Fletcher-Reeves Conjugate Gradient Research Articles

Evaluation of artificial neurocomputing algorithms and their metacognitive robustness in predictive modeling of fuel consumption rates during tillage

Artificial intelligence (AI) requires complex neurocomputing algorithms (NCAs) for robustness in predictive modeling. Since 1990, a plethora of NCAs have evolved, challenging selection of the most intelligent and error-tolerant model for predicting fuel consumption rate (ØFuel) in tillage. This study adopted 12 recent NCAs in modeling 72 neurocomputing architectures and evaluated their metacognitive robustness in predicting ØFuel using 80 tillage datasets. These included Levenberg-Marquardt (trainlm), Quasi-newton (trainbfg), Powell-Beale conjugate gradient (traincgb), Scaled conjugate gradient (trainscg), Fletcher-reeves conjugate gradient (traincgf), Polak-ribiére conjugate gradient (traincgp), Onestep secant (trainoss), Bayesian regularization (trainbr), Resilient backpropagation (trainrp), Gradient descent (traingd), Learning rate gradient descent (traingdx) and Gradient descent momentum (traingdm). Tillage variables were sequentially subjected to NCA architectures learning on logsig, Purelin, and tansig neuro-activation functions, targeting 1000 epochs. Neuro-cognitive performance was evaluated through broad multi-criteria of regressed neuron input–output functions using heuristic and accuracy metrics, i.e., training time (t), number of hidden layers (NL), and neurons (Nn), optimal epoch (Eopt), Coefficient of correlation (R) and determination (R2), Mean square error (MSE), Root mean square error (RMSE), Mean absolute error (MAE), Mean absolute percentage error (MAPE), Sum square error (SSE), Prediction scatter (Tscatter), Coefficient of variation (CV) and Prediction accuracy (PA). Prediction reliability and robustness were evaluated using a20-index (a20), Willmott’s index of agreement (IOA), Index of scatter (IOS), Variance accounted for (VAF), Performance index (PI), Total score rank (ξtotal), Sensitivity index (SAij) and Anderson-Darling (AD) test. Results indicated that varying NL and Nn did not correspond with t, Eopt and PA but only occurred in single-layered trainbr and double-layered trainlm. Although PA increased at reduced convergence error limits, relationships among Eopt, t, and PA were unclear. Single-layered trainbr (14-20-1) outperformed all NCAs with R (0.9993), R2 (0.9986), MSE (6.34e-06), RMSE (0.0025), MAE (0.003), MAPE (1.4e-06), SSE (8e-04), R2All (0.9998) Tvalue (1.0), CV (3.232 %) and PA (99.81 %). However, trainlm (14-20-10-1) most accurately modeled double-layered architectures i.e. R (0.9932), R2 (0.9864), MSE (7.4e-05), RMSE (0.009), MAE (0.004), MAPE (0.003), SSE (0.003), R2All (0.9929), Tvalue (0.9998), CV (3.212 %) and PA (97.8 %). Nonetheless, trainbr (14-20-1) achieved the best reliability metrics of a20 (100 %), VAF (99.98 %), IOA (1.00), PI (1.9971), IOS (0.0115), ξtotal (284) and AD-test (2.6852). Sensitivity analysis revealed that tractive force had the most significant influence on ØFuel while tire inflation pressure had the least. Learning on transig neuro-activation function in single-layered neural network, metacognitive robustness of trainbr is superiorly merited for predicting ØFuel during tillage.

A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration

A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration

A modified type of Fletcher-Reeves conjugate gradient method with its global convergence

<p><span>The conjugate gradient methods are one of the most important techniques used to address problems involving minimization or maximization, especially nonlinear optimization problems with no constraints at all. That is because of their simplicity and low memory needed. They can be applied in many areas, such as economics, engineering, neural networks, image restoration, machine learning, and deep learning. The convergence of Fletcher-Reeves (FR) conjugate gradient method has been established under both exact and strong Wolfe line searches. However, it is performance in practice is poor. In this paper, to get good numerical performance from the FR method, a little modification is done. The global convergence of the modified version has been established for general nonlinear functions. Preliminary numerical results show that the modified method is very efficient in terms of number of iterations and CPU time.</span></p>

