Effect of Deterministic and Continuous Design Space Resolution on Multiple-Objective Combustor Optimization

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Alejandro M. Briones ◽  
Markus P. Rumpfkeil ◽  
Nathan R. Thomas ◽  
Brent A. Rankin
Keyword(s):  
Computer Aided Design ◽  
Adaptive Mesh Refinement ◽  
Design Space ◽  
Cfd Simulation ◽  
Pareto Frontier ◽  
Wall Turbulence ◽  
Training Data ◽  
Supervised Machine Learning ◽  
Small Scale ◽  
Input Parameters

Abstract Supervised machine learning is used to classify a continuous and deterministic design space into a nondominated Pareto frontier and dominated design points. The effect of the initial training data quantity on the Pareto frontier and output parameter sensitivity is explored. The study is performed with the optimization of a subsonic small-scale cavity-stabilized combustor. A 3D geometry is created and parameterized using computer aided design (CAD) that is combined with a software for meshing, which automatically transfers grids and boundary conditions to the solver and postprocessing tool. Steady, compressible three-dimensional simulations are conducted employing a multiphase Realizable k–ε Reynolds-averaged Navier–Stokes (RANS) physics with an adiabatic flamelet progress variable (FPV) model. The near-wall turbulence modeling is computed with scalable wall functions (SWFs). For each computational fluid dynamics (CFD) simulation, four levels of adaptive mesh refinement (AMR) are utilized on the original cut-cell grid. There are 15 geometrical input parameters and three output parameters, viz., a pattern factor proxy, a combustion efficiency proxy, and total pressure loss (TPL). Three times the number of input parameters plus one (48) is necessary to yield an optimization independent of the initial sampling. This conclusion is drawn by examining and comparing the Pareto frontiers and global sensitivities. However, the latter provides a better metric. The relative influence of the input parameters on the outputs is assessed by Spearman's order-rank correlation and an active subspace analysis. Some persistent geometric features for nondominated designs are also discussed.

Effect of Deterministic and Continuous Design Space Resolution on Multiple-Objective Combustor Optimization

2019 ◽  
Author(s):  
Alejandro M. Briones ◽  
Markus P. Rumpfkeil ◽  
Nathan R. Thomas ◽  
Brent A. Rankin
Keyword(s):  
Design Space ◽  
Pareto Frontier ◽  
Output Parameter ◽  
Supervised Machine Learning ◽  
Small Scale ◽  
Multiple Objective ◽  
Fuel Injector ◽  
Progress Variable ◽  
Input Parameters ◽  
Exit Temperature

Abstract A supervised machine learning technique namely an Adaptive Multiple Objective (AMO) optimization algorithm is used to divide a continuous and deterministic design space into non-dominated Pareto frontier and dominated design points. The effect of the initial training data quantity, i.e., computational fluid dynamics (CFD) results, on the Pareto frontier and output parameter sensitivity is explored. The optimization study is performed on a subsonic small-scale cavity-stabilized combustor. A parametric geometry is created using CAD that is coupled with a meshing software. The latter automatically transfers meshes and boundary conditions to the solver, which is coupled with a post-processing tool. Steady, incompressible three-dimensional simulations are performed using a multi-phase realizable k-ε Reynolds-averaged Navier-Stokes (RANS) approach with an adiabatic flamelet progress variable (FPV). Scalable wall functions are used for modeling turbulence near the wall. For each CFD simulation four levels of adaptive mesh refinement (AMR) are utilized on the original cut-cell grid. The mesh is refined where the flow exhibits large progress variable curvature. There are fifteen geometrical input parameters and three output parameters, viz., a pattern factor proxy (maximum exit temperature), a combustion efficiency proxy (averaged exit temperature), and total pressure loss (TPL). The Pareto frontier and the input-to-output parameter sensitivities are reported for each meta-model simulation. For the investigated design space, three times the number of input parameters plus one (48) yields an optimization independent of the initial sampling. This conclusion is drawn by comparing the Pareto frontiers and global sensitivities. However, the latter provides a better metric. The relative influence of the input parameters on the outputs is assessed by using both a Spearman’s order-rank correlation approach as well as an active subspace analysis. In general, non-dominated design points exhibit persistent geometrical features such as offset opposed cavity forward and aft driver jet alignment. Larger cavities necessitate larger chutes and smaller outer liner jet diameters, whereas smaller cavities require smaller chutes and larger outer liner jet diameters. The fuel injector radial location varies, but can be located either radially inward or outward with respect to the forward dilution jet radial locations. For these non-dominated designs there is substantial burning inside and outside of the cavity. The downstream dilution jets quench the upstream hot gases.

