• Smart Structures and Systems
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• v.17 no.4
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• pp.611-629
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• 2016

This study presents a new approach of surrogate modeling for time-consuming finite element analysis. A surrogate model is widely used to reduce the computational cost under an iterative computational analysis. Although a variety of the methods have been widely investigated, there are still difficulties in surrogate modeling from a practical point of view: (1) How to derive optimal design of experiments (i.e., the number of training samples and their locations); and (2) diagnostics of the surrogate model. To overcome these difficulties, we propose a sequential surrogate modeling based on Gaussian process model (GPM) with self-adaptive sampling. The proposed approach not only enables further sampling to make GPM more accurate, but also evaluates the model adequacy within a sequential framework. The applicability of the proposed approach is first demonstrated by using mathematical test functions. Then, it is applied as a substitute of the iterative finite element analysis to Monte Carlo simulation for a response uncertainty analysis under correlated input uncertainties. In all numerical studies, it is successful to build GPM automatically with the minimal user intervention. The proposed approach can be customized for the various response surfaces and help a less experienced user save his/her efforts.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1219-1225
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• 2017

In this work, a scalable algorithm for model calibration in nuclear engineering applications is presented and tested. The algorithm relies on the construction of surrogate models to replace the original model within the region of interest. These surrogate models can be constructed efficiently via reduced order modeling and subspace analysis. Once constructed, these surrogate models can be used to perform computationally expensive mathematical analyses. This work proposes a surrogate based model calibration algorithm. The proposed algorithm is used to calibrate various neutronics and thermal-hydraulics parameters. The virtual environment for reactor applications-core simulator (VERA-CS) is used to simulate a three-dimensional core depletion problem. The proposed algorithm is then used to construct a reduced order model (a surrogate) which is then used in a Bayesian approach to calibrate the neutronics and thermal-hydraulics parameters. The algorithm is tested and the benefits of data assimilation and calibration are highlighted in an uncertainty quantification study and requantification after the calibration process. Results showed that the proposed algorithm could help to reduce the uncertainty in key reactor attributes based on experimental and operational data.

• Advances in Computational Design
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• v.1 no.3
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• pp.235-251
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• 2016

We have performed a design optimization of a stiffened panel with curvilinear stiffeners using an artificial neural network (ANN) residual kriging based surrogate modeling approach. The ANN residual kriging based surrogate modeling involves two steps. In the first step, we approximate the objective function using ANN. In the next step we use kriging to model the residue. We optimize the panel in an iterative way. Each iteration involves two steps-shape optimization and size optimization. For both shape and size optimization, we use ANN residual kriging based surrogate model. At each optimization step, we do an initial sampling and fit an ANN residual kriging model for the objective function. Then we keep updating this surrogate model using an adaptive sampling algorithm until the minimum value of the objective function converges. The comparison of the design obtained using our optimization scheme with that obtained using a traditional genetic algorithm (GA) based optimization scheme shows satisfactory agreement. However, with this surrogate model based approach we reach optimum design with less computation effort as compared to the GA based approach which does not use any surrogate model.

• International Journal of Fluid Machinery and Systems
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• v.2 no.1
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• pp.1-12
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• 2009

Surrogate modeling is applied to a compressor blade shape optimization to modify its stacking line and thickness to enhance adiabatic efficiency and total pressure ratio. Six design variables are defined by parametric curves and three objectives; efficiency, total pressure and a combined objective of efficiency and total pressure are considered to enhance the performance of compressor blade. Latin hypercube sampling of design of experiments is used to generate 55 designs within design space constituted by the lower and upper limits of variables. Optimum designs are found by formulating a PRESS (predicted error sum of squares) based averaging (PBA) surrogate model with the help of a gradient based optimization algorithm. The optimum designs using the current variables show that, to optimize the performance of turbomachinery blade, the adiabatic efficiency objective is improved substantially while total pressure ratio objective is increased a very small amount. The multi-objective optimization shows that the efficiency can be increased with the less compensation of total pressure reduction or both objectives can be increased simultaneously.

• Transactions of Materials Processing
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• v.27 no.1
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• pp.28-36
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• 2018

Electromagnetic forming is a type of high-speed forming process to deform a workpiece through a Lorentz force. As the high strain rate in an electromagnetic-forming simulation causes infeasibility in determining constitutive parameters, we employed inverse parameter estimation in the previous study. However, the inverse parameter estimation process required us to spend considerable time, which leads to an increase in computational cost. To overcome the computational obstacle, in this research, we applied two types of surrogate modeling methods and compared them to each other to evaluate which model is best for the electromagnetic-forming simulation. We exploited an artificial neural network and we reduced-order modeling methods. During the construction of a reduced-order model, we extracted orthogonal bases with proper orthogonal decomposition and predicted basis coefficients by utilizing an artificial neural network. After the construction of the surrogate models, we verified the artificial neural network and reduced-order models through training and testing samples. As a result, we determined the artificial neural network model is slightly more accurate than the reduced-order model. However, the construction of the artificial neural network model requires a considerably larger amount of time than that of the reduced-order model. Thus, a reduced order modeling method is more efficient than an artificial neural network for estimating the electromagnetic forming and for the rapid approximation of structural simulations which needs repetitive runs.

