Bayesian Regularization Research Articles

Artificial Neural Network for Benchmarking the Dimensional Accuracy of the PLA Fused Flament Fabrication Process

Fused Deposition Modeling (FDM) is an additive manufacturing technique that uses a 3D printer to extrude molten filament through a nozzle, which moves along the X, Y, and Z axes to create parts with the desired geometry. FDM offers numerous advantages, especially for producing parts with complex shapes, due to its ability to enable rapid and cost-effective manufacturing compared to traditional methods. This study implemented an Artificial Neural Network (ANN) to optimize process parameters aimed at minimizing dimensional inaccuracies in the FDM process. Key parameters considered for optimization included the number of shells, infill percentage, and nozzle temperature. The ANN utilized three algorithms: Scaled Conjugate Gradient, Bayesian Regularization, and Levenberg-Marquardt. Model performance was evaluated based on dimensional deviations along the X and Y axes, with a hidden layer of 25 neurons. Among the algorithms, Scaled Conjugate Gradient provided the most accurate results in minimizing dimensional errors.

A new approach for spatio-temporal interface treatment in fluid–solid interaction using artificial neural networks employing coupled partitioned fluid–solid solvers

Partitioned fluid–solid interaction (FSI) problems involving non-conforming grids pose formidable challenge in interface treatment, especially for information exchange, interface tracking, and field variable interpolation between solvers in both space and time. These demand special considerations for accurate and efficient simulations. This paper presents an application of artificial neural networks (ANN) for the interface treatment in a coupled FSI problem employing partitioned solvers. A shallow time-series ANN (nonlinear auto-regressive model with exogenous inputs, NARX) scheme is proposed to handle the exchange of Neumann/Dirichlet information at the coupling interface. This scheme involves two interface treatment models that were developed and analysed. The proposed models interpolate and transfer loads from the fluid to the solid domains, and conversely, displacements from the solid to the fluid domains between non-collocated grids. To validate this approach, we tested it on a 3D FSI problem, which involved damped oscillations of a flexible flap submerged in a fluid cavity. Adequately trained NARX interface models demonstrate reliable input–output mapping and accurate prediction of transient behaviour at the interface. Additionally, we explored the concept of reduced-order modelling (ROM) in the time domain. This allowed us to reduce the model’s complexity by half. Different training algorithms were evaluated to enhance the efficiency and performance of the proposed scheme. The study demonstrates that NARX networks trained with Bayesian Regularization (BR) and Levenberg–Marquardt (LM) algorithms exhibit the best accuracy, while the scaled conjugate gradient (SCG)-based training method provides better computational efficiency with acceptable accuracy. Overall, the NARX interface models provide precise performance and offer a viable potential for applications in FSI problems requiring accurate and faster computations.

Free vibration and nonlinear transient analysis of blast-loaded FGM sandwich plates with stepped face sheets: Analytical and artificial neural network approaches

This study investigates the free vibration and transient dynamic response of functionally graded material (FGM) sandwich plates with stepped face sheets (FGM-SPSFS) supported by viscoelastic foundation under blast loading. The research focuses on the effects of geometric configurations and material property variations across segments. Each plate comprises three layers: a homogeneous hard core and two FGM face sheets, divided horizontally into two segments with differing face sheet thicknesses, which enhance structural stiffness while maintaining a consistent total thickness. The material properties of the sandwich plates follow a power-law distribution. The formulations are based on higher-order shear deformation plate theory and von Kármán geometric nonlinearity, and are solved using Galerkin’s method. Validation is achieved by comparing the results with published literature and finite element analysis (FEA). Artificial neural network (ANN) models are developed to predict natural frequencies without extensive computational runs, employing Bayesian Regularization (BR) and Levenberg–Marquardt (LM) algorithms in MATLAB. A new graphical user interface (GUI) tool facilitates frequency predictions using the proposed ANN model. Key findings indicate that modifications to the stepped face sheets and core layers affect stiffness, natural frequency, and vibration amplitudes. Increasing the core-to-total thickness ratio enhances stiffness, resulting in higher frequencies and reduced displacement amplitudes. The LM algorithm outperforms the BR algorithm, with errors generally below 1%, compared to 2% to 4% for BR with the log-sigmoid function. This study offers valuable insights into the design and analysis of FGM sandwich structures for engineering applications.