A class of CG algorithms overcoming jamming of the iterative solving process and its application in image restoration

Intending to improve the numerical performance of the classic Fletcher–Reeves conjugate gradient method, Jiang and Jian embedded a shrinkage multiplier on the Fletcher–Reeves parameter which enhances its computational merits. As a matter of fact, we show that when the iterations jam, the line search turns to be approximately exact and so, search direction of the Jiang–Jian method automatically approaches the steepest descent direction which may lead to overcoming undesirable jamming effect of the classic Fletcher–Reeves method. A more detailed analysis of the numerical behavior of the Fletcher–Reeves method under the jamming phenomenon is presented as well. Then, on account of the advantages of the Jiang–Jian method, a conjugate gradient parameter is devised. Additionally, a descent spectral version of the proposed method is developed which fulfills the sufficient descent property regardless of the line search technique. Convergence of the proposed methods is addressed under classical suppositions. To gain support for our theoretical arguments, the computational merits of the given algorithms on a set of CUTEr test functions and the image restoration problem are depicted.

Development of a New Numerical Conjugate Gradient Technique for Image Processing

We present a new iterative conjugate gradient technique for image processing. The technique is based on a new derivation of the conjugacy coefficient and develops a variant of the classical Fletcher-Reeves conjugate gradient method. The derivation exploits a quadratic function model. The new method is intended to minimize the presence of noise by utilizing the adaptive median filter (AMF) to reduce salt-and-pepper noise, while the adaptive center-weighted median filter (ACWMF) is used to reduce random-valued noise. The theoretical convergence properties of the method are proven and then tested on a basic set of images using MATLAB. The results show that the proposed algorithm is more efficient than the classical Fletcher-Reeves (FR) method, as measured by the signal-to-noise ratio (PSNR). The number of iterations and the number of function evaluations are also lower for the proposed method. The favorable performance of the new algorithm provides promise for deriving similar techniques that enhance the speed and efficiency of image-processing libraries.

Prediksi Hasil Produksi Tanaman Tomat di Indonesia Menurut Provinsi Menggunakan Algoritma Fletcher-Reeves

Tomatoes are essential for Indonesians because they have high economic and nutritional value. In addition, as population growth increases, the demand for tomatoes also increases. Based on this, it is essential to research to predict the future development of tomato crop production. The research in this paper uses a dataset of tomato plant production in Indonesia, which is spread across 34 provinces in the last seven years, namely from 2015 to 2021), which is sourced from the Indonesian Central Bureau of Statistics and the District/City Agriculture Service of each Province. The algorithm proposed in this study is the Fletcher-Reeves Conjugate Gradient Algorithm which will be processed with the help of Matlab2011b. Research analysis with three network architectural models: 5-7-1, 5-13-1, and 5-17-1. Based on a network comparison of the three architectural models, the best result is the 5-17-1 model because the MSE value is the smallest compared to the other two models, namely 0.0009915 compared to 0.0010851 and 0.0049764, as well as the highest level of accuracy, namely by 94% versus 91% and 88%. Therefore the 5-17-1 model is used to predict the yield of tomato production in Indonesia for the future (2022 and 2023). Based on the prediction results at the end of 2022 and 2023, there are 18 provinces where tomato crop production has the potential to increase, although not too significantly. The prediction of tomato production using the Fletcher-Reeves algorithm is quite good because it produces a small error rate and high accuracy.

Comparison Fletcher-Reeves and Polak-Ribiere ANN Algorithm for Forecasting Analysis

Each method and algorithm ANN has different performances depending on the algorithm used and the parameters given. The purpose of this research is to obtain the best algorithm information from the two algorithms that will be compared based on the performance value or the smallest / lowest MSE value so that it can be used as a reference and information for solving forecasting problems. The ANN algorithms compared were Conjugate Gradient Fletcher-Reeves and Conjugate Gradient Polak-Ribiere. The conjugate gradient algorithm can solve unlimited optimization problems and is much more efficient than gradient descent-based algorithms because of its faster turnaround time and less iteration. The research data used for the forecasting analysis of the two algorithms are data on the number of rural poor people in Sumatra, Indonesia. 6-10-1, 6-15-1, and 6-20-1 architectural analysis. The results showed that the Polak-Ribiere Conjugate Gradient algorithm with the 6-10-1 architecture has the best performance results and the smallest / lowest MSE value compared to the Fletcher-Reeves algorithm and two other architectures. So it can be concluded that the 6-10-1 architectural architecture with the Conjugate Gradient Polak-Ribiere algorithm can be used to solve forecasting problems because the training time to achieve convergence is not too long, and the resulting performance is quite good.

