Optimal Number Of Neurons Research Articles

Prediction of operating parameters and output power of ducted wind turbine using artificial neural networks

The performance of a ducted wind turbine was simulated in this study utilizing an artificial neural network under various duct operating conditions. Ducted wind turbines have been identified as one of the cleanest and most effective future renewable energy possibilities. Different methods have been used throughout time to exploit the flow stream power successfully. However, the Ducted Wind Turbine System is one method that is still in its early phases. The operation of the ducted wind turbine is analyzed in this research under different wind conditions. The ANN algorithm is recommended for generating turbine power at various wind speeds. The proposed neural network model is shown to perform better for estimating turbine power curves. The ANN models used the free-stream wind speed, wind speed in the throat section, turbulence intensity, and wind power in the intake part of the duct as input datasets and the output power of wind in the throat section as output datasets. At the same time, a three-layer backpropagation training method from the Multilayer Perceptron algorithm approach, a Levenberg–Marquardt, was selected as the best ANN. It was evaluated by comparing to a Radial-based functions approach with a single hidden layer. The optimum number of neurons in the MLP method’s first and second hidden layers, as well as the RBF method’s single hidden layer, has been determined to be 55 and 70, respectively. At 77 and 70 epochs, the best MSE evaluation efficiency of MLP and RBF networks was estimated to be 0. 000103 and 0. 000353, respectively.

Impact of different arrangements of heated elliptical body, fins and differential heater in MHD convective transport phenomena of inclined cavity utilizing hybrid nanoliquid: Artificial neutral network prediction

In the current scenario, the impact of different arrangements of solid heated elliptical body, discrete heater (LH/H), array of fins with different sizes (1×2, 2×1, 2×2), conductivity ratio (r), magnetic field (Hartmann number, Ha), angle of inclination (β), nanoparticle volume fraction (χ) and Rayleigh number (Ra) is investigated for natural transport phenomena in the cavity containing hybrid nanoliquid. The cavity consists of three equally spaced fins on one wall and heated elliptical body inside the cavity. The homogeneous hybrid nanoliquid (Al2O3-Cu/water) model using experimental data is utilized and results are evaluated for different controlling parameters: Rayleigh numbers (Ra=103 to 106), Hartmann number (Ha=0 to 100), discrete heater (LH/H=0.1 to 0.9), angle of elliptical body (ω=0° to 180°) with three different positions (Center, POS I and II), angle of inclination (β=0 to π), thermal conductivity ratio (r=0.01–100), nanoparticle volume fraction (χ=0 to 0.02) using Galerkin Finite Element Method (GFEM). The mesh grid independency test is also performed for different combinations of meshes and a refined mesh with optimal degrees of freedom (DoFs=190275) has been considered for entire convection range (Ra=103−106).The impact of controlling parameters on average Nusselt number evaluated from the numerical heat transfer analysis has been compared and predicted using feed forward neural network model. The Levenberg-Marquardt back propagation algorithm is used for ANN training based on limited simulated data with optimal number of neurons and average R2 of 0.99988. The quadratic regression model, which is also determined using the MATLAB built-in subroutine ’fitlm’, demonstrates the greatest dependency of Nusselt number on nanoparticle concentration.

Robust adaptive self‐structuring neural networks tracking control of unmanned surface vessels with uncertainties and time‐varying disturbances

AbstractThe trajectory tracking control problem of unmanned surface vessels (USVs) with uncertainties and time‐varying disturbances is investigated. A robust adaptive trajectory tracking control scheme is proposed based on finite‐time control and a self‐structuring neural networks (SSNN) identifier, which can obtain satisfactory performance with an norm‐bounded, expected attenuation level within a finite time. The SSNN is developed to approximate USVs system uncertainties and external disturbances by online learning. Most importantly, a balance is achieved between the optimal number of neurons and the expected performance, which saves significant network resources. The Lyapunov stability analysis shows that the scheme ensures convergence of the tracking error to a small neighborhood around zero in finite time, while all the other closed‐loop signals remain bounded. Moreover, the application of a high‐gain observer effectively reduces the cost of velocity sensors. The feasibility and effectiveness of this control scheme are verified by theorem analysis and numerical simulations.

