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Weather forecasting is the trending topic around the world as it is the way to predict the threats posed by extreme rainfall conditions that lead to damage the human life and properties. These issues can be managed only when the occurrence of the worse weather is predicted in advance, and sufficient warnings can be executed in time. Thus, keeping in mind the importance of the rainfall prediction system, the purpose of this paper is to propose an effective rainfall prediction model using the nonlinear auto-regressive with external input (NARX) model.

The paper proposes a rainfall prediction model using the time-series prediction that is enabled using the NARX model. The time-series prediction ensures the effective prediction of the rainfall in a particular area or the locality based on the rainfall data in the previous term or month or year. The proposed NARX model serves as an adaptive prediction model, for which the rainfall data of the previous period is the input, and the optimal computation is based on the proposed algorithm. The adaptive prediction using the proposed algorithm is exhibited in the NARX, and the proposed algorithm is developed based on the Grey Wolf Optimization and the Levenberg–Marqueret (LM) algorithm. The proposed algorithm inherits the advantages of both the algorithms with better computational time and accuracy.

The analysis using two databases enables the better understanding of the proposed rainfall detection methods and proves the effectiveness of the proposed prediction method. The effectiveness of the proposed method is enhanced and the accuracy is found to be better compared with the other existing methods and the mean square error and percentage root mean square difference of the proposed method are found to be around 0.0093 and 0.207.

The rainfall prediction is enabled adaptively using the proposed Grey Wolf Levenberg–Marquardt (GWLM)-based NARX, wherein an algorithm, named GWLM, is proposed by the integration of Grey Wolf Optimizer and LM algorithm.

This study constructs time series model, artificial neural networks (ANNs) and statistical topologies to examine the volatility and forecast foreign exchange rates. The Mauritian forex market has been utilized as a case study, and daily data for nominal spot rate (during a time period of five years spanning from 2014 to 2018) for EUR/MUR, GBP/MUR, CAD/MUR and AUD/MUR have been applied for the predictions.

Autoregressive integrated moving average (ARIMA) and generalized autoregressive conditional heteroskedasticity (GARCH) models are used as a basis for time series modelling for the analysis, along with the non-linear autoregressive network with exogenous inputs (NARX) neural network backpropagation algorithm utilizing different training functions, namely, Levenberg–Marquardt (LM), Bayesian regularization and scaled conjugate gradient (SCG) algorithms. The study also features a hybrid kernel principal component analysis (KPCA) using the support vector regression (SVR) algorithm as an additional statistical tool to conduct financial market forecasting modelling. Mean squared error (MSE) and root mean square error (RMSE) are employed as indicators for the performance of the models.

The results demonstrated that the GARCH model performed better in terms of volatility clustering and prediction compared to the ARIMA model. On the other hand, the NARX model indicated that LM and Bayesian regularization training algorithms are the most appropriate method of forecasting the different currency exchange rates as the MSE and RMSE seemed to be the lowest error compared to the other training functions. Meanwhile, the results reported that NARX and KPCA–SVR topologies outperformed the linear time series models due to the theory based on the structural risk minimization principle. Finally, the comparison between the NARX model and KPCA–SVR illustrated that the NARX model outperformed the statistical prediction model. Overall, the study deduced that the NARX topology achieves better prediction performance results compared to time series and statistical parameters.

The foreign exchange market is considered to be instable owing to uncertainties in the economic environment of any country and thus, accurate forecasting of foreign exchange rates is crucial for any foreign exchange activity. The study has an important economic implication as it will help researchers, investors, traders, speculators and financial analysts, users of financial news in banking and financial institutions, money changers, non-banking financial companies and stock exchange institutions in Mauritius to take investment decisions in terms of international portfolios. Moreover, currency rates instability might raise transaction costs and diminish the returns in terms of international trade. Exchange rate volatility raises the need to implement a highly organized risk management measures so as to disclose future trend and movement of the foreign currencies which could act as an essential guidance for foreign exchange participants. By this way, they will be more alert before conducting any forex transactions including hedging, asset pricing or any speculation activity, take corrective actions, thus preventing them from making any potential losses in the future and gain more profit.

This is one of the first studies applying artificial intelligence (AI) while making use of time series modelling, the NARX neural network backpropagation algorithm and hybrid KPCA–SVR to predict forex using multiple currencies in the foreign exchange market in Mauritius.