• Ocean Systems Engineering
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• v.9 no.2
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• pp.111-133
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• 2019

Flow through a scaled horizontal axis marine current turbine was numerically simulated after validation and the turbine design was optimized. The computational fluid dynamics (CFD) code Ansys-CFX 16.1 for numerical modeling, an in-house blade element momentum (BEM) code for analytical modeling and an in-house surrogate-based optimization (SBO) code were used to find an optimal turbine design. The blade-pitch angle (${\theta}$) and the number of rotor blades (NR) were taken as design variables. A single objective optimization approach was utilized in the present work. The defined objective function was the turbine's power coefficient ($C_P$). A $3{\times}3$ full-factorial sampling technique was used to define the sample space. This sampling technique gave different turbine designs, which were further evaluated for the objective function by solving the Reynolds-Averaged Navier-Stokes equations (RANS). Finally, the SBO technique with search algorithm produced an optimal design. It is found that the optimal design has improved the objective function by 26.5%. This article presents the solution approach, analysis of the turbine flow field and the predictability of various surrogate based techniques.

• Nuclear Engineering and Technology
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• v.53 no.3
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• pp.715-731
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• 2021

Uncertainties are calculated for pressurized water reactor (PWR) spent nuclear fuel (SNF) characteristics. The deterministic code STREAM is currently being used as an SNF analysis tool to obtain isotopic inventory, radioactivity, decay heat, neutron and gamma source strengths. The SNF analysis capability of STREAM was recently validated. However, the uncertainty analysis is yet to be conducted. To estimate the uncertainty due to nuclear data, STREAM is used to perturb nuclear cross section (XS) and resonance integral (RI) libraries produced by NJOY99. The perturbation of XS and RI involves the stochastic sampling of ENDF/B-VII.1 covariance data. To estimate the uncertainty due to modeling parameters (fuel design and irradiation history), surrogate models are built based on polynomial chaos expansion (PCE) and variance-based sensitivity indices (i.e., Sobol' indices) are employed to perform global sensitivity analysis (GSA). The calculation results indicate that uncertainty of SNF due to modeling parameters are also very important and as a result can contribute significantly to the difference of uncertainties due to nuclear data and modeling parameters. In addition, the surrogate model offers a computationally efficient approach with significantly reduced computation time, to accurately evaluate uncertainties of SNF integral characteristics.

• The KSFM Journal of Fluid Machinery
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• v.14 no.5
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• pp.55-62
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• 2011

Shape optimization of a Printed circuit heat exchanger (PCHE) has been performed by using three-dimensional Reynolds-Averaged Navier-Stokes (3-D RANS) analysis and surrogate modeling techniques. The objective function is defined as a linear combination of effectiveness of the PCHE term and pressure drop in the cold channels of the PCHE. The cold channel angle and the ellipse aspect ratio of the cold channel are used as design variables for the optimization. Design points are selected through Latin-hypercube sampling. The optimal point is determined through surrogate-based optimization method which uses 3-D RANS analyses at design points. The results of three types of surrogate model are compared each other. The results of the optimizations indicate improved performance in friction loss but low performance in effectiveness than the reference shape.

• Transactions of Materials Processing
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• v.29 no.2
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• pp.89-96
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• 2020

The finite element method has been widely applied in the sheet metal forming process. However, the finite element method is computationally expensive and time consuming. In order to tackle this problem, surrogate modeling methods have been proposed. An artificial neural network (ANN) is one such surrogate model and has been well studied over the past decades. However, when it comes to ANN with two or more layers, so called deep neural networks (DNN), there is distinct a lack of research. We chose to use DNNs our surrogate model to predict the behavior of sheet metal in the deep drawing process. Thickness variation is selected as an output of the DNN in order to evaluate workpiece feasibility. Input variables of the DNN are radius of die, die corner and blank holder force. Finite element analysis was conducted to obtain data for surrogate model construction and testing. Sampling points were determined by full factorial, latin hyper cube and monte carlo methods. We investigated the performance of the DNN according to its structure, number of nodes and number of layers, then it was compared with a radial basis function surrogate model using various sampling methods and numbers. The results show that our DNN could be used as an efficient surrogate model for the deep drawing process.

• International Journal of Fluid Machinery and Systems
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• v.2 no.2
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• pp.179-188
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• 2009

Recent development of high speed computers and use of optimization techniques have given a big momentum of turbomachinery design replacing expensive experimental cost as well as trial and error approaches. The surrogate based optimization techniques being used for aerodynamic turbomachinery designs coupled with Reynolds-averaged Navier-Stokes equations analysis involve single- and multi-objective optimization methods. The objectives commonly tried to improve were adiabatic efficiency, pressure ratio, weight etc. Presently coupling the fluid flow and structural analysis is being tried to find better design in terms of weight, flutter and vibration, and turbine life. The present article reviews the surrogate based optimization techniques used recently in turbomachinery shape optimizations.