Regular Artificial Neural Network Research Articles

Robust prediction of workability properties for 3D printing with steel slag aggregate using bayesian regularization and evolution algorithm

This study addresses the growing interest in utilizing steel slag as a sustainable alternative to river sand in additive manufacturing of concrete, driven by the increasing scarcity of natural resources. The rheological properties of fresh material significantly impact the quality of 3D-printed filament, necessitating suitable workability for printability. The research focuses on evaluating the influence of steel slag aggregate and key admixtures, such as silica fume and superplasticizer, on the workability properties of fresh concrete. Through an extensive series of 90 slump tests, optimal combinations ensuring the desired workability for 3D printing applications were identified. To enhance the manufacturing of fresh concrete and develop user-friendly tools, a novel soft computing approach is introduced—Adaptive Elitist Differential Evolution coupled with Bayesian Regularization Artificial Neural Network (aeDE-BRANN). This advanced model considers five critical input parameters: silica fume to Portland cement ratio, steel slag to cement ratio, water to cement ratio, cement content, and superplasticizer dosage. The model outputs crucial workability metrics, including slump flow and slump. In a comprehensive comparative study, the aeDE-BRANN framework demonstrates superior performance in terms of both simplicity and efficiency when compared to other forecasting models. Feature analysis techniques, including Shapley values from game theory and partial dependence plots, provide valuable insights into the intricate relationships between input variables and workability properties. The findings underscore the water to cement ratio as the most influential factor on workability, followed by silica fume to Portland cement ratio and steel slag to cement ratio. This study contributes a reliable tool for predicting workability properties, aiding in the selection of suitable steel slag aggregate and admixtures. Ultimately, it facilitates the sustainable and innovative evolution of 3D concrete printing practices.

Tree Biomass Modeling Based on the Exploration of Regression and Artificial Neural Networks Approaches

Understanding the dynamics of tree biomass is a significant factor in forest ecosystems, and accurate quantitative knowledge of its development provides support for the optimization of forest management. This work aimed to employ innovative practices in tree biomass modeling, artificial neural network approaches along with the least-squares regression methodology, in order to construct reliable and accurate estimation and prediction models that contribute to solving the emerging problems in the field of sustainable forest management. Based on this aim, different modeling strategies were developed and explored. The nonlinear seemingly unrelated regression (NSUR) methodology, the generalized regression (GRNN), the resilient propagation (RPNN) and the Bayesian regularization (BRNN) artificial neural network algorithms were utilized for the construction of reliable biomass models to attain the most accurate and reliable tree biomass components and total tree biomass estimations. The work showed that GRNN models provided a significantly better performance compared with the other modeling methodologies tested. Considering the non-parametric nature of the GRNN neural network algorithm, the fact that it was designed for nonlinear regression-type problems capable of dealing with small datasets, this modeling approach warrants consideration as an effective alternative to nonlinear regression or to other neural network approaches to the field of tree biomass modeling.

The Predictive Power of Macroeconomic Variables on the Indian Stock Market Utilizing an Ann Model Approach: An Empirical Investigation Based on BSE Sensex

Abstract Research background The paper focuses on the use of Artificial Neural Networks (ANNs) for forecasting time series data of the stock market since ANNs are dynamic and are more capable of handling complex data sets in comparison to conventional forecasting techniques such as regression, Logistic regression, and have massive potential for the prediction of stock market prices. Purpose Artificial neural networks are an effective method for forecasting time series. Therefore, this study aims to forecast the closing price of the BSE Sensex using artificial neural networks (ANNs). Research methodology The study uses nine input variables, including macroeconomic and global stock market factors, to estimate the BSE Sensex using scaled conjugate gradient algorithm artificial neural networks (SCGANNs) and Bayesian regularized artificial neural networks (BRANN). Results As per the empirical results of the study, the ANN model can forecast the closing values of the BSE Sensex with a Bayesian Regularization (BR) method with an accuracy of over 99 percent, thus leading to significant implications for domestic institutional investors (DIIs), foreign institutional investors (FIIs), investment houses, and so on. This study adds more value to the existing literature by proving that the BRANN models outperform SCGANN in stock market forecasting. Novelty This is the first study to employ macroeconomic variables as input variables for predicting the Indian stock market using ANN. The study highlights the ANN model’s forecasting potential, giving investors robust and accurate stock value prediction capabilities.