There has been a growing concern about air quality because in recent years, industrial and vehicle emissions have resulted in unsatisfactory human health conditions. There is an urgent need for the measurements and estimations of particulate pollutants levels, especially in urban areas. As a contribution to this issue, the purpose of this paper is to use data from measured concentrations of particulate matter and meteorological conditions for the predictions of PM₁₀.

The procedure included daily data collection of current PM₁₀ concentrations for the city of São Carlos-SP, Brazil. These data series enabled to use an estimator based on artificial neural networks. Data sets were collected using the high-volume sampler equipment (VFA-MP10) in the period ranging from 1997 to 2006 and from 2014 to 2015. The predictive models were created using statistics from meteorological data. The models were developed using two neural network architectures, namely, perceptron multilayer (MLP) and non-linear autoregressive exogenous (NARX) inputs network.

It was observed that, over time, there was a decrease in the PM₁₀ concentration rates. This is due to the implementation of more strict environmental laws and the development of less polluting technologies. The model NARX that used as input layer the climatic variables and the PM₁₀ of the previous day presented the highest average absolute error. However, the NARX model presented the fastest convergence compared with the MLP network.

The presentation of a given PM₁₀ concentration of the previous day improved the performance of the predictive models. This paper brings contributions with the NARX model applications.

The purpose of this paper is to predict the daily accuracy improvement for the Jakarta Islamic Index (JKII) prices using deep learning (DL) with small and big data of symmetric volatility information.

This paper uses the nonlinear autoregressive exogenous (NARX) neural network as the optimal DL approach for predicting daily accuracy improvement through small and big data of symmetric volatility information of the JKII based on the criteria of the highest accuracy score of testing and training. To train the neural network, this paper employs the three DL techniques, namely Levenberg–Marquardt (LM), Bayesian regularization (BR) and scaled conjugate gradient (SCG).

The experimental results show that the optimal DL technique for predicting daily accuracy improvement of the JKII prices is the LM training algorithm based on using small data which provide superior prediction accuracy to big data of symmetric volatility information. The LM technique develops the optimal network solution for the prediction process with 24 neurons in the hidden layer across a delay parameter equal to 20, which affords the best predicting accuracy based on the criteria of mean squared error (MSE) and correlation coefficient.

This research would fill a literature gap by offering new operative techniques of DL to predict daily accuracy improvement and reduce the trading risk for the JKII prices based on symmetric volatility information.

This research is the first that predicts the daily accuracy improvement for JKII prices using DL with symmetric volatility information.

This paper aims to investigate the profile of the wind speed of a Cameroonian city for the very first time, as there is a growing trend for new wind energy installations in the West region of Cameroon. Two well-known artificial neural networks, namely, multi-layer perceptron (MLP) and nonlinear autoregressive network with exogenous inputs (NARX), were used to model the wind speed profile of the city of Bapouh in the West-region of Cameroon.

In this work, the profile of the wind speed of a Cameroonian city was investigated for the very first time since there is a growing trend for new wind energy installations in the West region of Cameroon. Two well-known artificial neural networks namely multi-layer perceptron (MLP) and nonlinear autoregressive network with exogenous inputs (NARX) were used to model the wind speed profile of the city of Bapouh in the West-region of Cameroon. The meteorological data were collected every 10 min, at a height of 50 m from the NASA website over a period of two months from December 1, 2016 to January 31, 2017. The performance of the model was evaluated using some well-known statistical tools, such as root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE). The input variables of the model were the mean wind speed, wind direction, maximum pressure, maximum temperature, time and relative humidity. The maximum wind speed was used as the output of the network. For optimal prediction, the influence of meteorological variables was investigated. The hyperbolic tangent sigmoid (Tansig) and linear (Purelin) were used as activation functions, and it was shown that the combination of wind direction, maximum pressure, maximum relative humidity and time as input variables is the best combination.

Maximum pressure, maximum relative humidity and time as input variables is the best combination. The correlation between MLP and NARX was computed. It was found that the MLP has the highest correlation when compared to NARX.

Two well-known artificial neural networks namely multi-layer perceptron (MLP) and nonlinear autoregressive network with exogenous inputs (NARX) were used to model the wind speed profile.