Box-Behnken Design for MAFM Precision Surface Finishing of Al-6063/SiC/B<sub>4</sub>C Composites: A Comparative Study with Nature-Inspired Algorithms

Precision polishing is difficult for advanced materials like silicon carbide and boron carbide. Magnetic abrasive flow machining (MAFM) has become an effective method for cleaning, deburring, and polishing metal and high-tech engineering parts. By finishing hybrid Al/SiC/B4C-metal matrix composites (MMCs), this research uses MAFM for experimental readings. The present work is innovative due to the aluminum workpiece fixture, hybrid composites, and response surface methodology (RSM) modeling. The neural simulation of the MAFM process and nature-inspired error reduction make it unique. Using six input and two output parameters, a generic framework is created. Box-Behnken design (BBD) of response surface methodology plans and executes 54 runs of experimentation. The hybrid artificial neural network (ANN) technique is used to compare the MAFM process systematically. ANN is used to model parameter input-output relations. To anticipate the created surface accurately, regression models must be precise. These hybrid particle swarm optimization (PSO)-genetic algorithm (GA)-simulated annealing (SA) algorithms optimize the MAFM process. Additionally, trained ANN models outperform the BBD model in prediction. For optimal error reduction, the neural network uses Bayesian regularization with 112 iterations. The ANN model regression graph shows a correlation between inputs and outputs. A scanning electron microscope (SEM) with 300-magnification examines the workpiece surface. According to SEM, MAFM provides fine surface textures, thus reducing abnormalities.

A short-term load demand forecasting: Levenberg–Marquardt (LM), Bayesian regularization (BR), and scaled conjugate gradient (SCG) optimization algorithm analysis

A short-term load demand forecasting: Levenberg–Marquardt (LM), Bayesian regularization (BR), and scaled conjugate gradient (SCG) optimization algorithm analysis

Modelling the properties of aerated concrete on the basis of raw materials and ash-and-slag wastes using machine learning paradigm

The thermal power industry, as a major consumer of hard coal, significantly contributes to harmful emissions, affecting both air quality and soil health during the operation and transportation of ash and slag waste. This study presents the modeling of aerated concrete using local raw materials and ash-and-slag waste in seismic areas through machine learning techniques. A comprehensive literature review and comparative analysis of normative documentation underscore the relevance and feasibility of employing non-autoclaved aerated concrete blocks in such regions. Machine learning methods are particularly effective for disjointed datasets, with neural networks demonstrating superior performance in modeling complex relationships for predicting concrete strength and density. The results reveal that neural networks, especially those with Bayesian Regularisation, consistently outperformed decision trees, achieving higher regression values (Rstrength = 0.9587 and Rdensity = 0.91997) and lower error metrics (MSE, RMSE, RIE, MAE). This indicates their advanced capability to capture intricate non-linear patterns. The study concludes that artificial neural networks are a robust tool for predicting concrete properties, crucial for producing non-autoclaved curing wall blocks suitable for earthquake-resistant construction. Future research should focus on optimizing the balance between density and strength of blocks by enhancing the properties of aerated concrete and utilizing reliable models.

