Ship Robust Design Optimization Based on Polynomial Chaos Expansions

2020 ◽  
Vol 36 (03) ◽  
pp. 213-225
Author(s):  
Xiao Wei ◽  
Haichao Chang ◽  
Baiwei Feng ◽  
Zuyuan Liu
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Optimization Design ◽  
Polynomial Chaos ◽  
Minimum Energy ◽  
Robust Design Optimization ◽  
Uncertain Variables ◽  
Polynomial Coefficients ◽  
Collocation Points ◽  
Polynomial Chaos Expansions

Considerable parameter perturbations occur owing to the influence of uncertain factors in actual ship transportation, resulting in a substantial decline in ship performance. These parameters should not be regarded as certain values but uncertain variables. Ship robust design optimization (RDO) is a method in which various uncertainties are fully considered in the early stages of ship design to ensure that the optimal case adapts to the perturbation of the uncertain parameters. In this study, instead of the commonly used Monte Carlo method, polynomial chaos expansions (PCEs) are adopted to quantify the uncertainty, and an improved probabilistic collocation method (PCM) based on the linear independence principle is proposed to select sample points for calculating polynomial coefficients of PCE, which not only reduces the number of collocation points compared with the traditional statistical sampling method but also avoids the problem that arises with the traditional PCM, which cannot maintain high calculation accuracy even with considerable collocation points. Finally, to ensure ship robustness, in comparison with deterministic optimization design, the proposed RDO framework is applied to minimum Energy Efficiency Design Index (EEDI) KRISO Container Ship hull form design.

scholarly journals Sensitivity Analysis Based on Polynomial Chaos Expansions and Its Application in Ship Uncertainty-Based Design Optimization

2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Xiao Wei ◽  
Haichao Chang ◽  
Baiwei Feng ◽  
Zuyuan Liu
Keyword(s):  
Sensitivity Analysis ◽  
Design Optimization ◽  
Polynomial Chaos ◽  
Early Stage ◽  
Computational Cost ◽  
Sensitivity Index ◽  
Uncertain Variables ◽  
Polynomial Coefficients ◽  
Sensitivity Indices ◽  
Polynomial Chaos Expansions

In order to truly reflect the ship performance under the influence of uncertainties, uncertainty-based design optimization (UDO) for ships that fully considers various uncertainties in the early stage of design has gradually received more and more attention. Meanwhile, it also brings high dimensionality problems, which may result in inefficient and impractical optimization. Sensitivity analysis (SA) is a feasible way to alleviate this problem, which can qualitatively or quantitatively evaluate the influence of the model input uncertainty on the model output, so that uninfluential uncertain variables can be determined for the descending dimension to achieve dimension reduction. In this paper, polynomial chaos expansions (PCE) with less computational cost are chosen to directly obtain Sobol' global sensitivity indices by its polynomial coefficients; that is, once the polynomial of the output variable is established, the analysis of the sensitivity index is only the postprocessing of polynomial coefficients. Besides, in order to further reduce the computational cost, for solving the polynomial coefficients of PCE, according to the properties of orthogonal polynomials, an improved probabilistic collocation method (IPCM) based on the linear independence principle is proposed to reduce sample points. Finally, the proposed method is applied to UDO of a bulk carrier preliminary design to ensure the robustness and reliability of the ship.

scholarly journals Intelligent Approach to Robust Design Optimization of a Rotor System due to Its Support Stiffness Uncertainty

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Bensheng Xu ◽  
Chaoping Zang ◽  
Genbei Zhang
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
System Performance ◽  
Polynomial Chaos ◽  
Low Pressure ◽  
Polynomial Chaos Expansion ◽  
Rotor System ◽  
Robust Design Optimization ◽  
Chaos Expansion ◽  
Vibration Responses

In this paper, an intelligent robust design approach combined with different techniques such as polynomial chaos expansion (PCE), radial basis function (RBF) neural network, and evolutionary algorithms is presented with a focus on the optimization of the dynamic response of a rotor system considering support stiffness uncertainty. In the proposed method, the PCE method instead of the traditional Monte Carlo uncertainty analysis is applied to analyze the uncertain propagation of system performance. The RBF network is introduced to establish the approximate models of the objective and constraint functions. Taking the low-pressure rotor of a gas turbine with support stiffness uncertainty as an example, the optimization model is established with the mean and variance of unbalanced response of the rotor system at different operating speeds as the objective function, and the maximum unbalance response is less than the upper limit as the constraint function. The polynomial chaos expansion is generated to facilitate a rapid analysis of robustness in the presence of support stiffness uncertainties that is defined in terms of tolerance with good accuracy. The optimal Hypercubus are used as experimental plans for building RBF approximation models of the objective and constraint functions. Finally, the robust solutions are obtained with the multiobject optimization algorithm NSGA-II. Monte Caro simulation analysis demonstrates that the qualified rate of maximum vibration responses of the low-pressure rotor system can be increased from 83.6% to over 99%. This approach to robust design optimization is shown to lead to designs that significantly decrease vibration responses of the rotor system and improved system performance with reduced sensitivity to support stiffness uncertainty.

Hybrid Discrete Variable Robust Design Optimization Based on the Intelligent Single Particle Algorithm

2013 ◽  
Vol 299 ◽  
pp. 143-147
Author(s):  
Mao Fu Liu ◽  
Hui Xian Han
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Single Particle ◽  
Optimization Design ◽  
Robust Design Optimization ◽  
Position Vector ◽  
Engineering Practice ◽  
Discretization Method ◽  
Discrete Variable ◽  
Robust Optimization Design

Aiming to solve the problems of hybrid discrete variable robust design optimization in engineering practice, Particle position vector discretization method is applied toimprove intelligence single particle algorithm. A program written by MATLAB is designed for solving the problems of hybrid discrete variable robust design optimization. The paper verified the effectiveness and practicability of the method through an example of plane dimension chain’s discrete tolerance robust optimization design in the field of mechanical manufacturing.

Study of Uncertainties and Objective Function Modeling Effects on Probabilistic Optimization Results

2019 ◽  
Vol 5 (4) ◽  
Author(s):  
Oussama Braydi ◽  
Pascal Lafon ◽  
Rafic Younes
Keyword(s):  
Standard Deviation ◽  
Objective Function ◽  
Design Optimization ◽  
Robust Design ◽  
Optimization Design ◽  
Robust Design Optimization ◽  
Deterministic Case ◽  
Objective Functions ◽  
Design Problems ◽  
Probabilistic Optimization

Abstract In this work, we study the effect of uncertainties modeling and the choice of objective function on the results of optimization design problems in deterministic and probabilistic contexts. Uncertainties modeling are studied in two cases identified in the literature. The results show how the choice of two different objective functions, which lead to the same results in deterministic case, may lead to opposite results in probabilistic case. Also, the results show how the uncertainties modeling type can affect the antagonism between mean and standard deviation in the reliability-based robust design optimization (RBRDO) problems. Three mechanical applications chosen from the literature are used to illustrate these cases.

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