Spectral CG Algorithm for Solving Fuzzy Nonlinear Equations

The nonlinear conjugate gradient method is an effective technique for solving large-scale minimizations problems, and has a wide range of applications in various fields, such as mathematics, chemistry, physics, engineering and medicine. This study presents a novel spectral conjugate gradient algorithm (non-linear conjugate gradient algorithm), which is derived based on the Hisham–Khalil (KH) and Newton algorithms. Based on pure conjugacy condition The importance of this research lies in finding an appropriate method to solve all types of linear and non-linear fuzzy equations because the Buckley and Qu method is ineffective in solving fuzzy equations. Moreover, the conjugate gradient method does not need a Hessian matrix (second partial derivatives of functions) in the solution. The descent property of the proposed method is shown provided that the step size at meets the strong Wolfe conditions. In numerous circumstances, numerical results demonstrate that the proposed technique is more efficient than the Fletcher–Reeves and KH algorithms in solving fuzzy nonlinear equations.

Optimal Operation of a Microgrid with Hydrogen Storage Based on Deep Reinforcement Learning

Microgrid with hydrogen storage is an effective way to integrate renewable energy and reduce carbon emissions. This paper proposes an optimal operation method for a microgrid with hydrogen storage. The electrolyzer efficiency characteristic model is established based on the linear interpolation method. The optimal operation model of microgrid is incorporated with the electrolyzer efficiency characteristic model. The sequential decision-making problem of the optimal operation of microgrid is solved by a deep deterministic policy gradient algorithm. Simulation results show that the proposed method can reduce about 5% of the operation cost of the microgrid compared with traditional algorithms and has a certain generalization capability.

Conjugate gradient algorithm for consistent generalized Sylvester-transpose matrix equations

<abstract><p>We develop an effective algorithm to find a well-approximate solution of a generalized Sylvester-transpose matrix equation where all coefficient matrices and an unknown matrix are rectangular. The algorithm aims to construct a finite sequence of approximated solutions from any given initial matrix. It turns out that the associated residual matrices are orthogonal, and thus, the desire solution comes out in the final step with a satisfactory error. We provide numerical experiments to show the capability and performance of the algorithm.</p></abstract>

Accelerated Reduced Gradient Algorithm with Constraint Relaxation in Differential Inverse Kinematics

The Moore-Penrose pseudoinverse-based solution of the differential inverse kinematic task of redundant robots corresponds to the result of a particular optimization underconstraints in which the implementation of Lagrange’s ReducedGradient Algorithm can be evaded simply by considering the zero partial derivatives of the ”Auxiliary Function” associated with this problem. This possibility arises because of the fact that the cost term is built up of quadratic functions of the variable of optimization while the constraint term is linear function of the same variables. Any modification in the cost and/or constraint structure makes it necessary the use of the numerical algorithm. Anyway, the penalty effect of the cost terms is always overridden by the hard constraints that makes practical problems in the vicinity of kinematic singularities where the possible solution stillexists but needs huge joint coordinate time-derivatives. While in the special case the pseudoinverse simply can be deformed, inthe more general one more sophisticated constraint relaxation can be applied. In this paper a formerly proposed acceleratedtreatment of the constraint terms is further developed by the introduction of a simple constraint relaxation. Furthermore, thenumerical results of the algorithm are smoothed by a third order tracking strategy to obtain dynamically implementable solution.The improved method’s operation is exemplified by computation results for a 7 degree of freedom open kinematic chain

Customer Decision Prediction Using Deep Neural Network on Telco Customer Churn Data

Customer churn is the most important problem in the business world, especially in the telecommunications industry, because it greatly influences company profits. Getting new customers for a company is much more difficult and expensive than retaining existing customers. Machine learning, part of data mining, is a sub-field of artificial intelligence widely used to make predictions, including predicting customer churn. Deep neural network (DNN) has been used for churn prediction, but selecting hyperparameters in modeling requires more time and effort, making the process more challenging for the researcher. Therefore, the purpose of this study is to propose a better architecture for the DNN algorithm by using a hard tuner to obtain more optimal hyperparameters. The tuning hyperparameter used is random search in determining the number of nodes in each hidden layer, dropout, and learning rate. In addition, this study also uses three variations of the number of hidden layers, two variations of the activation function, namely rectified linear unit (ReLu) and Sigmoid, then uses five variations of the optimizer (stochastic gradient descent (SGD), adaptive moment estimation (Adam), adaptive gradient algorithm (Adagrad), Adadelta, and root mean square propagation (RMSprop)). Experiments show that the DNN algorithm using hyperparameter tuning random search produces a performance value of 83.09 % accuracy using three hidden layers, the number of nodes in each hidden layer is [20, 35, 15], using the RMSprop optimizer, dropout 0.1, the learning rate is 0.01, with the fastest tuning time of 21 seconds. Better than modeling using k-nearest neighbor (K-NN), random forest (RF), and decision tree (DT) as comparison algorithms.

The Discrete Gaussian Expectation Maximization (Gradient) Algorithm for Differential Privacy

In this paper, we give a modified gradient EM algorithm; it can protect the privacy of sensitive data by adding discrete Gaussian mechanism noise. Specifically, it makes the high-dimensional data easier to process mainly by scaling, truncating, noise multiplication, and smoothing steps on the data. Since the variance of discrete Gaussian is smaller than that of the continuous Gaussian, the difference privacy of data can be guaranteed more effectively by adding the noise of the discrete Gaussian mechanism. Finally, the standard gradient EM algorithm, clipped algorithm, and our algorithm (DG-EM) are compared with the GMM model. The experiments show that our algorithm can effectively protect high-dimensional sensitive data.

Preconditioned Conjugate Gradient Algorithm-Based 2D Waveform Inversion for Shallow-Surface Site Characterization

The full-waveform inversion (FWI) of a Love wave has become a powerful tool for shallow-surface site characterization. In classic conjugate gradient algorithm- (CG) based FWI, the energy distribution of the gradient calculated with the adjoint state method does not scale with increasing depth, resulting in diminished illumination capability and insufficient model updating. The inverse Hessian matrix (HM) can be used as a preprocessing operator to balance, filter, and regularize the gradient to strengthen the model illumination capabilities at depth and improve the inversion accuracy. However, the explicit calculation of the HM is unacceptable due to its large dimension in FWI. In this paper, we present a new method for obtaining the inverse HM of the Love wave FWI by referring to HM determination in inverse scattering theory to achieve a preconditioned gradient, and the preconditioned CG (PCG) is developed. This method uses the Love wave wavefield stress components to construct a pseudo-HM to avoid the huge calculation cost. It can effectively alleviate the influence of nonuniform coverage from source to receiver, including double scattering, transmission, and geometric diffusion, thus improving the inversion result. The superiority of the proposed algorithm is verified with two synthetic tests. The inversion results indicate that the PCG significantly improves the imaging accuracy of deep media, accelerates the convergence rate, and has strong antinoise ability, which can be attributed to the use of the pseudo-HM.