Bayesian Regularization Algorithm Research Articles

Smart Detection of Faults in Beers Using Near-Infrared Spectroscopy, a Low-Cost Electronic Nose and Artificial Intelligence

Early detection of beer faults is an important assessment in the brewing process to secure a high-quality product and consumer acceptability. This study proposed an integrated AI system for smart detection of beer faults based on the comparison of near-infrared spectroscopy (NIR) and a newly developed electronic nose (e-nose) using machine learning modelling. For these purposes, a commercial larger beer was used as a base prototype, which was spiked with 18 common beer faults plus the control aroma. The 19 aroma profiles were used as targets for classification ma-chine learning (ML) modelling. Six different ML models were developed; Model 1 (M1) and M2 were developed using the NIR absorbance values (100 inputs from 1596–2396 nm) and e-nose (nine sensor readings) as inputs, respectively, to classify the samples into control, low and high concentration of faults. Model 3 (M3) and M4 were based on NIR and M5 and M6 based on the e-nose readings as inputs with 19 aroma profiles as targets for all models. A customized code tested 17 artificial neural network (ANN) algorithms automatically testing performance and neu-ron trimming. Results showed that the Bayesian regularization algorithm was the most adequate for classification rendering precisions of M1 = 95.6%, M2 = 95.3%, M3 = 98.9%, M4 = 98.3%, M5 = 96.8%, and M6 = 96.2% without statistical signs of under- or overfitting. The proposed system can be added to robotic pourers and the brewing process at low cost, which can benefit craft and larger brewing companies.

Electromagnetic field and artificial intelligence based fault detection and classification system for the transmission lines in smart grid

ABSTRACT An electromagnetic field and artificial intelligence-based transmission line protection system for smart grid is proposed in this paper. Bayesian regularization neural network is used as an intelligence technique. Instead of conventional current transformers, the use of magnetic field sensors for monitoring the current in transmission lines is proposed. A mathematical model of the magnetic field due to the current in transmission line is developed by considering two positions of the magnetic field sensors. The developed model is simulated for extensive scenarios. Line to ground, line to line, double line to ground and three-phase faults are created. The fault current values are transformed into magnetic field values and given to the dyadic analysis filter bank for feature extraction process. The extracted features are given as an input to the neural network for the training. The Bayesian regularization algorithm is used as a training algorithm. The performance of the proposed system is compared with other algorithms. It shows that the proposed system with Bayesian regularization have 96.11% of accuracy with the combination of different faults. The results obtained show that the proposed system outperforms the existing approaches.

COVID-19 Death Risk Assessment in Iran using Artificial Neural Network

Since the pandemic spread of COVID-19, it has posed a unique public health concern worldwide due to its increased death rate all around the world. The pandemic disease is caused by the SARS-CoV-2, which is the main cause of Middle East Respiratory Syndrome (MERS) and severe acute respiratory syndrome (SARS). Risk assessment is a vital action toward disease risk reduction as it increases the understanding of the risk factors associated with the disease and allows existing data to decide on adequate preventive and mitigation measures. Machine learning techniques have gained strength since 2000, as it has crucial role in data analysis and is really helpful to develop standard mortality models. This study aims to find the best model for data analysis using the Artificial Neural Network (ANN) and other risk factors, which contribute to the high mortality and morbidity associated with COVID-19 in Iran, to predict the risk of death for the people with different situation. A systematic review and meta-analysis were examined by using patient risk factor data from studies done by researchers to estimate COVID-19 death risk. Risk factors for the disease were extracted from an existing study. Using ANN, the best risk prediction for the disease is calculated. Assessment of a different number of hidden neurons with a different training function using the Bayesian Regularization algorithm, the best training function for the ANN model with 5 hidden neurons is found to have the most satisfying results. The coefficient of determination (R) and Root Mean Square Error (RMSE) was 9.99999e-1 and 4.54201e-19 respectively.

Optimization of Optical Machine Structure by Backpropagation Neural Network Based on Particle Swarm Optimization and Bayesian Regularization Algorithms.

Fit of the highly nonlinear functional relationship between input variables and output response is important and challenging for the optical machine structure optimization design process. The backpropagation neural network method based on particle swarm optimization and Bayesian regularization algorithms (called BMPB) is proposed to solve this problem. A prediction model of the mass and first-order modal frequency of the supporting structure is developed using the supporting structure as an example. The first-order modal frequency is used as the constraint condition to optimize the lightweight design of the supporting structure’s mass. Results show that the prediction model has more than 99% accuracy in predicting the mass and the first-order modal frequency of the supporting structure, and converges quickly in the supporting structure’s mass-optimization process. The supporting structure results demonstrate the advantages of the method proposed in the article in terms of high accuracy and efficiency. The study in this paper provides an effective method for the optimized design of optical machine structures.

