Surrogate-based Optimization Technique Research Articles

Optimization of the impeller for hydraulic performance improvement of a high-speed magnetic drive pump

Magnetic drive centrifugal pumps have compact structure and lower efficiency than ordinary centrifugal pumps. The surrogate-based optimization technique was applied to improve the performance of a high-speed magnetic drive pump with the help of numerical simulations. Eight geometrical parameters of the impeller were considered as the design variable. About 290 samples of impeller were generated by optimal Latin hypercube sampling (OLHS) method, and the corresponding efficiencies of all the impeller samplings were obtained from numerical simulation. The performance test of the prototype pump was carried out, and the experimental results were in good agreement with the numerical simulation results. The hydraulic efficiency at 1.2 Qd of the magnetic drive pump was set as the optimization objective. Using response surface methodology (RSM), surrogate models were established for the objective functions based on the numerical results. The multi-island genetic algorithm (MIGA) was used to optimize the impeller. The hydraulic efficiency of the optimal impeller at rated flow rate was 72.89%, which was 6.23% higher than the prototype impeller.

Surrogate-Based Optimization of a Centrifugal Pump with Volute Casing for an Automotive Engine Cooling System

This paper investigates the capability of a surrogate-based optimization technique for the advanced design of centrifugal pumps. The centrifugal pump considered in this work is designed for the automotive cooling system and consists of an impeller, a vaneless diffuser and a volute. A fully three-dimensional geometry parametrization based on Bézier surfaces is presented. The optimization procedure includes the following software packages: Scilab for the geometric parametrization, Ansys-CFX for the CFD simulations and DAKOTA for the optimization management. The initial geometry is defined by a 0D code that provides a preliminary design of the pump, given the operating conditions, i.e., the volumetric flow rate, the head and the rotating speed. In this work an operative point typical of high performance gasoline cars is considered.

Optimization of a vacuum cleaner fan suction and shaft power using Kriging surrogate model and MIGA

Optimization of vacuum cleaner fan components is a low-cost and time-saving solution to satisfy the increasing requirement for compact energy-efficient cleaners. In this study, surrogate-based optimization technique is used and for the first time it is focused on maximization of Airwatt parameter, which describes the fan suction power, as an objective function (Case II). Besides, the shaft power is minimized (Case I) as another optimization target in order to reduce the power consumption of the vacuum cleaner. 11 geometrical variables of 3 fan components including impeller, diffuser and return channel are selected as the optimization design variables. 80 training points are distributed in the sample space using Advanced Latin Hypercube Sampling (ALHS) technique and the outputs of sample points are calculated by means of CFD simulations. Kriging and RSA surrogate models have been fitted to the outputs of the sample space. Through coupling of constructed Kriging models and Multi-Island Genetic Algorithm (MIGA), the optimal design for each of the optimization cases is presented and evaluated using numerical simulations. A 20.22% reduction in shaft power in Case I and an improvement of 27.73% in Airwatt in Case II have been achieved as the overall results of this study. Despite achieving goals in both optimization cases, a slight decrease in Airwatt in Case I (−6.20%) and a slight increase in shaft power in Case II (+4.82%) are observed relative to primary fan. Furthermore, the Analysis of Variance (ANOVA) determines the importance level of design variables and their 2-way interactions on the objective functions. It was concluded that geometrical parameters related to all of the fan components must be considered simultaneously to conduct a comprehensive optimization. The reasons of enhancement in optimal cases compared with the reference design have been further investigated by analysis of the fan internal flow field. Post-processing of the CFD results demonstrates that the applied geometrical modifications cause a more uniform flow through the flow passages of the optimal fan components.

Surrogate-based aerodynamic shape optimization for delaying airfoil dynamic stall using Kriging regression and infill criteria

