Feed-forward Back-propagation Neural Network Research Articles

Artificial Neural Network Control Applied to a Photovoltaic-Battery Microgrid System

This paper deals with artificial neural network (ANN) applied to control a standalone microgrid in French Guiana. ANN is an artificial intelligence technique used to control non-linear and complex systems. ANN associated with the Levenberg–Marquardt (LM) algorithm has many advantages, such as rapid decision-making and improved system transients. Therefore, this technique should be adapted for the control of photovoltaic (PV) systems in the tropical climate of French Guiana with high variation in irradiance. The microgrid is composed of a PV source and a storage battery to supply an isolated building which is modeled by a DC load. The PV source is controlled by an ANN-based MPPT (Maximum Power Point Tracking) controller. To validate our ANN-MPPT, we compared it with one of the very popular MPPT algorithms, which is the P&O-MPPT algorithm. The comparison results show that our ANN-MPPT works well because it can find the maximum power point quickly. In the case of battery control, we tested two feed-forward backpropagation neural network (FFBNN) configurations called method1 and method2 associated with the Levenberg–Marquardt (LM) algorithm. We varied the number of hidden layers in each of these two FFBNN configurations to obtain the optimal number of hidden layers for each configuration which optimizes battery control. Method1 is chosen because it is better than method2, in a sense that it respects the maximum amplitude of the battery current for our application and improves the transient regimes of this current. This best configuration (method1) is then tested with two other learning algorithms for comparison: Bayesian regularization (BR) and scaled conjugate gradient (SCG) methods. The system performance with LM algorithm is better than SCG and BR algorithms. LM algorithm improves the performance of the system in transient regimes while the results obtained with the SGG and BR algorithms are similar. Then, we focused on the advantage of using ANN control compared to the conventional proportional integral control (PI control). The comparison results showed that ANN control associated with the LM algorithm (ANN-LM) made it possible to reduce battery current peaks by 26% in transient regimes compared to conventional PI control. Finally, we present and discuss the results of our simulation obtained with the MATLAB Simulink software.

Machine learning approach for prediction of ionospheric irregularities on ROTI index over the Northern anomaly crest in Egypt during solar cycle 24

This paper reports the prediction results of the ionospheric irregularities represented by the ROTI index close to the equatorial ionization anomaly's Northern peak. A feedforward backpropagation Neural Network (NN) approach is implemented using a time series Nonlinear Autoregressive approach with Exogenous inputs (NARX). We used the data from a dual frequency GPS-SCINDA station located at Helwan (geographic coordinates of 29.86°N, 31.32°E, and MLAT of 29.94°N) in Egypt. To allow the model to be independently tested during varying levels of solar activities, we collected a 5-minute resolution of ROTI data for the solar cycle 24 from 2009 to 2017. The factors that influence the development of ionospheric irregularities are involved in the established model representing the diurnal and seasonal variations as well as solar and geomagnetic activity parameters. To support learning, we included IRI-foF2 and IRI-hmF2 parameters in the input layer neurons to improve the model learning about the behavior of the ionospheric F layer. The results show that the NN-ROTI values precisely match the GPS-ROTI values with an RMSE of 0.106 TECU/min and a prediction efficiency of 95%. The predicted values are highly correlated with the originals, with a regression of 0.89. Furthermore, the irregularities were more prevalent during the equinox months than during the solstice months. It is also observed that predicted NN-ROTI values in all seasons have RMSEs less than 0.03 and 0.05 TECU/min for the low and high solar activity, respectively. The results also showed a clear correlation between solar activity and the occurrence percentage of ionospheric irregularities indicating a solar cycle dependency. The prediction values of the NN-ROTI occurrence % demonstrated a remarkable correlation with the observed GPS-ROTI occurrence % across SC24.

