Applications of Polynomial Chaos-Based Cokriging to Simulation-Based Analysis and Design Under Uncertainty

2020 ◽  
Author(s):  
Jethro Nagawkar ◽  
Leifur Leifsson
Keyword(s):  
Robust Design ◽  
Ultrasonic Testing ◽  
Polynomial Chaos ◽  
Robust Design Optimization ◽  
High Fidelity ◽  
Analysis And Design ◽  
Simulation Based ◽  
The Mean ◽  
Design Case ◽  
Global Accuracy

Abstract This paper demonstrates the use of the polynomial chaos-based Cokriging (PC-Cokriging) on various simulation-based problems, namely an analytical borehole function, an ultrasonic testing (UT) case and a robust design optimization of an airfoil case. This metamodel is compared to Kriging, polynomial chaos expansion (PCE), polynomial chaos-based Kriging (PC-Kriging) and Cokriging. The PC-Cokriging model is a multi-variate variant of PC-Kriging and its construction is similar to Cokriging. For the borehole function, the PC-Cokriging requires only three high-fidelity samples to accurately capture the global accuracy of the function. For the UT case, it requires 20 points. Sensitivity analysis is performed for the UT case showing that the F-number has negligible effect on the output response. For the robust design case, a 75 and 31 drag count reduction is reported on the mean and standard deviation of the drag coefficient, respectively, when compared to the baseline shape.

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.

scholarly journals Stochastic simulation and robust design optimization of integrated photonic filters

Nanophotonics ◽  
2017 ◽  
Vol 6 (1) ◽  
pp. 299-308 ◽  
Author(s):  
Tsui-Wei Weng ◽  
Daniele Melati ◽  
Andrea Melloni ◽  
Luca Daniel
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Ring Resonator ◽  
Process Variations ◽  
Robust Design Optimization ◽  
Generalized Polynomial ◽  
Optimization Simulation ◽  
The Mean ◽  
Sparsity Structure ◽  
Mean Square Errors

AbstractManufacturing variations are becoming an unavoidable issue in modern fabrication processes; therefore, it is crucial to be able to include stochastic uncertainties in the design phase. In this paper, integrated photonic coupled ring resonator filters are considered as an example of significant interest. The sparsity structure in photonic circuits is exploited to construct a sparse combined generalized polynomial chaos model, which is then used to analyze related statistics and perform robust design optimization. Simulation results show that the optimized circuits are more robust to fabrication process variations and achieve a reduction of 11%–35% in the mean square errors of the 3 dB bandwidth compared to unoptimized nominal designs.

Robust Design Optimization of an Industrial 1.5 Stage Axial Compressor Under Operational and Geometrical Uncertainties

2021 ◽  
Author(s):  
Alexandre Gouttière ◽  
Dirk Wunsch ◽  
Rémy Nigro ◽  
Virginie Barbieux ◽  
Charles Hirsch
Keyword(s):  
Robust Optimization ◽  
Design Optimization ◽  
Robust Design ◽  
Computational Cost ◽  
Axial Compressor ◽  
Secondary Flows ◽  
Robust Design Optimization ◽  
Original Design ◽  
The Mean ◽  
Standard Deviations

Abstract A robust design optimization of a 1.5 stage axial compressor with secondary flows from Safran Aero Boosters is investigated. A total of 9 simultaneous operational and geometrical uncertainties are propagated for the nominal design point as well as for two off-design points, close to stall and choke conditions respectively. These uncertainties, including mass flow rates of the secondary flows, tip gap size of the rotor and highly correlated profiles on the inlet condition, are propagated by the Non-Intrusive Probabilistic Collocation method. In order to understand the effects of the uncertainties on the performances and to minimize the computational cost of the robust optimization, a preliminary uncertainty quantification (UQ) study of the original design is performed to identify and rule out less influential uncertainties. Contrary to what was expected, the imposed geometrical uncertainties on the tip gap are identified to have the relatively smallest influence on the performances by means of scaled sensitivity derivatives. The global objective of the robust design optimization is to minimize the standard deviations of the main compressor performances at all three operating points and to preserve the mean values of these performances. Because the objective functions are standard deviations, this study is only possible in a robust optimization setting, by propagating the simultaneous operational and geometrical uncertainties. A total of 9 stochastic objectives and 15 stochastic constraints are taken into account. The best optimal design preserves the mean performances of the compressor, while the standard deviations are minimized compared with the original design, ensuring a more robust operation. This effect is very pronounced in the off-design points.

