Reliability-based design optimization under mixture of random, interval and convex uncertainties

Wang, Lei; Wang, Xiaojun; Wang, Ruixing; Chen, Xiao

doi:10.1007/s00419-016-1121-0

Cited by 53 publications

(21 citation statements)

References 40 publications

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“…According to equations (16) and (19), a l and a c influence the final total normal stiffness K n and total tangential stiffness directly. Moreover, from equations (5), (10), and (11), the uncertain parameters D and G determine a l and a c , respectively.…”

Section: Effects Of D and G On A C And A Lmentioning

confidence: 99%

“…In recent years, more and more attention has been paid to the uncertainty of engineering problem. 15,16 Many uncertain parameters such as external load, material characteristics, and machining error in the actual bolted joint exist. All these external uncertainties can vary micro-fractal parameters, and the uncertain parameters lead to the change of system's characteristics.…”

Section: Introductionmentioning

confidence: 99%

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Interval estimation for contact stiffness of bolted joint with uncertain parameters

Zhao

Yang

Liu

et al. 2019

Advances in Mechanical Engineering

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Bolted joints are elements used to create resistant assemblies in the mechanical system, whose overall performance is greatly affected by joints’ contact stiffness. Most of the researches on contact stiffness are based on certainty theory whereas in real applications the uncertainty characterizes the parameters such as fractal dimension D and fractal roughness parameter G. This article presents an interval estimation theory to obtain the stiffness of bolted joints affected by uncertain parameters. Topography of the contact surface is fractal featured and determined by fractal parameters. Joint stiffness model is built based on the fractal geometry theory and contact mechanics. Topography of the contact surface of bolted joints is measured to obtain the interval of uncertain fractal parameters. Equations with interval parameters are solved to acquire the interval of contact stiffness using the Chebyshev interval method. The relationship between the interval of contact stiffness and the uncertain parameters, that is, fractal dimension D, fractal roughness parameter G, and normal pressure, can be obtained. The presented model can be used to estimate the interval of stiffness for bolted joints in the mechanical systems. The results can provide theoretical reference for the reliability design of bolted joints.

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Section: Effects Of D and G On A C And A Lmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interval estimation for contact stiffness of bolted joint with uncertain parameters

Zhao

Yang

Liu

et al. 2019

Advances in Mechanical Engineering

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“…Other researchers optimized structures and studied their sensitivity through probabilistic and nonprobabilistic hybrid reliability methodology as well [25][26][27][28][29][30][31]. For example, Luo and Zhang investigated an adhesive bonded steel-concrete composite beam with probabilistic and nonprobabilistic uncertainties and mathematically formulated the reliability-based optimization, incorporating mixed reliability constraints as a nested problem.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, based on active learning International Journal of Aerospace Engineering 3 kriging, Yang et al investigated HRA. The nonprobabilistic set-theory convex model was combined with the classical probabilistic approach to optimize structures exhibiting random and uncertain-but-bounded mixed uncertainties in [31].…”

Section: Introductionmentioning

confidence: 99%

Application of Probabilistic and Nonprobabilistic Hybrid Reliability Analysis Based on Dynamic Substructural Extremum Response Surface Decoupling Method for a Blisk of the Aeroengine

Bai

Zhang

et al. 2017

International Journal of Aerospace Engineering

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For the nondeterministic factors of an aeroengine blisk, including both factors with sufficient and insufficient statistical data, based on the dynamic substructural method of determinate analysis, the extremum response surface method of probabilistic analysis, and the interval method of nonprobabilistic analysis, a methodology called the probabilistic and nonprobabilistic hybrid reliability analysis based on dynamic substructural extremum response surface decoupling method (P-NP-HRA-DS-ERSDM) is proposed. The model includes random variables and interval variables to determine the interval failure probability and the interval reliability index. The extremum response surface function and its flow chart of mixed reliability analysis are given. The interval analysis is embedded in the most likely failure point in the iterative process. The probabilistic analysis and nonprobabilistic analysis are investigated alternately. Tuned and mistuned blisks are studied in a complicated environment, and the results are compared with the Monte Carlo method (MCM) and the multilevel nested algorithm (MLNA) to verify that the hybrid model can better handle reliability problems concurrently containing random variables and interval variables; meanwhile, it manifests that the computational efficiency of this method is superior and more reasonable for analysing and designing a mistuned blisk. Therefore, this methodology has very important practical significance.

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“…This methodology ensures that the design solution remains feasible and close to optimal even if there is a change in data. Different methodologies for robust design and optimization in mechanical systems have been extensively discussed in literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Most of these methods assume some kind of distribution for the uncertain variable to optimize the problem.…”

Section: Introductionmentioning

confidence: 99%

Robust design optimization using the price of robustness, robust least squares and regularization methods

Bukhari¹

2017

Int. J. Simul. Multidisci. Des. Optim.

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Abstract. In this paper a framework for robust optimization of mechanical design problems and process systems that have parametric uncertainty is presented using three different approaches. Robust optimization problems are formulated so that the optimal solution is robust which means it is minimally sensitive to any perturbations in parameters. The first method uses the price of robustness approach which assumes the uncertain parameters to be symmetric and bounded. The robustness for the design can be controlled by limiting the parameters that can perturb. The second method uses the robust least squares method to determine the optimal parameters when data itself is subjected to perturbations instead of the parameters. The last method manages uncertainty by restricting the perturbation on parameters to improve sensitivity similar to Tikhonov regularization. The methods are implemented on two sets of problems; one linear and the other non-linear. This methodology will be compared with a prior method using multiple Monte Carlo simulation runs which shows that the approach being presented in this paper results in better performance.Keywords: robust design / optimization / price of robustness / control of robustness / robust least square

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Reliability-based design optimization under mixture of random, interval and convex uncertainties

Cited by 53 publications

References 40 publications

Interval estimation for contact stiffness of bolted joint with uncertain parameters

Interval estimation for contact stiffness of bolted joint with uncertain parameters

Application of Probabilistic and Nonprobabilistic Hybrid Reliability Analysis Based on Dynamic Substructural Extremum Response Surface Decoupling Method for a Blisk of the Aeroengine

Robust design optimization using the price of robustness, robust least squares and regularization methods

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