Scaled Conjugate Gradient Method Research Articles

Development and characterization of carboxylated copper oxide conjugated polymeric nanocomposites and correlating with computational techniques

The quality and effectiveness of composite-based components are influenced by their mechanical characteristics. Hence, a structured approach is essential to identify the key factors that contribute to achieving superior mechanical characteristics. This study investigates the utilization of an artificial neural network (ANN) to predict the mechanical characteristics, explicitly density, and hardness, of carboxyl copper oxide nanoparticle (CCONP)/DL-lactide and glycolide copolymer (PDLG) nanocomposites fabricated through microwave-assisted sintering. The research explores the effects of numerous microwave sintering conditions on the microstructure and mechanical properties of the nanocomposites. Physical characterization techniques including FTIR and TEM analysis are employed to confirm physical interactions and nanocomposite size. A back-propagation neural network with a 2–10-2 architecture was developed to predict density and hardness. The network was trained using the Levenberg-Marquardt algorithm and the Scaled Conjugate Gradient method. The predicted values are compared with experimental results, showing good agreement with correlation coefficients (R) of 0.883 for density and 0.9737 for hardness. This demonstrates the effectiveness of the ANN approach in evaluating the mechanical properties of CCONP/PDLG nanocomposites, providing a reliable tool for decision-making and potentially reducing experimental characterization costs.

A descent scaled conjugate gradient method for unconstrained optimization with its applications in image restoration problems

Based on combining the conjugate gradient method proposed by Hager and Zhang with the scaled gradient idea, we presented a new scaled conjugate gradient method which satisfies the sufficient descent condition. In our method, the scaled parameter is determined so that the search direction becomes close to the three-term HS method suggested by Zhang, Zhou and Li. It is proved that the new method is globally convergent for general nonlinear functions, under some standard assumptions. Numerical comparisons on some test problems from the CUTEst library and image restoration problems illustrate the efficiency and robustness of our proposed method in practice.

Development of Deep Learning for Power Energy Optimization in the Industrial Robot System

This paper established power consumption modeling and motion estimation optimization of industrial robots. We also studied factors affecting the use of electrical energy, such as friction, torque, and electric current. The energy consumption parameters of each coupling can be quantified through the Deep Learning (DL) technique, Scaled Conjugate Gradient (SCG) estimation, or Simulation and experimentation based on the movement posture of a given robot dynamic model to control the robot operation. The robot dynamic model parameters can be identified and expressed in mathematical equations. Electrical energy consumption estimates were analyzed using the SCG technique to compare with the Nonlinear Least Squares (NLS) method using a large dataset of approximately 60,000 samples. The results showed accurate parameter prediction and electrical energy consumption estimation of the robot locomotion pose. The maximum errors in the SCG and NLS methods were 0.89% and 1.54%, respectively. It indicated that the electric energy consumption model using the SCG estimation method is more efficient than the NLS method.

Effectiveness and number of transfer units of plate heat exchanger with Fe3O4–SiO2/Water hybrid nanofluids: Experimental and artificial neural network predictions

This paper analyses the effectiveness and number of transfer units of water dispersed Fe3O4–SiO2 hybrid fluids passing via plate heat exchanger experimentally. The flow of Fe3O4–SiO2/water hybrid nanofluids in plate heat exchanger remains the laminar flow conditions. The experimental studies were carried out with particle loadings ranging from 0.2 % to 1.0 % and flow rates ranging from 0.05 kg/s to 0.1166 kg/s. The obtained results of effectiveness and number of transfer units from these experiments were predicted with artificial neural network based scaled conjugate gradient (SCG) method. Based on the chemical reaction and in-situ growth methods, the Fe3O4–SiO2 nanoparticles were prepared and then characterized using x-ray diffraction (XRD) and vibrating sample magnetometer (VSM) equipment. Water diluted hybrid nanofluids were developed and used for the experimental studies. Results from the XRD indicates that, the particle size of synthesized Fe3O4–SiO2 nanoparticles were found to be 47 nm and the results from VSM shows, the final Fe3O4–SiO2 sample contains 67.8 % of SiO2 and 32.2 % of Fe3O4. Results also indicates with an increase of volume loadings and Reynolds number, the effectiveness and number of transfer units were enhanced. The effectiveness and number of transfer units were increased by 13.23 % and 24.51 % at 1.0 % vol. of hybrid nanofluid and at a Reynolds number of 571.89, over water data. Through the SCG method, the correlation coefficient R2 for effectiveness is 0.99040, and the R2 for number of transfer units is 0.98771, respectively. New generalized equation was proposed for the evaluation of effectiveness and number of transfer units.