AI-based predictive approach via FFB propagation in a driven-cavity of Ostwald de-Waele fluid using CFD-ANN and Levenberg–Marquardt

The integration of Artificial Intelligence (AI) and Machine Learning (ML) techniques into computational science has ushered in a new era of innovation and efficiency in various fields, with particular significance in computational fluid dynamics (CFD). Several methods based on AI and Machine Learning (ML) have been standardized in many fields of computational science, including computational fluid dynamics (CFD). This study aims to couple CFD with artificial neural networks (ANNs) to predict the fluid forces that arise when a flowing fluid interacts with obstacles installed in the flow domain. The momentum equation elucidating the flow has been simulated by adopting the finite element method (FEM) for a range of rheological and kinematic conditions. Hydrodynamic forces, including pressure drop between the back and front of the obstacle, surface drag, and lift variations, are measured on the outer surface of the cylinder via CFD simulations. This data has subsequently been fed into a Feed-Forward Back (FFB) propagation neural network for the prediction of such forces with completely unknown data. For all cases, higher predictivity is achieved for the drag coefficient (CD) and lift coefficient (CL) since the mean square error (MSE) is within ± 2% and the coefficient of determination (R) is approximately 99% for all the cases. The influence of pertinent parameters like the power law index (n) and Reynolds number (Re) on velocity, pressure, and drag and lift coefficients is also presented for limited cases. Moreover, a significant reduction in computing time has been noticed while applying hybrid CFD-ANN approach as compared with CFD simulations only.

ARIMA-BPNN based Stock Price Prediction Model Based on Fusion News Sentiment Analysis

In recent years, the prediction of stocks has mainly focused on improving and combining stock prediction algorithms, or analyzing news sentiment tendencies to simulate subjective investor consciousness. However, both methods have shortcomings in practicality and comprehensiveness. Therefore, based on the use of stock data, the sentiment propensity of vocabulary in the article was processed, and a new algorithm model was obtained by combining the differential integration moving average autoregressive model and backpropagation feedforward neural network model. Finally, sentiment propensity was integrated into the combination model to obtain an algorithm model that integrates sentiment analysis. After optimizing the sentiment vocabulary of news. The algorithm has improved its ability to recognize emotional tendency words, while traditional algorithms have been improved to improve the accuracy of stock prediction, further verifying the relationship curve between emotional tendency and stock prediction fluctuations. The experimental results show that the combined model of sentiment analysis is close to the true value in predicting stock results, with an error of less than 1.5%. The accuracy and stability of the model’s prediction results are significantly better than the uncombined model and traditional prediction models. The new combination model provides better judgment basis for investors through experimental prediction results, creating conditions for investors to avoid stock market risks and improve investment value.

WHITE BLOOD CELL CANCER CLASSIFICATION USING MODIFIED HONEY BEE OPTIMIZATION ALGORITHM (MHBO) BASED FEATURE SELECTION AND NEURAL NETWORK CLASSIFICATION MODEL

A blood malignancy known as leukemia is defined by the bone marrow's abnormal and uncontrollably high production of leukocytes, or white blood cells (WBCs). It is possible to identify and diagnose illnesses early by examining photographs of minute blood cells. lately, hematopathologists have been analyzing, detecting, and identifying leukemia kinds in patients utilizing image-processing techniques. Since no specialized equipment is required for lab testing, image detection is a quick and affordable way of detection. Several image processing tools are created for obtaining significant data from medical photos to enhance patient diagnosis. In this research, a feed forward-back propagation neural network framework is presented, and the kind of cancer found in the cells is ultimately predicted. First, the provided photos are subjected to the filtering procedure. The second method is the Fuzzy Inference System (FIS) technique, which is reliable in the face of changing illumination levels and considers the stability levels of color elements to identify edges among color bone marrow microscopic pictures. Third Active contour detection provides an accurate curve of the boundary edge of the cells. And then the background separation is done by Pinched Flow Fractionation (PFF). Then the feature extraction is carried out by the Modified Honey Bee optimization algorithm (MHBO). Finally, the Feed Forward Back Propagation Neural Network (FFBNN) framework-based classifier is proposed for predicting the white blood cells. Based on the findings, this suggested approach created an automated system that allows medical practitioners to accurately diagnose all forms and subtypes of the disease. Keywords: Bone marrow microscopic images, Fuzzy Inference System (FIS), Pinched Flow Fractionation (PFF), Modified honey bee optimization algorithm (MHBO), Feed Forward Back Propagation Neural Network framework

Condition Monitoring of Pneumatic Drive Systems Based on the AI Method Feed-Forward Backpropagation Neural Network.