Laplace based Bayesian inference for ordinary differential equation models using regularized artificial neural networks

Parameter estimation and associated uncertainty quantification is an important problem in dynamical systems characterised by ordinary differential equation (ODE) models that are often nonlinear. Typically, such models have analytically intractable trajectories which result in likelihoods and posterior distributions that are similarly intractable. Bayesian inference for ODE systems via simulation methods require numerical approximations to produce inference with high accuracy at a cost of heavy computational power and slow convergence. At the same time, Artificial Neural Networks (ANN) offer tractability that can be utilized to construct an approximate but tractable likelihood and posterior distribution. In this paper we propose a hybrid approach, where Laplace-based Bayesian inference is combined with an ANN architecture for obtaining approximations to the ODE trajectories as a function of the unknown initial values and system parameters. Suitable choices of customized loss functions are proposed to fine tune the approximated ODE trajectories and the subsequent Laplace approximation procedure. The effectiveness of our proposed methods is demonstrated using an epidemiological system with non-analytical solutions—the Susceptible-Infectious-Removed (SIR) model for infectious diseases—based on simulated and real-life influenza datasets. The novelty and attractiveness of our proposed approach include (i) a new development of Bayesian inference using ANN architectures for ODE based dynamical systems, and (ii) a computationally fast posterior inference by avoiding convergence issues of benchmark Markov Chain Monte Carlo methods. These two features establish the developed approach as an accurate alternative to traditional Bayesian computational methods, with improved computational cost.

Determining the Proper Times and Sufficient Actions for the Collision Avoidance of Navigator-Centered Ships in the Open Sea Using Artificial Neural Networks

Ship collisions are a major maritime accident; various systems have been proposed to prevent them. Through investigating and analyzing the causes of maritime accidents, it has been established that ship collisions can either caused by delaying actions or not taking the sufficient actions to avoid them. Recognizing the limitations in providing quantitative numerical values for avoiding ship collisions, this study aimed to use Bayesian regularized artificial neural networks (BRANNs) to suggest the proper time and sufficient actions required for ship collision avoidance consistent with the Convention on the International Regulations for Preventing Collisions at Sea. We prepared the data by calculating the proper times and sufficient actions based on precedent research and used them to train, validate, and assess the BRANNs. Subsequently, an artificial neural network controller was designed and proposed. The data of the proposed neural network controller were verified via simulation, validating the controller. This study is limited in cases such as overtaking a ship in front. However, it is expected that this controller can be improved by establishing the criteria for an appropriate overtaking distance after further examining the closest point of approach (CPA) and time to the CPA (TCPA) for overtaking a ship in front and using the method presented herein.

A spatiotemporal monitoring model of TSM and TDS in arid region lakes utilizing Sentinel-2 imagery

The assessment of lake water quality is crucial for protecting and managing natural resources. Total suspended matter (TSM) and total dissolved solids (TDS) are significant parameters in evaluating lake water quality, and their concentration levels provide useful information about the health of the ecosystem. However, measuring TSM and TDS concentrations in remote arid areas can be challenging, necessitating the development of a simple, efficient, and cost-effective monitoring system. In this study, the aim was to retrieve TDS and TSM concentrations in the arid region using an empirical and physics-based method simultaneously. Measured data and remote sensing images for Chah-Nimeh Reservoirs (CNRs), Iran, were used to establish the TSM and TDS concentration model. Twenty-seven Sentinel-2 multispectral instrument (MSI) data acquired from 2018 to 2021 were employed to determine the spatiotemporal distribution of TDS and TSM concentrations. The results indicate that Sentinel-2 MSI data is a productive tool for retrieving TSM concentration using the Case-2 Regional/Coastal Color (C2RCC) processor, with a high level of performance in the dry ecosystem of CNRs (R2 = 0.92). Furthermore, the Bayesian regularization artificial neural network (BRANN) algorithm was used to evaluate TDS concentration, and the results demonstrated that the BRANN algorithm outperforms other models, with a high level of performance (R2 = 0.89). It is noteworthy that evaluating TDS concentration is generally more challenging than TSM. The study provides a valuable model for monitoring TSM and TDS concentrations in remote arid areas using Sentinel-2 MSI data. The proposed approach can facilitate effective spatiotemporal monitoring of TSM and TDS concentrations and aid in the evaluation of lake water quality, specifically in regions where in-situ measurements are not feasible. The findings have significant implications for the management and conservation of natural resources in arid and remote regions.