A Quadratic Model based Conjugate Gradient Optimization Method

In this paper, we introduce a nonlinear scaled conjugate gradient method, operating on the premise of a descent and conjugacy relationship. The proposed algorithm employs a conjugacy parameter that is determined to ensure that the method generates conjugate directions. It also utilizes a parameter that scales the gradient to enhance the convergence behavior of the method. The derived method not only exhibits the crucial feature of global convergence but also maintains the generation of descent directions. The efficiency of the method is established through numerical tests conducted on a variety of high-dimensional nonlinear test functions. The obtained results attest to the improved behavior of the derived algorithm and support the presented theory.

Harmonics Forecasting of Wind and Solar Hybrid Model Driven by DFIG and PMSG Using ANN and ANFIS

Grid integration of Renewable Energy Systems (RES) involves various types of power electronics-based converters and inverters. The use of these electronic-based devices results in inducing both current and voltage harmonics to the grid. In order to reduce harmonics, especially for large-scale integration of RES, harmonic forecasting is one of many techniques used to design harmonic mitigation devices. The core objective of this work is to develop a novel forecasting model for accurate and reliable harmonic estimation for RES. To achieve this two hybrid generator models are used. First model consists of wind turbine coupled with Doubly Fed Induction Generator (DFIG) combined with Solar Photo Voltaic (PV) based power generator which are connected to common grid. The second model uses Permanent Magnet Synchronous Generator (PMSG) with wind turbine in conjunction with Solar-PV generator. With real world meteorological data (wind speed and solar irradiation) as inputs, these generators simulate and produce output power with current and voltage waveforms. Harmonics are extracted from these waveforms to record, analyze, arrange and forecast future harmonics. Three parameters namely, Total Harmonics Distortion (THD) and the dominant individual harmonic contents, 11 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> harmonic (h11) and 13 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> harmonic (h13) are forecasted for both voltage and current waveforms. Artificial Neural Networks (ANN) and Adaptive Neuro Fuzzy Inference Systems (ANFIS) are the prominent methods used for forecasting. Three types of three-layered ANN structures namely Cascaded Neural Network with Recurrent Local feedback (3LCRNNL), Cascaded Neural Network with Recurrent Global feedback (3LCRNNG) and Cascaded Neural Network with Local and Global feedback (CRNNGL) have been proposed and utilized in this work with hyperbolic tangent as transfer function to adjust weights and scaled conjugate gradient method as optimizer to reduce training error. ANFIS is also employed with subtractive clustering method to improve adaptability and accuracy of forecasts. The results are compared and presented which shows that ANFIS recorded the best performance for THDV and h13 and 3LCRNNGL for h11 for the Wind DFIG-PV model voltage harmonics forecast. For forecasts of the current harmonics, 3LCRNNGL performed best for THDI and h11, whereas ANFIS performed best for h13. For Wind PMSG-PV generator model, ANFIS yields the best results in every scenario involving voltage and current harmonics.