The dynamic stall phenomenon is characterized by the formation of a leading-edge vortex, which is responsible for adverse aerodynamic forces and moments adversely impacting the structural strength and life of a system. Aerodynamic shape optimization (ASO) provides a cost-effective approach to delay or mitigate the dynamic stall characteristics. Unfortunately, ASO requires multiple evaluations of accurate but time-consuming computational fluid dynamics (CFD) simulations to produce optimum designs rendering the optimization process computationally costly. The current work proposes a surrogate-based optimization (SBO) technique to alleviate the computational burden of ASO to delay and mitigate the deep dynamic stall characteristics of airfoils. In particular, the Kriging regression surrogate model is used for approximating the objective and constraint functions. The airfoil geometry is parametrized using six PARSEC parameters. The objective and constraint functions are evaluated with the unsteady Reynolds-averaged Navier-Stokes equations with a C-grid mesh topology and Menter's shear stress transport turbulence model. The approach is demonstrated on a vertical axis wind turbine airfoil at a Reynolds number of 135,000 and a Mach number of 0.1 undergoing a sinusoidal oscillation with a reduced frequency of 0.05. The surrogate model is constructed with 60 initial samples and further refined with 20 infill samples using expected improvement. The generated surrogate model is validated with the normalized root mean square error based on 20 test data samples. The refined surrogate model is utilized for finding the optimal design using multi-start gradient-based search. The optimal airfoil has a higher thickness, larger leading-edge radius, and an aft camber compared to the baseline. These geometric shape changes delay the dynamic stall angle by over 3∘ and reduces the severity of the pitching moment coefficient fluctuation. Finally, global sensitivity analysis is conducted on the optimal design using Sobol' indices revealing the most influential shape variables and their interaction effects impacting the airfoil dynamic stall characteristics.

A surrogate-based optimization method for the issuance of passenger evacuation orders under ship fires

In order to reduce assembly time and improve the computational efficiency under ship fires, a surrogate-based optimization technique is proposed to estimate the optimal time of the issuance of evacuation orders, which determines the passenger response times. The Legendre polynomial chaos expansion technique is employed to construct the surrogate model of passenger assembly time with response time parameters, and validated with the original computer evacuation model. The genetic algorithm (GA) is subsequently applied to find the optimal response time combination. A 3-storey passenger ship is presented and four different fire scenarios that involve typical fire locations are considered to address the validity of this proposed method. The results suggest that this proposed method can be used to determine the optimal and the worst response time parameters with a significantly reduced number of evaluation samples. The relative error of assembly time from the surrogate model follows the normal distribution. For evacuation zone with the longest average travel distance, passengers should be informed of the immediate evacuation. For evacuation zones with short average travel distances, the optimal response time may be larger than the worst solution. This work provides a new method to make a reasonable evacuation planning in ship fires.

Influence of stall fences on the performance of Wells turbine

The Wells turbine is one of the candidates for use in Oscillating Water Column (OWC) type wave energy conversion devices. The narrow operating range of a Wells turbine limits its application to a small range of ocean environments. At a high angle of attack, the turbine performance drops suddenly due to a phenomenon known as stall. The present study introduces stall fences in the Wells turbine blade to postpone stall and widen the operating range. The stall fences are defined by the length, height, and thickness in percentage of blade chord length. For the present study, dimensions of the stall fences are determined by using a surrogate-based optimization technique. The modified and reference turbine are numerically studied by solving the Reynolds-Averaged-Navier-Stokes equations in the commercial CFD software ANSYS CFX 16.1. The comparison of fenced turbine with reference turbine shows 16.6% improvement in operating range at the cost of peak torque developed by the turbine. The peak-to-average power ratio in the stall-free range is reduced by 16.7% when stall fences are used. The change in internal flow due to the presence of stall fences is analyzed in detail in the present work.

Optimization of a horizontal axis marine current turbine via surrogate models

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 (o) 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 (Cp). A 3x3 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.

On the optimal morphology and performance of a modeled dragonfly airfoil in gliding mode

Numerical investigation on the effect of wing morphology of the dragonfly Aeshna cyanea is carried out to understand its influence on the aerodynamic performance. The two-dimensional wing section has corrugation all over the surface along the chord length on both upper (suction side) and lower (pressure side) surfaces. By considering each corrugation separately on different airfoils at their different positions, 10 single corrugated airfoils were generated. Simulations are performed on these different airfoils to determine the effect of each corrugation on aerodynamic performance. The flow is modeled as incompressible, Newtonian, homogeneous, and unsteady. The angle of attack was varied from 0° to 20°, and the Reynolds number (Re) was varied from 150 to 10 000. The optimum morphology and angle of attack were predicted by using the surrogate-based optimization technique for a maximum gliding ratio at different Re. A fully corrugated pressure side gives the best performance at angles of attack of 9.79° and 14.83° at low Re. At high Re, corrugations on the pressure side which are in the middle and those near the trailing edge give a maximum gliding ratio at angles of attack 9.22° and 5.276°. The spatiotemporal dynamics indicate that corrugations near the leading edge on the upper surface and corrugations near the trailing edge for the lower surface and which are in the middle are beneficial. It is also found that shear drag due to corrugation decreases but pressure drag increases; therefore, the overall drag coefficient for a fully corrugated airfoil increases. Corrugations on the suction side have little influence, while those on the pressure side causes lift enhancement.