Graph Neural Network-Based Design Decision Support for Shared Mobility Systems

Abstract Emerging shared mobility systems are gaining popularity due to their significant economic and environmental benefits. In this paper, we present a network-based approach for predicting travel demand between stations (e.g., whether two stations have sufficient trips to form a strong connection) in shared mobility systems to support system design decisions. In particular, we answer the research question of whether local network information (e.g., the network neighboring station’s features of a station and its surrounding points of interest (POI), such as banks, schools, etc.) would influence the formation of a strong connection or not. If so, to what extent do such factors play a role? To answer this question, we propose using graph neural networks (GNNs), in which the concept of network embedding can capture and quantify the effect of local network structures. We compare the results with a regular artificial neural network (ANN) model that is agnostic to neighborhood information. This study is demonstrated using a real-world bike sharing system, the Divvy Bike in Chicago. We observe that the GNN prediction gains up to 8% higher performance than the ANN model. Our findings show that local network information is vital in the structure of a sharing mobility network, and the results generalize even when the network structure and density change significantly. With the GNN model, we show how it supports two crucial design decisions in bike sharing systems, i.e., where new stations should be added and how much capacity a station should have.

Automatic error function learning with interpretable compositional networks

In Constraint Programming, constraints are usually represented as predicates allowing or forbidding combinations of values. However, some algorithms exploit a finer representation: error functions. Their usage comes with a price though: it makes problem modeling significantly harder. Here, we propose a method to automatically learn an error function corresponding to a constraint, given a function deciding if assignments are valid or not. This is, to the best of our knowledge, the first attempt to automatically learn error functions for hard constraints. Our method uses a variant of neural networks we named Interpretable Compositional Networks, allowing us to get interpretable results, unlike regular artificial neural networks. Experiments on 5 different constraints show that our system can learn functions that scale to high dimensions, and can learn fairly good functions over incomplete spaces.

Multi-peak emission of In2O3 induced by oxygen vacancy aggregation

Oxygen vacancy is crucial to the optical properties in In2O3, however, the single oxygen vacancy model fails to explain the observed multi-peak emission in the experiment. Herein, we have theoretically investigated the diversity of oxygen vacancy distribution, revealing the relationship between the defect configurations and the optical properties. Combining the first-principles calculations and bayesian regularized artificial neural networks, we demonstrate that the structural stability can be remarkably enhanced by multi-oxygen vacancy aggregation, which will evolve with the defect concentration and temperature. Notably, our results indicate that the single oxygen vacancy will induce the emission peaks centered at 1.35 eV, while multi-peak emission near 2.35 eV will be attributed to the distribution of aggregated double oxygen vacancies. Our findings provide a comprehensive understanding of multi-peak emission observed in In2O3, and the rules of the vacancy distribution may be extended for other metal oxides to modulate the optical properties in practice.

Probability Prediction Approach of Fatigue Failure for the Subsea Wellhead Using Bayesian Regularization Artificial Neural Network

The subsea wellhead (SW) system is a crucial connection between blowout preventors (BOPs) and subsea oil and gas wells. Excited by cyclical fatigue dynamic loadings, the SW is prone to fatigue failure, which would lead to the loss of well integrity and catastrophic accidents. Based on the Bayesian Regularization Artificial Neuron Network (BRANN), this paper proposes an efficient probability approach to predict the fatigue failure probability of SW during its entire life. In the proposed method, the BRANN fatigue damage (BRANN-FD) model reflecting the non-linear relationship between the input and output data was developed by the limited fatigue damage analysis data, which was utilized to generate thousands of non-numerical fatigue damage data of SW rapidly. Combining parametric and non-parametric estimation methods, the probability density function (PDF) of SW fatigue damage was determined to calculate the accumulation fatigue damage during service life. Using the logistic regression, the fatigue failure probability of SW was predicted. The application of the proposed approach was demonstrated by a case study. The results illustrated that the fatigue damage of SW would be viewed as obeying the Lognormal distribution, which could be used to obtain the accumulation fatigue damage in operation conveniently. Furthermore, the fatigue failure probability of SW nonlinearly increased with the increment in the accumulation fatigue damage of SW, which could be helpful to ensure the operation safety of SW in deepwater oil and gas development, especially for aged wellhead.