Automated Design Optimization of a Small-Scale High-Swirl Cavity-Stabilized Combustor

2018 ◽  
Author(s):  
Alejandro M. Briones ◽  
David L. Burrus ◽  
Joshua P. Sykes ◽  
Brent A. Rankin ◽  
Andrew W. Caswell
Keyword(s):  
Total Pressure ◽  
Cfd Simulation ◽  
Rank Correlation ◽  
Coefficient Of Determination ◽  
Small Scale ◽  
Baseline Design ◽  
Design Point ◽  
Swirl Angle ◽  
Input Parameters ◽  
Exit Temperature

A numerical optimization study is performed on a small-scale high-swirl cavity-stabilized combustor. A parametric geometry is created in CAD software that is coupled with meshing software. The latter automatically transfers meshes and boundary conditions to the solver, which is coupled with a post-processing tool. Steady, incompressible three-dimensional simulations are performed using a multi-phase Realizable k-ϵ Reynolds-averaged Navier-Stokes (RANS) approach with the non-adiabatic flamelet progress variable (FPV). There are nine input parameters based on geometrical control variables. There are five output parameters, viz., pattern factor (PF), RMS of the profile factor deviation, averaged exit temperature, averaged exit swirl angle, and total pressure loss. An iterative design of experiments (DOE) with a recursive Latin Hypercube Sampling (LHS) is performed to filter the most important input parameters. The five major input parameters are found with Spearman’s order-rank correlation and R2 coefficient of determination. The five input parameters are used for the adaptive multiple objective (AMO) optimization. The AMO algorithm provided a candidate design point with the lowest weighted objective function. This design point was verified through CFD simulation. The combined filtering and optimization procedures improve the baseline design point in terms of pattern and profile factor. The former halved from that of the baseline design point whereas the latter turned from an outer peak to a center peak profile, closely mimicking an ideal profile. The exit swirl angle favorably increased 25%. The averaged exit temperature and the total pressure losses remained nearly unchanged from the baseline design point.

scholarly journals A Comparative Evaluation of Supervised Machine Learning Classification Techniques for Engineering Design Applications

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Conner Sharpe ◽  
Tyler Wiest ◽  
Pingfeng Wang ◽  
Carolyn Conner Seepersad
Keyword(s):  
Machine Learning ◽  
Engineering Design ◽  
Design Space ◽  
Optimization Problems ◽  
Machine Learning Algorithms ◽  
Training Data ◽  
Supervised Machine Learning ◽  
Machine Learning Techniques ◽  
Design Exploration ◽  
Machine Learning Classification

Abstract Supervised machine learning techniques have proven to be effective tools for engineering design exploration and optimization applications, in which they are especially useful for mapping promising or feasible regions of the design space. The design space mappings can be used to inform early-stage design exploration, provide reliability assessments, and aid convergence in multiobjective or multilevel problems that require collaborative design teams. However, the accuracy of the mappings can vary based on problem factors such as the number of design variables, presence of discrete variables, multimodality of the underlying response function, and amount of training data available. Additionally, there are several useful machine learning algorithms available, and each has its own set of algorithmic hyperparameters that significantly affect accuracy and computational expense. This work elucidates the use of machine learning for engineering design exploration and optimization problems by investigating the performance of popular classification algorithms on a variety of example engineering optimization problems. The results are synthesized into a set of observations to provide engineers with intuition for applying these techniques to their own problems in the future, as well as recommendations based on problem type to aid engineers in algorithm selection and utilization.