A Nonmonotone Scaled Fletcher–Reeves Conjugate Gradient Method with Application in Image Reconstruction

A Nonmonotone Scaled Fletcher–Reeves Conjugate Gradient Method with Application in Image Reconstruction

Assessment and mitigation of DC bias risk in power grids at provincial boundaries

With the wide application of high voltage/ultra-high voltage (HV/UHV) DC transmission technology, the impact of DC grounding electrode location selection on the surrounding power grid has become increasingly prominent, especially the problem of DC bias hazard caused by DC grounding electrodes at provincial grid boundaries needs to be solved urgently. This paper studies the assessment and prevention of trans-regional DC bias risk, and proposes an inversion method of earth resistivity model based on the measured data of neutral current in the provincial boundary area. Firstly, the DC bias risk of provincial boundary power grid is simulated and calculated, and the influence of reasonable selection of earth model on the accuracy of risk assessment results is explained. Based on the classical Fletcher-Reeves conjugate gradient method and the measured neutral current data, a reduced-order inversion method for the earth resistivity parameters of the provincial boundary power grid is proposed. On this basis, a set of DC bias risk control scheme is formulated for the actual project of Gannan power grid. Finally, the feasibility of the scheme is verified by simulation and measured data.

Pemanfaatan Algoritma Fletcher-Reeves untuk Penentuan Model Prediksi Harga Nilai Ekspor Menurut Golongan SITC

Conjugate gradient Fletcher-Reeves algorithm, according to some literature, is an optimization method that is suitable when juxtaposed with the backpropagation method because this method can speed up the training time to achieve a minimum convergence value. Therefore, this study aims to prove whether the algorithm has good performance and can provide efficient convergence results when used to solve prediction problems in the case of export values ​​according to the Standard International Trade Classification (SITC) class. The results of this study are a predictive model that can be used and developed to make predictions in seeing the development of the export value of the SITC class based on the US Dollar currency. The research data was taken from the website of the Central Statistics Agency for 2010-2020. Prediction models that will be analyzed using the Fletcher-Reeves algorithm include 5-20-1, 5-25-1, and 5-30-1, with the activation functions of tansig and logsig. Based on the analysis carried out through excel calculations from the training and testing process using the Matlab-2011b application, the results obtained that the 5-25-1 network model is the best model with a performance value or Mean Square Error 0.00287273 compared to the other four models. So it can be concluded that the Fletcher-Reeves algorithm is proven to produce faster convergence; it can be seen from the epoch generated from each model that it is not too large and the time required is relatively short

A New Spectral Conjugate Gradient Method for Nonlinear Unconstrained Optimization

Theconjugate gradient method is widely used to solve large scale unconstrainedoptimization problems. However, the rate of convergence conjugate gradient method is linearunless it restarted. In this study, we present a new spectral conjugategradient modification formula with restart property obtains the globalconvergence and descent properties.In addition, we proposed a new restart condition for Fletcher-Reeves conjugate gradient formula. The numerical resultsdemonstrated that the modified Fletcher-Reeves parameter and the new CG formulawith their restart conditions are more efficient and robustness than otherconventional methods.

Modeling of Cu(II) Adsorption from an Aqueous Solution Using an Artificial Neural Network (ANN).