An LSTM-PINN Hybrid Method to Estimate Lithium-Ion Battery Pack Temperature

Physics-based models for battery temperature prediction are often not suitable for online applications due to the large number of fitted parameters, low fidelity results from parameter inaccuracy and unaccounted model dynamics, limited high quality experimental data, and slow convergence of predictions from unknown initial conditions. On the other hand, data-driven models require much less computation power but a large dataset to learn the time dependent behavior. This paper proposes a physics-informed neural network (PINN) to take full advantage of both physics-based and data-driven models. Four comparative studies were performed to investigate the effectiveness of including chamber temperature with two different activation functions, the optimal number of neurons and hidden layers, the dependance on reversible heat generation, and the performance of long short-term memory (LSTM)-PINN model. The results show that the LSTM-PINN with chamber temperature as one of the inputs delivers better prediction accuracy. The LSTM-PINN with an exponential activation function for the chamber temperature has a more accurate prediction for the direct current fast charge (DCFC) test profile and similar prediction accuracy for the grade load (GL) 100 test profile. The root mean square errors (RMSEs) of the LSTM-PINN are 0.57°C for DCFC and 0.52°C for GL 100, respectively. In addition, having 55 neurons and 4 hidden layers gives the lowest prediction error. Furthermore, the improvement by having reversible heat generation is negligible. At last, the LSTM-PINN model has less prediction error than the LSTM model, especially when the battery temperature range is enormous.

The Optimal Artificial Neural Network for Small Datasets on Shear Resistance Prediction of Steel Fibre Reinforced Concrete Beam

This study presents an approach for the prediction of the shear strength of steel fiber reinforced concrete (SFRC) beams using the Artificial Neural Network (ANN) developed based on existing experimental shear resistance results from various researchers. The experimental results database containing 42 sample numbers of SFRC beams (with shear span-to-depth ratio exceeding 2.5) without stirrups, with compressive strength of concrete varying from 24.9 to 68.6 MPa and steel fibers of hooked end type are used to develop an ANN model. The developed ANN model is trained by using 70% and 90% of the data and another 30 to 10% served as the validation data purpose. The shear strengths prediction based on ANN model was found to be in perfect agreement with the experimental values when the optimal neuron number is 2 and by fixing the training set size as 90%. Results showed that this ANN model has strong potential as a feasible design tool for predicting the shear strength of SFRC beams without transverse reinforcement or stirrups within the range of input parameters considered in this study.

Prediction and classification of suspended sediment and zooplankton signals from acoustic Doppler current profiler backscatter data using artificial neural networks

Characterization of each underwater object has its challenges, especially for small objects. The process of quantifying acoustic signals for these small objects can be done using high-frequency hydroacoustic instruments such as an acoustic Doppler current profiler (ADCP) combined with the artificial intelligence (AI) technique. This paper presents an artificial neural network (ANN) methodology for classifying an object from acoustic and environmental data in the water column. In particular, the methodology was tuned for the recognition of suspended sediments and zooplankton. Suspended sediment concentration and zooplankton abundance, which extracted from ADCP acoustic data, were used as input in the backpropagation method along with other environmental data such as effects of tides, currents, and vertical velocity. The classifier used an optimal number of neurons in the hidden layer and a feature selection based on a genetic algorithm. The ANN method was also used to estimate the suspended sediment concentration in the future. This study provided new implications for predicting and classifying suspended sediment and zooplankton using the ADCP instrument. The proposed methodology allowed us to identify the objects with an accuracy of more than 95%.

