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1

Blanchard, Tyler, and Biswanath Samanta. "Wind speed forecasting using neural networks." Wind Engineering 44, no. 1 (2019): 33–48. http://dx.doi.org/10.1177/0309524x19849846.

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The prediction of wind speed is critical in the assessment of feasibility of a potential wind turbine site. This work presents a study on prediction of wind speed using artificial neural networks. Two variations of artificial neural networks, namely, nonlinear autoregressive neural network and nonlinear autoregressive neural network with exogenous inputs, were used to predict wind speed utilizing 1 year of hourly weather data from four locations around the United States to train, validate, and test these networks. This study optimized both neural network configurations and it demonstrated that both models were suitable for wind speed prediction. Both models outperformed persistence model (with a factor of about 2 to 10 in root mean square error ratio). Both artificial neural network models were implemented for single-step and multi-step-ahead prediction of wind speed for all four locations and results were compared. Nonlinear autoregressive neural network with exogenous inputs model gave better prediction performance than nonlinear autoregressive model and the difference was statistically significant.
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2

Grande, Davide, Catherine A. Harris, Giles Thomas, and Enrico Anderlini. "Data-Driven Stability Assessment of Multilayer Long Short-Term Memory Networks." Applied Sciences 11, no. 4 (2021): 1829. http://dx.doi.org/10.3390/app11041829.

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Recurrent Neural Networks (RNNs) are increasingly being used for model identification, forecasting and control. When identifying physical models with unknown mathematical knowledge of the system, Nonlinear AutoRegressive models with eXogenous inputs (NARX) or Nonlinear AutoRegressive Moving-Average models with eXogenous inputs (NARMAX) methods are typically used. In the context of data-driven control, machine learning algorithms are proven to have comparable performances to advanced control techniques, but lack the properties of the traditional stability theory. This paper illustrates a method to prove a posteriori the stability of a generic neural network, showing its application to the state-of-the-art RNN architecture. The presented method relies on identifying the poles associated with the network designed starting from the input/output data. Providing a framework to guarantee the stability of any neural network architecture combined with the generalisability properties and applicability to different fields can significantly broaden their use in dynamic systems modelling and control.
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3

Boynton, R. J., M. A. Balikhin, and S. A. Billings. "Online NARMAX model for electron fluxes at GEO." Annales Geophysicae 33, no. 3 (2015): 405–11. http://dx.doi.org/10.5194/angeo-33-405-2015.

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Abstract. Multi-input single-output (MISO) nonlinear autoregressive moving average with exogenous inputs (NARMAX) models have been derived to forecast the > 0.8 MeV and > 2 MeV electron fluxes at geostationary Earth orbit (GEO). The NARMAX algorithm is able to identify mathematical model for a wide class of nonlinear systems from input–output data. The models employ solar wind parameters as inputs to provide an estimate of the average electron flux for the following day, i.e. the 1-day forecast. The identified models are shown to provide a reliable forecast for both > 0.8 and > 2 MeV electron fluxes and are capable of providing real-time warnings of when the electron fluxes will be dangerously high for satellite systems. These models, named SNB3GEO > 0.8 and > 2 MeV electron flux models, have been implemented online at http://www.ssg.group.shef.ac.uk/USSW/UOSSW.html.
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4

Talla Konchou, Franck Armel, Pascalin Tiam Kapen, Steve Brice Kenfack Magnissob, Mohamadou Youssoufa, and René Tchinda. "Prediction of wind speed profile using two artificial neural network models: an ab initio investigation in the Bapouh’s city, Cameroon." International Journal of Energy Sector Management 15, no. 3 (2021): 566–77. http://dx.doi.org/10.1108/ijesm-04-2020-0008.

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Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.
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5

Laadissi, El Mehdi, Anas El Filali, and Malika Zazi. "A Nonlinear TSNN Based Model of a Lead Acid Battery." Bulletin of Electrical Engineering and Informatics 7, no. 2 (2018): 169–75. http://dx.doi.org/10.11591/eei.v7i2.675.

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The paper studies a nonlinear model based on time series neural network system (TSNN) to improve the highly nonlinear dynamic model of an automotive lead acid cell battery. Artificial neural network (ANN) take into consideration the dynamic behavior of both input-output variables of the battery charge-discharge processes. The ANN works as a benchmark, its inputs include delays and charging/discharging current values. To train our neural network, we performed a pulse discharge on a lead acid battery to collect experimental data. Results are presented and compared with a nonlinear Hammerstein-Wiener model. The ANN and nonlinear autoregressive exogenous model (NARX) models achieved satisfying results.
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El, Mehdi Laadiss, El Filali Anas, and Zazi Malika. "A Nonlinear TSNN Based Model of a Lead Acid Battery." Bulletin of Electrical Engineering and Informatics 7, no. 2 (2018): 169–75. https://doi.org/10.11591/eei.v7i2.675.

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The paper studies a nonlinear model based on time series neural network system (TSNN) to improve the highly nonlinear dynamic model of an automotive lead acid cell battery. Artificial neural network (ANN) take into consideration the dynamic behavior of both input-output variables of the battery charge-discharge processes. The ANN works as a benchmark, its inputs include delays and charging/discharging current values. To train our neural network, we performed a pulse discharge on a lead acid battery to collect experimental data. Results are presented and compared with a nonlinear Hammerstein-Wiener model. The ANN and nonlinear autoregressive exogenous model (NARX) models achieved satisfying results.
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7

Ghalei, Pouya, Alireza Fatehi, and Mohamadreza Arvan. "Two-Degree-of-Freedom Helicopter Closed-Loop Identification through a Cascade Controller." Advanced Materials Research 403-408 (November 2011): 4649–58. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.4649.

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Input-Output data modeling using multi layer perceptron networks (MLP) for a laboratory helicopter is presented in this paper. The behavior of the two degree-of-freedom platform exemplifies a high order unstable, nonlinear system with significant cross-coupling between pitch and yaw directional motions. This paper develops a practical algorithm for identifying nonlinear autoregressive model with exogenous inputs (NARX) and nonlinear output error model (NOE) through closed loop identification. In order to collect input-output identifier pairs, a cascade state feedback (CSF) controller is introduced to stabilize the helicopter and after that the procedure of system identification is proposed. The estimated models can be utilized for nonlinear flight simulation and control and fault detection studies.
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8

Whyte, J. M., A. Plumridge, and A. V. Metcalfe. "Comparison of predictions of rainfall-runoff models for changes in rainfall in the Murray-Darling Basin." Hydrology and Earth System Sciences Discussions 8, no. 1 (2011): 917–55. http://dx.doi.org/10.5194/hessd-8-917-2011.

