Multilayer Artificial Neural Network Research Articles

Experimental study and machine learning simulation of Pb (II) separation from aqueous solutions via a nanocomposite adsorbent

BackgroundClean water is the most basic human need for life and for other purposes. The existence of water sources contaminated with heavy metals (HMs) and the need to separate them from wastewater is not a secret. For this reason, the production of various adsorbents has been carried out, and the use of data science to advance the goals of water purification has been considered. MethodsIn this study, a zeolite ZSM-5/silica aerogel (ZSM5/SA) composite was synthesized as a mesoporous adsorbent in three different ratios (including 25, 50, and 75% silica aerogel). Then the characterization of adsorbents was performed by Field-Emission Scanning Electron Microscopy (FESEM), Energy Dispersive X-Ray (EDX), and Surface area and pore size (BET-BJH) analyses. Adsorbents were tested under the same conditions to compare the adsorption capacities. After data collection, multilayer linear regression (MLR) was used to predict the removal of lead ions from an aqueous solution. For this purpose, multilayer artificial neural networks (MLP-ANN) with error backpropagation functions and support vector regression (SVR) were coded with MATLAB software. The effect of effective parameters on the adsorption was investigated using experimental design and the general 2 K full factorial method. Significant findingBy ANOVA analysis of variance, the linear regression equation was obtained with a prediction accuracy of 87.3%. The best-predicted percentages (with 70% data) for ANN and SVR were 99.52% and 98.43%, respectively. In addition, the mean square error (MSE) for ANN and SVR was 0.00037 and 0.0083, respectively. Neural network training functions were compared using ANN model performance (MSE, SSE, SAE, MAE) and R2. Examination of neural network and SVR predictive behavior showed that SVR performs data training better, but neural network data testing performs 1.16% better than SVR. Data prediction performance indicated that neural networks and SVR were successful in data prediction.

Using artificial neural networks to predict the reference evapotranspiration

Artificial neural network models (ANNs) were used in this study to predict reference evapotranspiration ( ETo) using climatic data from the meteorological station at the test station in Kafr El-Sheikh Governorate as inputs and reference evaporation values computed using the Penman–Monteith (PM) equation. These datasets were used to train and test seven different ANN models that included different combinations of the five diurnal meteorological variables used in this study, namely, maximum and minimum air temperature ( Tmax and Tmin), dew point temperature ( Tdw), wind speed ( u), and precipitation (P), how well artificial neural networks could predict ETo values. A feed- forward multi-layer artificial neural network was used as the optimization algorithm. Using the tansig transfer function, the final architected has a 6-5-1 structure with 6 neurons in the input layer, 5 neurons in the hidden layer, and 1 neuron in the output layer that corresponds to the reference evapotranspiration. The root mean square error ( RMSE) of 0.1295 mm∙day –1 and the correlation coefficient ( r) of 0.996 are estimated by artificial neural network ETo models. When fewer inputs are used, ETo values are affected. When three separate variables were employed, the RMSE test values were 0.379 and 0.411 mm∙day –1 and r values of 0.971 and 0.966, respectively, and when two input variables were used, the RMSE test was 0.595 mm∙day –1 and the r of 0.927. The study found that including the time indicator as an input to all groups increases the prediction of ETo values significantly, and that including the rain factor has no effect on network performance. Then, using the Penman–Monteith method to estimate the missing variables by using the ETo calculator the normalised root mean squared error ( NRMSE) reached about 30% to predict ETo if all data except temperature is calculated, while the NRMSE reached about of 13.6% when used ANN to predict ETo using variables of temperature only.