Natural flood disasters frequently happen in Malaysia especially during monsoon season and Kuala Kangsar, Perak, is one of the cities with the frequent record of natural flood disasters. Previous flood disaster faced by this city showed the failure in notifying the citizen with sufficient time for preparation and evacuation. The authority in charge of the flood disaster in Kuala Kangsar depends on the real-time monitoring from the hydrological sensor located at several stations along the main river. The real-time information from hydrological sensor failed to provide early notification and warning to the public. Although many hydrological sensors are available at the stations, only water level sensors and rainfall sensors are used by authority for flood monitoring. This study developed a flood prediction model using artificial intelligence to predict the incoming flood in Kuala Kangsar area based on artificial neural network (ANN). The flood prediction model is expected to predict the incoming flood disaster by using information from the variety of hydrological sensors. The study finds that the proposed ANN model based on nonlinear autoregressive network with exogenous inputs (NARX) has better performance than other models with the correlation coefficient that is equal to 0.98930. The NARX model of flood prediction developed in this study can be referred to as the future flood prediction model in Kuala Kangsar, Perak.

This paper aims to establish a multi-input equilibrium manifold expansion (EME) model for gas turbine (GT). It proposes that the extension of model input dimension is realized based on similarity theory and affine structure in the framework of single-input EME model. The study aims to expand the scope of application of the EME model so that it can be used for the control or fault diagnosis of GTs.

In this paper, the concepts of corrected equilibrium manifold expansion (CEME) model and multi-cell equilibrium manifold expansion (MEME) model are first proposed. This paper uses theoretical analysis and simulation experiments to demonstrate the effectiveness of the bilayer equilibrium manifold expansion (BEME) model, which is a combination of the CEME and the MEME models. Simulation experiments include confirmatory experiments and comparative experiments.

The paper provides a new sight into building a multiple-input EME (MI-EME) model for GTs. The proposed method can build an accurate and robust MI-EME model that has superior performance compared with widely used nonlinear models including Wiener model (WM), Hammerstein model (HM), Hammerstein–Wiener model (HWM) and nonlinear autoregressive with exogenous inputs (NARX) network model. In terms of accuracy, the maximum error percentage of the proposed model is just 1.309%, far less than WM, HM and HWM. In terms of the stability of model calculation, the range of the mean error percentage of the proposed model is just a quarter of that of NARX network model.

The paper fulfills the construction of a novel multi-input nonlinear model, which has laid a foundation for the follow-up research of model-based GT fault detection and isolation or GT control.

The purpose of this paper is to investigate the dynamic relationship between inflation, interest rate differential, the exchange trade and exchange rate parities, i.e. (USD/TND, EUR/TND and JPY/TND).

Given the existing non-linear form between the different time series in this study, the empirical analysis is based on the using of non-parametric method such as the artificial neural networks. In order to detect the causality relationship between the variables, the authors use an NARX model.

Mixed results were found; there is a bidirectional relationship between inflation and exchange rate among others. Results also show that there is a strong correlation between the terms of trade and inflation, which says that trade openness increases the demand for imported goods and, therefore, causes more inflation for Tunisia.

After these results, it is important for policymakers to know which factors influence exchange rate stability, especially in developing countries like Tunisia.

This paper seeks to present a feedback error learning neuro‐controller for an unstable research helicopter.

Three neural‐aided flight controllers are designed to satisfy the ADS‐33 handling qualities specifications in pitch, roll and yaw axes. The proposed controller scheme is based on feedback error learning strategy in which the outer loop neural controller enhances the inner loop conventional controller by compensating for unknown non‐linearity and parameter uncertainties. The basic building block of the neuro‐controller is a nonlinear auto regressive exogenous (NARX) input neural network. For each neural controller, the parameter update rule is derived using Lyapunov‐like synthesis. An offline finite time training is used to provide asymptotic stability and on‐line learning strategy is employed to handle parameter uncertainty and nonlinearity.

The theoretical results are validated using simulation studies based on a nonlinear six degree‐of‐freedom helicopter undergoing an agile maneuver. The neural controller performs well in disturbance rejection is the presence of gust and sensor noise.

The neuro‐control approach presented in this paper is well suited to unmanned and small‐scale helicopters.

The study shows that the neuro‐controller meets the requirements of ADS‐33 handling qualities specifications of a helicopter.