Neural Approach in Short-Term Outdoor Temperature Prediction for Application in HVAC Systems

An accurate air-temperature prediction can provide the energy consumption and system load in advance, both of which are crucial in HVAC (heating, ventilation, air conditioning) system operation optimisation as a way of reducing energy losses, operating costs, as well as pollution and dust emissions while maintaining residents’ thermal comfort. This article presents the results of an outdoor air-temperature time-series prediction for a multifamily building with the use of artificial neural networks during the heating period (October–May). The aim of the research was to analyse in detail the created neural models with a view to select the best combination of predictors and the optimal number of neurons in a hidden layer. To meet that task, the Akaike information criterion was used. The most accurate results were obtained by MLP 3-3-1 (r = 0.986, AIC = 1300.098, SSE = 4467.109), with the ambient-air-temperature time series observed 1, 2, and 24 h before the prognostic temperature as predictors. The AIC proved to be a useful method for the optimum model selection in a machine-learning modelling. What is more, neural network models provide the most accurate prediction, when compared with LR and SVR. Additionally, the obtained temperature predictions were used in HVAC applications: entering-water temperature and indoor temperature modelling.

Prediction of Total Electron Content (TEC) using Neural Network over Anomaly Crest Region Bhopal

In the present work neural network has been developed for the prediction of Vertical Total Electron Content (VTEC) over Bhopal (23.2°N, 77.4°E & MLAT 14.2°N), an equatorial anomaly crest region. The study is based on the VTEC data recorded by a multi-frequency multi-constellation GNSS receiver installed at Bhopal during May 2016 to August 2017. Neural Network (NN) consists of artificial neurons that are used to learn data patterns adjusting weights between input, hidden and output layers by computational modelling. In order to obtain the optimal number of neurons in the hidden layer, the performance of four systems of neural network have been tested. Out of which, the fourth neural network has been used to predict VTEC with 7 input neurons in the present study. The number of hidden layer neurons is a factor that affects the performance of the trained networks. The input layer of the network includes the year, day of the year, hour of the day, geographic latitude, geographic longitude, SSN and IRI NmF2. We have compared the TEC obtained from the neural network prediction (NN TEC), GPS derived TEC (GPS TEC) and TEC from IRI-2016 model (IRI TEC) and analysis has been made. We observed that the Root Mean Square Error (RMSE) decreases with increase in the number of hidden layer neurons. The RMSE comes out to be lowest (1.96 TECU), when the number of hidden layer neurons are 41.The TEC predicted from the NN model and estimated from GPS receiver have same trend at 01:00 and 07:00 UT. The modelled NN TEC values are in good agreement with GPS TEC values for all seasons and 0.99 correlation coefficient was calculated for summer months, but IRI TEC always underestimates GPS TEC in all seasons. The NN model excellently predicted the TEC values of August 2017 by putting the credentials of August 2016 and only 0.55–32.16% relative errors were estimated between them whereas it reaches up to 93.86% with IRI TEC. Thus, the result shows that the proposed NN model can predict the diurnal and seasonal GPS TEC more accurate than IRI over anomaly crest region Bhopal. However, the inclusion of IRI-NmF2 as input layer neuron increases the network performance.

Response estimation of reinforced concrete shear walls using artificial neural network and simulated annealing algorithm

Reinforced concrete (RC) shear walls constitute a lateral load resisting system which is utilized in medium-rise and high-rise buildings. Recent earthquakes and corresponding studies have highlighted the importance of understanding the performance of reinforced concrete shear walls. Hence, there is an essential need to estimate the response of RC shear walls. However, predicting the response of the RC walls is difficult in this form due to the complex nature of the problem. In this research, a hybrid technique, the artificial neural network (ANN) and Simulated Annealing (SA), is considered to solve such complicated problems. (SA) algorithm is utilized to determine the optimal number of neurons of ANN and the percentage of data that should be used in the training and testing set. 14 learning algorithms are used and their performance is compared. The database, which is utilized in this study, consists of 150 RC shear walls. The coefficient of determination (R2) and root mean square error (RMSE) values of the best ANN model (ANN with Conjugate gradient backpropagation with Fletcher-Reeves updates learning algorithm) were found to be 0.97 and 1.66, respectively, which demonstrate a high capability of the SA-ANN algorithm in predicting RC shear walls’ responses.