Shape optimization of the ERCOFTAC centrifugal pump impeller using open-source software

This paper investigates a surrogate-based optimization technique with a genetic algorithm for fast and robust improvement of centrifugal pump performance. The optimization strategy is based only on open-source software, i.e. Scilab for the geometric parametrization, OpenFOAM for the CFD simulations and DAKOTA for the optimization. This choice aims to achieve widespread diffusion of the proposed methodology. A fully three-dimensional geometry parametrization based on Bezier surfaces is presented, allowing both the impeller and the vaned diffuser to be parametrized. Moreover, we present a comparison of different surrogate models (Kriging and artificial neural network), investigating their performance in pump optimization. We validate the proposed methodology using the ERCOFTAC centrifugal pump, because of the availability of experimental and numerical data. The results of this study demonstrate the potential of surrogate-based optimization techniques to improve the performance of centrifugal pumps.

Design Optimization of the Centrifugal Pumps via Low Fidelity Models

Low fidelity model assisted design optimization of turbomachines has reduced the total computational and experimental costs. These models are called surrogate models which mimic the actual experiments or simulations. The surrogate models can generate thousands of approximate results from a few samples, making it easy to locate the optimal solution. Ample articles reported surrogate assisted design optimization of centrifugal pumps. In this article, the authors try to give a brief overview of the surrogate based optimization technique along with its historical applications and trend of the recent use. The various key design parameters which affect the performance of the centrifugal pump have also been discussed. The effectiveness of the surrogate based optimization technique and corresponding performance metrics have been discussed.

Design of a novel gas cyclone vortex finder using the adjoint method

Gas cyclones have many industrial applications in solid–gas separation. The vortex finder is an essential part in gas cyclones where the shape and diameter highly affect the cyclone performance. Many optimization studies have been conducted to optimize the cylindrical vortex finder diameter. This study introduces a new vortex finder shape optimized for minimum pressure drop using the discrete adjoint method. The new optimum cyclone will save 66% from the driving power needed for the Stairmand cyclone. To efficiently perform the grid independence study for the new cyclone, a new framework using the adjoint solver and the grid convergence index is proposed and tested. The proposed framework relies on local mesh adaptation instead of the global mesh refinement approach. A comparison of numerical simulation of the new cyclone and the Stairmand cyclone confirms the superior performance of the new vortex finder shape for the pressure drop and the cut-off diameter. The results of this study open a new era gas cyclones geometry optimization by using the adjoint method instead of the traditional surrogate based optimization technique. Moreover, the computational costs for the grid independence studies will be reduced via the application of the adjoint methods.

Warpage reduction with variable pressure profile in plastic injection molding via sequential approximate optimization

Warpage reduction is one of the important issues in plastic injection molding (PIM). In order to resolve this issue, there are mainly two ways to reduce warpage: One is to design the mold, and the other is to optimize the process parameters such as the mold temperature, the melt temperature, and so on. In this paper, the latter approach is employed. In particular, variable pressure profile approach is adopted for the warpage reduction. Besides the variable pressure profile, the melt temperature and the mold temperature are taken as the design variables. Also, short shot that the melt plastic is not filled into the cavity is one of the fatal defects in PIM. Unlike the literature, in this paper, the short shot is handled as the design constraint. PIM simulation is generally so costly and time consuming, and then the surrogate-based optimization technique is used. The radial basis function (RBF) network is used throughout sequential approximate optimization (SAO) procedure. Moldex3D is used for PIM simulation. In order to compare the effectiveness of the variable pressure profile, the traditional process parameter optimization considered in the literature is also carried out. Numerical results show that the variable pressure profile is one of the effective ways to warpage reduction compared to the traditional process parameter optimization.