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Abstract. Management of water resources requires an appreciation for how climate change, in particular changes in rainfall, affects the volume of water available in runoff. While there are many studies that use hydrological models for this purpose, comparisons of predictions appear much less commonly in the literature. This paper aims to contribute to this discussion by proposing methods for evaluating the effect on daily runoff projections of rainfall-runoff models when historical daily rainfall inputs are scaled by factors that increase and decrease the rainfall. Considered are the widely used lumped conceptual model SIMHYD and a selection of time series models which feature lagged runoff and rainfall terms. In particular these are AutoRegressive with eXogenous input (ARX), a variant containing nonlinear autoregressive runoff terms (NARX), a model for the log transform of runoff, a finite impulse response model (FIR) and a two regime threshold autoregressive model with exogenous input (TARX). Results show that SIMHYD and the single regime time series models considered have very different behaviour under scaled input rainfall. Reasons for the discrepancy are discussed. The amplification of the rainfall change observed for SIMHYD is consistent with claims that a 1% change in rainfall leads to a 2–3% change in runoff in the Murray-Darling Basin.
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9

Hou, Dehao, Wenjun Ma, Lingyan Hu, et al. "Modeling of Nonlinear SOEC Parameter System Based on Data-Driven Method." Atmosphere 14, no. 9 (2023): 1432. http://dx.doi.org/10.3390/atmos14091432.

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Based on the basic nonlinear parameter system of the solid oxide electrolysis cell, the data-driven method was used for system identification. The basic model of the solid oxide electrolysis cell was accomplished in Simulink and experiments were performed under a diversified input/output operating environment. The experimental results of the solid oxide electrolysis cell basic parameter system generated 15 datasets. The system identification process involved the utilization of these datasets with the application of nonlinear autoregressive-exogenous models. Initially, data identification came from the Matlab mechanism model. Then, the nonlinear autoregressive-exogenous structures were estimated and selected exploratively through an individual operating condition. In terms of fitness, we conclude that the solid oxide electrolysis cell parameter system cannot be satisfied by a solitary autoregressive-exogenous model for all datasets. Nevertheless, the nonlinear autoregressive-exogenous model utilized S-type nonlinearities to fit a total of 2 validation datasets and 15 estimated datasets. The obtained results were compared with the basic parameter system of a solid oxide electrolysis cell, and the nonlinear autoregressive-exogenous projected output demonstrated an accuracy of over 93% across diverse operational circumstances—regardless of whether there was noise interference. This result has positive significance for the future use of the solid oxide electrolysis cell to achieve the dual carbon goal in China.
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10

Khan, Mushtaq Hussain, Shreya Macherla, and Angesh Anupam. "Nonlinear connectedness of conventional crypto-assets and sustainable crypto-assets with climate change: A complex systems modelling approach." PLOS ONE 20, no. 2 (2025): e0318647. https://doi.org/10.1371/journal.pone.0318647.

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Earlier studies used classical time series models to forecast the nonlinear connectedness of conventional crypto-assets with CO2 emissions. For the first time, this study aims to provide a data-driven Nonlinear System Identification technique to study the nonlinear connectedness of crypto-assets with CO2 emissions. Using daily data from January 2, 2019, to March 31, 2023, we investigate the nonlinear connectedness among conventional crypto-assets, sustainable crypto-assets, and CO2 emissions based on our proposed model, Multiple Inputs Single Output (MISO) Nonlinear Autoregressive with Exogenous Inputs (NARX). Intriguingly, the forecasting accuracy of the proposed model improves with the inclusion of exogenous input variables (conventional and sustainable crypto-assets). Overall, our results reveal that conventional crypto-assets exhibit slightly stronger connectedness with CO2 emissions compared to sustainable crypto-assets. These findings suggest that, to some extent, sustainable crypto-assets provide a solution to the environmental issues related to CO2 emissions. However, further improvements in sustainable crypto-assets through technological advances are required to develop more energy-efficient decentralised finance consensus algorithms, with the aim of reshaping the cryptocurrency ecosystem into an environmentally sustainable market.
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11

Li, Guoqi, Changyun Wen, Wei Xing Zheng, and Yan Chen. "Identification of a Class of Nonlinear Autoregressive Models With Exogenous Inputs Based on Kernel Machines." IEEE Transactions on Signal Processing 59, no. 5 (2011): 2146–59. http://dx.doi.org/10.1109/tsp.2011.2112355.

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12

Sani, Muhammad Gaya, Norhaliza Abdul Wahab, Yahya M. Sam, Sharatul Izah Samsudin, and Irma Wani Jamaludin. "Comparison of NARX Neural Network and Classical Modelling Approaches." Applied Mechanics and Materials 554 (June 2014): 360–65. http://dx.doi.org/10.4028/www.scientific.net/amm.554.360.

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Classical optimization tools are effective when precise mechanistic models exist to support their design and implementation. However, most of the real-world processes are complex due to either nonlinearities or uncertainties (or both) and environmental variations, thus making realizing accurate mathematical models for such processes quite difficult or often impossible. Black box approach tends to present a better alternative in such situations. This paper presents a comparison of nonlinear autoregressive with eXogenous (NARX) neural network and traditional modelling techniques [autoregressive with exogenous input (ARX) and autoregressive moving average with exogenous input (ARMAX)]. The models were validated using experimental data from full-scale plants. Simulation results revealed that the performance of the NARX neural network is better compared to the ARMAX and ARX. The NARX neural network may serve as a valuable forecasting tool for the plants.
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13

El Ghazouli, Khalid, Jamal El Khattabi, Isam Shahrour, and Aziz Soulhi. "Wastewater flow forecasting model based on the nonlinear autoregressive with exogenous inputs (NARX) neural network." H2Open Journal 4, no. 1 (2021): 276–90. http://dx.doi.org/10.2166/h2oj.2021.107.