Study on the Optimal Double-Layer Electrode for a Non-Aqueous Vanadium-Iron Redox Flow Battery Using a Machine Learning Model Coupled with Genetic Algorithm

To boost the operational performance of a non-aqueous DES electrolyte-based vanadium-iron redox flow battery (RFB), our previous work proposed a double-layer porous electrode spliced by carbon paper and graphite felt. However, this electrode’s architecture still needs to be further optimized under different operational conditions. Hence, this paper proposes a multi-layer artificial neural network (ANN) model to predict the relationship between vanadium-iron RFB’s performance and double-layer electrode structural characteristics. A training dataset of ANN is generated by three-dimensional finite-element numerical simulations of the galvanostatic discharging process. In addition, a genetic algorithm (GA) is coupled to an ANN regression training process for optimizing the model parameters to elevate the accuracy of ANN prediction. The novelty of this work lies in this modified optimal method of a double-layer electrode for non-aqueous RFB driven by a machine learning (ML) model coupled with GA. The comparative result shows that the ML model reaches a satisfactory predictive accuracy, and the mean square error of this model is lower than other popular ML regression models. Based on the known region of operating conditions, the obtained results prove that this well-trained ML algorithm can be used to estimate whether a double-layer electrode should be applied to a non-aqueous vanadium-iron RFB and determine an appropriate thickness ratio for this double-layer electrode.

Prediction of Rock Tensile Strength Using Soft Computing and Statistical Methods

The tensile strength of the rocks is one of the effective factors in the rupture of structure foundations and underground spaces, the stability of rocky slopes, and the ability to drill and explode in rocks. This research was conducted to estimate tensile strength using methods such as simple regression (SR), multivariate linear regression (MVLR), support vector regression (SVR) with radial basis kernel function, multilayer feed-forward artificial neural network (MFF-ANN), Gaussian process regression (GPR) using squared exponential kernel (SEK) function, and adaptive neuro-fuzzy inference system (ANFIS) based on Gaussian membership function. For this purpose, petrography, and engineering features of the limestone, sandstone, and argillaceous limestone samples in the south of Iran, were assessed. The results obtained from this study were compared with those of previous research, revealing a strong correlation (R2=0.95 to 1.00) between our findings and the published works. To estimate Brazilian tensile strength (BTS), the index properties including water absorption by weight, point load index (PLI), porosity%, P-wave velocity (Vp), and density were considered as inputs. Methods were compared using various criteria. The SVR precision (R=0.96) was higher than MFF-ANN (R=0.92), ANFIS (R=0.95), GPR (R=0.945), and MVLR (R=0.89) to estimate the tensile strength. The average BTS measured in the laboratory and predicted by all 5 methods is 6.62 and 6.71 MPa, respectively, which shows the very high precision of the investigated methods. Analysis of model criteria using statistical analysis for developed relationships revealed that there is sufficient accuracy to use the empirical equations.

Reliability study of generalized Rayleigh distribution based on inverse power law using artificial neural network with Bayesian regularization

Using the generalized Rayleigh distribution and the inverse power law, this paper proposes a new reliability model and investigates the effect of the key parameters on reliability measurements. This proposed new model offers a more accurate way to model the performance of electronic components over their lifetimes. In order to analyze the reliability parameters, a multi-layer artificial neural network model has been developed by using the datasets generated by numerical methods and obtained in four different scenarios. Using the artificial neural network model with 5 neurons in the hidden layer, the reliability parameters Hazard Rate Function, Odds function, Reversed Hazard Rate Function, Mean Time to Failure and Mean Time Between Failures have been estimated. The results obtained have been analyzed comprehensively and explained with graphics. The study findings showed that there was a direct relationship between the reliability parameters examined in all scenarios and an increase in the Mean Time Between Failures value appeared for each scenario. However, it has also been seen that the developed artificial neural network can make predictions with very high accuracy and is a powerful engineering tool that can be utilized in reliability analysis.

Reliability study of generalized exponential distribution based on inverse power law using artificial neural network with Bayesian regularization

AbstractThe investigation of lifetime reliability analysis is vital for confirming the quality of devices, equipment, electronic tube flops, and so forth. Statistical investigators have become more interested in lifetime model exploration in recent years, particularly in the last decade, without considering the issue of modeling the metrics of model reliability using artificial neural networks (ANNs). This study addresses this vacuum by discussing the multilayer ANN with Bayesian regularization modeling for reliability metrics of generalized exponential model based on inverse power law (IPL). The numerical findings of the reliability investigations and the values obtained from the ANN have been examined and analyzed carefully. The findings show that ANNs are a powerful and useful mathematical tool for analyzing the reliability of lifetime model based on IPL. Finally, a real life framework is implemented that support the theory of a research study.