This research optimized the adsorption performance of rice husk char (RHC4) for copper (Cu(II)) from an aqueous solution. Various physicochemical analyses such as Fourier transform infrared spectroscopy (FTIR), field-emission scanning electron microscopy (FESEM), carbon, hydrogen, nitrogen, and sulfur (CHNS) analysis, Brunauer–Emmett–Teller (BET) surface area analysis, bulk density (g/mL), ash content (%), pH, and pHZPC were performed to determine the characteristics of RHC4. The effects of operating variables such as the influences of aqueous pH, contact time, Cu(II) concentration, and doses of RHC4 on adsorption were studied. The maximum adsorption was achieved at 120 min of contact time, pH 6, and at 8 g/L of RHC4 dose. The prediction of percentage Cu(II) adsorption was investigated via an artificial neural network (ANN). The Fletcher–Reeves conjugate gradient backpropagation (BP) algorithm was the best fit among all of the tested algorithms (mean squared error (MSE) of 3.84 and R2 of 0.989). The pseudo-second-order kinetic model fitted well with the experimental data, thus indicating chemical adsorption. The intraparticle analysis showed that the adsorption process proceeded by boundary layer adsorption initially and by intraparticle diffusion at the later stage. The Langmuir and Freundlich isotherm models interpreted well the adsorption capacity and intensity. The thermodynamic parameters indicated that the adsorption of Cu(II) by RHC4 was spontaneous. The RHC4 adsorption capacity is comparable to other agricultural material-based adsorbents, making RHC4 competent for Cu(II) removal from wastewater.

Model Order Reduction of Port-Hamiltonian Systems by Riemannian Modified Fletcher–Reeves Scheme

Based on the Riemannian modified Fletcher–Reeves conjugate gradient scheme, we propose a new model order reduction algorithm to reduce port-Hamiltonian (PH) systems by the two-sided projection. Making full use of the geometric notions and geometrical characteristics of the Stiefel manifold, the proposed algorithm is not only computationally efficient, but also globally convergent. Additionally, it can preserve the PH structure and the passivity of the original system. A numerical example is simulated to demonstrate the efficiency of our algorithm.

DWT-based electromyogram signal classification using maximum likelihood-estimated features for neurodiagnostic applications

Automated diagnosis of neuromuscular disorders such as myopathy and neuropathy can be done by measuring and analyzing the nonlinear and non-stationary trends in electromyogram (EMG) signals. This paper introduces a new automated diagnostic approach with the combination of discrete wavelet transform (DWT) and maximum likelihood estimation (ML-estimation) for analysis and classification of EMG signals into healthy, myopathy, or neuropathy classes. DWT decomposes the considered EMG signals into frequency sub-bands, and ML-estimation is used for extracting the features from the discrete wavelet sub-bands. Subsequently, obtained feature vectors are used for classifying the EMG signals using multilayer perceptron neural network (MLPNN). Comparative analysis of various performance measures has been performed with all the 71 wavelets of DWT and 13 training algorithms of MLPNN. Results are promising with specificity of 83.33%, sensitivity (myopathy) of 91.66%, sensitivity (neuropathy) of 83.33%, and total classification accuracy of 86.5%, which are obtained using the combination of Daubechies-11 wavelet and Fletcher–Reeves conjugate gradient training algorithm.

A Modified Fletcher–Reeves Conjugate Gradient Method for Monotone Nonlinear Equations with Some Applications

One of the fastest growing and efficient methods for solving the unconstrained minimization problem is the conjugate gradient method (CG). Recently, considerable efforts have been made to extend the CG method for solving monotone nonlinear equations. In this research article, we present a modification of the Fletcher–Reeves (FR) conjugate gradient projection method for constrained monotone nonlinear equations. The method possesses sufficient descent property and its global convergence was proved using some appropriate assumptions. Two sets of numerical experiments were carried out to show the good performance of the proposed method compared with some existing ones. The first experiment was for solving monotone constrained nonlinear equations using some benchmark test problem while the second experiment was applying the method in signal and image recovery problems arising from compressive sensing.

A Nonlinear Conjugate Gradient Algorithm under Strong Wolfe-Powell Line Search for Large Scale Unconstrained Optimization Problems

The conventional conjugate gradient method solves linear and quadratic optimization problems but most real life problems consist of nonquadratic functions of several variables. In this work a nonlinear conjugate gradient algorithm for solving large scale optimization problems is presented. The new algorithm is a modification of the Fletcher-Reeves conjugate gradient method and it is proved to achieve global convergence under the strong Wolfe-Powell inexact line search technique. Computational experiments show that the new algorithm presented performs better than the Fletcher-Reeves exact line search algorithm in solving high dimensional nonlinear optimization problems.