Automated Design Optimization of a Small-Scale High-Swirl Cavity-Stabilized Combustor

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Alejandro M. Briones ◽  
David L. Burrus ◽  
Joshua P. Sykes ◽  
Brent A. Rankin ◽  
Andrew W. Caswell
Keyword(s):  
Total Pressure ◽  
Cfd Simulation ◽  
Fluid Dynamic ◽  
Coefficient Of Determination ◽  
Small Scale ◽  
Baseline Design ◽  
Design Point ◽  
Swirl Angle ◽  
Input Parameters ◽  
Exit Temperature

A numerical optimization study is performed on a small-scale high-swirl cavity-stabilized combustor. A parametric geometry is created in cad software that is coupled with meshing software. The latter automatically transfers meshes and boundary conditions to the solver, which is coupled with a postprocessing tool. Steady, incompressible three-dimensional simulations are performed using a multiphase Realizable k-ε Reynolds-averaged Navier-Stokes (RANS) approach with a nonadiabatic flamelet progress variable (FPV) model. There are nine geometrical input parameters. There are five output parameters, viz., pattern factor (PF), RMS of the profile factor deviation, averaged exit temperature, averaged exit swirl angle, and total pressure loss. An iterative design of experiments (DOE) with a recursive Latin hypercube sampling (LHS) is performed to filter the most important input parameters. The five major input parameters are found with Spearman's order-rank correlation and R2 coefficient of determination. The five input parameters are used for the adaptive multiple objective (AMO) optimization. This provided a candidate design point with the lowest weighted objective function, which was verified through computational fluid dynamic (CFD) simulation. The combined filtering and optimization procedures improve the baseline design point in terms of pattern and profile factor. The former halved from that of the baseline design point, whereas the latter turned from an outer peak to a center peak profile, closely mimicking an ideal profile. The exit swirl angle favorably increased 25%. The averaged exit temperature and the total pressure losses remained nearly unchanged from the baseline design point.

On-Design Component-Level Multiple-Objective Optimization of a Small-Scale Cavity-Stabilized Combustor

2021 ◽  
Author(s):  
Alejandro Briones ◽  
Timothy Erdmann ◽  
Brent Rankin
Keyword(s):  
Pareto Frontier ◽  
Supervised Machine Learning ◽  
Combustion Model ◽  
Small Scale ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Component Level ◽  
Baseline Design ◽  
Design Point ◽  
Design Component

Abstract This work presents an on-design component-level multiple-objective optimization of a small-scaled uncooled cavity-stabilized combustor. Optimization is performed at the maximum power condition of the engine thermodynamic cycle. The CFD simulations are managed by a supervised machine learning algorithm to divide a continuous and deterministic design space into non-dominated Pareto frontier and dominated design points. Steady, compressible three-dimensional simulations are performed using a multi-phase Realizable k-? RANS and non-adiabatic FPV combustion model. Conjugate heat transfer through the combustor liner is also considered. There are fifteen geometrical input parameters and four objective functions viz., maximization of combustion efficiency, and minimization of total pressure losses, pattern factor, and critical liner area factor. The baseline combustor design is based on engineering guidelines developed over the past two decades. The small-scale baseline design performs remarkably well. Direct optimization calculations are performed on this baseline design. In terms of Pareto optimality, the baseline design remains in the Pareto frontier throughout the optimization. However, the optimization calculations show improvement from an initial design point population to later iteration design points. The optimization calculations report other non-dominated designs in the Pareto frontier. The Euclidean distance from design points to the utopic point is used to select a "best" and "worst" design point for future fabrication and experimentation. The methodology to perform CFD optimization calculations of a small-scale uncooled combustor is expected to be useful for guiding the design and development of future gas turbine combustors.

On-Design Component-Level Multiple-Objective Optimization of a Small-Scale Cavity-Stabilized Combustor

2021 ◽  
Author(s):  
Alejandro M. Briones ◽  
Timothy J. Erdmann ◽  
Brent A. Rankin
Keyword(s):  
Pareto Frontier ◽  
Supervised Machine Learning ◽  
Combustion Model ◽  
Small Scale ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Component Level ◽  
Baseline Design ◽  
Design Point ◽  
Design Component