Smart Grid Forecasting with MIMO Models: A Comparative Study of Machine Learning Techniques for Day-Ahead Residual Load Prediction

With the fast expansion of intermittent renewable energy sources in the upcoming smart grids, simple and accurate day-ahead systems for residual load forecasts are urgently needed. Machine learning strategies can facilitate towards drastic cost minimizations in terms of operating-reserves avoidance to compensate the mismatches between the actual and forecasted values. In this study, a multi-input/multi-output model is developed based on artificial neural networks to map the relationship between different predictor inputs, including time indices, weather variables, human activity parameters, and energy price indicators, and target outputs such as wind and photovoltaic generation. While the information flows in only one direction (from the predictor nodes through the hidden layers to the target node), benchmark training algorithms are employed and assessed under different case studies. The model is evaluated under both parametric and non-parametric formulations, namely neural networks and Gaussian process regression. Essential improvements are achieved by enhancing the number of embedded predictors, while superior performance is observed by using Bayesian regularization mechanisms. In terms of mean-error indices and determination coefficient, this opens the pathway towards minimization via Bayesian inference-based approaches in the presence of increased and highly stochastic renewable inputs.

Experimental study of the surface finishing of CNC magnetic abrasive finishing based on ANN

ABSTRACT CNC Magnetic Abrasive Finishing (CNC MAF) is famous for aluminium sheet processing. This study used an artificial neural network (ANN) analytical model with a Bayesian regularisation algorithm (BR) to examine how machine parameters (rotation speed, feed rate, depth of cut, and several passes) affect surface roughness during CNC MAF of aluminium sheet. Experimental and quantitative data proved its prediction ability. ANN model to select the best machine parameters for low surface roughness. The perfect numerical solution was experimentally tested, and surface morphology and roughness were used to evaluate processing quality under optimal machine parameters. The ANN model is also compared to Taguchi L16 for prediction and optimisation. Compared to ANN, prediction and optimal surface finishing mean absolute error are 96% lower. The results show that the ANN model is better at studying machine configuration during CNC MAF of Al sheet. SEM and 3D Optical profilometer were also used to analyze the Al sheet. The UV-VIS Spectrophotometer measures Al polished sample reflectance at 200–700 nm.

On the thermal performance of a three-dimensional cross-ternary hybrid nanofluid over a wedge using a Bayesian regularization neural network approach

Abstract Significance Studying the flow of ternary nanofluids [Ag, Cu, MoS2] holds significant importance in both science and engineering. Ternary nanofluids are vital in advancing thermal management systems, heat exchangers, aerospace, and materials processing applications. Purpose This study investigates the ternary hybrid Carreau nanofluid numerically for thermal proficiency in the inclined magnetized environment. In this study, three distinct nanoparticles of [Ag, Cu, MoS2] and base fluid water over the wedge are used. The velocity of nanofluids is judged under the influence of an inclined magnetic field, and the thermal performance is scrutinized by incorporating the thermal radiation effect. Methodology The physical problem generates partial differential equations, which are transformed into ordinary differential equations (ODEs) through similarity variables. These ODEs are linearized into a system of ODEs and then passed under the bvp4c Matlab program to get the solution. This solution is again trained by an artificial neural network, and further results are obtained with both schemes and compared. Findings The most rapid heat transport analysis is found for ternary hybrid nanofluids compared to bi-hybrid nanofluids. The thermal radiation parameters and the magnetic environment augment the rate of heat transport.

A besyian regularisation neural network approach for hepatitis B virus spread prediction and immune system therapy model

The primary aim of the article is to analyze the response of the human immune system when it encounters the hepatitis B virus. This is done using a mathematical system of differential equations. The differential equation system has six components, likely representing various aspects of the immune response or virus dynamics. A Bayesian regularization neural network has been presented in the process of training. These networks are employed to find solutions for different categories or scenarios related to hepatitis B infection. The Adams method is used to generate reference data sets. The back-propagated artificial neural network, based on Bayesian regularization, is trained and validated using the generated data. The data is divided into three sets: 90% for training and 5% each for testing and validation. The correctness and effectiveness of the proposed neural network model have been assessed using various evaluation metrics. The metrics have been used in this study are Mean Square Error (MSE), histogram errors, and regression plots. These measures provide support to the neural network to approximate the immune response to the hepatitis B virus.