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Abstract Wastewater flow forecasts are key components in the short- and long-term management of sewer systems. Forecasting flows in sewer networks constitutes a considerable uncertainty for operators due to the nonlinear relationship between causal variables and wastewater flows. This work aimed to fill the gaps in the wastewater flow forecasting research by proposing a novel wastewater flow forecasting model (WWFFM) based on the nonlinear autoregressive with exogenous inputs neural network, real-time, and forecasted water consumption with an application to the sewer system of Casablanca in Morocco. Furthermore, this research compared the two approaches of the forecasting model. The first approach consists of forecasting wastewater flows on the basis of real-time water consumption and infiltration flows, and the second approach considers the same input in addition to water distribution flow forecasts. The results indicate that both approaches show accurate and similar performances in predicting wastewater flows, while the forecasting horizon does not exceed the watershed lag time. For prediction horizons that exceed the lag time value, the WWFFM with water distribution forecasts provided more reliable forecasts for long-time horizons. The proposed WWFFM could benefit operators by providing valuable input data for predictive models to enhance sewer system efficiency.
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Khalid, EL GHAZOULI, EL KHATABI Jamal, SHAHROUR Isam, and SOULHI Aziz. "Comparison of M5 Model Tree and Nonlinear Autoregressive with eXogenous inputs (NARX) Neural Network for urban stormwater discharge modelling." MATEC Web of Conferences 295 (2019): 02002. http://dx.doi.org/10.1051/matecconf/201929502002.

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This paper presents a comparative study of two data-driven modelling techniques in forecasting urban drainage stormwater discharge based on rainfall prediction. Both M5T and NARX (Nonlinear Autoregressive with eXogenous inputs) Neural Network are used for 30 minutes storm water forecasting. Data are collected from watershed area of 3315 ha, located in the city of Casablanca in Morocco. The results show that both models provide good results, but however with better performances of the NARX model.
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Meriem, Mossaddek, Mehdi Laadissi El, Ennawaoui Chouaib, Bouzaid Sohaib, and Hajjaji Abdelowahed. "Enhancing battery system identification: nonlinear autoregressive modeling for Li-ion batteries." International Journal of Electrical and Computer Engineering (IJECE) 14, no. 3 (2024): 2449–56. https://doi.org/10.11591/ijece.v14i3.pp2449-2456.

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Precisely characterizing Li-ion batteries is essential for optimizing their performance, enhancing safety, and prolonging their lifespan across various applications, such as electric vehicles and renewable energy systems. This article introduces an innovative nonlinear methodology for system identification of a Li-ion battery, employing a nonlinear autoregressive with exogenous inputs (NARX) model. The proposed approach integrates the benefits of nonlinear modeling with the adaptability of the NARX structure, facilitating a more comprehensive representation of the intricate electrochemical processes within the battery. Experimental data collected from a Li-ion battery operating under diverse scenarios are employed tovalidate the effectiveness of the proposed methodology. The identified NARX model exhibits superior accuracy in predicting the battery's behavior compared to traditional linear models. This study underscores the importance of accounting for nonlinearities in battery modeling, providing insights into the intricate relationships between state-of-charge, voltage, and current under dynamic conditions.
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Nikolic, Sasa S., Miroslav B. Milovanovic, Nikola B. Dankovic, et al. "Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions." Elektronika ir Elektrotechnika 29, no. 2 (2023): 4–11. http://dx.doi.org/10.5755/j02.eie.33838.

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Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, and a new improvement is proposed, which is consisted of the basic structure of Hammerstein-Wiener models with an improved orthogonal function of Müntz-Legendre type. We present an extension of generalised Malmquist polynomials that represent Müntz polynomials. Also, a detailed mathematical background for performing improved almost orthogonal polynomials, in combination with Hammerstein-Wiener models, is proposed. The proposed approach is used to identify the strongly nonlinear hydraulic system via the transfer function. To compare the results obtained, well-known orthogonal functions of the Legendre, Chebyshev, and Laguerre types are exploited.
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Alsumaiei, Abdullah A. "A Nonlinear Autoregressive Modeling Approach for Forecasting Groundwater Level Fluctuation in Urban Aquifers." Water 12, no. 3 (2020): 820. http://dx.doi.org/10.3390/w12030820.

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The application of a nonlinear autoregressive modeling approach with exogenous input (NARX) neural networks for modeling groundwater level fluctuation has been examined by several researchers. However, the suitability of NARX in modeling groundwater level dynamics in urbanized and arid aquifer systems has not been comprehensively investigated. In this study, a NARX-based modeling approach is presented to establish a robust water management tool to aid urban water managers in controlling the development of shallow water tables induced by artificial recharge activity. Temperature data series are used as exogenous inputs for the NARX network, as they better reflect the intensity of artificial recharge activities, such as excessive lawns irrigation. Input delays and feedback delays for the NARX networks are determined based on the autocorrelation and cross-correlation analyses of detrended groundwater levels and monthly temperature averages. The validation of the proposed approach is assessed through a rolling validation procedure. Four observation wells in Kuwait City are selected to test the applicability of the proposed approach. The results showed the superiority of the NARX-based approach in modeling groundwater levels in such an urbanized and arid aquifer system, with coefficient of determination (R2) values ranging between 0.762 and 0.994 in the validation period. Comparison with other statistical models applied to the same study area shows that NARX models presented here reduced the mean absolute error (MAE) of groundwater levels forecasts by 50%. The findings of this paper are promising and provide a valuable tool for the urban city planner to assist in controlling the problem of shallow water tables for similar climatic and aquifer systems.
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18

Zhang, Wanxin, Jihong Zhu, and Dongbing Gu. "Identification of robotic systems with hysteresis using Nonlinear AutoRegressive eXogenous input models." International Journal of Advanced Robotic Systems 14, no. 3 (2017): 172988141770584. http://dx.doi.org/10.1177/1729881417705845.

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19

El Hamidi, Khadija, Mostafa Mjahed, Abdeljalil El Kari, and Hassan Ayad. "Adaptive Control Using Neural Networks and Approximate Models for Nonlinear Dynamic Systems." Modelling and Simulation in Engineering 2020 (August 26, 2020): 1–13. http://dx.doi.org/10.1155/2020/8642915.