Antioxidant increase by response surface optimization and Bayesian neural network modelling of pumpkin (Cucurbita moschata Duch) freezing

Pumpkin antioxidants have been found to benefit diabetics. This current study was attempted to optimize slow freezing treatment for a pumpkin to obtain maximum antioxidant gain using response surface methodology (RSM) and Bayesian regularized neural network (BRANN) approaches. A central composite design was used to generate the freezing experiment and to examine response change as a function of temperature and freezing time. Feedforward neural networks with a 2-15-1 structure were developed and trained using the Bayesian regularization algorithm. The results showed that the freezing data were well fitted to quadratic models generating R2 for total phenolic compounds (TPC), flavonoid of 0.850 and 0.857 respectively. The RSM optimized freezing of -20oC for 9 hrs were well confirmed to produce an increase in TPC and flavonoid by 54.44% and 60.4% respectively. The BRANN performances were found to be similar to that of RSM. While overfitting was mitigated during the supervised training, the BRANN model served excellent predictive and confirmatory tool for the optimization. In conclusion, slow freezing at -20oC for 9 hrs significantly increases TPC and flavonoid of pumpkin. This novel process may be adopted to provide healthier pumpkins food products for targeted consumers.

Performance Analysis of Traffic Congestion Using Designated Neural Network Training Algorithms

A lot of neural network training algorithms on prediction exist and these algorithms are being used by researchers to solve evaluation, forecasting, clustering, function approximation etc. problems in traffic volume congestion. This study is aimed at analysing the performance of traffic congestion using some designated neural network training algorithms on traffic flow in some selected corridors within Akure, Ondo state, Nigeria. The selected corridors were Oba Adesida road, Oyemekun road and Oke Ijebu road all in Akure. The traffic flow data were collected manually with the help of field observers who monitored and record traffic movement along the corridors. To accomplish this, three common training algorithms were selected to train the traffic flow data. The data were trained using Bayesian Regularization (BR), Scaled Conjugate Gradient (SCG) and Levenberg-Marquardt (LM) training algorithms. The outputs/performances of these training functions were evaluated by using the Mean Square Error (MSE) and Coefficient of Regression (R) to find the best training algorithms. The results show that, the Bayesian regularization algorithm, performs better with MSE of 2.37e-13 and R of 0.9999 than SCG and LM algorithms.

Artificial neural network based water quality index (WQI) for river Godavari (India)

Abstract The water quality index has been universally accepted as an indicator to represent the water quality status of the surface water body comprehensively. The prevalent conventional Water Quality Indices (WQIs) suffer from limitations such as 'eclipsing' and 'ambiguity'. Artificial intelligence techniques such as artificial neural networks (ANNs) have gained importance to overcome the limitations of conventional WQIs. In the present study, the Levenberg Marquardt (LM) algorithm and the Scaled Conjugate Gradient (SCG) algorithm have been compared to develop WQI based on the ANN approach (i.e ANNWQI). It is observed that the LM algorithm outperforms the SCG algorithm for prediction of ANNWQI of Indian streams, while the Bayesian Regularization algorithm has not been found suitable for the same purpose in the present study. It is also observed that both LM and SCG algorithm gives robust predictions when the hidden layer contains ten neurons. The combination of data set partitioning of training (75%), Validation (15%), and testing (10%) have been found to give the robust performance of prediction of ANNWQI for Indian streams. The predicted ANNWQI model using the LM algorithm has a very high correlation with the measured WQI values and therefore recommended to be adopted as an effective alternative, to avoid lengthy calculations involved in prevalent conventional WQI.

Performance Analysis of Traffic Congestion Using Designated Neural Network Training Algorithms

A lot of neural network training algorithms on prediction exist and these algorithms are being used by researchers to solve evaluation, forecasting, clustering, function approximation etc. problems in traffic volume congestion. This study is aimed at analysing the performance of traffic congestion using some designated neural network training algorithms on traffic flow in some selected corridors within Akure, Ondo state, Nigeria. The selected corridors were Oba Adesida road, Oyemekun road and Oke Ijebu road all in Akure. The traffic flow data were collected manually with the help of field observers who monitored and record traffic movement along the corridors. To accomplish this, three common training algorithms were selected to train the traffic flow data. The data were trained using Bayesian Regularization (BR), Scaled Conjugate Gradient (SCG) and Levenberg-Marquardt (LM) training algorithms. The outputs/performances of these training functions were evaluated by using the Mean Square Error (MSE) and Coefficient of Regression (R) to find the best training algorithms. The results show that, the Bayesian regularization algorithm, performs better with MSE of 2.37e-13 and R of 0.9999 than SCG and LM algorithms.