Simulating Ship Manoeuvrability with Artificial Neural Networks Trained by a Short Noisy Data Set

Artificial neural networks are applied to model the manoeuvrability characteristics of a ship based on empirical information acquired from experiments with a scaled model. This work aims to evaluate the performance of the proposed method of training the artificial neural network model even with a very small quantity of noisy data. The data used for the training consisted of zig-zag and circle manoeuvres carried out in agreement with the IMO standards. The wind effect is evident in some of the recorded experiments, creating additional disturbance to the fitting scheme. The method used for the training of the network is the Levenberg–Marquardt algorithm, and the results are compared with the scaled conjugate gradient method and the Bayesian regularization. The results obtained with the different methodologies show very suitable accuracy in the prediction of the referred manoeuvres.

New scaled algorithm for non-linear conjugate gradients in unconstrained optimization

&lt;p&gt;A new scaled conjugate gradient (SCG) method is proposed throughout this paper, the SCG technique may be a special important generalization conjugate gradient (CG) method, and it is an efficient numerical method for solving nonlinear large scale unconstrained optimization. As a result, we proposed the new SCG method with a strong Wolfe condition (SWC) line search is proposed. The proposed technique's descent property, as well as its global convergence property, are satisfied without the use of any line searches under some suitable assumptions. The proposed technique's efficiency and feasibility are backed up by numerical experiments comparing them to traditional CG techniques.&lt;/p&gt;

An extension of the type-1 and singleton fuzzy logic system trained by scaled conjugate gradient methods for multiclass classification problems

This paper proposes an extension of the type-1 and singleton fuzzy logic system for dealing with multiclass classification problems. The proposed extension enables a fuzzy classifier to generate more than one output, thereby avoiding the use of binary decomposition strategies when multiclass classification problems are considered. Additionally, with the goal of improving classifier performance, the scaled conjugate gradient training method was applied, as well as its modified version using the differential operator R·. The effectiveness of the proposed extension was evaluated using data from the UCI Machine Learning Repository based on well-established classification metrics. The numerical results reveal a significant reduction in computational complexity when using the proposed extension compared to the traditional decomposition strategy, as well as improved convergence speed when using the scaled conjugate gradient training method.

Rambutan (Nephelium lappaceum) seeds for the treatment of Palm Oil Mill Effluent (POME) and its Feedforward Artificial Neural Network (FANN) modeling

In the present research, local rambutan seed extract was used as a bio-coagulant for the treatment of palm oil mill effluent (POME). Jar test experiments were conducted to find the optimal operating conditions for the removal of turbidity and total suspended solids from POME. At an optimal pH of 3, bio-coagulant dosage of 600 mg/L and room temperature of 28⁰C, an impressive removal of 65% of total suspended solids and 79% of turbidity was achieved. Along with this, a Feedforward Artificial Neural Network (FANN) was used to model the coagulation mechanism. Three different training algorithms were tested on the FANN, namely the Lavenberg-Marquardt, Bayesian Regularization and Scaled Conjugate Gradient methods. The best training algorithm was found to be Bayesian Regularization, based on the fact that it was in closer agreement with the experiment results and gave very low error percentage. The results of this study suggest that rambutan seeds have potential in being used as a bio-coagulant for POME treatment. Treatment efficiencies were reasonably high, and less sludge was produced using this natural treatment method, thus deemed to be more economical and environmentally friendly.

ANN based method for improving gold price forecasting accuracy through modified gradient descent methods

