This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solve...This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.展开更多
For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversio...For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized. we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.展开更多
The steepest descent(or ascent)search is employed for finding optimum diffusion coefficients in T42L9G model,with a view to improving the model's computational stability or prediction accuracy.The method of the st...The steepest descent(or ascent)search is employed for finding optimum diffusion coefficients in T42L9G model,with a view to improving the model's computational stability or prediction accuracy.The method of the steepest descent search is first described,in which the golden section search is chosen as the fundamental one- dimensional search used in the multi-dimentional steepest descent search,and then the optimization of the dif- fusion coefficients is described.展开更多
The safety and reliability of battery storage systems are critical to the mass roll-out of electrified transportation and new energy generation.To achieve safe management and optimal control of batteries,the state of ...The safety and reliability of battery storage systems are critical to the mass roll-out of electrified transportation and new energy generation.To achieve safe management and optimal control of batteries,the state of charge(SOC)is one of the important parameters.The machine-learning based SOC estimation methods of lithium-ion batteries have attracted substantial interests in recent years.However,a common problem with these models is that their estimation performances are not always stable,which makes them difficult to use in practical applications.To address this problem,an optimized radial basis function neural network(RBF-NN)that combines the concepts of Golden Section Method(GSM)and Sparrow Search Algorithm(SSA)is proposed in this paper.Specifically,GSM is used to determine the optimum number of neurons in hidden layer of the RBF-NN model,and its parameters such as radial base center,connection weights and so on are optimized by SSA,which greatly improve the performance of RBF-NN in SOC estimation.In the experiments,data collected from different working conditions are used to demonstrate the accuracy and generalization ability of the proposed model,and the results of the experiment indicate that the maximum error of the proposed model is less than 2%.展开更多
基金the National Science and Tech-nology Council,Taiwan for their financial support(Grant Number NSTC 111-2221-E-019-048).
文摘This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.
基金supported by Specialized Research Fund for the Doctoral Program of Higher Education of China(20110022120004)the Fundamental Research Funds for the Central Universities
文摘For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized. we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.
文摘The steepest descent(or ascent)search is employed for finding optimum diffusion coefficients in T42L9G model,with a view to improving the model's computational stability or prediction accuracy.The method of the steepest descent search is first described,in which the golden section search is chosen as the fundamental one- dimensional search used in the multi-dimentional steepest descent search,and then the optimization of the dif- fusion coefficients is described.
基金This work was supported by the Fundamental Research Funds for the Central Universities(2022MS015)。
文摘The safety and reliability of battery storage systems are critical to the mass roll-out of electrified transportation and new energy generation.To achieve safe management and optimal control of batteries,the state of charge(SOC)is one of the important parameters.The machine-learning based SOC estimation methods of lithium-ion batteries have attracted substantial interests in recent years.However,a common problem with these models is that their estimation performances are not always stable,which makes them difficult to use in practical applications.To address this problem,an optimized radial basis function neural network(RBF-NN)that combines the concepts of Golden Section Method(GSM)and Sparrow Search Algorithm(SSA)is proposed in this paper.Specifically,GSM is used to determine the optimum number of neurons in hidden layer of the RBF-NN model,and its parameters such as radial base center,connection weights and so on are optimized by SSA,which greatly improve the performance of RBF-NN in SOC estimation.In the experiments,data collected from different working conditions are used to demonstrate the accuracy and generalization ability of the proposed model,and the results of the experiment indicate that the maximum error of the proposed model is less than 2%.