Novel Analytical Method for Mix Design and Performance Prediction of High Calcium Fly Ash Geopolymer Concrete.

Despite extensive in-depth research into high calcium fly ash geopolymer concretes and a number of proposed methods to calculate the mix proportions, no universally applicable method to determine the mix proportions has been developed. This paper uses an artificial neural network (ANN) machine learning toolbox in a MATLAB programming environment together with a Bayesian regularization algorithm, the Levenberg-Marquardt algorithm and a scaled conjugate gradient algorithm to attain a specified target compressive strength at 28 days. The relationship between the four key parameters, namely water/solid ratio, alkaline activator/binder ratio, Na2SiO3/NaOH ratio and NaOH molarity, and the compressive strength of geopolymer concrete is determined. The geopolymer concrete mix proportions based on the ANN algorithm model and contour plots developed were experimentally validated. Thus, the proposed method can be used to determine mix designs for high calcium fly ash geopolymer concrete in the range 25–45 MPa at 28 days. In addition, the design equations developed using the statistical regression model provide an insight to predict tensile strength and elastic modulus for a given compressive strength.

Performance Analysis of Learning Rate Parameter on Prediction of Signal Power Loss for Network Optimization and Better Generalization

This research work explores the neural network learning capabilities by using a multi-layer perceptron artificial neural network to predict signal power loss by means of dataset from long term evolution network. The analysis of the effect of the learning rate parameter and the adoption of early stopping method during network training have been executed by using varied values of learning rate to ascertain the best learning rate during the neural network training. Also, there were neural network training without the application of learning rate and early stopping method and comparison have been made with the output results as shown in different tables. Output results comparisons have been performed using training regression and performance mean squared error. Two back propagation training algorithms, the Levenberg–Marquardt and the Bayesian Regularization algorithms were employed for the network training and comparison of their prediction abilities examined using same values of learning rates and on application of early stopping method as well as without learning rate and without early stopping method. The result shows an optimal performance of the neural network model on application of 0.005 learning rate and using 75%:15%:15% early stopping method with training regression 0.99267 and performance mean squared error 2.47 using Levenberg–Marquardt and training regression 0.99488 and performance mean squared error of 1.910 using Bayesian Regularization algorithms, respectively. Without application of learning rate and early stopping method, training the network using Levenberg–Marquardt algorithm gives training regression of 0.97111 and performance mean squared error of 7.38 using Levenberg–Marquart algorithm and training regression of 0.99248 and performance mean squared error of 4.42 using Bayesian Regularization algorithm. The margin between the two output results demonstrates the impact and importance of learning rate parameter as well as adopting early stopping method for neural network training for network optimization and better network generalization.

Chitin from seafood waste: particle swarm optimization and neural network study for the improved chitinase production

AbstractBACKGROUNDThe current system in the processing of seafood leads to accumulation of many waste products, such as shells, tails, heads and bones. This seafood waste can be exploited for the extraction of chitin, with numerous applications in different fields. Seafood waste treatment can produce some valuable products. For the valorization of chitin, its degradation is an important step that can be achieved using the chitinase enzyme. Interestingly, chitin can also be used as a significant substrate for chitinase production. In this study, chitinase activity was enhanced by optimizing the fermentation medium, and chitin was used as the substrate. The polynomial model obtained by central composite design was employed in a particle swarm optimization algorithm and artificial neural network to optimize the final optimal concentration factors. The optimization results were compared for the better activity of chitinase. From the authors' best knowledge, the optimization of fermentation medium for chitinase production by particle swarm optimization was performed for the first time.RESULTSThe highest activity optimized by particle swarm optimization and artificial neural network/ Bayesian regularization algorithm) was 115.8 and 124.78 U L–1, respectively, with the optimized variables.CONCLUSIONThis study concluded that particle swarm optimization and artificial neural network are the best optimization methods for medium optimization. Among the multilayer feed‐forward algorithms in the artificial neural network, the Bayesian regularization algorithm was useful in optimizing medium components. © 2020 Society of Chemical Industry