Abstract This work presents an on-design component-level multiple-objective optimization of a small-scaled uncooled cavity-stabilized combustor. Optimization is performed at the maximum power condition of the engine thermodynamic cycle. The CFD simulations are managed by a supervised machine learning algorithm to divide a continuous and deterministic design space into non-dominated Pareto frontier and dominated design points. Steady, compressible three-dimensional simulations are performed using a multi-phase Realizable k-ε RANS and non-adiabatic FPV combustion model. Conjugate heat transfer through the combustor liner is also considered. There are fifteen geometrical input parameters and four objective functions viz., maximization of combustion efficiency, and minimization of total pressure losses, pattern factor, and critical liner area factor. The baseline combustor design is based on engineering guidelines developed over the past two decades. The small-scale baseline design performs remarkably well. Direct optimization calculations are performed on this baseline design. In terms of Pareto optimality, the baseline design remains in the Pareto frontier throughout the optimization. However, the optimization calculations show improvement from an initial design point population to later iteration design points. The optimization calculations report other non-dominated designs in the Pareto frontier. The Euclidean distance from design points to the utopic point is used to select a “best” and “worst” design point for future fabrication and experimentation. The methodology to perform CFD optimization calculations of a small-scale uncooled combustor is expected to be useful for guiding the design and development of future gas turbine combustors.

scholarly journals Data Quality Measures and Efficient Evaluation Algorithms for Large-Scale High-Dimensional Data

2021 ◽  
Vol 11 (2) ◽  
pp. 472
Author(s):  
Hyeongmin Cho ◽  
Sangkyun Lee
Keyword(s):  
Machine Learning ◽  
Data Quality ◽  
Large Scale ◽  
High Dimensional Data ◽  
Quality Measures ◽  
Training Data ◽  
Measure Data ◽  
High Dimensional ◽  
Small Scale ◽  
Class Separability

Machine learning has been proven to be effective in various application areas, such as object and speech recognition on mobile systems. Since a critical key to machine learning success is the availability of large training data, many datasets are being disclosed and published online. From a data consumer or manager point of view, measuring data quality is an important first step in the learning process. We need to determine which datasets to use, update, and maintain. However, not many practical ways to measure data quality are available today, especially when it comes to large-scale high-dimensional data, such as images and videos. This paper proposes two data quality measures that can compute class separability and in-class variability, the two important aspects of data quality, for a given dataset. Classical data quality measures tend to focus only on class separability; however, we suggest that in-class variability is another important data quality factor. We provide efficient algorithms to compute our quality measures based on random projections and bootstrapping with statistical benefits on large-scale high-dimensional data. In experiments, we show that our measures are compatible with classical measures on small-scale data and can be computed much more efficiently on large-scale high-dimensional datasets.

scholarly journals Effects of Training Set Size on Supervised Machine-Learning Land-Cover Classification of Large-Area High-Resolution Remotely Sensed Data

2021 ◽  
Vol 13 (3) ◽  
pp. 368
Author(s):  
Christopher A. Ramezan ◽  
Timothy A. Warner ◽  
Aaron E. Maxwell ◽  
Bradley S. Price
Keyword(s):  
Machine Learning ◽  
Sample Size ◽  
Remotely Sensed ◽  
Training Data ◽  
Supervised Machine Learning ◽  
Sample Sizes ◽  
Remotely Sensed Data ◽  
Large Area ◽  
Training Set ◽  
Set Size

The size of the training data set is a major determinant of classification accuracy. Nevertheless, the collection of a large training data set for supervised classifiers can be a challenge, especially for studies covering a large area, which may be typical of many real-world applied projects. This work investigates how variations in training set size, ranging from a large sample size (n = 10,000) to a very small sample size (n = 40), affect the performance of six supervised machine-learning algorithms applied to classify large-area high-spatial-resolution (HR) (1–5 m) remotely sensed data within the context of a geographic object-based image analysis (GEOBIA) approach. GEOBIA, in which adjacent similar pixels are grouped into image-objects that form the unit of the classification, offers the potential benefit of allowing multiple additional variables, such as measures of object geometry and texture, thus increasing the dimensionality of the classification input data. The six supervised machine-learning algorithms are support vector machines (SVM), random forests (RF), k-nearest neighbors (k-NN), single-layer perceptron neural networks (NEU), learning vector quantization (LVQ), and gradient-boosted trees (GBM). RF, the algorithm with the highest overall accuracy, was notable for its negligible decrease in overall accuracy, 1.0%, when training sample size decreased from 10,000 to 315 samples. GBM provided similar overall accuracy to RF; however, the algorithm was very expensive in terms of training time and computational resources, especially with large training sets. In contrast to RF and GBM, NEU, and SVM were particularly sensitive to decreasing sample size, with NEU classifications generally producing overall accuracies that were on average slightly higher than SVM classifications for larger sample sizes, but lower than SVM for the smallest sample sizes. NEU however required a longer processing time. The k-NN classifier saw less of a drop in overall accuracy than NEU and SVM as training set size decreased; however, the overall accuracies of k-NN were typically less than RF, NEU, and SVM classifiers. LVQ generally had the lowest overall accuracy of all six methods, but was relatively insensitive to sample size, down to the smallest sample sizes. Overall, due to its relatively high accuracy with small training sample sets, and minimal variations in overall accuracy between very large and small sample sets, as well as relatively short processing time, RF was a good classifier for large-area land-cover classifications of HR remotely sensed data, especially when training data are scarce. However, as performance of different supervised classifiers varies in response to training set size, investigating multiple classification algorithms is recommended to achieve optimal accuracy for a project.