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In this research, a comparative study of two recurrent neural networks, nonlinear autoregressive with exogenous input (NARX) neural network and nonlinear autoregressive moving average (NARMA-L2), and a feedforward neural network (FFNN) is performed for their ability to provide adaptive control of nonlinear systems. Three dynamical nonlinear systems of different complexity are considered. The aim of this work is to make the output of the plant follow the desired reference trajectory. The problem becomes more challenging when the dynamics of the plants are assumed to be unknown, and to tackle this problem, a multilayer neural network-based approximate model is set up which will work in parallel to the plant and the control scheme. The network parameters are updated using the dynamic backpropagation (BP) algorithm.
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20

Mossaddek, Meriem, El Mehdi Laadissi, Chouaib Ennawaoui, Sohaib Bouzaid, and Abdelowahed Hajjaji. "Enhancing battery system identification: nonlinear autoregressive modeling for Li-ion batteries." International Journal of Electrical and Computer Engineering (IJECE) 14, no. 3 (2024): 2449. http://dx.doi.org/10.11591/ijece.v14i3.pp2449-2456.

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Precisely characterizing Li-ion batteries is essential for optimizing their performance, enhancing safety, and prolonging their lifespan across various applications, such as electric vehicles and renewable energy systems. This article introduces an innovative nonlinear methodology for system identification of a Li-ion battery, employing a nonlinear autoregressive with exogenous inputs (NARX) model. The proposed approach integrates the benefits of nonlinear modeling with the adaptability of the NARX structure, facilitating a more comprehensive representation of the intricate electrochemical processes within the battery. Experimental data collected from a Li-ion battery operating under diverse scenarios are employed to validate the effectiveness of the proposed methodology. The identified NARX model exhibits superior accuracy in predicting the battery's behavior compared to traditional linear models. This study underscores the importance of accounting for nonlinearities in battery modeling, providing insights into the intricate relationships between state-of-charge, voltage, and current under dynamic conditions.
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21

Kacimi, Houda, Sara Fennane, Hamza Mabchour, Fatehi ALtalqi, Ibtissam El Moury, and Adil Echchelh. "Comparison of multilayer perceptron and nonlinear autoregressive models for wind speed prediction." Bulletin of Electrical Engineering and Informatics 14, no. 3 (2025): 1591–601. https://doi.org/10.11591/eei.v14i3.8541.

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Wind energy is a critical component of the global shift to renewable energy sources, with significant growth driven by the need to reduce carbon emissions. Accurate wind speed prediction is crucial for increasing wind energy output since it directly influences wind farm design and performance. The purpose of this study is to compare two artificial neural network (ANN) models for predicting wind speed in Dakhla City, a place with a high wind energy potential. The first model is a multilayer perceptron (MLP) trained with the backpropagation algorithm, while the second is a nonlinear autoregressive with exogenous inputs (NARX) model, a form of recurrent neural network (RNN) noted for its ability to handle time-series data more well. The comparative analysis results show that the NARX model outperforms the MLP model in terms of wind speed forecast accuracy. The NARX model achieved a near-perfect regression coefficient (R) of 0.9998 and a root mean square error (RMSE) of 1.02899, indicating that it can represent complex, nonlinear wind speed patterns. These findings indicate that the NARX model could be a beneficial tool for increasing the efficiency of Dakhla City’s wind energy infrastructure, assisting the region in meeting its renewable energy ambitions.
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Nikentari, Nerfita, and Hua-Liang Wei. "Multi-task learning using non-linear autoregressive models and recurrent neural networks for tide level forecasting." International Journal of Electrical and Computer Engineering (IJECE) 14, no. 1 (2024): 960–70. https://doi.org/10.11591/ijece.v14i1.pp960-970.

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Tide level forecasting plays an important role in environmental management and development. Current tide level forecasting methods are usually implemented for solving single task problems, that is, a model built based on the tide level data at an individual location is only used to forecast tide level of the same location but is not used for tide forecasting at another location. This study proposes a new method for tide level prediction at multiple locations simultaneously. The method combines nonlinear autoregressive moving average with exogenous inputs (NARMAX) model and recurrent neural networks (RNNs), and incorporates them into a multi-task learning (MTL) framework. Experiments are designed and performed to compare single task learning (STL) and MTL with and without using non-linear autoregressive models. Three different RNN variants, namely, long short- term memory (LSTM), gated recurrent unit (GRU) and bidirectional LSTM (BiLSTM) are employed together with non-linear autoregressive models. A case study on tide level forecasting at many different geographical locations (5 to 11 locations) is conducted. Experimental results demonstrate that the proposed architectures outperform the classical single-task prediction methods.
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Wan, Sicheng, Yibo Wang, Youshuang Zhang, Beibei Zhu, Huakun Huang, and Jia Liu. "Fusion of Hierarchical Optimization Models for Accurate Power Load Prediction." Sustainability 16, no. 16 (2024): 6903. http://dx.doi.org/10.3390/su16166903.

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Accurate power load forecasting is critical to achieving the sustainability of energy management systems. However, conventional prediction methods suffer from low precision and stability because of crude modules for predicting short-term and medium-term loads. To solve such a problem, a Combined Modeling Power Load-Forecasting (CMPLF) method is proposed in this work. The CMPLF comprises two modules to deal with short-term and medium-term load forecasting, respectively. Each module consists of four essential parts including initial forecasting, decomposition and denoising, nonlinear optimization, and evaluation. Especially, to break through bottlenecks in hierarchical model optimization, we effectively fuse the Nonlinear Autoregressive model with Exogenous Inputs (NARX) and Long-Short Term Memory (LSTM) networks into the Autoregressive Integrated Moving Average (ARIMA) model. The experiment results based on real-world datasets from Queensland and China mainland show that our CMPLF has significant performance superiority compared with the state-of-the-art (SOTA) methods. CMPLF achieves a goodness-of-fit value of 97.174% in short-term load prediction and 97.162% in medium-term prediction. Our approach will be of great significance in promoting the sustainable development of smart cities.
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Boynton, R. J., M. A. Balikhin, S. A. Billings, and O. A. Amariutei. "Application of nonlinear autoregressive moving average exogenous input models to geospace: advances in understanding and space weather forecasts." Annales Geophysicae 31, no. 9 (2013): 1579–89. http://dx.doi.org/10.5194/angeo-31-1579-2013.