Automatic Hybrid Access Control in SCADA-Enabled IIoT Networks Using Machine Learning.

The recent advancements in the Internet of Things have made it converge towards critical infrastructure automation, opening a new paradigm referred to as the Industrial Internet of Things (IIoT). In the IIoT, different connected devices can send huge amounts of data to other devices back and forth for a better decision-making process. In such use cases, the role of supervisory control and data acquisition (SCADA) has been studied by many researchers in recent years for robust supervisory control management. Nevertheless, for better sustainability of these applications, reliable data exchange is crucial in this domain. To ensure the privacy and integrity of the data shared between the connected devices, access control can be used as the front-line security mechanism for these systems. However, the role engineering and assignment propagation in access control is still a tedious process as its manually performed by network administrators. In this study, we explored the potential of supervised machine learning to automate role engineering for fine-grained access control in Industrial Internet of Things (IIoT) settings. We propose a mapping framework to employ a fine-tuned multilayer feedforward artificial neural network (ANN) and extreme learning machine (ELM) for role engineering in the SCADA-enabled IIoT environment to ensure privacy and user access rights to resources. For the application of machine learning, a thorough comparison between these two algorithms is also presented in terms of their effectiveness and performance. Extensive experiments demonstrated the significant performance of the proposed scheme, which is promising for future research to automate the role assignment in the IIoT domain.

Better decision-making strategy with target seeking approach of humanoids using hybridized SOARANN-fuzzy technique

The prediction and decision-making features of the artificial neural network have been applied to several robotic related research works. Humanoid robot navigation is a challenging task for the researchers with best decision making. Simple artificial neural network (ANN) is the connection models which are poor in multistep decision making with long term planning and logical reasoning. So, in this study artificial neural network is improved in long term cognitive planning by SOAR (State Operator and Result) with powerful feature prediction through ANN (SANN) and hybridized with Fuzzy system for generation effective turning angle value, which will guide the humanoids to reach target location with better decision target seeking ability. An intelligent data fusion model is embedded between SOAR and ANN for converting the logical sequence information of SOAR to probabilistic vectors in multilayer ANNs. The obstacle distances are the input parameters to the SANN model and turning angle (TA) is the output from SANN. The obstacle distances along with the TA obtained from SANN is fed to the fuzzy system as input value and effective turning angle (ETA) is obtained to guide the humanoids towards reaching target. The proposed novel technique and ANN is used by both single and multiple humanoids in both simulation and experimental platforms. The novelty of the research focuses on the development of the new SOAR-ANN technique with better decision strategy for effective turning angle value, to obtain global optimal path by avoiding trapping in local optima and dead ends. The simulation and experimental results in terms of path length travelled and time spent to reach target are obtained from both ANN and novel SANN-Fuzzy technique. When the developed novel technique is compared with standalone ANN method during single humanoid navigation then, a significant improvement of 2–5% and 14–15% is observed in related to trajectory path span and trajectory time spent respectively. Similarly, during multiple humanoid navigation percentage improvement of 5–9% and 14–18% is obtained for humanoids in terms of navigational parameters respectively. The results clearly shows the developed technique requires less time and travels less path to reach target as compared to ANN and the percentage of error is also quite low. Statistical analysis is performed from the results of both the techniques and reflects the effectiveness of the proposed technique in comparison to ANN. Further the developed technique is compared against another existing methodologies like Fuzzy-ANN and Boundary Node Approach and, significant enhancements of 5.64% and 9.72% is attained in terms of track span respectively.