Global convergence of a modified Fletcher–Reeves conjugate gradient method with Wolfe line search

In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. we propose a modified Fletcher–Reeves (abbreviated FR) [Function minimization by conjugate gradients, Comput. J. 7 (1964) 149–154] conjugate gradient algorithm satisfying a parametrized sufficient descent condition with a parameter [Formula: see text] is proposed. The parameter [Formula: see text] is computed by means of the conjugacy condition, thus an algorithm which is a positive multiplicative modification of the Hestenes and Stiefel (abbreviated HS) [Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards Sec. B 48 (1952) 409–436] algorithm is obtained, which produces a descent search direction at every iteration that the line search satisfies the Wolfe conditions. Under appropriate conditions, we show that the modified FR method with the strong Wolfe line search is globally convergent of uniformly convex functions. We also present extensive preliminary numerical experiments to show the efficiency of the proposed method.

New Hybrid Conjugate Gradient Method As A Convex Combination of Ls and Fr Methods

In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate gradient methods, satisfies the famous D-L conjugacy condition and in the same time accords with the Newton direction with the suitable condition. Furthermore, this property doesn’t depend on any line search. Next, we also prove that, moduling the value of the parameter t, the Newton direction condition is equivalent to Dai-Liao conjugacy condition. The strong Wolfe line search conditions are used. The global convergence of this new method is proved. Numerical comparisons show that the present hybrid conjugate gradient algorithm is the efficient one.

Evaluation on Partial Discharge Intensity of Electrical Equipment Based on Improved ANFIS and Ultraviolet Pulse Detection Technology

The ultraviolet pulse detection technology has superiorities in response speed and antijamming capability, so it is extensively applied to insulation detection for electrical equipment. The existing detection and analysis methods have defects, such as failure of precise modeling caused by incomplete analysis of influence factor, poor model adaptability, and complex operation. In allusion to the problems, the ultraviolet pulse detection circuit was optimized and its sensitivity was analyzed through tests. Then, a partial discharge intensity evaluation method for electrical equipment based on the improved adaptive network based fuzzy inference system (improved ANFIS) was proposed combined with the detected pulse count (P), temperature (T) and humidity (H). The initial fuzzy inference system structure was established with the subtractive clustering method (SCM) and fuzzy C-means (FCM) algorithm, and the traditional ANFIS learning algorithm was improved via Fletcher-Reeves conjugate gradient method. In this way, the model parameters were optimized continuously, and the system ability of ignoring small changes in the network was improved. Finally, the effectiveness and practicability of the method were verified through field test. The experimental results demonstrated that the improved ANFIS reduced the model error by 2% when compared with traditional ANFIS, and the model accuracy is improved. Besides, the quantitative precision of the discharge intensity is higher than that of the traditional ANFIS by the contrastive analysis of field test data, indicating that the improved ANFIS evaluate the partial discharge intensity of electrical equipment more accurately. Thus, a decision basis can be provided for the equipment protection and charged maintenance of the electric system.

A Riemannian variant of the Fletcher–Reeves conjugate gradient method for stochastic inverse eigenvalue problems with partial eigendata

SummaryIn this paper, we focus on the stochastic inverse eigenvalue problem with partial eigendata of constructing a stochastic matrix from the prescribed partial eigendata. A Riemannian variant of the Fletcher–Reeves conjugate gradient method is proposed for solving a general unconstrained minimization problem on a Riemannian manifold, and the corresponding global convergence is established under some assumptions. Then, we reformulate the inverse problem as a nonlinear least squares problem over a matrix oblique manifold, and the application of the proposed geometric method to the nonlinear least squares problem is investigated. The proposed geometric method is also applied to the case of prescribed entries and the case of column stochastic matrix. Finally, some numerical tests are reported to illustrate that the proposed geometric method is effective for solving the inverse problem.