Environmental High Frequency Characterization of Fabrics Based on a Novel Surrogate Modelling Antenna Technique

Wearable antennas are mostly constructed from fabric or foam, whereas e-textiles are often used as conductive parts. A design obstacle is the lack of knowledge about the electromagnetic properties of these materials. Moreover, most of these fabrics exhibit electromagnetic properties that depend on prevailing atmospheric conditions. In this work, we present a dedicated characterization method to determine the complex permittivity of fabrics or foams, as well as the effective conductivity of e-textiles, and this as a function of relative humidity. The method extracts the constitutive parameters by comparing measured and simulated antenna figures of merit such as input impedance and antenna efficiency. This inverse problem is solved using a surrogate-based optimization technique as implemented in the Surrogate Modeling Toolbox, yielding a fast and accurate characterization. The method is evaluated by characterizing six materials which are exposed to relative humidity levels ranging from 10% to 90%. From the extracted complex permittivities of the six materials, two-phase dielectric mixing models based on the volumetric fractions of the absorbed moisture in the substrates are developed and evaluated in terms of accuracy. For the materials exhibiting a high sensitivity to moisture, the model is observed to be less accurate. However, the worst model accuracy is shown to be comparable with the estimated accuracy of the characterization procedure. For materials with low sensitivity to moisture, the model fits the measured values very well.

Accelerated parameter identification in a 3D marine biogeochemical model using surrogate-based optimization

We present the application of the Surrogate-based Optimization (SBO) method on a parameter identification problem for a 3-D biogeochemical model. SBO is a method for acceleration of optimization processes when the underlying model itself is of very high computational complexity. In these cases, coupled simulation runs require large amounts of computer time, where optimization runs may become unfeasible even with high-performance hardware. As a consequence, the key idea of SBO is to replace the original and computationally expensive (high-fidelity) model by a so-called surrogate, which is created from a less accurate but computationally cheaper (low-fidelity) model and a suitable correction approach to increase its accuracy. To date, the SBO approach has been widely and successfully used in engineering applications and also for parameter identification in a 1-D marine ecosystem model of NPZD type. In this paper, we apply the approach onto a two-component biogeochemical model. The model is spun-up into a steady seasonal cycle via the Transport Matrix Approach. The low-fidelity model we use consists of a reduced number of spin-up iterations (several decades instead of millennia used for the original model). A multiplicative correction operator is further exploited to extrapolate the rather inaccurate low-fidelity model onto the original one. This corrected model builds our surrogate. We validate this SBO method by twin-experiments that use synthetic observations generated by the original model. We motivate our choice of the low-fidelity model and the multiplicative correction and discuss the computational advantage of SBO in comparison to an expensive parameter optimization in the context of the high-fidelity model. The proposed SBO technique is shown to yield a solution close to the target at a significant gain of computational efficiency. Without further regularization techniques, the method is able to identify most model parameters. The method is simple to implement and presents a promising and pragmatic tool to calibrate biogeochemical models in a global three-dimensional setting.

Low-Fidelity Model Mesh Density and the Performance of Variable-Resolution Shape Optimization Algorithms

Surrogate based optimization (SBO) provides an interesting alternative to conventional aerodynamic shape optimization methods. By shifting the optimization burden to a cheap and yet reasonably accurate surrogate model, the design cost can be substantially reduced. SBO methods exploiting physically based surrogates can be particularly efficient because underlying low-fidelity models embed some knowledge about the system under consideration (e.g., by sharing the simulation tools with the high-fidelity models) so that good accuracy and even better generalization capability can be obtained through a correction based on a very limited number of high-fidelity model samples. The major open problem here is the proper selection of the low-fidelity model. The type of simplifications made to construct the model, as well as its level of accuracy (e.g., mesh density) may be crucial for the algorithm performance both in terms of the quality of the final design and the computational cost of the design process. Here, we investigate this trade off using space mapping (SM) as an exemplary SBO technique and two dimensional airfoil shape optimization as a representative design problem. Both lift maximization and drag minimization test cases are considered.

World bank endorses water resources strategy

Gas cyclones have many industrial applications in solid–gas separation. The vortex finder is an essential part in gas cyclones where the shape and diameter highly affect the cyclone performance. Many optimization studies have been conducted to optimize the cylindrical vortex finder diameter. This study introduces a new vortex finder shape optimized for minimum pressure drop using the discrete adjoint method. The new optimum cyclone will save 66% from the driving power needed for the Stairmand cyclone. To efficiently perform the grid independence study for the new cyclone, a new framework using the adjoint solver and the grid convergence index is proposed and tested. The proposed framework relies on local mesh adaptation instead of the global mesh refinement approach. A comparison of numerical simulation of the new cyclone and the Stairmand cyclone confirms the superior performance of the new vortex finder shape for the pressure drop and the cut-off diameter. The results of this study open a new era gas cyclones geometry optimization by using the adjoint method instead of the traditional surrogate based optimization technique. Moreover, the computational costs for the grid independence studies will be reduced via the application of the adjoint methods.