Multipoint optimization of an axial turbine cascade using a hybrid algorithm

2020 ◽  
pp. 1-15
Author(s):  
Arnaud Châtel ◽  
Tom Verstraete ◽  
Grégory Coussement
Keyword(s):  
Evolutionary Algorithm ◽  
Hybrid Algorithm ◽  
Search Space ◽  
Benchmark Problems ◽  
Flow Angle ◽  
Operating Range ◽  
Trailing Edges ◽  
Gradient Based ◽  
Outlet Flow ◽  
Multipoint Optimization

Abstract This paper presents a multipoint optimization of the LS89 cascade. The objective of the optimization consists in minimizing the entropy losses generated inside the cascade over a predefined operating range. Two aerodynamic constraints are imposed in order to conserve the same performance as the original cascade. The first constraint is established on the outlet flow angle in order to achieve at least the same flow turning as the LS89. The second constraint limits the mass-flow passing through the cascade. The optimization is performed using a hybrid algorithm which combines a classical evolutionary algorithm with a gradient-based method. The hybridization between both methods is based on the Lamarckian approach which consists in incorporating the gradient method inside the loop of the evolutionary algorithm. In this methodology, the evolutionary method allows to globally explore the design space while the gradient-based method locally improves certain designs located in promising regions of the search space. First, the better performance of the hybrid method compared to the performance of an evolutionary algorithm is demonstrated on benchmark problems. Then, the methodology is applied on the LS89 application. The optimization allows to find a new profile which reduces the entropy losses over the entire operating range by at least 9.5 %. Finally, the comparison of the flows computed in the baseline and in the optimized cascades demonstrates that the reduction of the losses is due to a decrease of the entropy generated downstream the trailing edges and within the passages between the optimized blades.

Multipoint Optimization of an Axial Turbine Cascade Using a Hybrid Algorithm

2019 ◽  
Author(s):  
Arnaud Châtel ◽  
Tom Verstraete ◽  
Grégory Coussement
Keyword(s):  
Evolutionary Algorithm ◽  
Hybrid Algorithm ◽  
Search Space ◽  
Benchmark Problems ◽  
Turbine Cascade ◽  
Flow Angle ◽  
Operating Range ◽  
Overall Design ◽  
Gradient Based ◽  
Multipoint Optimization

Abstract This paper presents a constrained multipoint optimization of the LS89 turbine cascade. The objective of the optimization consists in minimizing the entropy losses generated inside the cascade over a predefined operating range. The operating range is bounded by two operating points respectively characterized by a downstream isentropic Mach number of 0.9 and 1.01. During the optimization, two aerodynamic constraints are imposed in order to conserve the same performance as the original cascade. The first constraint is established on the outlet flow angle in order to achieve at least the same flow turning as the LS89 turbine. The second constraint limits the mass-flow passing through the optimized cascade. The optimization is performed using a hybrid algorithm which combines efficiently a classical evolutionary algorithm with a gradient-based method. The hybridization process between both methods is based on the Lamarckian approach which consists in incorporating directly the gradient method inside the loop of the evolutionary algorithm. In this methodology, the evolutionary method allows to globally explore the overall design space while the gradient-based method locally improves certain designs located in the most promising regions of the search space. First, the better performance of the proposed hybrid method compared to the performance of a classical evolutionary algorithm is demonstrated on two benchmark problems. Then, the methodology is applied on a turbomachinery application in order to minimize the losses in the linear LS89 cascade. The optimization process allows to find a new blade profile which reduces the entropy losses over the entire operating range by at least 9.5 %. Finally, the comparison of the flows computed in the baseline and in the optimized cascades demonstrates that the reduction of the losses is due to a decrease of the entropy generated downstream the trailing edges and within the passages between the optimized blades.

