An iterative dimension-by-dimension method for structural interval response prediction with multidimensional uncertain variables

Xiong, Congcong; Wang, Lei; Liu, Guanhua; Shi, Qinghe

doi:10.1016/j.ast.2019.01.032

Cited by 62 publications

(15 citation statements)

References 32 publications

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“…不确定性. 以飞行器结构为例, 其在制造、装配及服役过程中存在着多源不确定性: 因加工工艺等引起的材料属性分散性、由于制造及安装误差导致的几何尺寸不确定性以及由于外界扰动引起的载荷不确定性等 [21,22] . 这些不确定性相互作用会引起结构系统性能的巨大变化, 在高性能设计的需求下有必要在Birkhoff 系统构建以及保辛求解的过程中考虑不确定性的影响.…”

Section: 对于实际的动力学系统将不可避免地存在多种unclassified

Random and interval uncertain symplectic methods for linear Birkhoff equations and their comparison study

Zhu¹,

Qiu²

2020

Sci. Sin.-Phys. Mech. Astron.

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Section: 对于实际的动力学系统将不可避免地存在多种unclassified

Random and interval uncertain symplectic methods for linear Birkhoff equations and their comparison study

Zhu¹,

Qiu²

2020

Sci. Sin.-Phys. Mech. Astron.

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“…The nonprobabilistic method is suitable to address the uncertain variables with upper and lower bounds, 28 including the interval, ellipsoid, super parametric, and exponential convex models, among others 29‐31 . Wang et al 32 used the interval set‐theoretic model to describe the uncertain‐but‐bounded uncertainties in TO problems, and the iterative dimension‐by‐dimension method was further constructed to accelerate the convergence rate considerably 33 . The fuzzy method adopted the membership level to describe the uncertain parameters to achieve design results under different safety targets 34,35 .…”

Section: Introductionmentioning

confidence: 99%

Robust topology optimization methodology for continuum structures under probabilistic and fuzzy uncertainties

Meng

Wang

et al. 2021

Numerical Meth Engineering

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Owing to the variations in geometric dimensions, material properties and external loads in engineering applications, robust topology optimization (RTO) has garnered increasing attention in recent years to account for the uncertain behaviors during the preliminary concept design phases. This paper presents a hybrid RTO method to simultaneously resolve the epistemic and aleatory uncertainties. First, based on the probabilistic and fuzzy methodologies, the hybrid RTO model is formulated with nested double optimization loops using Monte Carlo simulations. Second, an efficient iterative method is proposed based on the perturbation method to accelerate the rate of convergence of the proposed hybrid RTO model. The derivatives of the hybrid robust compliance objective function with respect to the deterministic design variables, random parameters, and fuzzy parameters are then derived using the adjoint variable method. Finally, a T-shaped beam design, an L-shaped beam design, and a three-dimensional cantilever beam design are tested to validate the proposed hybrid RTO method.

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“…At present, the methods to deal with the uncertainty include the probability method [5], [6], the fuzzy method [7], [8], and the interval method [9], [10], etc. Among them, the fuzzy method uses membership function to describe the uncertain quantity, and uses the fuzzy mathematics to solve the membership function of the state quantity; the probability method uses random variables to describe the uncertainty, and uses Monte Carlo simulation [11], point estimation [12], semi-invariant method [13] to obtain the probability distribution characteristics of state variables; the interval method uses interval number to describe the uncertainty, and uses interval analysis theory to solve the equation with interval number.…”

Section: Introductionmentioning

confidence: 99%

Utilizing Statistical Information for Interval Analysis: A Method for Analyzing the Interval Uncertainty of Line-of-Sight Measurement Error of Space-Borne Observation Platforms

Ding

Yang

et al. 2020

IEEE Access

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Analyzing the space-borne observation platform's line-of-sight measurement error (SOPLME) is of great significance for the improvement of the space-borne optical tracking system. In this regard, we consider the space-borne observation platform (SOP) as a multi-body system and build both the target imaging model from the inertial space to the optical camera image plane and the line-of-sight measurement model. The relationship between the SOPLME and the satellite's orbit error, attitude error, platform angular vibration error, inner and outer frame rotation error, and position quantization error of target image point is deduced theoretically. However, since there are many error sources and the modeling process is highly nonlinear, the amplification of the output range caused by the ''wrapping effect'' may occur when using the interval calculation method to analyze the output range of the SOPLME. To solve this problem, we propose a novel method of interval analysis by using statistical information. This method combines the convenience of interval representation with the high accuracy of probability calculation, which can effectively avoid the overestimation problem caused by the inherent ''wrapping effect'' of the interval calculation method. Firstly, we describe the parameters of each error source with the interval constructed by upper and lower bounds. Secondly, the optimal Latin hypercube sampling (LHS) matrix of error source parameters is designed by the quasi-optimization method. Then we use the Gaussian mixture model (GMM) to approximate the distribution function of the SOPLME. Finally, the output range of the SOPLME is estimated by Taylor expansion. The simulation test verifies the reliability of the model and interval calculation method in this paper. The simulation example shows that the proposed method can get a more reliable error output interval with less sampling amount, which is suitable for analyzing the dynamic process of the output interval of the SOPLME. INDEX TERMS Space-borne observation platform, line-of-sight measurement error, interval analysis, Latin hypercube sampling, Gaussian mixture model.

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An iterative dimension-by-dimension method for structural interval response prediction with multidimensional uncertain variables

Cited by 62 publications

References 32 publications

Random and interval uncertain symplectic methods for linear Birkhoff equations and their comparison study

Random and interval uncertain symplectic methods for linear Birkhoff equations and their comparison study

Robust topology optimization methodology for continuum structures under probabilistic and fuzzy uncertainties

Utilizing Statistical Information for Interval Analysis: A Method for Analyzing the Interval Uncertainty of Line-of-Sight Measurement Error of Space-Borne Observation Platforms

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