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Abstract. The nonlinear autoregressive moving average with exogenous inputs (NARMAX) system identification technique is applied to various aspects of the magnetospheres dynamics. It is shown, from an example system, how the inputs to a system can be found from the error reduction ratio (ERR) analysis, a key concept of the NARMAX approach. The application of the NARMAX approach to the Dst (disturbance storm time) index and the electron fluxes at geostationary Earth orbit (GEO) are reviewed, revealing new insight into the physics of the system. The review of studies into the Dst index illustrate how the NARMAX approach is able to find a coupling function for the Dst index from data, which was then analytically justified from first principles. While the review of the electron flux demonstrates how NARMAX is able to reveal new insight into the physics of the acceleration and loss processes within the radiation belt.
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Wang, Lan, Yu Cheng, Jinglu Hu, Jinling Liang, and Abdullah M. Dobaie. "Nonlinear System Identification Using Quasi-ARX RBFN Models with a Parameter-Classified Scheme." Complexity 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/8197602.

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Quasi-linear autoregressive with exogenous inputs (Quasi-ARX) models have received considerable attention for their usefulness in nonlinear system identification and control. In this paper, identification methods of quasi-ARX type models are reviewed and categorized in three main groups, and a two-step learning approach is proposed as an extension of the parameter-classified methods to identify the quasi-ARX radial basis function network (RBFN) model. Firstly, a clustering method is utilized to provide statistical properties of the dataset for determining the parameters nonlinear to the model, which are interpreted meaningfully in the sense of interpolation parameters of a local linear model. Secondly, support vector regression is used to estimate the parameters linear to the model; meanwhile, an explicit kernel mapping is given in terms of the nonlinear parameter identification procedure, in which the model is transformed from the nonlinear-in-nature to the linear-in-parameter. Numerical and real cases are carried out finally to demonstrate the effectiveness and generalization ability of the proposed method.
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Lee, Ya Wei. "Dynamic Modeling and Identification of an Electric-Hydraulic Controlled Fuel Injection System." Advanced Materials Research 918 (April 2014): 206–11. http://dx.doi.org/10.4028/www.scientific.net/amr.918.206.

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Fuel consumption, related to engine operation and performance, has always been emphasized in the modern design of heavy vehicles. For identifying the operational mechanism of a novel hydraulically actuated electronic unit injection (HEUI) system from the viewpoint of energy conversion, this study presents the estimation of a nonlinear autoregressive moving average with exogenous inputs (NARMAX) models. By this modeling approach, the correlation between injection pressure and fuel rate under normal operations is detected. When mapping the NARMAX models into the frequency domain, the frequency response functions (FRFs) representing the energy transfer mechanisms in the system can then be precisely obtained. Due to the high-order FRFs responsible for the non-linear coupling between the various input spectral components, the HEUI dynamics can be demonstrated as an energy resonance of 22.5 Hz.
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Jiang, Han, Yajie Zou, Shen Zhang, Jinjun Tang, and Yinhai Wang. "Short-Term Speed Prediction Using Remote Microwave Sensor Data: Machine Learning versus Statistical Model." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/9236156.

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Recently, a number of short-term speed prediction approaches have been developed, in which most algorithms are based on machine learning and statistical theory. This paper examined the multistep ahead prediction performance of eight different models using the 2-minute travel speed data collected from three Remote Traffic Microwave Sensors located on a southbound segment of 4th ring road in Beijing City. Specifically, we consider five machine learning methods: Back Propagation Neural Network (BPNN), nonlinear autoregressive model with exogenous inputs neural network (NARXNN), support vector machine with radial basis function as kernel function (SVM-RBF), Support Vector Machine with Linear Function (SVM-LIN), and Multilinear Regression (MLR) as candidate. Three statistical models are also selected: Autoregressive Integrated Moving Average (ARIMA), Vector Autoregression (VAR), and Space-Time (ST) model. From the prediction results, we find the following meaningful results: (1) the prediction accuracy of speed deteriorates as the prediction time steps increase for all models; (2) the BPNN, NARXNN, and SVM-RBF can clearly outperform two traditional statistical models: ARIMA and VAR; (3) the prediction performance of ANN is superior to that of SVM and MLR; (4) as time step increases, the ST model can consistently provide the lowest MAE comparing with ARIMA and VAR.
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Hermansah, Hermansah, Dedi Rosadi, Abdurakhman Abdurakhman, and Herni Utami. "Automatic time series forecasting using nonlinear autoregressive neural network model with exogenous input." Bulletin of Electrical Engineering and Informatics 10, no. 5 (2021): 2836–44. http://dx.doi.org/10.11591/eei.v10i5.2862.

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This study aims to determine an automatic forecasting method of univariate time series, using the nonlinear autoregressive neural network model with exogenous input (NARX). In this automatic setting, users only need to supply the input of time series. Then, an automatic forecasting algorithm sets up the appropriate features, estimate the parameters in the model, and calculate forecasts, without the users’ intervention. The algorithm method used include preprocessing, tests for trends, and the application of first differences. The time series were tested for seasonality, and seasonal differences were obtained from a successful analysis. These series were also linearly scaled to [−1, +1]. The autoregressive lags and hidden neurons were further selected through the stepwise and optimization algorithms, respectively. The 20 NARX models were fitted with different random starting weights, and the forecasts were combined using the ensemble operator, in order to obtain the final product. This proposed method was applied to real data, and its performance was compared with several available automatic models in the literature. The forecasting accuracy was also measured by mean squared error (MSE) and mean absolute percent error (MAPE), and the results showed that the proposed method outperformed the other automatic models.
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De Freitas Lopes, Gisele, Manoel Henrique Reis Nascimento, Alexandra Amaro de Lima, et al. "APPLICATION OF THE NONLINEAR AUTOREGRESSIVE MODEL WITH EXOGENOUS INPUTS FOR RIVER LEVEL FORECAST IN THE AMAZON." International Journal for Innovation Education and Research 10, no. 3 (2022): 304–23. http://dx.doi.org/10.31686/ijier.vol10.iss3.3696.

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The present work is justified by three basic lines that involve the problem of the theme, which are the use of Artificial Intelligence, the problem of floods in the Amazon and the issue of technology in favor of decision making. The environmental impacts caused by economic and social factors are problems portrayed in scenarios such as floods and ebbs of rivers, bringing up situations such as an increase in diseases, reduction of agricultural production in locations that depend on accurate geological control, in addition to the increase in erosive processes. in risk locations. Thus, the use of AI to predict the river level, which consequently can minimize problems arising from floods that cause an environmental impact, is highly possible, since when it is known in advance that an event is close to happening, decisions can be taken so that the impacts be smaller. This work models and applies NARX to forecast the river level in the Amazon with variables of easy access and implementation through the MATLAB software, in order to contribute with a forecast model capable of predicting a possible flood from the river level..
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Nikentari, Nerfita, and Hua-Liang Wei. "Multi-task learning using non-linear autoregressive models and recurrent neural networks for tide level forecasting." International Journal of Electrical and Computer Engineering (IJECE) 14, no. 1 (2024): 960. http://dx.doi.org/10.11591/ijece.v14i1.pp960-970.