Construction of an Optimized Multilayer Neural Network Within a Nonlinear Model of Generalized Error

In this paper, we propose a method for optimizing the structure of a multilayer neural network based on minimizing nonlinear generalized error, which is based on the principle of minimum length of description. According to this principle, the generalized error is determined by the error in the description of the model and the error in the approximation of the data by the neural network in the nonlinear approximation. From the condition of minimizing the generalized network error, the expressions for calculating the optimal network size are given (the number of synaptic connections and the number of neurons in hidden layers). The graphic dependences of the generalized error of the network on the number of synaptic connections between the neurons with different values of input images and the fixed number of educational examples and the graphic dependences of the optimal number of synaptic connections from the number of educational examples with different values of the input images are constructed. The assessment of the degree of complexity of the training of the neural network is carried out on the basis of the ratio of the optimal number of synaptic connections between the neurons and the optimal number of neurons in the hidden layers.

Improving energy storage and performance through implementing artificial neural network modeling to forecast heat transfer and entropy generation within a wavy‐wall microchannel under discontinuous‐boundary condition–hybrid nanofluid utilization

Numerous industries deal with heat transfer looking for a new technique to boost efficiency. Using nonuniform condition and making a wavy wall and microchannel are the conventional techniques to increase heat transfer which consequently lead to intensification in energy storage potential. In the present study, forced convection heat transfer of nanofluid through the slippage microchannel is investigated by utilizing numerical methods. Moreover, the results of the artificial neural network in determining the parameters involved in the first and second laws of thermodynamics are discussed; so it is necessary to determine the optimal number of neurons in the middle layer. In addition, the current study aims to examine the effects of Reynolds number, slip wall, and locations of thermal boundary condition on heat transfer and irreversibility. However, thermal entropy generation becomes 1.52 times worse. It is also revealed that the slippage wall can enhance the heat transfer up to 15.6%. The best thing about slippage microchannel is creating slip wall raises the thermal entropy generation and declines the viscous entropy generation.

Using Artificial Neural Networks in Predicting the Level of Stress among Military Conscripts

The present study aims to elucidate the main variables that increase the level of stress at the beginning of military conscription service using an artificial neural network (ANN)-based prediction model. Random sample data were obtained from one battalion of the Lithuanian Armed Forces, and a survey was conducted to generate data for the training and testing of the ANN models. Using nonlinearity in stress research, numerous ANN structures were constructed and verified to limit the optimal number of neurons, hidden layers, and transfer functions. The highest accuracy was obtained by the multilayer perceptron neural network (MLPNN) with a 6-2-2 partition. A standardized rescaling method was used for covariates. For the activation function, the hyperbolic tangent was used with 20 units in one hidden layer as well as the back-propagation algorithm. The best ANN model was determined as the model that showed the smallest cross-entropy error, the correct classification rate, and the area under the ROC curve. These findings show, with high precision, that cohesion in a team and adaptation to military routines are two critical elements that have the greatest impact on the stress level of conscripts.

Producing non-traditional flour from watermelon rind pomace: Artificial neural network (ANN) modeling of the drying process

An artificial neural network (ANN) model was developed to simulate the convective drying process of watermelon rind pomace used in the fabrication of non-traditional flour. Also, the drying curves obtained experimentally were fitted with eleven different empirical models to compare both modeling approaches. Lastly, to reduce the required fossil fuel in the convective drying process, two types of solar air heaters (SAH) were presented and experimentally evaluated.The optimization of the ANN by a genetic algorithm (GA) resulted in an optimal number of neurons of nine (9) for the first hidden layer and ten (10) for the second hidden layer. Also, the ANN performed better than the best fitted empirical model. Simulations with the trained ANN showed very promising generalization capabilities.The type II SAH showed the best performance and the highest air temperature it reached was 45 °C. The specific energy consumption (SEC) needed to dry the watermelon rind at this temperature and the CO2 emissions were 609 kWh.kg−1 and 318 kg CO2.kWh−1, respectively. Using the type II SAH, this energy amount would be saved without CO2 emissions. To reach higher drying temperatures the combination of the SAH and the electrical convective dryer is possible.

