Novel solution framework for inverse problem considering interval uncertainty

Abstract

This article proposes a novel solution framework for the inverse problem considering interval uncertainty in structural or systemic responses, which provides an efficient tool for the uncertain inverse problems of nonlinear structures or systems. Interval is used to model and characterize the uncertainty, and the bounds of uncertain structural responses are only required. In each iterative step, the approximate deterministic inverse problem is constructed according to the interval analysis results, and then the identified intervals of inputs are updated by solving the approximate deterministic inverse problem. Therefore, the interval inverse problem is decoupled into a series of interval analyses and deterministic inverse problems that are alternately solved, which dramatically promotes the computational efficiency of the interval inverse problem. Besides, an iterative mechanism is proposed to ensure the convergence of the whole procedure. Finally, two numerical examples and an engineering application are investigated to demonstrate the accuracy and efficiency of the proposed method.

An efficient method for estimating failure probability bounds under random‐interval mixed uncertainties by combining line sampling with adaptive Kriging

“…The illustration of design points under RIMU (6).If j = N, turn to step (7). Otherwise, let j = j + 1 and turn to step (3).…”

“…The problem for solving the intersection zj of l j (c, e 𝜶 ) and the extremum limit state surface under the RIMU. To solve the design point under the RIMU, the performance function g z ( z, x I ) in the standard normal space is firstly obtained by the transformation in Equation (6). The design point is defined as the failure point closest to the coordinate origin in the standard normal space.…”

“…However, due to the limitation of the data information in practice, it is almost impossible to assume that all uncertain input variables in the structure can be characterized by probabilistic model. The input variables with the limited experimental data in the practical engineering are generally quantified by interval model [3][4][5][6] lying within the certain lower bound and upper bound. In this paper, both the random and interval input variables are considered in the structural reliability analysis, and the motivation and importance of the work are discussed as follows in detail.…”

A novel univariate dimension‐reduction based interval finite element method for static response prediction of uncertain structures

“…Uncertainties of things are divided into three types: stochastic uncertainty, [4][5][6] fuzzy uncertainty 7,8 and interval uncertainty. [9][10][11][12] They belong to the research areas of probability theory and mathematical statistics, fuzzy mathematics and interval mathematics, respectively. Probabilistic/ stochastic models deal with uncertain engineering problems under the premise that empirical data are sufficient to determine the probability density function of uncertainty.…”

“…Uncertainties of things are divided into three types: stochastic uncertainty, 4‐6 fuzzy uncertainty 7,8 and interval uncertainty 9‐12 . They belong to the research areas of probability theory and mathematical statistics, fuzzy mathematics and interval mathematics, respectively.…”