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Tide level forecasting plays an important role in environmental management and development. Current tide level forecasting methods are usually implemented for solving single task problems, that is, a model built based on the tide level data at an individual location is only used to forecast tide level of the same location but is not used for tide forecasting at another location. This study proposes a new method for tide level prediction at multiple locations simultaneously. The method combines nonlinear autoregressive moving average with exogenous inputs (NARMAX) model and recurrent neural networks (RNNs), and incorporates them into a multi-task learning (MTL) framework. Experiments are designed and performed to compare single task learning (STL) and MTL with and without using non-linear autoregressive models. Three different RNN variants, namely, long short-term memory (LSTM), gated recurrent unit (GRU) and bidirectional LSTM (BiLSTM) are employed together with non-linear autoregressive models. A case study on tide level forecasting at many different geographical locations (5 to 11 locations) is conducted. Experimental results demonstrate that the proposed architectures outperform the classical single-task prediction methods.
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Natsheh and Samara. "Toward Better PV Panel’s Output Power Prediction; a Module Based on Nonlinear Autoregressive Neural Network with Exogenous Inputs." Applied Sciences 9, no. 18 (2019): 3670. http://dx.doi.org/10.3390/app9183670.

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Much work has been carried out for modeling the output power of photovoltaic panels. Using artificial neural networks (ANNS), one could efficiently model the output power of heterogeneous photovoltaic (HPV) panels. However, due to the existing different types of artificial neural network implementations, it has become hard to choose the best approach to use for a specific application. This raises the need for studies that develop models using the different neural networks types and compare the efficiency of these different types for that specific application. In this work, two neural network types, namely, the nonlinear autoregressive network with exogenous inputs (NARX) and the deep feed-forward (DFF) neural network, have been developed and compared for modeling the maximum output power of HPV panels. Both neural networks have four exogenous inputs and two outputs. Matlab/Simulink is used in evaluating the proposed two models under a variety of atmospheric conditions. A comprehensive evaluation, including a Diebold-Mariano (DM) test, is applied to verify the ability of the proposed networks. Moreover, the work further investigates the two developed neural networks using their actual implementation on a low-cost microcontroller. Both neural networks have performed very well; however, the NARX model performance is much better compared with DFF. Using the NARX network, a prediction of PV output power could be obtained, with half the execution time required to obtain the same prediction with the DFF neural network, and with accuracy of ±0.18 W.
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Banihabib, Mohammad Ebrahim, Arezoo Ahmadian, and Mohammad Valipour. "Hybrid MARMA-NARX model for flow forecasting based on the large-scale climate signals, sea-surface temperatures, and rainfall." Hydrology Research 49, no. 6 (2018): 1788–803. http://dx.doi.org/10.2166/nh.2018.145.

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Abstract In this study, to reflect the effect of large-scale climate signals on runoff, these indices are accompanied with rainfall (the most effective local factor in runoff) as the inputs of the hybrid model. Where one-year in advance forecasting of reservoir inflows can provide data to have an optimal reservoir operation, reports show we still need more accurate models which include all effective parameters to have more forecasting accuracy than traditional linear models (ARMA and ARIMA). Thus, hybridization of models was employed for improving the accuracy of flow forecasting. Moreover, various forecasters including large-scale climate signals were tested to promote forecasting. This paper focuses on testing MARMA-NARX hybrid model to enhance the accuracy of monthly inflow forecasts. Since the inflow in different periods of the year has in linear and non-linear trends, the hybrid model is proposed as a means of combining linear model, monthly autoregressive moving average (MARMA), and non-linear model, nonlinear autoregressive model with exogenous (NARX) inputs to upgrade the accuracy of flow forecasting. The results of the study showed enhanced forecasting accuracy through using the hybrid model.
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Sultana, Nahid, S. M. Zakir Hossain, Salma Hamad Almuhaini, and Dilek Düştegör. "Bayesian Optimization Algorithm-Based Statistical and Machine Learning Approaches for Forecasting Short-Term Electricity Demand." Energies 15, no. 9 (2022): 3425. http://dx.doi.org/10.3390/en15093425.

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This article focuses on developing both statistical and machine learning approaches for forecasting hourly electricity demand in Ontario. The novelties of this study include (i) identifying essential factors that have a significant effect on electricity consumption, (ii) the execution of a Bayesian optimization algorithm (BOA) to optimize the model hyperparameters, (iii) hybridizing the BOA with the seasonal autoregressive integrated moving average with exogenous inputs (SARIMAX) and nonlinear autoregressive networks with exogenous input (NARX) for modeling separately short-term electricity demand for the first time, (iv) comparing the model’s performance using several performance indicators and computing efficiency, and (v) validation of the model performance using unseen data. Six features (viz., snow depth, cloud cover, precipitation, temperature, irradiance toa, and irradiance surface) were found to be significant. The Mean Absolute Percentage Error (MAPE) of five consecutive weekdays for all seasons in the hybrid BOA-NARX is obtained at about 3%, while a remarkable variation is observed in the hybrid BOA-SARIMAX. BOA-NARX provides an overall steady Relative Error (RE) in all seasons (1~6.56%), while BOA-SARIMAX provides unstable results (Fall: 0.73~2.98%; Summer: 8.41~14.44%). The coefficient of determination (R2) values for both models are >0.96. Overall results indicate that both models perform well; however, the hybrid BOA-NARX reveals a stable ability to handle the day-ahead electricity load forecasts.
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Golob, Marjan. "NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic Processes." Mathematics 11, no. 2 (2023): 304. http://dx.doi.org/10.3390/math11020304.