Machine condition monitoring is used in a variety of industries as a very efficient strategy for equipment maintenance. This paper presents a study on monitoring a pneumatic system using a feed-forward backpropagation neural network as a classifier and compares the results obtained with different sensor signals and associated extracted features as input for classification. The vibrations of the body of a pneumatic cylinder are acquired using both common industrial sensors and low-cost sensors integrated into an Arduino board. Pressure sensors for both chambers and a position sensor are also used. Power spectral density (PSD) is used to extract features from the acceleration signals, as well as statistical indices. Statistical indices are considered for pressure and position sensors. The results, which are based on experimental data obtained on a test bench, show that a feed-forward neural network makes it possible to identify the operating states with a good degree of reliability. Even with low-cost instrumentation, it is possible to realize reliable condition monitoring based on vibrations. This last result is particularly important as it can help to further increase the uptake of this maintenance approach in the industrial environment.

Comparative study of different training algorithms in backpropagation neural networks for generalized biomass higher heating value prediction

When selecting biomass feedstock for sustainable heat and electricity generation, higher heating value (HHV) is an important consideration. Meanwhile, the laboratory procedures of using an adiabatic oxygen bomb calorimeter to determine the HHV are strenuous, costly, and time-consuming. As a result, researchers have turned to artificial intelligence techniques such as artificial neural networks (ANN) to predict HHV using data from proximate analysis. Notwithstanding, this approach has been hampered by different case-specific techniques and methodologies given the heterogeneous nature of biomass materials and intricate ANN structures. This study, therefore, examined and compared the efficacy of six training algorithms comprising thirteen distinct training functions of feedforward backpropagation neural networks to predict the HHV of a variety of biomass materials as a function of the proximate analysis. In creating the networks, the neurons of the hidden layer were iterated from 1 to 20 leading to 260 investigated scenarios. Compared to other training algorithms, the Bayesian Regularization and Levenberg-Marquardt with 15 and 12 hidden neurons respectively, demonstrated superior prediction performances based on the Nash-Sutcliff's efficiencies of 0.9044 and 0.8877, and mean squared errors of 0.002271 and 0.00267. It is envisaged that this study will create an insightful paradigm for a rapid selection of best-performing ANN algorithms for biomass HHV prediction.

FFBP Neural Network Optimized with Woodpecker Mating Algorithm for Dynamic Cluster-based Secure Routing in WSN

Feed Forward Back Propagation Neural Network (FFBPNN) Optimized with Woodpecker Mating Algorithm is proposed in this manuscript for Dynamic Cluster-Based Secure Routing in Wireless Sensor Networks (FFBPNN-WMA-ECHC-WSN). The proposed method contains three different stages: first stage is dynamically clustered sensor network formation based on FFBPNN, second stage is Key generation for data encryption and decryption using Elliptic Curve-based Hill Cipher (ECHC), third stage is Homomorphic encryption scheme, which is used to deliver the aggregated data in-time. Woodpecker Mating Algorithm (WMA) is proposed to optimize the parameter values of FFBPNN. The proposed FFBPNN-WMA ECHC-WSN method was implemented in NS2 tool and its efficiency is evaluated under some metrics, like alive nodes, packet drop, network lifetime, delay, throughput, and energy consumption, Packet Delivery Ratio (PDR). The performance of FFBPNN-WMA-ECHC-WSN method provides lower delay 99.01%, 98.34%, 95.23% and 97.45%, and higher throughput 97.25%, 90.12%, 89.39% and 95.47% compared with existing models, such as EHCERA-SDT-WSN, DSA-ECC-PSO-SDT-WSN, IPECC-PDF-ABC-SDT-WSN and IBFA-LDCSN-BSHHO-SDT-WSN, respectively.

Enhancing infrastructure sustainability: reliability and sensitivity analysis of localized integrated renewable energy systems using feed forward backpropagation neural network

Enhancing infrastructure sustainability: reliability and sensitivity analysis of localized integrated renewable energy systems using feed forward backpropagation neural network

Prediction of quality characteristics of micro-channels by deep learning algorithm during laser transmission ablation of PMMA

Underwater laser transmission micro-channelling of thick transparent polymethyl methacrylate (PMMA) using a neodymium-doped yttrium aluminium garnet (Nd: YAG) laser is the focus of this study. Experiments are conducted to determine the effect of three significant variables, namely pulse frequency, lamp current, and cutting speed, on heat-affected zone (HAZ) width, cut depth, and kerf width. Experiments are designed systematically utilising the full factorial design method. The purpose of constructing empirical models, specifically non-linear ones, is to establish and clarify the relationship between control factors and corresponding responses. A feed forward backpropagation neural network (FF-BPNN) is employed for predicting the measured response. Additionally, an assessment is made between the FF-BPNN results and the values predicted by the model. On the basis of the anticipated results, it can be concluded that the FF-BPNN model is preferable in predicting both the depth of cut and kerf width. In contrast, when specifically contemplating the measurement of HAZ width, the application of a non-linear model is more advantageous. As a measure of accuracy, the mean absolute error is computed for both the feedforward backpropagation neural network (FF-BPNN) and the nonlinear modelling technique.