Robust Design Optimization of Gear Parameters for a Wind Turbine Using Interval Analysis

2010 ◽  
Vol 224 (10) ◽  
pp. 2235-2245 ◽  
Author(s):  
R Dong ◽  
W Sun ◽  
H Xu
Keyword(s):  
Wind Turbine ◽  
Design Optimization ◽  
Robust Design ◽  
Optimization Method ◽  
Mean Value ◽  
Robust Design Optimization ◽  
Upper And Lower Bounds ◽  
Interval Numbers ◽  
Minimum Sensitivity ◽  
The Mean

A robust design optimization method is suggested to optimize the system parameters of a gear transmission for a wind turbine with minimum sensitivity of fatigue strength to variations in uncertain application factor, dynamic load coefficient, material property parameters, and other coefficients representing unknown working condition. Interval numbers are employed to model the uncertainties by which only the upper and lower bounds are needed. Based on interval mathematics, the original real-valued objective and constraint functions are replaced by the interval-valued functions, which directly represent the variation bounds of the new functions under uncertainty. The single-objective function is converted into two-objective functions for minimizing the mean value and the variation, and the constraint functions are reformulated with the acceptable robustness level, resulting in a bi-level mathematical model. The optimization results of gear parameter demonstrate the validity and feasibility of the presented method.

Empirical Models for Non-Deterministic Simulation-Based Robust Design

2007 ◽  
Author(s):  
Hae-Jin Choi ◽  
Janet K. Allen
Keyword(s):  
Robust Design ◽  
Cell Walls ◽  
Linear Models ◽  
Simulation Models ◽  
Simulation Based ◽  
Alloy Heat ◽  
Mean And Variance ◽  
The Mean ◽  
Uncertainty Analyses ◽  
Computationally Intensive

We propose a method for metamodeling non-deterministic computer intensive simulations for use in robust design. Generalized linear models for mean responses and heteroscadastic response variances are iteratively estimated in an integrated manner. Estimators that may be used for predicting the mean and variance models are introduced and metamodels of variance are developed. The usefulness of this metamodeling approach in efficient uncertainty analyses of non-deterministic, computationally-intensive simulation models for robust design methods is illustrated with the example of the design of a linear cellular alloy heat exchanger with randomly distributed cracks in the cell walls.

Simulation-based robust design of complex product considering uncertainties of metamodel, design variables, and noise parameters

2016 ◽  
Vol 231 (20) ◽  
pp. 3715-3727 ◽  
Author(s):  
Zhenyu Liu ◽  
Xiang Peng ◽  
Chan Qiu ◽  
Jianrong Tan ◽  
Guifang Duan ◽  
...  
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Product Performance ◽  
Robust Design Optimization ◽  
Complex Product ◽  
Noise Parameters ◽  
Design Variables ◽  
Simulation Based ◽  
Metamodel Uncertainty ◽  
Performance Uncertainty

The uncertainties of design variables, noise parameters, and metamodel are important factors in simulation-based robust design optimization. Most conventional metamodel construction methods only consider one or two uncertainties. In this paper, a new surrogate modeling method simultaneously measuring all the uncertainties is proposed for simulation-based robust design optimization of complex product. The effect of metamodel uncertainty on product performance uncertainty is quantified through uncertainty propagation analysis among design variables uncertainty, noise parameters uncertainty, metamodel uncertainty, and performance uncertainty. Then, the sampling points are selected and the metamodel is constructed based on the predictive interval of product performance and mean square error of the Kriging metamodel. The constructed metamodel is applied to robust design optimization considering multiple uncertainties. Results of two mathematical examples show that the proposed metamodel considering multiple uncertainties increases the result accuracy of robust design optimization. Finally, the proposed algorithm is applied to robust design optimization of a heat exchanger, and the total heat transfer rate is enhanced under uncertainties of fin structural parameters, operation conditions parameters and simulation metamodel.

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