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This paper presents a new approach for modelling nonlinear dynamic processes (NDP). It is based on a nonlinear autoregressive with exogenous (NARX) inputs model structure and a deep convolutional fuzzy system (DCFS). The DCFS is a hierarchical fuzzy structure, which can overcome the deficiency of general fuzzy systems when facing high dimensional data. For relieving the curse of dimensionality, as well as improving approximation performance of fuzzy models, we propose combining the NARX with the DCFS to provide a good approximation of the complex nonlinear dynamic behavior and a fast-training algorithm with ensured convergence. There are three NARX DCFS structures proposed, and the appropriate training algorithm is adapted. Evaluations were performed on a popular benchmark—Box and Jenkin’s gas furnace data set and the four nonlinear dynamic test systems. The experiments show that the proposed NARX DCFS method can be successfully used to identify nonlinear dynamic systems based on external dynamics structures and nonlinear static approximators.
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Aquize, Rubén, Armando Cajahuaringa, José Machuca, David Mauricio, and Juan M. Mauricio Villanueva. "System Identification Methodology of a Gas Turbine Based on Artificial Recurrent Neural Networks." Sensors 23, no. 4 (2023): 2231. http://dx.doi.org/10.3390/s23042231.

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The application of identification techniques using artificial intelligence to the gas turbine (GT), whose nonlinear dynamic behavior is difficult to describe through differential equations and the laws of physics, has begun to gain importance for a little more than a decade. NARX (Nonlinear autoregressive network with exogenous inputs) is one of the models used to identify GT because it provides good results. However, existing studies need to show a systematic method to generate robust NARX models that can identify a GT with satisfactory accuracy. In this sense, a systematic method is proposed to design NARX models for identifying a GT, which consists of nine precise steps that go from identifying GT variables to obtaining the optimized NARX model. To validate the method, it was applied to a case study of a 215 MW SIEMENS TG, model SGT6-5000F, using a set of 2305 real-time series data records, obtaining a NARX model with an MSE of 1.945 × 10−5, RMSE of 0.4411% and a MAPE of 0.0643.
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Almuhaini, Salma Hamad, and Nahid Sultana. "Forecasting Long-Term Electricity Consumption in Saudi Arabia Based on Statistical and Machine Learning Algorithms to Enhance Electric Power Supply Management." Energies 16, no. 4 (2023): 2035. http://dx.doi.org/10.3390/en16042035.

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This study aims to develop statistical and machine learning methodologies for forecasting yearly electricity consumption in Saudi Arabia. The novelty of this study include (i) determining significant features that have a considerable influence on electricity consumption, (ii) utilizing a Bayesian optimization algorithm (BOA) to enhance the model’s hyperparameters, (iii) hybridizing the BOA with the machine learning algorithms, viz., support vector regression (SVR) and nonlinear autoregressive networks with exogenous inputs (NARX), for modeling individually the long-term electricity consumption, (iv) comparing their performances with the widely used classical time-series algorithm autoregressive integrated moving average with exogenous inputs (ARIMAX) with regard to the accuracy, computational efficiency, and generalizability, and (v) forecasting future yearly electricity consumption and validation. The population, gross domestic product (GDP), imports, and refined oil products were observed to be significant with the total yearly electricity consumption in Saudi Arabia. The coefficient of determination R2 values for all the developed models are >0.98, indicating an excellent fit of the models with historical data. However, among all three proposed models, the BOA–NARX has the best performance, improving the forecasting accuracy (root mean square error (RMSE)) by 71% and 80% compared to the ARIMAX and BOA–SVR models, respectively. The overall results of this study confirm the higher accuracy and reliability of the proposed methods in total electricity consumption forecasting that can be used by power system operators to more accurately forecast electricity consumption to ensure the sustainability of electric energy. This study can also provide significant guidance and helpful insights for researchers to enhance their understanding of crucial research, emerging trends, and new developments in future energy studies.
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Ghahari, SeyedAli, Cesar Queiroz, Samuel Labi, and Sue McNeil. "Cluster Forecasting of Corruption Using Nonlinear Autoregressive Models with Exogenous Variables (NARX)—An Artificial Neural Network Analysis." Sustainability 13, no. 20 (2021): 11366. http://dx.doi.org/10.3390/su132011366.

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Any effort to combat corruption can benefit from an examination of past and projected worldwide trends. In this paper, we forecast the level of corruption in countries by integrating artificial neural network modeling and time series analysis. The data were obtained from 113 countries from 2007 to 2017. The study is carried out at two levels: (a) the global level, where all countries are considered as a monolithic group; and (b) the cluster level, where countries are placed into groups based on their development-related attributes. For each cluster, we use the findings from our previous study on the cluster analysis of global corruption using machine learning methods that identified the four most influential corruption factors, and we use those as independent variables. Then, using the identified influential factors, we forecast the level of corruption in each cluster using nonlinear autoregressive recurrent neural network models with exogenous inputs (NARX), an artificial neural network technique. The NARX models were developed for each cluster, with an objective function in terms of the Corruption Perceptions Index (CPI). For each model, the optimal neural network is determined by fine-tuning the hyperparameters. The analysis was repeated for all countries as a single group. The accuracy of the models is assessed by comparing the mean square errors (MSEs) of the time series models. The results suggest that the NARX artificial neural network technique yields reliable future values of CPI globally or for each cluster of countries. This can assist policymakers and organizations in assessing the expected efficacies of their current or future corruption control policies from a global perspective as well as for groups of countries.
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Chreng, Karodine, Han Soo Lee, and Soklin Tuy. "A Hybrid Model for Electricity Demand Forecast Using Improved Ensemble Empirical Mode Decomposition and Recurrent Neural Networks with ERA5 Climate Variables." Energies 15, no. 19 (2022): 7434. http://dx.doi.org/10.3390/en15197434.

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By conserving natural resources and reducing the consumption of fossil fuels, sustainable energy development plays a crucial role in energy planning. Specifically, demand-side planning must be researched and anticipated based on electricity consumption at the grounded level. Due to the global warming crisis, atmospheric conditions are among the most influential components that have altered electricity consumption patterns. In this study, 66 climate variables from the ERA5 reanalysis and the observed power demand at four grid substations (GSs) in Cambodia were examined using recurrent neural networks (RNNs). Using the cross-correlation function between power demand and each climate variable, statistically significant climate variables were sorted out. In addition, a wide range of feedback delays (FDs) was generated from the data on power demand and defined using 95% confidence intervals. The combination of the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) technique with a nonlinear autoregressive neural network with exogenous inputs (NARX) and a nonlinear autoregressive neural network (NAR) produced a hybrid electricity forecasting model. The data were decomposed into the intrinsic mode functions (IMFs) and were then used as inputs in optimized NARX and NAR models. The performance of the various benchmarked models was analyzed and compared using mainly statistical indicators such as the normalized root mean square error (NMSE) and the coefficient of determination (R2). The hybrid models perform exceptionally well in predicting electricity demand, and the ICEEMDAN-NARX hybrid model with correlated climate variables performs the best among the tested experiments as a useful prediction tool.
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Lee, Y. W. "Assessment of the Shock-Absorption Performance of a High Capacity Suspension System by Neural Networks." Journal of Mechanics 30, no. 1 (2013): 39–48. http://dx.doi.org/10.1017/jmech.2013.66.