Exploring artificial neural networks for the forward kinematics of a SCARA robotic manipulator using varied datasets and training optimizers

Abstract Although analytical methods are traditionally employed, the solution to the Forward Kinematics (FK) problem for Selective Compliance Assembly Robot Arm (SCARA) manipulator robots can prove intricate and computationally demanding. Recognizing this challenge, this study endeavors to introduce an intelligent approach by leveraging Artificial Neural Networks (ANNs) to address the FK problem specifically tailored for a four-degree-of-freedom (4-DoF) SCARA robot. To train the ANNs, we employ three distinct datasets, one with a fixed step size, one with a random step size, and one based on a sinusoidal signal. Moreover, the objective is to scrutinize the ANNs performance under the influence of three distinct training algorithms: Levenberg-Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG). Through a systematic comparison of various ANN models, diverse training algorithms, and the three chosen datasets, the investigation reveals that optimal Mean Squared Error (MSE) results are achieved with random step size datasets for models with two hidden layers using the LM algorithm (MSE = 8.6099e-05). For the BR algorithm, the best MSE (8.0535e-05) was obtained with sinusoidal datasets and three hidden layers. For the SCG algorithm, the optimal MSE (1.1144e-04) was achieved with fixed step size datasets and one hidden layer. The accuracy of the ANN model is significantly influenced by the dataset, the choice of training optimizer, and the configuration of hidden layers. Consequently, further research could explore hybrid approaches that integrate evolutionary algorithms to leverage their respective strengths and improve overall ANN model performance.

Efficiency analysis of solar radiation on chemical radioactive nanofluid flow over a porous surface with magnetic field

Artificial neural networks have revolutionized machine learning by providing exceptional capabilities for modeling complicated mechanisms and solving various challenges. Backpropagation is an important training technique in the field of artificial neural networks. However, this technique must be optimized when working with complicated fluid dynamics. This study analyzes the three-dimensional radiative flow of a tangent hyperbolic fluid driven by the Cattaneo-Christov flux system across a porous stretching sheet using ANN backpropagation enhanced by Bayesian Regularization approach. Heat and mass transfer analysis includes thermal radiation, chemical reactions and Cattaneo-Christov flux model. Porosity, radiation, chemical reaction rate, and ion slip effect are among the important physical characteristics that are modified to see how they affect fluid dynamics. Using MATLAB's BVP4C solver, the velocity, temperature, and concentration profiles that result from these model equations provide the training dataset for ANNs. The dataset is divided into 80 % for training, 10 % for testing, and 10 % for validation. Performance plots, regression graphs, and error histograms are used to analyze the performance of the LMT-based ANN and demonstrate its high accuracy and efficiency. With an R2 value of 1, the ANN produced a mean squared error of around 10⁻11. Fluid mobility drops as the magnetic parameter grows, while the thermal profile exhibits an increasing trend. Similarly, decreasing fluid velocity is the outcome of raising the porosity parameter. The study's conclusions have great potential for use in sectors that need sophisticated cooling and heating equipment.

A Bayesian regularization radial basis neural network novel procedure for the fractional economic and environmental system

The motive of current work is to design a novel radial basis Bayesian regularization neural network (RB-BRNN) for solving the nonlinear fractional economic and environmental system (FEES). A radial basis activation function in the hidden layers is applied by taking 20 numbers of neurons. The mathematical FEES is presented in three classes, named as cost of control accomplishment, manufacturing elements competence and technical exclusion’s diagnostics cost. A reference dataset is obtained using the Adams numerical results to reduce the mean square error (MSE) by taking the data for training 70%, while 15% is used for both testing and validation. The negligible absolute error values and comparison of the solutions develop the worth of computing RB-BRNN in order to solve the nonlinear dynamics of the FEES. Error diagrams, regression values, and the MSE performances are implemented to assess the precision of the designed solver.