A Comparative Performance Analysis of ANN Algorithms for MPPT Energy Harvesting in Solar PV System

In this paper, artificial neural network (ANN) based Levenberg-Marquardt (LM), Bayesian Regularization (BR) and Scaled Conjugate Gradient (SCG) algorithms are deployed in maximum power point tracking (MPPT) energy harvesting in solar photovoltaic (PV) system to forge a comparative performance analysis of the three different algorithms. A comparative analysis among the algorithms in terms of the performance of handling the trained dataset is presented. The MATLAB/Simulink environment is used to design the maximum power point tracking energy harvesting system and the artificial neural network toolbox is utilized to analyze the developed model. The proposed model is trained with 1000 dataset of solar irradiance, temperature, and voltages. Seventy percent data is used for training, while 15% data is employed for validation, and 15% data is utilized for testing. The trained datasets error histogram represents zero error in the training, validation, and test phase of data matching. The best validation performance is attained at 1000 epochs with nearly zero mean squared error where the trained data set is converged to the best training results. According to the results, the regression and gradient are 1, 1, 0.99 and 0.000078, 0.0000015739 and 0.26139 for Levenberg-Marquardt, Bayesian Regularization and Scaled Conjugate Gradient algorithms, respectively. The momentum parameters are 0.0000001 and 50000 for Levenberg-Marquardt and Bayesian Regularization algorithms, respectively, while the Scaled Conjugate Gradient algorithm does not have any momentum parameter. The Scaled Conjugate Gradient algorithm exhibit better performance compared to Levenberg-Marquardt and Bayesian Regularization algorithms. However, considering the dataset training, the correlation between input-output and error, the Levenberg-Marquardt algorithm performs better.

Performance Comparison of Non-Linear Median Filter Built on MLP-ANN and Conventional MLP-ANN: Using Improved Dataset Training in Micro-Cell Environment

This research work explores the Levenberg- Marquardt training algorithm used for Artificial Neural Network (ANN) optimization during training and the Bayesian Regularization algorithm for the enhanced generalized trained network in training a designed non-linear vector median filter built on Multi-Layer Perceptron (MLP) ANN called model-1 and a conventional MLP ANN called model-2. The model-1 employed in the design helps in dataset de-noising to ensure the removal of unwanted signals for the improved training dataset. An early stopping method in the ratio of 80:10:10 for training, testing, and validation to overcome the problem of over-fitting during network training was employed. First-order statistical indices, the standard deviation, root mean squared error, mean absolute error, and correlation coefficient were adopted for network training analysis and comparative analysis of the designed model-1 and model-2, respectively. Two locations, Line-of-sight (location-1) and non-Line-of-Sight (location-2), were considered where the dataset was captured. The training results from the two locations for the two models demonstrated improved prediction of signal power loss using model-1 in comparison to model-2. For instance, the correlation coefficient, which shows the strength of the predicted value to the measured values (closer to 1) establishing a strong connection, gives 0.990 and 0.995 using model-1 for location-1, training with Lavenberg-Marquardt and Bayesian Regularization algorithm, respectively and 0.965 and 0.980 for model-2 using the same algorithms. It is seen that the Bayesian regularization algorithm, which optimizes the network in accordance with the Levenberg- Marquardt algorithm, gave better prediction results. The same sequence of improved perditions using designed model-1 in comparison to model-2 were seen with training results in location-2 while also adopting other employed 1st order statistical indices.

АНАЛИЗ МАТЕМАТИЧЕСКИХ МОДЕЛЕЙ ПРИ ПОСТРОЕНИИ НЕЙРОННОЙ СЕТИ ДЛЯ ОЦЕНКИ РАБОТОСПОСОБНОСТИ АГРЕГАТА

Prevention of emergencies in aviation technology is largely ensured by diagnostics of the functioning of its units. Often the performance criterion is the level of vibration that influences the decision to adjust the load or shut down the unit. The article discusses mathematical models when applying neural network methods for vibration diagnostics. When using cross-validation, the initial sample with vibration data is divided into several blocks, which are grouped into three samples: training, control, and test. To assess the effectiveness of diagnostics, three different quality criteria were used: mean error in the test sample, AUC, and F-measure. For a given set of initial data, the best fitted configuration turned out to be a neural network of three layers with 18 neurons in each layer, implemented in the MATLAB package. It uses a Bayesian regularization algorithm as a learning function. The percentage of the average error in recognizing the state of the considered aggregate using the neural network turned out to be 4.85, the AUC value was 0.885, and the F-measure was 0.827. Compared to a network built in automatic mode using the Statistics and Machine Learning Toolbox and Neural Network Toolbox machine learning libraries, the F-measure of the fitted network configuration is 6.7% higher.