Prediction of axial load bearing capacity of PHC nodular pile using Bayesian regularization artificial neural network

Pre-stressed precast high strength concrete (PHC) nodular piles with hyper-MEGA construction method are favorably used in medium to high-rise building foundations. In this study, a feed-forward neural network (FFNN) was adopted to investigate the ultimate axial load bearing capacity of the PHC nodular pile. The network receives the composite pile and geotechnical conditions with eight input neurons and outputs the nodular pile's ultimate axial load bearing capacity. Among numerous possible FFNN network architectures, the most accurate one is determined by optimizing the hidden layer. Network training is conducted with Bayesian regularization backpropagation (BRB); the training datasets consist of static pile load test and standard penetration test index of soil profile collected from various projects in Vietnam. The significance of each input parameter is quantified with importance-based sensitivity analysis. An explicit function has been constructed from weights and bias values at each neuron in the FFNN to estimate the axial load bearing capacity. The excellent agreement of all output values by the proposed FFNN with the measured values proved the model’s robustness and reliability. The predictive capacity of the proposed FFNN model has significantly outperformed all current empirical formulas. The outcome of this study can be directly put into engineering practice to furnish an economically optimal design of the composite nodular pile.

Prediction of Casing Collapse Strength Based on Bayesian Neural Network

With the application of complex fracturing and other complex technologies, external extrusion has become the main cause of casing damage, which makes non-API high-extrusion-resistant casing continuously used in unconventional oil and gas resources exploitation. Due to the strong sensitivity of string ovality, uneven wall thickness, residual stress, and other factors to high anti-collapse casing, the API formula has a big error in predicting the anti-collapse strength of high anti-collapse casing. Therefore, Bayesian regularization artificial neural network (BRANN) is used to predict the external collapse strength of high anti-collapse casing. By collecting full-scale physical data, including initial defect data, geometric size, mechanical parameters, etc., after data preprocessing, the casing collapse strength data set is established for model training and blind measurement. Under the classical three-layer neural network, the Bayesian regularization algorithm is used for training. Through empirical formula and trial and error method, it is determined that when the number of hidden neurons is 12, the model is the best prediction model for high collapse resistance casing. The prediction results of the blind test data imported by the model show that the coincidence rate of BRANN casing collapse strength prediction can reach 96.67%. Through error analysis with API formula prediction results and KT formula prediction results improved by least square fitting, the BRANN-based casing collapse strength prediction has higher accuracy and stability. Compared with the traditional prediction method, this model can be used to predict casing strength under more complicated working conditions, and it has a certain guiding significance.

Forecasting of groundwater level fluctuations using a hybrid of multi-discrete wavelet transforms with artificial intelligence models

Abstract Groundwater is often one of the significant natural sources of freshwater supply, especially in arid and semi-arid regions, and is of paramount importance. This study provides a new and high accurate technique for forecasting groundwater level (GWL). The artificial intelligence (AI) models include the artificial neural network (ANN) of multi-layer perceptron (MLP) and radial basis function network (RBF), and adaptive neural-fuzzy inference system (ANFIS) models. Input data to the models is the monthly average GWL of 17 piezometers. In this study, a preprocessing of data including the discrete wavelet transform (DWT) and multi-discrete wavelet transform (M-DWT) simultaneously was utilized. The results showed that the hybrid M-DWT-ANN, M-DWT-RBF, and M-DWT-ANFIS models compared to the DWT-ANN, DWT-RBF, and DWT-ANFIS models as well as than regular ANN, RBF, and ANFIS models, had the highest accuracy in forecasting GWL for the 1-, 2-, 3-, and 6-months ahead. Also, the M-DWT-ANN model had the best performance. Overall, the results illustrated that using the M-DWT method as preprocessing of input data can be a valuable tool to increase the predictive model's accuracy and efficiency. The results of this study indicate the potential of M-DWT-AI hybrid models to improve GWL forecasting.

