scholarly journals Optimization of a Stirling Engine by Variable-Step Simplified Conjugate-Gradient Method and Neural Network Training Algorithm

Energies ◽  
2020 ◽  
Vol 13 (19) ◽  
pp. 5164
Author(s):  
Chin-Hsiang Cheng ◽  
Yu-Ting Lin
Keyword(s):  
Neural Network ◽  
Optimal Design ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Stirling Engine ◽  
Neural Network Training ◽  
Training Algorithm ◽  
Network Training ◽  
Variable Step

The present study develops a novel optimization method for designing a Stirling engine by combining a variable-step simplified conjugate gradient method (VSCGM) and a neural network training algorithm. As compared with existing gradient-based methods, like the conjugate gradient method (CGM) and simplified conjugate gradient method (SCGM), the VSCGM method is a further modified version presented in this study which allows the convergence speed to be greatly accelerated while the form of the objective function can still be defined flexibly. Through the automatic adjustment of the variable step size, the optimal design is reached more efficiently and accurately. Therefore, the VSCGM appears to be a potential and alternative tool in a variety of engineering applications. In this study, optimization of a low-temperature-differential gamma-type Stirling engine was attempted as a test case. The optimizer was trained by the neural network algorithm based on the training data provided from three-dimensional computational fluid dynamic (CFD) computation. The optimal design of the influential parameters of the Stirling engine is yielded efficiently. Results show that the indicated work and thermal efficiency are increased with the present approach by 102.93% and 5.24%, respectively. Robustness of the VSCGM is tested by giving different sets of initial guesses.

scholarly journals An Advanced Conjugate Gradient Training Algorithm Based on a Modified Secant Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Ioannis E. Livieris ◽  
Panagiotis Pintelas
Keyword(s):  
Neural Network ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
High Order Accuracy ◽  
Conjugate Gradient Methods ◽  
Training Methods ◽  
Neural Network Training ◽  
Training Algorithm ◽  
Error Surface ◽  
Network Training

Conjugate gradient methods constitute excellent neural network training methods characterized by their simplicity, numerical efficiency, and their very low memory requirements. In this paper, we propose a conjugate gradient neural network training algorithm which guarantees sufficient descent using any line search, avoiding thereby the usually inefficient restarts. Moreover, it achieves a high-order accuracy in approximating the second-order curvature information of the error surface by utilizing the modified secant condition proposed by Li et al. (2007). Under mild conditions, we establish that the proposed method is globally convergent for general functions under the strong Wolfe conditions. Experimental results provide evidence that our proposed method is preferable and in general superior to the classical conjugate gradient methods and has a potential to significantly enhance the computational efficiency and robustness of the training process.

Experimental Identification of a Flow Orifice Using a Neural Network and the Conjugate Gradient Method

1996 ◽  
Vol 118 (2) ◽  
pp. 272-277 ◽  
Author(s):  
X. P. Xu ◽  
R. T. Burton ◽  
C. M. Sargent
Keyword(s):  
Neural Network ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Experimental Approach ◽  
Stable Solution ◽  
Training Algorithm ◽  
The Neural Network ◽  
Trained Neural Network ◽  
Flow Valve

An experimental approach of using a neural network model to identifying a nonlinear non-pressure-compensated flow valve is described in this paper. The conjugate gradient method with Polak-Ribiere formula is applied to train the neural network to approximate the nonlinear relationships represented by noisy data. The ability of the trained neural network to reproduce and to generalize is demonstrated by its excellent approximation of the experimental data. The training algorithm derived from the conjugate gradient method is shown to lead to a stable solution.

scholarly journals Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method

Energies ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7835
Author(s):  
Chin-Hsiang Cheng ◽  
Duc-Thuan Phung
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Thermodynamic Model ◽  
Thermal Efficiency ◽  
Engine Performance ◽  
Stirling Engine ◽  
Positive Effects ◽  
Baseline Case ◽  
Variable Step

This study focuses on optimizing a 100-W-class β-Type Stirling engine by combining the modified thermodynamic model and the variable-step simplified conjugate gradient (VSCGM) method. For the modified thermodynamic model, non-uniform pressure is directly introduced into the energy equation, so the indicated power and heat transfer rates can reach energy balance while the VSCGM is an updated version of the simplified conjugate gradient method (SCGM) with adaptive increments and step lengths to the optimization process; thus, it requires fewer iterations to reach the optimal solution than the SCGM. For the baseline case, the indicated power progressively raises from 88.2 to 210.2 W and the thermal efficiency increases from 34.8 to 46.4% before and after optimization, respectively. The study shows the VSCGM possesses robust property. All optimal results from the VSCGM are well-matched with those of the computational fluid dynamics (CFD) model. Heating temperature and rotation speed have positive effects on optimal engine performance. The optimal indicated power rises linearly with the charged pressure, whereas the optimal thermal efficiency tends to decrease. The study also points out that results of the modified thermodynamic model with fixed values of unknowns agree well with the CFD results at points far from the baseline case.

scholarly journals Machine-learning in astronomy

2014 ◽  
Vol 10 (S306) ◽  
pp. 279-287 ◽  
Author(s):  
Michael Hobson ◽  
Philip Graff ◽  
Farhan Feroz ◽  
Anthony Lasenby
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Neural Networks ◽  
Gamma Ray ◽  
Neural Network Training ◽  
Training Algorithm ◽  
Data Description ◽  
Astronomical Data ◽  
Machine Learning Methods ◽  
Network Training

AbstractMachine-learning methods may be used to perform many tasks required in the analysis of astronomical data, including: data description and interpretation, pattern recognition, prediction, classification, compression, inference and many more. An intuitive and well-established approach to machine learning is the use of artificial neural networks (NNs), which consist of a group of interconnected nodes, each of which processes information that it receives and then passes this product on to other nodes via weighted connections. In particular, I discuss the first public release of the generic neural network training algorithm, calledSkyNet, and demonstrate its application to astronomical problems focusing on its use in the BAMBI package for accelerated Bayesian inference in cosmology, and the identification of gamma-ray bursters. TheSkyNetand BAMBI packages, which are fully parallelised using MPI, are available athttp://www.mrao.cam.ac.uk/software/.

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