Structural Shape Optimization Wth Error Control

1994 ◽  
Author(s):  
Pierre Duysinx ◽  
WeiHong Zhang ◽  
HaiGuang Zhong ◽  
Pierre Beckers ◽  
Claude Fleury
Keyword(s):  
Shape Optimization ◽  
Computer Aided Design ◽  
Adaptive Mesh Refinement ◽  
Error Control ◽  
Optimization Procedure ◽  
Adaptive Mesh ◽  
Structural Shape ◽  
Structural Shape Optimization ◽  
Design Variables ◽  
Recent Developments

Abstract A robust and automatic shape optimization procedure is presented in this paper, which incorporates recent developments in the field of computer-aided design (CAD) of mechanical structures, such as geometric modelling, automatic selection of independent design variables, sensitivity analysis using reliable mesh perturbation schemes, error estimation and adaptive mesh refinement. A numerical example is given to show the efficiency of the procedure.

Adaptive Geometry Representation of Turbine Vane Frames for Use in Optimization

2021 ◽  
Author(s):  
Sebastian F. Riebl ◽  
Christian Wakelam ◽  
Reinhard Niehuis
Keyword(s):  
Design Space ◽  
Cfd Simulation ◽  
A Priori ◽  
Three Dimensional ◽  
Optimization Method ◽  
Three Dimensions ◽  
Design Parameters ◽  
Adjustment Process ◽  
Turbine Vane ◽  
Integrated Concept

Abstract Turbine Vane Frames (TVF) are a way to realize more compact jet engine designs. Located between the high pressure turbine (HPT) and the low pressure turbine (LPT), they fulfill structural and aerodynamic tasks. When used as an integrated concept with splitters located between the structural load-bearing vanes, the TVF configuration contains more than one type of airfoil with sometimes pronouncedly different properties. This system of multidisciplinary demands and mixed blading poses an interesting opportunity for optimization. Within the scope of the present work, a full geometric parameterization of a TVF with splitters is presented. The parameterization is chosen as to minimize the number of parameters required to automatically and flexibly represent all blade types involved in a TVF row in all three dimensions. Typical blade design parameters are linked to the fourth order Bézier-curve controlled camber line-thickness parameterization. Based on conventional design rules, a procedure is presented, which sets the parameters within their permissible ranges according to the imposed constraints, using a proprietary developed code. The presented workflow relies on subsequent three dimensional geometry generation by transfer of the proposed parameter set to a commercially available CAD package. The interdependencies of parameters are discussed and their respective significance for the adjustment process is detailed. Furthermore, the capability of the chosen parameterization and adjustment process to rebuild an exemplary reference TVF geometry is demonstrated. The results are verified by comparing not only geometrical profile data, but also validated CFD simulation results between the rebuilt and original geometries. Measures taken to ensure the robustness of the method are highlighted and evaluated by exploring extremes in the permissible design space. Finally, the embedding of the proposed method within the framework of an automated, gradient free numerical optimization is discussed. Herein, implications of the proposed method on response surface modeling in combination with the optimization method are highlighted. The method promises to be an option for improvement of optimization efficiency in gradient free optimization of interdependent blade geometries, by a-priori excluding unsuitable blade combinations, yet keeping restrictions to the design space as limited as possible.

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