Predicting electrical power output of combined cycle power plants using a novel artificial neural network optimized by electrostatic discharge algorithm

Combined cycle power plants (CCPP) are among the most sophisticated, yet efficient, systems for producing electrical energy. Hence, simulating their performance has been an engineering hotspot toward sustainable developments. This paper employs novel soft computing methods for predicting electrical power (PE) output of CCPPs. To this end, a metaheuristic technique called electrostatic discharge algorithm (ESDA) is coupled with an artificial neural network (ANN) to create the proposed hybrid. Its performance is compared to several conventionally trained ANNs to investigate the effect of hybridization. By considering the influence of ambient temperature, exhaust vacuum, atmospheric pressure, and relative humidity, the PE is predicted through a 4 × 9 × 1 network. Among the conventional trainers, Levenberg-Marquardt emerged as the most promising one. However, the ESDA outperformed this algorithm in both training and testing phases. Accordingly, the used metaheuristic optimization could improve the robustness of the regular ANN in surmounting computational drawbacks. The ESDA-ANN is, therefore, introduced as a reliable predictive tool for the PE modeling, and the corresponding predictive formula is presented in the last part of this research.

Artificial neural networks and phenomenological degradation models for fatigue damage tracking and life prediction in laser induced graphene interlayered fiberglass composites

The mechanical properties of fiber reinforced polymer matrix composites are known to gradually deteriorate as fatigue damage accumulates under cyclic loading conditions. While the steady degradation in elastic stiffness throughout fatigue life is a well-established and studied concept, it remains difficult to continuously monitor such structural changes during the service life of many dynamic engineering systems where composite materials are subjected to random and unexpected loading conditions. Recently, laser induced graphene (LIG) has been demonstrated to be a reliable, in-situ strain sensing and damage detection component in fiberglass composites under both quasi-static and dynamic loading conditions. This work investigates the potential of exploiting the piezoresistive properties of LIG interlayered fiberglass composites in order to formulate cumulative damage parameters and predict both damage progression and fatigue life using artificial neural networks (ANNs) and conventional phenomenological models. The LIG interlayered fiberglass composites are subjected to tension–tension fatigue loading, while changes in their elastic stiffness and electrical resistance are monitored through passive measurements. Damage parameters that are defined according to changes in electrical resistance are found to be capable of accurately describing damage progression in LIG interlayered fiberglass composites throughout fatigue life, as they display similar trends to those based on changes in elastic stiffness. These damage parameters are then exploited for predicting the fatigue life and future damage state of fiberglass composites using both trained ANNs and phenomenological degradation and accumulation models in both specimen-to-specimen and cycle-to-cycle schemes. When used in a specimen-to-specimen scheme, the predictions of a two-layer Bayesian regularized ANN with 40 neurons in each layer are found to be at least 60% more accurate than those of phenomenological degradation models, displaying R 2 values greater than 0.98 and root mean square error (RMSE) values smaller than 10−3. A two-layer Bayesian regularized ANN with 25 neurons in each layer is also found to yield accurate predictions when used in a cycle-to-cycle scheme, displaying R 2 values greater than 0.99 and RMSE values smaller than 2 × 10−4 once more than 30% of the initial measurements are used as inputs. The final results confirm that piezoresistive LIG interlayers are a promising tool for achieving accurate and continuous fatigue life predictions in multifunctional composite structures, specifically when coupled with machine learning algorithms such as ANNs.

난류 유동에서 다변수 인자에 대한 기계 학습 기법 비교 연구

It is important to predict spatially varying parameters to model turbulent flows. In this study, the spatially varying parameters are modeled via machine learning techniques using experiment-based turbulent bubble flow data and DNS-based turbulent Prandtl number data. The prediction and generalization errors of machine learning models are evaluated, and the different techniques are compared. Among the artificial neural network (ANN) techniques, the regular ANN using the full-batch training and the stochastic gradient descent (SGD) ANN based on mini-batch training are compared with the random forest (RF) method. The prediction and generalization errors show different characteristics according to the data resolution. For the coarsest bubbly flow data set, SGD ANN shows stable training and prediction, which leads to the smallest prediction and generalization errors. For the data sets with a finer resolution, the generalization error of SGD ANN is smallest, whereas the average prediction errors of regular ANN and RF method are smaller compared to SGD ANN. When evaluated using the trained models, all machine learning techniques show similar spatial distribution to the original data.

