasticityandincremental collapse, besidesplastic collapse, are also widely used to identify failure modes under variable loadings. A structure undergoesalternating plasticitywhen the fluctuating loading program produces, after any arbitrarily large time, some plastic deformation as well as a subsequent vanishing of the net plastic deformation. This induces failure due to low‐cycle fatigue. Likewise, the structure fails byincremental collapsewhen plastic deformations accumulate in the form of a compatible strain distribution that leads to excessive inelastic deformation.Shakedown analysis allows working under the realistic assumption that only the range of variable loadings is known, unlike the usual prescription of a particular loading history. That is, we deal withdirect methodsthat are based solely on the knowledge of a range of load variations (or a reference loading, in limit analysis) in this chapter. It is worth emphasizing that the differences between incremental and direct methods go beyond the computational advantages frequently obtained with the latter ones. In fact, the fundamental questions about whether or not critical loads or cycles do exist, independently from loading histories, can only be answered by the theories of direct methods.The mathematical foundations of shakedown theory strongly rest on optimization theory and the related areas of convex analysis and mathematical programming. The present chapter contains simplified derivations of the statical, kinematical, and mixed variational principles of shakedown theory by means of the basic techniques of convex analysis. Moreover, numerical procedures suitable to solve the shakedown analysis problem are discussed here in the framework of mathematical programming techniques combined with common procedures in the field of finite element methods.Applications in fundamental examples are then presented, namely, (a) a restrained block under thermo‐mechanical loadings, (b) the classical Bree problem of a tube under variable pressure and temperature, with a more realistic model and including an exact solution, (c) a plate with a circular hole subjected to variable tractions, and (d) a plate with simulated imperfections showing critical mechanisms with strongly localized deformations.

In this paper we present a mathematical programming based approach for revenue management in cargo airlines. The approach is based on a modified version of a multicommodity network flow model which has been developed in a decision support approach for schedule planning in cargo airlines. We think that using the same concept for planning and revenue management is essential for consistency of planning and operation. To meet the real-time requirements of revenue management special computational strategies for solving the large models are necessary.

Aggregating classifiers with mathematical programming

This paper proposes fuzzy-based multi-objective design optimization approach for the optimal analysis of buried pipe based on the expected value of a fuzzy output variable when the membership function is computed. The design of pipe structures is usually associated with uncertainties. Therefore, the principle of fuzzy set and a multi-objective optimization algorithm is applied to account for the variabilities associated with the uncertain parameters to ensure an acceptable performance against the impact of uncertainties. Different methods such as deterministic and non-deterministic methods have been proposed to model the effect of uncertainties and analyse the performance of engineering structure in the literature. Herein, a fuzzy-based uncertainty modelling approach that employs the optimal performance of a hybrid GA-GAM for the analysis of a buried pipeline is proposed. The purpose of the strategy is to optimise the design variable while considering the adverse effect of the uncertain fuzzy variables and variability of the structural performance. The uncertain fuzzy variable is used in the analysis to take into account the subjective nature of the corrosion process, while the entropy of a fuzzy variable used as a global measure of variable dispersion is employed to measure the variability and sensitivity of the structural response. The outcome of the fuzzy-based multi-objective design optimization provides a set of optimal solution for the analysis of fuzzy structure. Finally, the applicability and characteristic of this method are demonstrated using a numerical example, and the outcome denotes acceptable analytical tools for design engineers and can be applied to analyse other engineering structures.

Classical limit analysis of structures by the statical approach computationally means maximization of a load multiplier under equilibrium and yield condition constraints, namely convex mathematical programming. In elastoplasticity, generalizations of limit analysis had been proposed in order to achieve, still by load factor constrained optimization, the safety factor with respect to plastic collapse. This paper presents similar generalization in two-phase poroelastoplasticity. A method is here developed (and validated by numerical application to a masonry dam) apt to assess the safety factor of a structure interpretable as a poroplastic system, with respect to both plastic collapse and critical thresholds on deformations, by solving a nonconvex nonsmooth constrained optimization problem usually referred to in the literature as “mathematical program under equilibrium constraints”. Piece-wise linearization of yield surfaces and reduction of yield planes by a “sifting” procedure are adopted to reduce computing efforts.

Heat transfer principles in thermal calculation of structures in fire

A new risk criterion in fuzzy environment and its application

In this study, extended two-stage stochastic programming with fuzzy variables is developed for water resources management under uncertainty. First, the problem is formulated and solved by an extended interval-parameter two-stage stochastic programming (ITSP) approach for retrieving water shortages. To this end, some alternatives are considered to retrieve the difference between the quantities of promised water-allocation targets and the actual allocated water. An extended ITSP is then developed for the problem under the fuzzy uncertainty by using fuzzy variables and solved using fuzzy chance-constrained programming based on the idea of possibility theory. Furthermore, an illustrative example is also given to clarify the methods discussed in this paper.

This paper proposes a strict constructing approach for a reasonable membership function as objectively as possible. It is important to set a reasonable membership function to parameters for real-world decision making interactively and objectively. The main contribution of our proposed approach is to integrate a general continuous function derived from mathematical programming under a given probability density function based on real-world data into subjective interval estimation by a heuristic method. The interval estimation is to set intervals that a decision maker confidently judges whether an element is completely or never included in the given set. The main steps of our proposed approach are to solve the mathematical programming problem in terms of objectivity. It is hard to solve the problem with nonlinear function directly and efficiently. In this paper, the given nonlinear membership function is approximately transformed into a piecewise linear membership function, and the appropriate membership values are determined based on the strict optimal solution.

Returns to beef research in Canada: A comparison of time series and mathematical programming approaches