Forecasting the Tourism Demand of Türkiye Using Artificial Neural Network (ANN) Approach

Modelling and forecasting the tourism demand is an important research area for both public and private sectors for planning the travel and accommodation facilities in advance. Therefore, modelling the tourism demand in terms of the number of tourists is an active research area for both tourism, economics and financial studies. In this work, the tourism demand of Türkiye is modelled using artificial neural network methods. The tourism demand represented by the number of tourists is taken as the dependent variable while the past values of the number of tourists is considered as the inputs. Furthermore, the tourism revenue is also modelled employing the same autoregressive artificial neural network approach. Monthly data in the period of 2008-2022 which are taken from the official sources are used as the research material. The multilayer perceptron type artificial neural networks with nonlinear neural activation functions is selected for the accurate modelling of the highly seasonal tourism demand data. The modelling and forecasting results show that the developed artificial neural network reaches high accuracy for modelling both the tourism demand and the tourism revenue such that the coefficient of determination of the developed artificial neural network models have the values of R2=0.949 and R2=0.840 for the tourism demand and tourism revenue, respectively, providing an objective assessment of the accuracy of the developed models. It is concluded that the multilayer perceptron based artificial neural network methods can be used to model the tourism demand therefore this type of modelling is expected to be helpful for tourism planners by providing them the tourism demand forecast in advance.

Urban development modeling in Al Diwaniyah province of Iraq using RS-GIS

The rapid growth of the population and the consequent increase in migration to the cities during the past decades have caused the expansion of many urban areas. In this study, the growth and development of the urban areas of Al-Diwaniyeh during the recent decades using three categories: 1. urban limits layer extracted from land use maps during the period, 2. population density layers and 3. Degree of urbanization in the period 1975 to 2015 It was investigated, monitored and modeled. Modeling and forecasting for the future was done using layers of population density and degree of urbanization. The population density map for 2025 was implemented based on population changes in the last two decades using the multilayer artificial neural network method. While the prediction of the degree of urbanization was operationalized by creating and applying a multi-layer neural network model for 2030. The results of the study showed that the general trend of the expansion of Al-Diwaniye city limits during the period of 1975 to 205 was increasing. The degree of urbanization in Al Diwaniyah has been increasing since 1975. After 1975, the initial cores of the dense areas were formed, and gradually, in the following periods, the expansion of the urban areas of Al-Diwaniyeh was observed around the cores. The class of rural areas has shown an upward trend with a more uniform slope compared to other classes of the degree of urbanization. While after 1990, high density and low density classes with close areas have also gone through an upward trend. The rate of population density and, accordingly, the rate of population in Al-Diwaniye has been increasing between 1975 and 2015. The trend of maximum population changes has been downward; therefore, it can be claimed that the initial dense cores of the urban population of Al-Diwaniyeh have moved to the surrounding areas. In the estimated degree of urbanization in 2030, the class with high density has faced a decrease in area compared to the previous period. In general, the area of ​​built-up areas in 2030 will increase compared to previous periods, but this will be achieved with a slower acceleration and slope compared to previous periods.

A sensor-agnostic albedo retrieval method for realistic sea ice surfaces: model and validation

Abstract. A framework was established for remote sensing of sea ice albedo that integrates sea ice physics with high computational efficiency and that can be applied to optical sensors that measure appropriate radiance data. A scientific machine learning (SciML) approach was developed and trained on a large synthetic dataset (SD) constructed using a coupled atmosphere–surface radiative transfer model (RTM). The resulting RTM–SciML framework combines the RTM with a multi-layer artificial neural network SciML model. In contrast to the Moderate Resolution Imaging Spectroradiometer (MODIS) MCD43 albedo product, this framework does not depend on observations from multiple days and can be applied to single angular observations obtained under clear-sky conditions. Compared to the existing melt pond detection (MPD)-based approach for albedo retrieval, the RTM–SciML framework has the advantage of being applicable to a wide variety of cryosphere surfaces, both heterogeneous and homogeneous. Excellent agreement was found between the RTM–SciML albedo retrieval results and measurements collected from airplane campaigns. Assessment against pyranometer data (N=4144) yields RMSE = 0.094 for the shortwave albedo retrieval, while evaluation against albedometer data (N=1225) yields RMSE = 0.069, 0.143, and 0.085 for the broadband albedo in the visible, near-infrared, and shortwave spectral ranges, respectively.

