Zhiping Qiu

Anti-optimization technique – a generalization of interval analysis for nonprobabilistic treatment of uncertainty

Abstract Anti-optimization technique, on the one hand, represents an alternative and complement to traditional probabilistic methods, and on the other hand, it is a generalization of the mathematical theory of interval analysis. In this study, in terms of interval analysis or interval mathematics, the arithmetic operations and the partial order relation of anti-optimization technique can be defined, and the convex model variables and the convex model extension function of convex models can also be introduced. The comparison of the Lagrange multiplier method with the convex model extension method for evaluating the region of static displacements of structures with uncertain-but-bounded parameters shows that the width of the upper and lower bounds on the static displacement yielded by the Lagrange multiplier method of convex models is tighter than those produced by the convex model extension.

Interval Analysis Method for Damage Identification of Structures

description was adopted for the measured natural frequencies in this paper. Via the first-order Taylor series expansion, the interval bounds of the elemental stiffness parameters of both undamaged and damaged structures were derived by using the model updating based on the initial analytical finite element model. The damage can be identified by comparing the differences between the two models, where the quantitative measure of the possibility of damage existence in the elements is introduced. A larger value of possibility of damage existence implied a higher possibility of damage occurrence. The damage identifications for a steel cantilever beam and a steel cantilever plate were performed by the presented method, which is validated by Monte Carlo simulation. Moreover, the case of the multidamage identification, the number of the used natural frequencies, and the effects of damage level and uncertainty level on the damage detection were studied as well. The numerical results proved the validity and applicability of the presented interval analysis method.

Membership-Set Identification Method for Structural Damage Based on Measured Natural Frequencies and Static Displacements

Based on measured natural frequencies and static displacements, an improved interval analysis technique is proposed for structural damage detection by adopting membership-set identification and two-step model updating procedures. Due to the scarcity of uncertain information, the uncertainties are considered as interval numbers in this article. Via the first-order Taylor series expansion, the interval bounds of the elemental stiffness parameters of undamaged and damaged structures are obtained. The structural damage is detected by the quantitative measure of the possibility of damage existence in elements, which is more reasonable than the probability of damage existence in the condition of less measurement data. In this study, the conversation of the interval analysis method is remarkably reduced by the membership-set identification technique. The present method is applied to a truss structure and a steel cantilever plate for damage identification, and the damage identification results obtained by the interval analysis method and probabilistic method are compared. This article also discusses the effects of damage level and uncertainty level on detection results. The numerical examples show that the wide intervals resulting from the interval operation can be narrowed by the proposed non-probabilistic approach, and the feasibility and applicability of the present method are validated.

PROBABILISTIC DAMAGE IDENTIFICATION OF STRUCTURES WITH UNCERTAINTY BASED ON DYNAMIC RESPONSES

The probabilistic damage identification problem with uncertainty in the FE model parameters, external-excitations and measured acceleration responses is studied. The uncertainty in the system is concerned with normally distributed random variables with zero mean value and given covariance. Based on the theoretical model and the measured acceleration responses, the probabilistic structural models in undamaged and damaged states are obtained by two-stage model updating, and then the Probabilities of Damage Existence (PDE) of each element are calculated as the damage criterion. The influences of the location of sensors on the damage identification results are also discussed, where one of the optimal sensor placement techniques, the effective independence method, is used to choose the nodes for measurement. The damage identification results by different numbers of measured nodes and different damage criterions are compared in the numerical example.

Non-Probabilistic Methods for Natural Frequency and Buckling Load of Composite Plate Based on the Experimental Data

A hybrid experimental-theoretical method is proposed to investigate the influence of unavoidable scatter in elastic moduli on the natural frequency and axial buckling load of composite plate using ellipsoidal and interval analyses. The elastic moduli for material T300-QY8911 are quantified by use of the smallest ellipsoid or smallest hyper-rectangle based on a set of real experimental data. Then the bounds of the natural frequency of axial buckling load of composite plate in virtue of the obtained ellipsoid and hyper-rectangle are evaluated. Numerical examples are provided to illustrate the feasibility and validity of the proposed method.