An efficient nonlinear interval uncertain optimization method using Legendre polynomial chaos expansion

Wang, Liqun; Yang, Guolai; Li, Zixuan; Xu, Fengjie

doi:10.1016/j.asoc.2021.107454

Cited by 24 publications

(4 citation statements)

References 42 publications

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“…After normalization, the grey relational coefficient γ i (k), which is used to quantify the relationship between the target and actual normalized results, can be formulated as [26]:…”

Section: Multi-criteria Decision Making (Mcdm) Methodsmentioning

confidence: 99%

“…The GRA with entropy weight method is applied to choose the most satisfactory solution in Pareto sets. The objective weight is calculated by using the entropy weight method, and the grey relational grade is calculated by Equation (26).…”

Section: Main Processes Of Muodmentioning

confidence: 99%

“…The method uses the Chebyshev interval inclusion function to realize the non-invasiveness of the interval algorithm. Wang et al [26] developed an effective interval uncertain optimization design strategy using Legendre polynomial chaotic expansion, which is more efficient than the conventional method. Hou et al [27] carried out the uncertainty optimization, pertaining to the energy efficiency of ships in icy areas, considering the interval parameters; the optimization results provided practical guidance for the energy-saving design of ships in the case of uncertainty in the actual environment.…”

Section: Introductionmentioning

confidence: 99%

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Optimization Design for the Planetary Gear Train of an Electric Vehicle under Uncertainties

Chen

Lin

et al. 2022

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The planetary gear train is often used as the main device for decelerating and increasing the torque of the drive motor of electric vehicles. Considering the lightweight requirement and existing uncertainty in structural design, a multi-objective uncertainty optimization design (MUOD) framework is developed for the planetary gear train of the electric vehicle in this study. The volume and transmission efficiency of the planetary gear train are taken into consideration as optimization objectives. The manufacturing size, material, and load input of the planetary gear train are considered as uncertainties. An approximate direct decoupling model, based on subinterval Taylor expansion, is applied to evaluate the propagation of uncertainties. To improve the convergence ability of the multi-objective evolutionary algorithm, the improved non-dominated sorting genetic algorithm II (NSGA-II) is designed by using chaotic and adaptive strategies. The improved NSGA-II has better convergence efficiency than classical NSGA-II and multi-objective particle swarm optimization (MOPSO). In addition, the multi-criteria decision making (MCDM) method is applied to choose the most satisfactory solution in Pareto sets from the multi-objective evolutionary algorithm. Compared with the multi-objective deterministic optimization design (MDOD), the proposed MUOD framework has better reliability than MDOD under different uncertainty cases. This MUOD method enables further guidance pertaining to the uncertainty optimization design of transportation equipment, containing gear reduction mechanisms, in order to reduce the failure risk.

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“…After normalization, the grey relational coefficient γ i (k), which is used to quantify the relationship between the target and actual normalized results, can be formulated as [26]:…”

Section: Multi-criteria Decision Making (Mcdm) Methodsmentioning

confidence: 99%

Section: Main Processes Of Muodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimization Design for the Planetary Gear Train of an Electric Vehicle under Uncertainties

Chen

Lin

et al. 2022

Actuators

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“…Wang et al 41 proposed an interval uncertain optimization method using genetic algorithm to optimize the inner layer and non-dominated sorting genetic algorithm to optimize the outer layer. Wang et al 42 proposed a Legendre polynomial expansion method combined with subinterval technique to optimize nonlinear interval uncertain problems. Rahman et al 43 proposed the concept of type-2 interval order relation and type-2 interval valued function.…”

Section: Introductionmentioning

confidence: 99%

An interval particle swarm optimization method for interval nonlinear uncertain optimization problems

Zheng

Xie

2023

Advances in Mechanical Engineering

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For nonlinear optimization problems involving interval variables or parameters, the interval possibility degree or interval order relation is conventionally adopted to convert them into a deterministic corresponding counterpart and then can be solved with linear programing approaches, through which computational resources and costs have been preserved to a certain extent. However, some information and computational accuracy will be discounted during the model transformation. In this paper, an interval optimization algorithm based on particle swarm optimization is proposed aiming to cut down the loss of useful information by means of straight optimization instead of model deterministic converting so as to enhance calculation accuracy with few growths of computing expenses. The proposed method firstly employs an interval satisfaction value to cope with the constraints. Consequently, the particle swarm optimization method is used to seek the optimum solution sets without the model deterministic converting. And a criterion based on the satisfaction value model of interval possibility degree plays the role in individual selecting out of the above solution sets. Finally, the effectiveness of the proposed method is verified by investigating four examples.

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An adaptive bivariate decomposition method for interval optimization problems with multiple uncertain parameters

Wei

Feng

2022

Engineering with Computers

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An efficient nonlinear interval uncertain optimization method using Legendre polynomial chaos expansion

Cited by 24 publications

References 42 publications

Optimization Design for the Planetary Gear Train of an Electric Vehicle under Uncertainties

Optimization Design for the Planetary Gear Train of an Electric Vehicle under Uncertainties

An interval particle swarm optimization method for interval nonlinear uncertain optimization problems

An adaptive bivariate decomposition method for interval optimization problems with multiple uncertain parameters

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