Speed and accuracy investigations of neural network algorithms for ionospheric modelling at an equatorial region

Neural networks are very efficient tools for modeling, including ionospheric modeling. The training algorithm is important for achieving the optimum performance of the trained network. This research is therefore meant to evaluate and compare the performances of ten neural network training algorithms based on their prediction accuracies, and the duration/times taken by each of the algorithms to establish the optimum result. The neural networks were trained using electron density measurements by Radio Occultation (RO) technique from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) satellites. Data for the period 2006 through 2021 was used. The networks were trained using about 2.9 million data points collected from the Kano region, Nigeria (5-degree rectangular region around geographic: 12.00° N, 8.59° E) after performing data quality control. The training algorithms considered in the work include: Bayesian Regularization (BR); Broyden-Fletcher-Goldfarb-Shanno Quasi-Newton (BFG); Conjugate Gradient with Powell/Beale (CGB); Fletcher-Reeves Conjugate Gradient (CGF); Gradient descent with momentum and adaptive learning rate (GDX); Levenberg Marquardt (LM); One Step Secant (OSS); Polak-Ribiére Conjugate Gradient (CGP); Resilient Backpropagation (RP); and Scaled Conjugate Gradient (SCG). The results showed that the BR and the LM algorithms gave the best performances in minimizing the errors of prediction (the mean RMSEs are respectively 112 and 114 ×103 electrons/cm3), but the RP algorithm, which came third in terms of accuracy, was significantly faster than both the LM and BR algorithms. The worst-performing algorithm in terms of accuracy was the GDX algorithm, although it was the fastest algorithm. The BFG algorithm was the worst-performing algorithm in terms of a combination of speed and accuracy. The developed neural network model was validated using ionosonde electron density measurements obtained from Ilorin, Nigeria (geographic: 8.5° N, 4.5° E; geomagnetic: 1.8° S). A comparison of the neural network, the NeQuick, and the IRI model predictions relative to the ionosonde measurements indicate that the neural network model was the best-performing model; the NN model predictions minimized the mean absolute errors (MAEs) in ∼44% of 399 ionosonde profiles investigated, the IRI model did so in ∼32%, and the NeQuick did so in ∼24%. The MAEs of the NeQuick however exhibited the best (least) variance. In overall, the NN model gave the least (best) mean of the MAEs (∼73 × 103 cm−3), compared to ∼82 × 103 cm−3 given by both the NeQuick and the IRI models, further supporting the idea that neural networks are excellent for present-day ionospheric modeling.

Inverse algorithm for boundary heat flux density based on the NARX neural network

Abstract The inverse heat transfer problem is vital for scientific research and engineering applications. This paper introduces a method using the Nonlinear Autoregressive with Exogenous Inputs (NARX) neural network to identify heat boundary conditions in nonlinear transient heat transfer processes in real time. This method has two notable advantages: (1) It relies solely on surface temperature time series to obtain inversion results; (2) Even in the absence of knowledge regarding the system’s state equations, it can estimate heat flux density. The NARX neural network is trained by using Bayesian regularization with surface temperature and heat flux data. (3) As per the inversion results, the NARX neural network’s accuracy in predicting the boundary heat flux density (BHFD) increases as the temperature measurement points approach the heat flux boundary. This neural network calculates the current heat flux density by incorporating both present and past surface temperature measurements as inputs. Through numerical simulation experiments, the efficacy of the NARX method is confirmed, showcasing its exceptional accuracy, robustness against noise, and broad suitability.