Development of a method for optimizing the structure of static neural networks intended for categorizing technical state of gas-turbine engines

A process of creating a static neural network intended for diagnosing bypass gas turbine aircraft engines by a method of categorizing the technical state of the engine flow path was considered. Diagnostics depth was "to the structural assembly". A variant of diagnosing single faults of the flow path was considered.The following tasks were set:‒ select the best neuron activation functions in the network layers;‒ determine the number of layers;‒ determine the optimal number of neurons in layers;‒ determine the optimal size of the training set.The problem was solved taking into account the influence of parameter measurement errors.The method of structure optimization implies training the network of the selected configuration using a training data set. The training was periodically interrupted to analyze the results of the network operation according to the criterion characterizing the quality of classification of the engine technical state. The assessment was performed with training and control sets. The network that provides the best value of the classification quality parameter assessed by the test set was selected as the final network.The PS-90A turbojet engine was selected as the object of diagnostics. Diagnostics was carried out on takeoff mode and during the initial climb.Primary optimization was carried out according to the data with no measurement errors. It was shown that a two-layer network with the use of neurons having a hyperbolic tangent function in both layers is sufficient to solve the problem. The size of the first network layer was finally optimized according to the data containing measurement errors. A two-layer network with eight neurons in the first layer was obtained. The share of erroneous diagnoses measured 14.5 %

SELECTION OF INPUT VARIABLES OF NONLINEAR AUTOREGRESSIVE NEURAL NETWORK MODEL FOR TIME SERIES DATA FORECASTING

NARNN is a type of ANN model consisting of a limited number of parameters and widely used for various applications. This study aims to determine the appropriate NARNN model, for the selection of input variables of nonlinear autoregressive neural network model for time series data forecasting, using the stepwise method. Furthermore, the study determines the optimal number of neurons in the hidden layer, using a trial and error method for some architecture. The NARNN model is combined in three parts, namely the learning method, the activation function, and the ensemble operator, to get the best single model. Its application in this study was conducted on real data, such as the interest rate of Bank Indonesia. The comparison results of MASE, RMSE, and MAPE values with ARIMA and Exponential Smoothing models shows that the NARNN is the best model used to effectively improve forecasting accuracy.

Comparative study of methods to obtain the number of hidden neurons of an auto-encoder in a high-dimensionality context

Fourteen formulas from the state-of-art were used in this paper to find the optimal number of neurons in the hidden layer of an autoencoder neural network. The latter is employed to reduce the dataset dimension on high-dimensionality scenarios with not significant reduction in classification accuracy in comparison to the use of the whole dataset. A Deep Learning neural network was employed to analyze the effectiveness of the studied formulas in classification terms (accuracy). Eight high-dimensional datasets were processed in an experimental set in order to assess this proposal. Results presented in this work show that formula 13 (used to find the number of hidden neurons of the auto-encoder) is effective to reduce the data dimensionality without a statistically significant reduction of the classification performance, as it was confirmed by the Freidman test and the Holm's post-hoc test.

Determining the Number of Neurons in Artificial Neural Networks for Approximation, Trained with Algorithms Using the Jacobi Matrix

How can we determine the optimal number of neurons when constructing an artificial neural network? This is one of the most frequently asked questions when working with this type of artificial intelligence. Experience has brought the understanding that it takes an individual approach for each task to specify the number of neurons. Our method is based on the requirement of algorithms looking for a minimum of functions of type 𝑺􁈺𝒛􁈻 􀵌 Σ 􁈾𝝋𝒊 𝒎 􁈺𝒛 􁈻􁈿𝟐 𝒊􀭀𝟏 that satisfy the inequality 𝒑 􀵑 𝒎, where p is the dimensionality of the argument z, and m is the number of functions. Formulas for an upper limit of the required neurons are proposed for networks with one hidden layer and for networks with r hidden layers with an equal number of neurons.