Prediction and optimization of Nd: YAG laser transmission micro-channelling on PMMA employing an artificial neural network model

In the present research work, performance enhancement which plays pivotal role in the modern machining techniques during machining of advanced engineering materials has been attributed. An investigation is conducted on the laser transmission micro-channeling of thick transparent PMMA using Nd: YAG laser. The objective is to examine the impact of three key factors, namely pulse frequency, lamp current and cutting speed, on several quality aspects including depth of cut, kerf width, and heat-affected zone (HAZ) width. General full factorial design is used to design the experiments and empirical models (non-linear) are developed to establish the relationship between the control factors and responses. A feed forward back-propagation neural network (FF-BPNN) is used to model the process and subsequently to predict the responses. The successful capability of FF-BPNN in predicting and enhancing the characteristics of micro-channels fabricated on PMMA has been observed. Furthermore, it has been shown that feedforward backpropagation neural networks (FF-BPNN) can serve as a highly effective tool for acquiring a comprehensive model and determining the ideal configuration of process parameters in laser transmission micro-channeling operations. Additionally, FF-BPNN results and model predicted values are compared with non-linear modelling technique. Finally, mean absolute error is calculated to find out the accuracy of both the techniques.

ANN based prediction of ligand binding sites outside deep cavities to facilitate drug designing

The ever-changing environmental conditions and pollution are the prime reasons for the onset of several emerging and re-merging diseases. This demands the faster designing of new drugs to curb the deadly diseases in less waiting time to cure the animals and humans. Drug molecules interact with only protein surface on specific locations termed as ligand binding sites (LBS). Therefore, the knowledge of LBS is required for rational drug designing. Existing geometrical LBS prediction methods rely on search of cavities based on the fact that 83% of the LBS found in deep cavities, however, these methods usually fail where LBS localize outside deep cavities. To overcome the challenge, the present work provides an artificial neural network (ANN) based method to predict LBS outside deep cavities in animal proteins including human to facilitate drug designing. In the present work a feed-forward backpropagation neural network was trained by utilizing 38 structural, atomic, physiochemical, and evolutionary discriminant features of LBS and non-LBS residues localized in the extracted roughest patch on protein surface. The performance of this ANN based prediction method was found 76% better for those proteins where cavity subspace (extracted by MetaPocket 2.0, a consensus method) failed to predict LBS due to their localization outside the deep cavities. The prediction of LBS outside deep cavities will facilitate in drug designing for the proteins where it is not possible due to lack of LBS information as the geometrical LBS prediction methods rely on extraction of deep cavities.

An artificial neural network for predicting air traffic demand based on socio-economic parameters

Over the past five years, emerging economies have consistently progressed toward achieving greater economic independence. The aviation industry has played a significant role in driving this progress. Accurately forecasting the future demand for air travel is crucial for making long-term commitments to these economies. The findings of this study provide valuable insights into the provision of low-cost passenger carrier demand. They can assist low-cost carriers, airports, airport consultants, and government agencies in their strategic planning and development processes. The primary objective of this study is to identify and evaluate artificial intelligence-based solutions, specifically, Artificial Neural Networks (ANN), to determine the most effective model for projecting domestic demand for low-cost carriers. The study analyzes nine variables that impact the accuracy of predicting domestic air passenger demand in emerging countries using a Multilayer Feed-Forward Backpropagation Neural (MFFBPN) network. The performance of the developed ANN model for predicting air passenger demand is assessed through training, validation, and testing using 240 data sets. The evaluation metrics employed, including mean square error (MSE), root mean square error (RMSE), accuracy, precision, sensitivity, and specificity, indicate the effectiveness of the developed ANN model, with results of 0.0019 for MSE, 0.0440 for RMSE, 0.92 for accuracy, 0.92 for precision, 0.93 for sensitivity, and 0.95 for specificity. We show that modeling based on artificial intelligence approaches and ANN is more effective than conventional linear regression models.