Fragility assessment approach of deepwater drilling risers subject to harsh environments using Bayesian regularization artificial neural network

The drilling risers are the most critical and vulnerable connection of floating drilling platform and subsea wellhead. In order to improve the operation efficiency, the operators have attempted to suspend the drilling operations and keep the drilling risers connected to the wellhead to survive in the storm, thus the fragility of the drilling risers under storm is of paramount importance to drilling operations. This paper is aimed at proposing an efficient and robust BRANN-based non-intrusive approach for the fragility assessment of the deepwater drilling riser subject to storms. The proposed approach, which could effectively reflect the non-linear relationship between the input and output data, can generate thousands of non-numerical data under limited Finite Element Analysis (FEA) of the drilling risers, while the Monte Carlo Simulation (MCS) could be further incorporated to calculate the fragility curve. A case study was conducted to demonstrate the characteristics with respect to significantly computational reduction of the proposed approach compared to the conventional MCS method, and the proposed approach was verified to be robust and efficient in assessing the fragility of the drilling risers under storms. The related conclusions could be used to provide reference for operations of drilling risers under harsh environment.

Prediction of Flood in Barak River using Hybrid Machine Learning Approaches: A Case Study

Flooding causes several threats with outcomes which include peril to human and animal life, damage to property, and adversity to agricultural fields. Therefore, flood prediction is of prime importance for reducing loss of life and devastation to property. To model complex nature of hydrologic processes artificial neural network (ANN) tool is effectively being utilized for modelling different nonlinear relationships, and has proved to be an appropriate method for flood prediction. Present study investigated relative accuracy of radial basis function neural network (RBFNN) and support vector machine (SVM) models combined with Firefly Algorithm (FA) in predicting river flood discharge and contrasted with that of regular ANN, RBFNN and SVM models. Monthly river flow data of Silchar and Dholai stations located in Cachar district of Assam, India are utilized for the present study. For assessing model performance, coefficient of determination (R2), mean square error (MSE) and root mean square error (RMSE) were measured. Evaluation of outcomes shows that both RBF-FA (radial basis function — firefly algorithm) and SVM-FA (support vector machine — firefly algorithm) hybrid models give more precise forecasting results than RBFNN, FFBPNN (feed forward back propagation neural network) and SVM models. Yet, it can be observed that SVM-FA model give better forecasting outputs with R2 value 0.9818 than RBF-FA model. Results also reveal that simple SVM model performs marginally better than simple ANN model.

An integrated method of flammable cloud size prediction for offshore platforms

Abstract Response Surface Method (RSM) has been widely used for flammable cloud size prediction as it can reduce computational intensity for further Explosion Risk Analysis (ERA) especially during the early design phase of offshore platforms. However, RSM encounters the overfitting problem under very limited simulations. In order to overcome the disadvantage of RSM, Bayesian Regularization Artificial Neural (BRANN)-based model has been recently developed and its robustness and efficiency have been widely verified. However, for ERA during the early design phase, there seems to be room to further reduce the computational intensity while ensuring the model's acceptable accuracy. This study aims to develop an integrated method, namely the combination of Center Composite Design (CCD) method with Bayesian Regularization Artificial Neural Network (BRANN), for flammable cloud size prediction. A case study with constant and transient leakages is conducted to illustrate the feasibility and advantage of this hybrid method. Additionally, the performance of CCD-BRANN is compared with that of RSM. It is concluded that the newly developed hybrid method is more robust and computational efficient for ERAs during early design phase.

Weight and volume estimation of single and occluded tomatoes using machine vision

ABSTRACT The fundamental characteristics of agricultural products are appearance, size, and weight, which affect their market value, consumer preference, and choice. Thus, food and agricultural industries seek rapid, simple, and nondestructive approaches to assess real-time measurements at the post-harvest stage before packaging for the consumer market. While sorting and grading may be performed by humans, it is unreliable, time-consuming, complicated, subjective, onerous, expensive, and easily influenced by surroundings. Therefore, an astute sorting and grading method for tomato fruit is required. We evaluated two tomato configurations on a conveyor belt: single tomatoes (no occlusion) and multi-tomatoes (partially occluded). We used polygon approximation for concave and convex point extraction algorithms to segment the occluded tomatoes. We developed seven models for regression using single-tomato image features. The Bayesian regularization artificial neural network outranked all the trained models in weight estimation with a root-mean-square error (RMSE) of 1.468 g and R 2 of 0.971. For volume estimation, the RBF SVM had the best performance with R 2 of 0.982 and RMSE of 1.2683 cm3. It is feasible to implement a proposed system as a noninvasive in-line sorting technique for tomatoes.