Forecast of prices of financial assets including gold is of considerable importance for planning the economy. For centuries, people have been holding gold for many important reasons such as smoothening inflation fluctuations, protection from an economic crisis, sound investment etc.. Forecasting of gold prices is therefore an ever important exercise undertaken both by individuals and groups. Various local, global, political, psychological and economic factors make such a forecast a complex problem. Data analysts have been increasingly applying Artificial Intelligence (AI) techniques to make such forecasts. In the present work an inter comparison of gold price forecasting in Indian market is first done by employing a few classical Artificial Neural Network (ANN) techniques, namely Gradient Descent Method (GDM), Resilient Backpropagation method (RP), Scaled Conjugate Gradient method (SCG), Levenberg-Marquardt method (LM), Bayesian Regularization method (BR), One Step Secant method (OSS) and BFGS Quasi Newton method (BFG). Improvement in forecasting accuracy is achieved by proposing and developing a few modified GDM algorithms that incorporate different optimization functions by replacing the standard quadratic error function of classical GDM. Various optimization functions investigated in the present work are Mean median error function (MMD), Cauchy error function (CCY), Minkowski error function (MKW), Log cosh error function (LCH) and Negative logarithmic likelihood function (NLG). Modified algorithms incorporating these optimization functions are referred to here by GDM_MMD, GDM_CCY, GDM_KWK, GDM_LCH and GDM_NLG respectively. Gold price forecasting is then done by employing these algorithms and the results are analysed. The results of our study suggest that the forecasting efficiency improves considerably on applying the modified methods proposed by us.

New Investigation for the Liu-Story Scaled Conjugate Gradient Method for Nonlinear Optimization

This article considers modified formulas for the standard conjugate gradient (CG) technique that is planned by Li and Fukushima. A new scalar parameter θkNew for this CG technique of unconstrained optimization is planned. The descent condition and global convergent property are established below using strong Wolfe conditions. Our numerical experiments show that the new proposed algorithms are more stable and economic as compared to some well-known standard CG methods.

Design of a New Method for Detection of Occupancy in the Smart Home Using an FBG Sensor.

This article introduces a new way of using a fibre Bragg grating (FBG) sensor for detecting the presence and number of occupants in the monitored space in a smart home (SH). CO2 sensors are used to determine the CO2 concentration of the monitored rooms in an SH. CO2 sensors can also be used for occupancy recognition of the monitored spaces in SH. To determine the presence of occupants in the monitored rooms of the SH, the newly devised method of CO2 prediction, by means of an artificial neural network (ANN) with a scaled conjugate gradient (SCG) algorithm using measurements of typical operational technical quantities (indoor temperature, relative humidity indoor and CO2 concentration in the SH) is used. The goal of the experiments is to verify the possibility of using the FBG sensor in order to unambiguously detect the number of occupants in the selected room (R104) and, at the same time, to harness the newly proposed method of CO2 prediction with ANN SCG for recognition of the SH occupancy status and the SH spatial location (rooms R104, R203, and R204) of an occupant. The designed experiments will verify the possibility of using a minimum number of sensors for measuring the non-electric quantities of indoor temperature and indoor relative humidity and the possibility of monitoring the presence of occupants in the SH using CO2 prediction by means of the ANN SCG method with ANN learning for the data obtained from only one room (R203). The prediction accuracy exceeded 90% in certain experiments. The uniqueness and innovativeness of the described solution lie in the integrated multidisciplinary application of technological procedures (the BACnet technology control SH, FBG sensors) and mathematical methods (ANN prediction with SCG algorithm, the adaptive filtration with an LMS algorithm) employed for the recognition of number persons and occupancy recognition of selected monitored rooms of SH.

A Scaled Conjugate Gradient Method Based on New BFGS Secant Equation with Modified Nonmonotone Line Search

In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-Moré performance profiles.

Type-1 and singleton fuzzy logic system trained by a fast scaled conjugate gradient methods for dealing with binary classification problems

This work introduces the type-1 and singleton fuzzy logic system trained by scaled conjugate gradient method and its usage for binary classification problems. Aiming to improve the performance of the training procedure, we propose the multiplication of the Hessian matrix by the directional vector using the so-called differential operator R{·}, which results in another proposal for training the aforementioned fuzzy logic system. In order to evaluate the proposals, performance analyses based on well-known data sets provided by UCI Machine Learning Repository and Knowledge Extraction based on Evolutionary Learning Repository together with well-established metrics are detailed. The numerical results show that the proposals achieve improvements in comparison with others gradient based training methods applied to the type-1 fuzzy logic system present in the literature. These improvements regard to the fast convergence speed under the constraint over the number of epochs during the training phase.