Colorimetric characterization of the wide-color-gamut camera using the multilayer artificial neural network.

In order to realize colorimetric characterization for the wide-color-gamut camera, we propose using the multilayer artificial neural network (ML-ANN) with the error-backpropagation algorithm, to model the color conversion from the RGB space of camera to theX Y Z space of the CIEXYZ standard. In this paper, the architecture model, forward-calculation model, error-backpropagation model, and the training policy of the ML-ANN were introduced. Based on the spectral reflectance curves of the ColorChecker-SG blocks and the spectral sensitivity functions of the RGB channels of typical color cameras, the method of producing the wide-color-gamut samples for the training and testing of the ML-ANN was proposed. Meanwhile, the comparative experiment employing different polynomial transforms with the least-square method was conducted. The experimental results have shown that, with the increase of the hidden layers and the neurons in each hidden layer, the training and testing errors can be decreased obviously. The mean training errors and mean testing errors of the ML-ANN with optimal hidden layers have been decreased to 0.69 and 0.84 (color difference of CIELAB), respectively, which is much better than all the polynomial transforms, including quartic polynomial transform.

Development of welding discontinuity identification system using statistical texture feature extraction and ANN classification on digital radiographic image

Discontinuity in welds is one of the causes of the quality of a connection in the material decreases function. Undamaged test with radiographic method is one of the tests to see the quality of a weld. The test results are radiograph images and evaluated by a radiographer. So this research is designed by optimizing a system to help the work of a radiography expert in identifying discontinuities by utilizing the Matlab Application. On this system uses the method of characteristic extraction and classification of neural networks (AAN). The system uses a characteristic extraction method with geometric invariant moment (GIM) algorithms and a gray level co-occurenece matrix (GLCM) as identification values used in the classification process. The calcification process uses a backpropagation-type multilayer Artificial Neural Network. The types of discontinuities used as data in this system are incompleted of penetration, crack, wormhole, and distributed porosity using a total of 800 datasets of radiograph imagery data. This data sharing is organized using k fold cross validation. The study conducted 15 experiments in system testing to prove the truth in identifying. The results of the experiment resulted in the highest average performance score reaching 93.33%

Estimation of reference evapotranspiration using artificial neural network models for semi-arid region of Haryana

The study was conducted to evaluate performance of artificial neural network (ANN) models for estimating reference evapotranspiration (ET0) for semi-arid region of Haryana state. Ten years (2011-2020) daily weather data of maximum and minimum temperature, relative humidity, wind speed and sun shine hours was collected from the meteorological observatory at CCS HAU, Hisar. Multilayer perceptron feed forward back propagation ANN models were evaluated for different training algorithms (10), number of hidden layers (1-3) and number of neurons in hidden layers (1-30). Training algorithms compared in the study were heuristic techniques (GDA, GDX, RP), conjugate gradient (CGF, CGP, CGB, SCG), quasi-Newton (BFG, OSS) and Levenberg-Marquardt (LM). Results were compared against standard FAO Penman-Monteith method. The study revealed that best performance for ANN was found with LM algorithm in single layer of 13 neurons exhibiting RMSE, R, ME and RPD values 0.306, 0.986, 0.976 and 6.63, respectively. ANN models showed good performance in prediction of reference evapotranspiration.