Single-Point Optimization of the LS89 Turbine Cascade Using a Hybrid Algorithm

2018 ◽  
Author(s):  
Arnaud Châtel ◽  
Tom Verstraete ◽  
Grégory Coussement ◽  
Lasse Mueller
Keyword(s):  
Evolutionary Algorithm ◽  
Hybrid Algorithm ◽  
Design Space ◽  
Single Point ◽  
Flow Analysis ◽  
Optimization Methods ◽  
Benchmark Problems ◽  
Turbine Vane ◽  
Gradient Based ◽  
The One

This paper presents a single point optimization of the LS89 turbine vane cascade for a downstream isentropic Mach number of 0.9. The objective of the optimization is to minimize the entropy generation through the cascade while maintaining the flow turning of the baseline geometry. The optimization is performed using a hybrid optimization algorithm which combines two main families of optimization methods, namely an evolutionary algorithm and a gradient-based method. The combination of these two methods aims to correct their respective main disadvantage which are the poor convergence performance of the evolutionary and the trend to get trapped in local minima of the gradient-based method. The hybrid algorithm implemented in this work is based on the Lamarckian evolution and consists in incorporating directly the gradient-based method inside the loop of the evolutionary algorithm. In this approach, the evolutionary algorithm performs a global exploration of the design space while the gradient-based method improves the convergence rate of the evolutionary algorithm. The better performance of the developed hybrid method, compared to a classical evolutionary algorithm, is first demonstrated on two analitycal functions used as benchmark problems. Subsequently, the hybrid algorithm is used to optimize LS89 turbine vane, resulting in a new design with about 20 percent lower entropy production compared to baseline geometry. A thorough flow analysis shows that the improvements are largely due to a significant decrease in trailing edge losses, which is characterized by a higher base pressure. A previous optimization of the LS89 cascade has been already realized using a classical gradient-based method. This optimization converged towards a new design which reduces the entropy rise by a factor of 11 percent. Therefore, the comparison between this optimum and the one found using the proposed method demonstrates that the hybrid algorithm allows to locate a better minimum by performing a global exploration of the design space.

Matrix Solution of Compressible Flow on S1 Surface Through a Turbomachine Blade Row With Splitter Vanes or Tandem Blades

1984 ◽  
Vol 106 (2) ◽  
pp. 449-454 ◽  
Author(s):  
Chung-Hua Wu ◽  
Baoguo Wang
Keyword(s):  
Compressible Flow ◽  
Present Method ◽  
Curvilinear Coordinates ◽  
Flow Ratio ◽  
Matrix Solution ◽  
Flow Angle ◽  
Trailing Edges ◽  
Blade Row ◽  
Outlet Flow ◽  
Turbomachine Blade

The basic aerothermodynamic equations of turbomachine flow expressed with respect to nonorthogonal curvilinear coordinates and corresponding nonorthogonal velocity components are used to solve the compressible flow S1 surface in a turbomachine blade row with splitter vanes or tandem blades. The equation of stream function is solved by matrix technique, and the mass flow ratio and outlet flow angle are determined by applying the Kutta-Joukowsky condition to the trailing edges of the main blade and the splitter vane. Typical examples are given to illustrate the effectiveness of the present method.

scholarly journals An Effective Variable Transformation Strategy in Multitasking Evolutionary Algorithms

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Qingzheng Xu ◽  
Lei Wang ◽  
Jungang Yang ◽  
Na Wang ◽  
Rong Fei ◽  
...  
Keyword(s):  
Knowledge Transfer ◽  
Evolutionary Algorithm ◽  
Simulated Data ◽  
Search Space ◽  
Benchmark Problems ◽  
Inverse Transformation ◽  
Optimal Solutions ◽  
Variable Transformation ◽  
Algorithm Performance ◽  
Transformation Strategy