Effect of Architectural Composition of MLP ANN in Neural Network Learning for Signal Power Loss Prediction

This work analyzes the architectural complexity of a Multi-Layer Perceptron (MLP) Artificial Neural Network (ANN) model suitable for modeling and predicting signal power loss in micro-cellular environments. The MLP neural network model with one, two, and three hidden layers respectively were trained using measurement datasets used as the target values collected from a micro-cell environment that is suitable to describe different propagation paths and conditions. The neural network training has been performed by applying different training techniques to ensure a well-trained network for good generalization and avoid over-fitting during network training. Bayesian regularization algorithm (that updates weights and biases during network training) following the Levenberg-Marquardt optimization training algorithm was used as the training algorithm. A comparative analysis of training results from one, two, and three hidden layers MLP neural networks show the best prediction result of the signal power loss using a neural network with one hidden layer. A complex architectural composition of the MLP neural network involved very high training time and higher prediction errors.

Spatiotemporal Bayesian Regularization for Cardiac Strain Imaging: Simulation and In Vivo Results.

Cardiac strain imaging (CSI) plays a critical role in the detection of myocardial motion abnormalities. Displacement estimation is an important processing step to ensure the accuracy and precision of derived strain tensors. In this paper, we propose and implement Spatiotemporal Bayesian regularization (STBR) algorithms for two-dimensional (2-D) normalized cross-correlation (NCC) based multi-level block matching along with incorporation into a Lagrangian cardiac strain estimation framework. Assuming smooth temporal variation over a short span of time, the proposed STBR algorithm performs displacement estimation using at least four consecutive ultrasound radio-frequency (RF) frames by iteratively regularizing 2-D NCC matrices using information from a local spatiotemporal neighborhood in a Bayesian sense. Two STBR schemes are proposed to construct Bayesian likelihood functions termed as Spatial then Temporal Bayesian (STBR-1) and simultaneous Spatiotemporal Bayesian (STBR-2). Radial and longitudinal strain estimated from a finite-element-analysis (FEA) model of realistic canine myocardial deformation were utilized to quantify strain bias, normalized strain error and total temporal relative error (TTR). Statistical analysis with one-way analysis of variance (ANOVA) showed that all Bayesian regularization methods significantly outperform NCC with lower bias and errors (p < 0.001). However, there was no significant difference among Bayesian methods. For example, mean longitudinal TTR for NCC, SBR, STBR-1 and STBR-2 were 25.41%, 9.27%, 10.38% and 10.13% respectively An in vivo feasibility study using RF data from ten healthy mice hearts were used to compare the elastographic signal-to-noise ratio (SNRe) calculated using stochastic analysis. STBR-2 had the highest expected SNRe both for radial and longitudinal strain. The mean expected SNRe values for accumulated radial strain for NCC, SBR, STBR-1 and STBR-2 were 5.03, 9.43, 9.42 and 10.58, respectively. Overall results suggest that STBR improves CSI in vivo.

Intelligent Model Of Ecosystem For Smart Cities Using Artificial Neural Networks

A Smart City understands the infrastructure, facilities, and schemes open to its citizens. According to the UN report, at the end of 2050, more than half of the rural population will be moved to urban areas. With such an increase, urban areas will face new health, education, Transport, and ecological issues. To overcome such kinds of issues, the world is moving towards smart cities. Cities cannot be smart without using Cloud computing platforms, the Internet of Things (IoT). The world has seen such incredible and brilliant ideas for rural areas and smart cities. While considering the Ecosystem in Smart Cities, there is a considerable requirement to improve the model to make life better. This proposed research integrates a city into a smart city using the Internet of Things (IoT) which focuses on the smart ecosystem. In this research work, a model is proposed to overcome an ecosystem’s IoT and Machine Learning techniques issues. The Levenberg-Marquardt (LM), Bayesian Regularization (BR), and the Scaled Conjugate Gradient (SCG) algorithms are implemented with an ANN-based approach named to empower the ecosystem of the smart city while developing an efficient and smart ecosystem model. The proposed method’s evaluation indicates that the BR algorithm achieves promising results concerning accuracy and miss rates. The predicted accuracy of the proposed model shows 91.55% performance of the ecosystem on the given factors.