Artificial neural network modeling of cefixime photodegradation by synthesized CoBi2O4 nanoparticles.

CoBi2O4 (CBO) nanoparticles were synthesized by sol-gel method using polyvinylpyrrolidone (PVP) as a complexing reagent. For a single phase with the spinel structure, the formed gel was dried and calcined at four temperatures stages. Various methods were used to identify and characterize the obtained spinel, such as X-ray diffraction (XRD), scanning electron micrograph (SEM-EDX), transmission electron microscope (TEM), Fourier transform infrared (FT-IR), X-ray fluorescence (XRF), Raman, and UV-Vis spectroscopies. The photocatalytic activity of CBO was examined for the degradation of a pharmaceutical product cefixime (CFX). Furthermore, for the prediction of the CFX degradation rate, an artificial neural network model was used. The network was trained using the experimental data obtained at different pH with different CBO doses and initial CFX concentrations. To optimize the network, various algorithms and transfer functions for the hidden layer were tested. By calculating the mean square error (MSE), 13 neurons were found to be the optimal number of neurons and produced the highest coefficient of correlation R2 of 99.6%. The relative significance of the input variables was calculated, and the most impacting input was proved to be the initial CFX concentration. The effects of some scavenging agents were also studied. The results confirmed the dominant role of hydroxyl radical OH• in the degradation process. With the novel CoBi2O4/ZnO hetero-system, the photocatalytic performance has been enhanced, giving an 80% degradation yield of CFX (10mg/L) at neutral pH in only 3h.

Using Committee Neural Network for Prediction of Pressure Drop in Two-Phase Microchannels

Numerous studies have proposed to correlate experimental results, however there are still significant errors in those predictions. In this study, an artificial neural network (ANN) is considered for a two-phase flow pressure drop in microchannels incorporating four neural network structures: multilayer perceptron (MLP), radial basis function (RBF), general regression (GR), and cascade feedforward (CF). The pressure drop predication by ANN uses six inputs (hydraulic diameter of channel, critical temperature of fluid, critical pressure of fluid, acentric factor of fluid, mass flux, and quality of vapor). According to the experimental data, for each network an optimal number of neurons in the hidden layer is considered in the range 10–11. A committee neural network (CNN) is fabricated through the genetic algorithm to improve the accuracy of the predictions. Ultimately, the genetic algorithm designates a weight to each ANN model, which represents the relative contribution of each ANN in the pressure drop predicting process for a two-phase flow within a microchannel. The assessment based on the statistical indexes reveals that the results are not similar for all models; the absolute average relative deviation percent for MLP, CF, GR, and CNN were obtained to be equal to 10.89, 10.65, 7.63, and 5.79, respectively. The CNN approach is demonstrated to be superior to many ANN techniques, even with simple linearity in the model.

Application of static and dynamic artificial neural networks for forecasting inflow discharges, case study: Sefidroud Dam reservoir

Accurate forecasting of reservoir inflow is of great importance in water resources planning and management and it can highly affect decisions and policies of reservoir operation with respect to flood control, drought management, water supply, and hydropower generation. In this study, different models of static and dynamic artificial neural networks (ANN) including static feed forward neural network (FFNN), non-linear autoregressive (NAR), and nonlinear autoregressive with exogenous inputs (NARX) are employed in order to forecast Sefidroud Dam reservoir inflows. The capability of studied networks with a range of different input variables in predicting reservoir inflows are then compared. All employed models are trained using inflow discharge and precipitation data with different time delays and an optimum number of neurons in the hidden layers are obtained. In addition, the time index (T) is also employed as the input data to the proposed models in order to increase the accuracy of the estimates. The obtained results indicate that NAR dynamic neural network has a better performance in comparison with FFNN and NARX models. Furthermore, using 12 time delays for inflow discharges and precipitation data leads to the best accessible results where adding time index (T) increases the accuracy. The results obtained from this study provide useful information for reservoir inflow simulation. In other words, these results are critical for water resources management and planning particularly in the field of dam reservoir operation which is crucial under reported water crisis in Iran.