Multitasking evolutionary algorithm (MTEA), which solves multiple optimization tasks simultaneously in a single run, has received considerable attention in the community of evolutionary computation, and several algorithms have been proposed in the literature. Unfortunately, knowledge transfer between constituent tasks may cause negative effect on algorithm performance, especially when the optimal solutions of all tasks are in different locations of the unified search space. To address this issue, an effective variable transformation strategy and the corresponding inverse transformation are proposed in multitasking optimization scenario. After using variable transformation strategy, the estimated optimal solutions of all tasks are both near the center point of the unified search space. More importantly, this strategy can enhance the task similarity, and then the effectiveness of knowledge transfer will probably be positive in this case, which can help us to improve the algorithm performance. Keeping this in mind, a multitasking evolutionary algorithm (named MTDE-VT) is realized as an instance by embedding the proposed variable transformation strategy into multitasking differential evolution. In MTDE-VT, the individuals in the original population are first transformed into new locations by the variable transformation strategy. Once the offspring is generated in the transformed unified search space, it must be transformed back to the original unified search space. The statistical analysis of experimental results on some multitasking optimization benchmark problems illustrates the superiority of the proposed MTDE-VT algorithm in terms of solution accuracy and robustness. Furthermore, the basic principle and the good parameter combination are also provided based on massive simulated data.

scholarly journals Flow Studies in a Centrifugal Compressor Stage

2014 ◽  
Author(s):  
R. Rajendran
Keyword(s):  
Centrifugal Compressor ◽  
Flow Behavior ◽  
Compressor Stage ◽  
Impeller Blade ◽  
Vaned Diffuser ◽  
Flow Angle ◽  
Centrifugal Compressor Stage ◽  
Operating Range ◽  
Impeller Outlet ◽  
Outlet Flow

The overall efficiency of a compressor is dependent on the design of both the impeller and the diffuser. The vaned diffuser reduces the operating range compared to the vaneless diffuser. However, by proper setting of the diffuser with reference to the impeller, it is possible to achieve a good stage performance. This paper describes the experimental investigation of the detailed flow behavior inside a centrifugal compressor stage for three different setting angles of the vaned diffuser with reference to the fixed impeller blade outlet angle. It is seen that diffuser setting angles lower than the impeller outlet flow angle gives wide operating range.

Placement of Digital Microfluidic Biochips via a New Evolutionary Algorithm

2021 ◽  
Vol 26 (6) ◽  
pp. 1-22
Author(s):  
Chen Jiang ◽  
Bo Yuan ◽  
Tsung-Yi Ho ◽  
Xin Yao
Keyword(s):  
Evolutionary Algorithm ◽  
Resource Constraints ◽  
Scheduling Algorithm ◽  
Search Space ◽  
Placement Problem ◽  
Heuristic Scheduling ◽  
Microfluidic Biochips ◽  
Feasible Solutions ◽  
Digital Microfluidic ◽  
Operation Scheduling

Digital microfluidic biochips (DMFBs) have been a revolutionary platform for automating and miniaturizing laboratory procedures with the advantages of flexibility and reconfigurability. The placement problem is one of the most challenging issues in the design automation of DMFBs. It contains three interacting NP-hard sub-problems: resource binding, operation scheduling, and module placement. Besides, during the optimization of placement, complex constraints must be satisfied to guarantee feasible solutions, such as precedence constraints, storage constraints, and resource constraints. In this article, a new placement method for DMFB is proposed based on an evolutionary algorithm with novel heuristic-based decoding strategies for both operation scheduling and module placement. Specifically, instead of using the previous list scheduler and path scheduler for decoding operation scheduling chromosomes, we introduce a new heuristic scheduling algorithm (called order scheduler) with fewer limitations on the search space for operation scheduling solutions. Besides, a new 3D placer that combines both scheduling and placement is proposed where the usage of the microfluidic array over time in the chip is recorded flexibly, which is able to represent more feasible solutions for module placement. Compared with the state-of-the-art placement methods (T-tree and 3D-DDM), the experimental results demonstrate the superiority of the proposed method based on several real-world bioassay benchmarks. The proposed method can find the optimal results with the minimum assay completion time for all test cases.