Enhanced efficiency prediction of an electrified off-highway vehicle transmission utilizing machine learning methods

The increasingly noticeable effects of climate change require action to reduce greenhouse gas emissions. In the transport sector, the increase in electromobility is an important tool for reducing CO2 emissions. In order to meet the essential requirements, a particularly detailed system knowledge, for example on energy efficiency in the powertrain, is needed for the development and improvement of electric vehicles.The present work contributes to this by mapping the efficiency of a planetary gearbox for an electric vehicle. The mapping is done by experimental modelling with machine learning methods based on a standard efficiency description. The data necessary for the neural network training is generated by efficiency experiments on the powertrain test rig. For suitable results the data was pre-processed by applying relevant low-pass filters. A comparison of the Bayesian-Regularization algorithm, the Levenberg-Marquardt algorithm and the scaled-conjugate-gradient algorithm for training exhibited the strengths and weaknesses of the individual algorithms for the efficiency mapping. By comparing each algorithms performance metrics, the one matching the requirements best is chosen for the efficiency mapping.The result is a continuous function that determines the efficiency based on speed- and torque-inputs. Based on a key performance indicator, statistical validation by evaluating the standard deviations is used to ensure the quality of the results. In this paper the suitable algorithm for the given use case was determined. It can be applied for further research due to the significant results shown.

Evaluation of Normalization Techniques on Neural Networks for the Prediction of 305-Day Milk Yield

In this study, the impact of data preprocessing on the prediction of 305-day milk yield using neural networks were investigated with regard to the effect of different normalization techniques. Eight normalization techniques “Z-Score, Min-Max, D-Min-Max, Median, Sigmoid, Decimal Scaling, Median and MAD, TanhEstimators" and five different back propagation algorithms “Levenberg-Marquardt (LM), Bayesian Regularization (BR), Scaled Conjugate Gradient (SCG), Conjugate Gradient Back propagation with Powell-Beale Restarts (CGB) and Brayde Fletcher Gold Farlo Shanno Quasi Newton Back propagation (BFG)” were examined and tested comparatively for the analysis. Neural network architecture was optimized and tested with several experiments. Results of the analysis show that applying different normalization techniques affect the performance and the distribution of outputs influences the learning process of the neural network. The magnitude of the effects varied with the type of back propagation algorithms, activation functions, and network's architectural structure. According to the results of the analysis, the most successful performance value in the 305-day milk yield estimation was obtained by using the neural network structured by using the Decimal Scaling normalization technique with the Bayesian Regulation algorithm (R2Adj = 0.8181, RMSE= 0.0068, MAPE= 160.42 for test set; R2Adj =0.8141, RMSE= 0.0067, MAPE= 114.12 for validation set).

Assessment of Various Pedotransfer Functions for the Prediction of the Dry Bulk Density of Cultivated Soils in a Semiarid Environment

ABSTRACT Bulk density (BD) is a key soil indicator for the assessment of the sustainability of production from agricultural land. However, it is difficult to obtain data on BD from field studies because sampling is an extremely labor-intensive, time-consuming and expensive task at the large scale needed to generate meaningful amounts of data. Therefore, the purpose of this study was to evaluate different pedotransfer functions (PTFs) for their usefulness in the estimation of the BD values of an intensely cultivated area through the use of different geostatistical methods. PTFs are estimation functions of certain soil properties derived from raw data for other soil properties. Different approaches have been used for the development of PTFs, including regression methods and artificial neural networks. In this study, the multivariate analysis methods, general and stepwise regression, were used for BD estimation. In addition, different learning algorithms were evaluated with artificial neural networks (ANN) for their efficacy in estimating the BD. Seven basic soil properties, namely, sand, silt, clay, organic matter, pH, EC and CaCO3, were used in the development of models. The estimation power of the general regression model (normalized root mean square error (NRMSE): 7.10%) was higher than that of stepwise regression (NRMSE: 19.93%). Additionally, the lowest NRMSE (6.74%) and the highest R2 for BD estimation determined with different learning algorithms through artificial neural networks (ANN) were obtained with the Levenberg-Marguardt algorithm. Moreover, for BD estimation, ANN performed better than the multivariate regression equations. Spatial distribution maps of soil BD were generated with the commonly used ordinary kriging method by utilizing the real BD values in combination with BD values obtained from estimation models. Maps of BD values produced by stepwise regression estimation deviated significantly from maps generated with real values whereas ANN-II (Bayesian regularization algorithm) values were closest to the real values and that was reflected in the increased accuracy of mapping.