Anti-optimisation of uncertain structures using interval analysis

McWilliam, Stewart

doi:10.1016/s0045-7949(00)00143-7

Cited by 163 publications

(61 citation statements)

References 9 publications

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“…As a result, it debased the accuracy of the calculation. Mcwilliam [12] put forward an improved method which may partly consider the interactions. Based on the operation characteristic of the interval number, the interval finite element equations are divided into the common linear equations by Guo and Lü [13] , however, the method has a particular demand for the intervals.…”

Section: Interval Analysis Methodsmentioning

confidence: 99%

Sensitivity analysis of soil parameters based on interval

Shao

Chu

2008

Appl. Math. Mech.-Engl. Ed.

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Interval analysis is a new uncertainty analysis method for engineering structures. In this paper, a new sensitivity analysis method is presented by introducing interval analysis which can expand applications of the interval analysis method. The interval analysis process of sensitivity factor matrix of soil parameters is given. A method of parameter intervals and decision-making target intervals is given according to the interval analysis method. With FEM, secondary developments are done for Marc and the Duncan-Chang nonlinear elastic model. Mutual transfer between FORTRAN and Marc is implemented.With practial examples, rationality and feasibility are validated. Comparison is made with some published results.

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Section: Interval Analysis Methodsmentioning

confidence: 99%

Sensitivity analysis of soil parameters based on interval

Shao

Chu

2008

Appl. Math. Mech.-Engl. Ed.

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“…The corresponding algorithm consists of a sequence of IFE problems defined on the deterministic linear systems of equations resulting from substituting discrete values for the frequency in Equation (1). However, it has been shown in literature that the solution set of the corresponding interval problem can only be approximated [18,19]. Furthermore, the numerical procedures to calculate this approximation are very computationally expensive.…”

Section: Mathematical Formulation Of the Ifem Frf Problemmentioning

confidence: 99%

An interval finite element approach for the calculation of envelope frequency response functions

Moens

Vandepitte

2004

Numerical Meth Engineering

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SUMMARYThis paper focusses on the application of the interval finite element method in dynamic analyses. It describes a methodology for calculating frequency response function envelopes from a finite element model containing imprecise parameters defined as interval uncertainties. The resulting envelope functions give a conservative approximation of the possible range of the frequency response function, taking into account that the uncertain parameters in the model can adopt any value in their presumed uncertainty intervals. The methodology is based on the modal superposition principle. It consists of an interval aritmethic algorithm which processes the results of a preliminary global optimization performed on the modal parameters. The algorithm is constructed such that it optimally combines the advantages of both the anti-optimization and the interval arithmetic strategy for general numerical interval calculations.In the first stage of the development, the modal parameter ranges of each individual mode are independently combined in the modal response contributions. This yields the modal rectangle (MR) method. In order to remedy the high conservatism inherent to the MR method, the exact eigenfrequency ranges are added to the analysis. This results in the modal rectangle method with eigenfrequency interval correction (MRE). A second improvement consists of adding extra delimiters to the MRE modal parameter range approximation. This is achieved by performing an extra optimization on the modal response contributions at discrete frequencies. The method is referred to as the locally optimized modal rectangle method with eigenfrequency interval correction (OMRE). Finally, a numerical example illustrates the different algorithms.

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“…Unfortunately, this approach shows the drawback of being less and less accurate, augmenting the level of the uncertainty of the parameters. As the method above relates to operations of interval multiplication and interval division, the method would have the drawback of overestimation of the interval of the eigenvalues of uncertain structures [10] . To overcome this drawback, making use of the information of the first-order partial derivatives of eigenvalues and the first-order parameter perturbation, Chen et al [11] introduce a parameter perturbation method to approximate the bounds of the structural eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

Eigenvalue analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

Qiu

Zhang³

2017

Applied Mathematical Modelling

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a b s t r a c tWhen the uncertainties in interval parameters are fairly large, the current analysis methods, which are usually based on the information of the first-order partial derivatives of eigenvalues, may not work well for the structural eigenvalue problem with interval parameters. To overcome this drawback, in this work, the structural eigenvalue problem with interval parameters is modeled as a series of QB (quadratic programming with box constrains) problems by taking advantage of the information of the second-order partial derivatives of eigenvalues. Then the series of QB problems would be solved by using the DCA (difference of convex functions algorithm) which is turn out be very effective for the QB problem. The specific examples, a concrete frame with sixty bars and a plate discretized with 300 finite elements, are given to show the effectiveness and feasibility of the proposed method compared with other methods.

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Anti-optimisation of uncertain structures using interval analysis

Cited by 163 publications

References 9 publications

Sensitivity analysis of soil parameters based on interval

Sensitivity analysis of soil parameters based on interval

An interval finite element approach for the calculation of envelope frequency response functions

Eigenvalue analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

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