A new model to distinguish welds performed by short-circuit GMAW based on FRESH algorithm and MLP ANN

The short-circuit gas metal arc welding has been continuously studied over the years, due to its important role in manufacturing processes. Concerning the process, many kinds of research are carried out aiming to understand the influence of the shielding gas in welds quality. In this context, this work treats the voltage and current welding signals as time series and applies a feature extraction based on scalable hypothesis tests, which is called FRESH algorithm, in order to obtain the signal features. After that, these features are applied in a multilayer perceptron artificial neural network, trained by the scaled conjugate gradient method, which classifies the welds according to the flow rate and type of shielding gas used in the process. The model presented excellent performance, which shows that the proposal is suitable to be used in welding quality monitoring.

A new modified scaled conjugate gradient method for large-scale unconstrained optimization with non-convex objective function

In this paper, according to the fifth-order Taylor expansion of the objective function and the modified secant equation suggested by Li and Fukushima, a new modified secant equation is presented. Also, a new modification of the scaled memoryless BFGS preconditioned conjugate gradient algorithm is suggested which is the idea to compute the scaling parameter based on a two-point approximation of our new modified secant equation. A remarkable feature of the proposed method is that it possesses a globally convergent even without convexity assumption on the objective function. Numerical results show that the proposed new modification of scaled conjugate gradient is efficient.

Automated sleep staging of OSAs based on ICA preprocessing and consolidation of temporal correlations.

An automated sleep staging based on analyzing long-range time correlations in EEG is proposed. These correlations, indicating time-scale invariant property or self-similarity at different time scales, are known to be salient dynamical characteristics of stage succession for a sleeping brain even when the subject suffers a destructive disorder such as Obstructive Sleep Apnea (OSA). The goal is to extract a set of complementary features from cerebral sources mapped onto the scalp electrodes or from a number of denoised EEG channels. For this purpose, source localization/extraction and noise reduction approaches based on Independent Component Analysis were used prior to correlation analysis. Feature extracted segments were then classified in one of the five classes including WAKE, STAGE1, STAGE2, SWS and REM via an ensemble neuro-fuzzy classifier. Some techniques were employed to improve the classifier's performance including Scaled Conjugate Gradient Method to speed up learning the ANFIS classifiers, a pruning algorithm to eliminate irrelevant fuzzy rules and the 10-fold cross-validation technique to train and test the system more efficiently. The performance of classification for two strategies including (1) feature extraction from effective cerebral sources and (2) feature extraction from selected channels of denoised EEG signals was compared and contrasted in terms of training errors and test accuracies. The first and second strategies achieved 92.23 and 88.74% agreement with human expert respectively which indicates the effectiveness of the staging system based on cerebral sources of activity. Our results further indicate that the misclassification rates were almost below 10%. The proposed automated sleep staging system is reliable due to the fact that it is based on the underlying dynamics of sleep staging which is less likely to be affected by sleep fragmentations occurred repeatedly in OSA.

A new derivative-free SCG-type projection method for nonlinear monotone equations with convex constraints

Based on a modified line search scheme, this paper presents a new derivative-free projection method for solving nonlinear monotone equations with convex constraints, which can be regarded as an extension of the scaled conjugate gradient method and the projection method. Under appropriate conditions, the global convergence and linear convergence rate of the proposed method is proven. Preliminary numerical results are also reported to show that this method is promising.

A scaled conjugate gradient method for nonlinear unconstrained optimization

We propose a new optimization problem which combines the good features of the classical conjugate gradient method using some penalty parameter, and then, solve it to introduce a new scaled conjugate gradient method for solving unconstrained problems. The method reduces to the classical conjugate gradient algorithm under common assumptions, and inherits its good properties. We prove the global convergence of the method using suitable conditions. Numerical results show that the new method is efficient and robust.