scholarly journals APPROACHES TO ADAPTIVE STOCHASTIC SEARCH BASED ON THE NONEXTENSIVE q-DISTRIBUTION

2006 ◽  
Vol 16 (07) ◽  
pp. 2081-2091 ◽  
Author(s):  
GEORGE D. MAGOULAS ◽  
ARISTOKLIS ANASTASIADIS
Keyword(s):  
Search Space ◽  
Stochastic Search ◽  
Diffusion Method ◽  
Benchmark Problems ◽  
Adaptive Search ◽  
Particle Swarm Optimizer ◽  
Network Training ◽  
Nonextensive Entropy ◽  
Potential Benefits ◽  
Entropic Index

This paper explores the use of the nonextensive q-distribution in the context of adaptive stochastic searching. The proposed approach consists of generating the "probability" of moving from one point of the search space to another through a probability distribution characterized by the q entropic index of the nonextensive entropy. The potential benefits of this technique are investigated by incorporating it in two different adaptive search algorithmic models to create new modifications of the diffusion method and the particle swarm optimizer. The performance of the modified search algorithms is evaluated in a number of nonlinear optimization and neural network training benchmark problems.

scholarly journals Differential Evolution with Population and Strategy Parameter Adaptation

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
V. Gonuguntla ◽  
R. Mallipeddi ◽  
Kalyana C. Veluvolu
Keyword(s):  
Differential Evolution ◽  
Population Size ◽  
Optimization Problems ◽  
Search Space ◽  
Benchmark Problems ◽  
Parameter Adaptation ◽  
De Algorithm ◽  
Probabilistic Technique ◽  
Number Of Individuals ◽  
Strategy Parameters

Differential evolution (DE) is simple and effective in solving numerous real-world global optimization problems. However, its effectiveness critically depends on the appropriate setting of population size and strategy parameters. Therefore, to obtain optimal performance the time-consuming preliminary tuning of parameters is needed. Recently, different strategy parameter adaptation techniques, which can automatically update the parameters to appropriate values to suit the characteristics of optimization problems, have been proposed. However, most of the works do not control the adaptation of the population size. In addition, they try to adapt each strategy parameters individually but do not take into account the interaction between the parameters that are being adapted. In this paper, we introduce a DE algorithm where both strategy parameters are self-adapted taking into account the parameter dependencies by means of a multivariate probabilistic technique based on Gaussian Adaptation working on the parameter space. In addition, the proposed DE algorithm starts by sampling a huge number of sample solutions in the search space and in each generation a constant number of individuals from huge sample set are adaptively selected to form the population that evolves. The proposed algorithm is evaluated on 14 benchmark problems of CEC 2005 with different dimensionality.

Genetic Diversity as an Objective in Multi-Objective Evolutionary Algorithms

2003 ◽  
Vol 11 (2) ◽  
pp. 151-167 ◽  
Author(s):  
Andrea Toffolo ◽  
Ernesto Benini
Keyword(s):  
Genetic Diversity ◽  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Selection Pressure ◽  
Evaluation Method ◽  
State Of The Art ◽  
Search Space ◽  
Test Problems ◽  
Multi Objective ◽  
Diversity Evaluation

A key feature of an efficient and reliable multi-objective evolutionary algorithm is the ability to maintain genetic diversity within a population of solutions. In this paper, we present a new diversity-preserving mechanism, the Genetic Diversity Evaluation Method (GeDEM), which considers a distance-based measure of genetic diversity as a real objective in fitness assignment. This provides a dual selection pressure towards the exploitation of current non-dominated solutions and the exploration of the search space. We also introduce a new multi-objective evolutionary algorithm, the Genetic Diversity Evolutionary Algorithm (GDEA), strictly designed around GeDEM and then we compare it with other state-of-the-art algorithms on a well-established suite of test problems. Experimental results clearly indicate that the performance of GDEA is top-level.

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