Long term demand forecasting in Jakarta distribution grid system using fuzzy logic and artificial neural network method

Abstract In order to attain equilibrium between energy supply and demand, reliance on conventional methods for precise long-term electricity demand forecasting is no longer viable. The utilization of artificial intelligence, such as fuzzy logic and artificial neural network (ANN) models, emerges as a prospective solution in the current dynamic scenario. This research explores long-term electricity demand forecasting within the Jakarta distribution grid system, employing various fuzzy logic and ANN approaches including Sugeno, Mamdani, Bayesian Regularization, and the Levenberg algorithm. The analysis incorporates time series data spanning 2016 to 2019, encompassing electricity load demand, economic factors, and demographic variables, processed using MATLAB. The outcomes of the four forecasting methods reveal an average error range of 2 to 3%. The findings indicate that employing fuzzy logic and ANN methods for long-term electricity demand forecasting can yield a forecast error of less than 3%. The study recommends future research enhancements through the inclusion of additional time series data and a more refined system.

Removal of zinc from wastewaters using Turkish bentonite and artificial neural network [ANN] modeling

In this study, Ordu-Unye bentonite was used as an adsorbent in the removal of zinc from aqueous solutions. The aim of the experimental part of the study was to ascertain how zinc removal was affected by variables such as pH, adsorbent amount, contact time, and initial zinc concentration. In the second part of the experiments, bentonite was modified with two different acids and the adsorption performance of modified bentonite was also investigated. Characterization of raw and modified bentonites was also carried out using FTIR and XRD. It was observed that acid modification of bentonite negatively affected the zinc removal process from aqueous solutions. In this study, higher zinc removal (95 %) was obtained with raw bentonite compared to acid modified bentonites (58.4 % in HNO3 activated, 43.8 % for H2SO4 activated). Equilibrium isotherms were obtained and modelled to explain the adsorption mechanism. Adsorption isotherm studies showed that zinc adsorption fits well with Langmuir (R2: 0.99) and Temkin (R2: 0.97) models. Besides from these experimental investigations, various artificial neural network (ANN) training techniques were used to optimize the zinc adsorption process. By trial and error, the optimal performance was obtained by changing the number of hidden neurons in each layer of the neural network architecture. These models under study were analyzed to determine their R2 and mean square error (MSE) values, and the optimal outcomes were identified. Among the various training models of ANN, it was determined that the Bayesian Regularization method exhibited the optimum network architecture with the highest R2 (R2:0.995) and lowest MSE (MSE:0.0008) ratio.

An improved identification method based on Bayesian regularization optimization for the imbalanced proportion plastics recycling using NIR spectroscopy

An improved identification method based on Bayesian regularization optimization for the imbalanced proportion plastics recycling using NIR spectroscopy

Average Wind Speed Prediction in Giresun-Kümbet Plateau Region with Artificial Neural Networks

In order to estimate the electricity generation capacity and schedule the supply for vendor needs, wind speed prediction is crucial for wind power plant frameworks. Prior to the installation of the wind power plants, a reliable wind behaviour model is neccesary. To have such a model, wind data is recorded periodically. In this study, hourly recorded meteorological data of actual pressure, relative humidity, temperature, wind direction and average wind speed for the year 2023 were obtained from the General Directorate of Meteorology for the Kümbet plateau region of Giresun province. The data is used to accurately predict the future wind speed for the region. Matlab Artificial Neural Networks (ANN) is utilized. Actual pressure, relative humidity, temperature and wind direction parameters are defined as input in the prediction process. 85% of the data set is used as training data and remainin 15% data set is used for testing data. An optimization process is applied to determine the number of hidden layers to have the prediction value with the smallest error. Bayesian Regularization training process was performed by seeing that the hidden layer has the lowest error at 90 neurons. Performance evaluations are performed with Mean Square Error (MSE), Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Pearson Correlation Coefficient (R) metrics. The values of the metrics for the test data are 26.7137, 5.1685, 3.5055 and 0.7457 respectively. The results show that, ANN based model is useful for the wind speed prediction over the region.

Computing intelligence for the magnetised chemically reactive bidirectional radiative nanofluid flow through the Bayesian regularisation back-propagated neural network

Computing intelligence for the magnetised chemically reactive bidirectional radiative nanofluid flow through the Bayesian regularisation back-propagated neural network