Investigation on Tensile and Flexural Behaviour of Fibre Reinforced Concrete Using Artificial Neural Network

<p>The purpose of this study is to investigate the impact that using marble sludge powder as a partial replacement for cement in concrete can have. Experiments were conducted to investigate a variety of characteristics of fiber-reinforced concrete using both fresh concrete and concrete that had been allowed to solidify. In order to determine the split tensile and flexural property of FRC, two water binder ratios, such as 0.35 and 0.40, as well as percentage re-placements of 0%, 5%, 10%, 15%, 20%, and 25% of marble sludge powder and 0.5% of polypropylene 3S fibre were used. After curing for 7, 14, 28, and 56 days, the samples were put through a battery of mechanical tests to evaluate their qualities. The flexural strength and split tensile strength of the material were evaluated over the course of this investigation. In the end, an artificial neural network, also known as an ANN, was utilised in order to create a prediction model for split tensile and flexural strength. We displayed the experimentally obtained Split Tensile Strength and Flexural Strength against the regression analysis strength after 56 days for ANN. This was done so that we could compare the two. According to the findings of the experiments, using powder made from marble waste might lessen the damage that concrete causes to the environment while also providing economic benefits. In this study, dependable mechanical strength was developed by the use of a feed-forward back-propagation neural network, which consisted of eight input neurons, two hidden neurons, and one output neuron. According to the findings, it was discovered that the mechanical properties of concrete might be improved by using dry marble sludge powder as a substitute for up to 15% of the normal aggregate.</p>

Investigating Feed-Forward Back-Propagation Neural Network with Different Hyperparameters for Inverse Kinematics of a 2-DoF Robotic Manipulator: A Comparative Study

Inverse kinematics is a significant challenge in robotic manipulators, and finding practical solutions plays a crucial role in achieving precise control. This paper presents a study on solving inverse kinematics problems using the Feed-Forward Back-Propagation Neural Network (FFBP-NN) and examines its performance with different hyperparameters. By utilizing the FFBP-NN, our primary objective is to ascertain the joint angles required to attain precise Cartesian coordinates for the end-effector of the manipulator. To accomplish this, we first formed three input-output datasets (a fixed-step-size dataset, a random-step-size dataset, and a sinusoidal-signal-based dataset) of joint positions and their respective Cartesian coordinates using direct geometrical formulations of a two-degree-of-freedom (2-DoF) manipulator. Thereafter, we train the FFBP-NN with the generated datasets using the MATLAB Neural Network Toolbox and investigate its potential by altering the hyperparameters (e.g., number of hidden neurons, number of hidden layers, and training optimizer). Three different training optimizers are considered, namely the Levenberg-Marquardt (LM) algorithm, the Bayesian Regularization (BR) algorithm, and the Scaled Conjugate Gradient (SCG) algorithm. The Mean Squared Error is used as the main performance metric to evaluate the training accuracy of the FFBP-NN. The comparative outcomes offer valuable insights into the capabilities of various network architectures in addressing inverse kinematics challenges. Therefore, this study explores the application of the FFBP-NNs in tackling the inverse kinematics, and facilitating the choice of the most appropriate network design by achieving a portfolio of various experimental results by considering and varying different hyperparameters of the FFBP-NN.

Feedforward neural network-based augmented salp swarm optimizer for accurate software development cost forecasting

This research proposes the use of feed-forward backpropagation neural networks (FFNN) to develop an accurate cost forecasting model in light of the challenges associated with forecasting software development costs (FSDC). The salp swarm algorithm (SSA) is first augmented and then employed to optimize the parameters of the developed FFNN predictor. A search enhancement mechanism and an elitism technique have been developed and incorporated into the SSA optimization process as two fresh and effective techniques for this goal. The search enhancement mechanism is employed to keep up a high rate of global exploration while also driving convergence towards the optimal area. Whereas elitism is used throughout the research phase to prevent stagnation in the local optima. Nineteen benchmark test functions and twelve benchmark software development cost forecasting data sets are utilized to assess the performance of the recommended enhancement techniques and developed algorithms. The results obtained from experiments show the superiority of the proposed techniques. In addition, the developed technique has been compared with many state-of-the-art methods, which demonstrates its durability. This is in addition to the statistical validation carried out on the results obtained, which also supports the robustness of the proposed technique.