Thickness and refractive index measurements of a thin-film using an artificial neural network algorithm

Thin-film thickness and refractive index measurements are important for quality control in many high-tech industrial manufacturing processes, such as the semiconductor, display, and battery. Many studies have been carried out to measure the thickness and refractive index of thin-films, and recently studies using an artificial neural network (ANN) algorithm have also been conducted. However, strict evaluations of ANNs were not reported in all previous studies. In this study, a multilayer perceptron type of ANN algorithm for simultaneously analyzing the thickness and refractive index of a thin-film is designed and verified by using four thin-film certified reference materials (CRMs) being traceable to the length standard. According to the number of hidden layers and the number of nodes for each hidden layer, 12 multilayer perceptron type ANN algorithms were designed and trained with a theoretical dataset generated through optics theory based on multiple interferences. Subsequently, the interference spectra measured by the four CRMs were put into the 12 trained ANNs as input, and it was checked whether or not the output values were in good agreement with the corresponding certified values of both the thickness and refractive index. As a result, an ANN algorithm having two hidden layers with 100 nodes was selected as the final algorithm and an uncertainty evaluation was performed. Finally, the combined uncertainties for the thickness and refractive index were estimated to be 2.0 nm and 0.025 at a wavelength of 632.8 nm, respectively, as measured using a spectral reflectometer with the well-trained ANN algorithm.

High-dimensional multi-objective optimization algorithm for combustion chamber of aero-engine based on artificial neural network-multi-objective particle swarm optimization

This paper considers optimizing the performance of high-temperature combustion chamber of an aero-engine based on a concentric and hierarchical model. First, sample data for the design variables are obtained based on Latin hypercube sampling method, and a one-dimensional program is used to obtain the true values of combustion efficiency and total pressure loss corresponding to each group of variables. The obtained data are then pre-processed to establish a dataset. Second, a multi-layer artificial neural network (ANN) architecture is designed and a surrogate model of the combustion-related performance of the combustor is established using a data-driven method. The results of global sensitivity analysis based on variance show that ratio of fuel flow to air flow (fuel–air ratio) and the total inlet pressure are the most important factors influencing the two objective functions. Finally, we optimize the multi-objective combustion-related performance of the surrogate model by applying the particle swarm optimization algorithm to it. The results of experiments show that the ANN-based model could accurately predict the efficiency of combustion and total pressure loss of the chamber, yielding root mean-squared errors of 0.0107 and 0.3032%, respectively. It also had better generalization ability than the cubic polynomial surrogate model. Compared with the cubic polynomial model, it generated an optimal Pareto solution set as prediction that had higher values in both objective functions. The proposed model might require better data that can be obtained using intelligent sampling methods so that deeper neural networks can be designed to reduce error and improve its optimization design.

Prediction of Compressive Strength of Fly Ash-Slag Based Geopolymer Paste Based on Multi-Optimized Artificial Neural Network.

The fly ash-slag geopolymer is regarded as one of the new green cementitious materials that can replace cement, but it is difficult to predict its mechanical properties by conventional methods. Therefore, in the present study, the back propagation (BP) artificial neural network technique is used to predict the compressive strength of the fly ash-slag geopolymer. In this paper, data from the published literature were collected as the training set and the experimental results from laboratory experiments were used as the test set. Eight input parameters were determined, as follows: the percentage of fly ash, the percentage of slag, the water-cement ratio, the curing age, the modulus of alkali activator, the mass ratio of NaOH to Na2SiO3 and the moles of Na2O and SiO2 in the alkali activator. Three multilayer artificial neural network models were constructed using the Levenberg-Marquardt (LM), Bayesian regularization (BR) and scaled conjugate gradient (SCG) algorithms to compare the prediction accuracy of the compressive strength of the fly ash-slag geopolymer paste at different ages (3, 7, and 28 d). It was concluded that the training set error of the BR-BP neural network was the smallest. Ultimately, the hyperparameter optimization of the BR-BP neural network was carried out to compare the training set and the test set errors before and after the optimization, and the results show that the BR-BP neural network model with hyperparameter optimization had the highest prediction accuracy.

A Comparative Study in Forming Behavior of Different Grades of Steel in Cold Forging Backward Extrusion by Integrating Artificial Neural Network (ANN) with Differential Evolution (DE) Algorithm

The cold forging backward extrusion is employed to produce parts that are characterized by better mechanical strength. However, in this process, punches are often prone to breakages because of the large forces encountered in deforming the steel billets. The service life of the punches is affected majorly by the geometrical attributes, the type of steel undergoing deformation, and hence the present investigation focuses on the applications of natural computing algorithms such as artificial neural network (ANN) and differential evolution (DE) optimization algorithm to study the differential influence on the forming behavior of different grades steel and enhance the punch service life. The AISI steel grades, such as AISI 1010, 1018, and 1045, employed extensively in the production of automotive components, have been compared in terms of forming behavior, such as effective stress, strain, strain rate, and punch force. The multi-layer feed-forward ANN architecture was utilized for process modeling with forming responses of finite element (FE) simulations that are strategically planned through the design of experiments (DoE) approach. Considerable variations were found for the effective stress and punch force amongst the steels, while marginal deviations were observed for effective strain and strain rates. Confirmatory experiments were conducted to validate the results of optimal combinations obtained through the DE optimization technique, and the deviations were observed to be in the acceptable range. The cold forging backward extruded components have also been examined for better mechanical soundness through microstructure and micro-hardness analysis that clearly revealed the mechanical integrity and strength enhancement within the forged components. The proposed study would assist the industries engaged in the production of cold-forged steel components in determining the appropriate values of variables to minimize the forming responses and, thus, help in enhancing the life of the tooling.

Ultra-fast Surrogate Model for Magnetic Field Computation of a Superconducting Magnet Using Multi-layer Artificial Neural Networks

Due to the inherent nonlinear and sophisticated nature of superconducting wires/tapes, magnetic field computation of superconducting magnets by means of finite element methods (FEMs) is a time-consuming and complicated procedure. Although Legendre series method (LSM) was proposed as an alternative of FEMs, LSMs are not still fast enough. In current research, a surrogate model based on multi-layer artificial neural networks (ANNs) was introduced for the first time to dramatically reduce the computation time of a magnetic resonance imaging (MRI) magnet. To do this, firstly, the data related to the magnetic field were extracted based on LSM simulations for around 5000 different coil geometries. After that, the geometries of coils were used as inputs to a semi-deep learning ANN-based model in MATLAB software package. The minimum magnetic field in diameter spherical volume, maximum and minimum of total magnetic field were considered as outputs of the model, known as field indices. Then, ANN model was trained to calculate these field indices for any coil geometry. By doing so, magnetic field indices were estimated with a high accuracy based on the target values and also with extremely higher speed, comparing to FEM and LSM. Results showed that it takes 15 to 17 s for the proposed model to calculate the field indices for 750 different geometries whereas it takes for LSM-based model about 4 h.

Predicting the buckling behaviour of thin-walled structural elements using machine learning methods

The design process of thin-walled structural members is highly complex due to the possible occurrence of multiple instabilities. This research therefore aimed to develop machine learning algorithms to predict the buckling behaviour of thin-walled channel elements subjected to axial compression or bending. Feed-forward multi-layer Artificial Neural Networks (ANNs) were trained, in which the input variables comprised the cross-sectional dimensions and thickness, the presence/location of intermediate stiffeners, and the element length. The output data consisted of the elastic critical buckling load or moment, while also providing an immediate modal decomposition of the buckled shape into the traditionally defined ‘pure’ buckling mode categories (i.e. local, distortional and global buckling). The sample output for training was prepared using a combination of the Finite Strip Method (FSM) and the Equivalent Nodal Force Method (ENFM). The ANN models were subjected to a K-fold cross-validation technique and the hyperparameters were tuned using a grid search technique. The results indicated that the trained algorithms were capable of predicting the elastic critical buckling loads and carrying out the modal decomposition of the critical buckled shapes with an average accuracy (R2-value) of 98%. The influence of the various channel parameters on the output was assessed using the SHapley Additive exPlanations (SHAP) method.