Boosting flood routing prediction performance through a hybrid approach using empirical mode decomposition and neural networks: a case study of the Mera River in Ankara

Abstract Flood routing is vital in helping to reduce the impact of floods on people and communities by allowing timely and appropriate responses. In this study, the empirical mode decomposition (EMD) signal decomposition technique is combined with cascade forward backpropagation neural network (CFBNN) and feed-forward backpropagation neural network (FFBNN) machine learning (ML) techniques to model 2014 floods in Ankara, Mera River. The data are split in order to avoid the underfitting and overfitting problems of the algorithm. While establishing the algorithm, 70% of the data were divided into training, 15% testing and 15% validation. Graphical indicators and statistical parameters were used for the analysis of model performance. As a result, the EMD signal decomposition technique has been found to improve the performance of ML models. In addition, the EMD-FFBNN hybrid model showed the most accurate estimation results in the flood routing calculation. The study's outputs can assist in designing flood control structures such as levees and dams to help reduce flood risk.

Jellyfish optimized recurrent neural network for state of health estimation of lithium-ion batteries

The state of health (SOH) of lithium-ion batteries is considered an important health indicator to evaluate different features such as efficiency, robustness, and accuracy. The SOH of the lithium-ion battery is investigated to determine the advent of failures to mitigate the battery risk, avoid uneven fault occurrences and ensure safe battery operation. Nonetheless, the accurate assessment of SOH is difficult due to the occurrence of capacity degradation and performance deviation with temperature and aging impacts. Therefore, this work presents an improved hybrid recurrent neural network (RNN) and jellyfish optimization (JFO) to estimate the SOH of lithium-ion batteries. A total of 124 lithium-ion battery cells classified in three batches, namely ‘2017-05-12’, ‘2017-06-30’, and ‘2018-04-12’ from the MIT Stanford- Toyota Research Institute battery database, are used for the proposed work. The systematic sampling method is utilized for developing a 31-dimensional data format. The 31-dimensional data format is developed considering various critical battery parameters such as capacity, voltage, current, and temperature. The JFO is applied to achieve the best suitable RNN model hyperparameters for accurate estimation outcomes. The validation of the hybrid RNN-JFO method is conducted with other JFO-optimized neural network (NN) models, such as feedforward neural network (FFNN) and backpropagation neural network (BPNN). Compared with FFNN-JFO and BPNN-JFO models, the experiment conducted with the RNN-JFO method delivered accurate outcomes. For the batches ‘2017-05-12’, ‘2017-06-30’, and ‘2018-04-12’, the average root mean square error (RMSE) error achieved with the RNN-JFO model was 0.0529, 0.2674, and 0.1638. The SOH estimation outcomes confirm the effectiveness of the RNN-JFO method for SOH estimation on different lithium-ion batteries.

Comparative study of surface roughness prediction using neural-network and quadratic-rotatable-central-composite-design

The act of sustainable manufacturing lies in the response's prediction analysis, such as surface roughness during machining operations with nano-lubricant. This research focuses on developing a mathematical model to predict the experimental results of surface roughness of AA8112 alloys obtained during the end-milling process with an eco-friendly nano-lubricant. The study employed vegetable oil as the base cutting fluid (copra oil) and Titanium-dioxide (TiO2) nanoparticles as an additive. The end-milling machining was carried out with five machining parameters. The prediction analysis was done with a backpropagation feed-forward neural network (BPNN) and quadratic rotatable central composite design (QRCCD). The results show that the BPNN predicted the experimental results with 99.85%, and the QRCCD predicted 91.1%. The error percentage from both prediction analyses is 0.2% from the BPNN and 0.9% from the QRCCD. Therefore, the application of BPNN has proven viable in predicting surface roughness in machining operations. It will also improve the manufacturing industry's productivity and eliminate the high rate of waste materials during machining.

A new comprehensive model of thermal conductivity for hydrofluoroolefins refrigerants using feed-forward back-propagation neural networks

A new comprehensive model of thermal conductivity for hydrofluoroolefins refrigerants using feed-forward back-propagation neural networks