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ABSTRACTThe objective of this study is to develop a framework using nonlinear autoregressive model process with exogenous inputs (NARX) neural networks (NNs) to identify the dynamic hysteresis of high load capacity suspension systems. Here, a vertical excitation test is used to simulate various terrains at an oscillation frequency range from 0.1Hz to 10Hz by using NARX NNs. The model results are in good agreement with suspension component oscillation responses that manifest as variations in model order selection as the excitation frequency approaches 7Hz. Furthermore, mapping the models into generalized frequency response functions (GFRFs), elucidates any unanticipated couplings between surroundings and mechanical hysteresis within the suspension. The proposed approach's systematic design procedure is advantageous because it provides a cost-efficient method that achieves precise identification of online data.
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Gao, Xiaoshu, Hetao Hou, Liang Huang, Guangquan Yu, and Cheng Chen. "Evaluation of Kriging-NARX Modeling for Uncertainty Quantification of Nonlinear SDOF Systems with Degradation." International Journal of Structural Stability and Dynamics 21, no. 04 (2021): 2150060. http://dx.doi.org/10.1142/s0219455421500607.

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Structural assessment for collapse is commonly approached by observing the failure or collapse of systems fully incorporating degradation. Challenges however exist in the performance indicator or damage measure due to compound impacts of uncertainties of external (seismic excitation) and internal (structural properties) characteristics with degradation behavior. To account for the impacts of uncertainties, the state-of-the-art kriging nonlinear autoregressive with exogenous (NARX) model is explored in this study to replicate the response of nonlinear single-degree-of-freedom systems. The generalized hysteretic Bouc-Wen model with internal uncertainties is selected to emulate the stiffness and strength degradation. A probabilistic stochastic ground motion model is introduced to represent the external uncertainties. The global terms of NARX model are selected by least-angle regression algorithm and the kriging model is utilized to surrogate uncertain parameters into corresponding NARX model coefficients. The predictions of kriging NARX models are further compared with that of the polynomial chaos nonlinear autoregressive with exogenous input form model as well as Monte Carlo simulation. The comparisons show that kriging NARX model presents an effective and efficient meta-model technique for uncertainty quantification of systems with degradation.
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Eikenberry, Steffen E., and Vasilis Z. Marmarelis. "Principal Dynamic Mode Analysis of the Hodgkin–Huxley Equations." International Journal of Neural Systems 25, no. 02 (2015): 1550001. http://dx.doi.org/10.1142/s012906571550001x.

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We develop an autoregressive model framework based on the concept of Principal Dynamic Modes (PDMs) for the process of action potential (AP) generation in the excitable neuronal membrane described by the Hodgkin–Huxley (H–H) equations. The model's exogenous input is injected current, and whenever the membrane potential output exceeds a specified threshold, it is fed back as a second input. The PDMs are estimated from the previously developed Nonlinear Autoregressive Volterra (NARV) model, and represent an efficient functional basis for Volterra kernel expansion. The PDM-based model admits a modular representation, consisting of the forward and feedback PDM bases as linear filterbanks for the exogenous and autoregressive inputs, respectively, whose outputs are then fed to a static nonlinearity composed of polynomials operating on the PDM outputs and cross-terms of pair-products of PDM outputs. A two-step procedure for model reduction is performed: first, influential subsets of the forward and feedback PDM bases are identified and selected as the reduced PDM bases. Second, the terms of the static nonlinearity are pruned. The first step reduces model complexity from a total of 65 coefficients to 27, while the second further reduces the model coefficients to only eight. It is demonstrated that the performance cost of model reduction in terms of out-of-sample prediction accuracy is minimal. Unlike the full model, the eight coefficient pruned model can be easily visualized to reveal the essential system components, and thus the data-derived PDM model can yield insight into the underlying system structure and function.
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Ahmed, Duraid F., and Ali H. Khalaf. "Development of Artificial Neural Network Model of Crude Oil Distillation Column." Tikrit Journal of Engineering Sciences 22, no. 1 (2015): 24–37. http://dx.doi.org/10.25130/tjes.22.1.03.

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Artificial neural network in MATLAB simulator is used to model Baiji crude oil distillation unit based on data generated from aspen-HYSYS simulator. Thirteen inputs, six outputs and over 1487 data set are used to model the actual unit. Nonlinear autoregressive network with exogenous inputs (NARX) and back propagation algorithm are used for training. Seventy percent of data are used for training the network while the remaining thirty percent are used for testing and validating the network to determine its prediction accuracy. One hidden layer and 34 hidden neurons are used for the proposed network with MSE of 0.25 is obtained. The number of neuron are selected based on less MSE for the network. The model founded to predict the optimal operating conditions for different objective functions within the training limit since ANN models are poor extrapolators. They are usually only reliable within the range of data that they had been trained for.
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ZHANG, LI, YU-GENG XI, and WEI-DA ZHOU. "IDENTIFICATION AND CONTROL OF DISCRETE-TIME NONLINEAR SYSTEMS USING AFFINE SUPPORT VECTOR MACHINES." International Journal on Artificial Intelligence Tools 18, no. 06 (2009): 929–47. http://dx.doi.org/10.1142/s0218213009000469.

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Support vector machine (SVM) is a universal learning method. In this paper, an affine support vector machine (ASVM) for regression is presented for identification and control of input-affine nonlinear models. ASVM is a variant of SVM and so inherits its merits. The solution to ASVM is cast into a convex quadratic programming (QP). Hence ASVM has a unique global solution. In addition, the curse of dimensionality is avoided because ASVM is insensitive to the dimensionality of data. A commonly used model for a nonlinear system is a nonlinear autoregressive exogenous (NARX) model. ASVM could get good performance in both identification and control if a NARX model can be well represented by an input-affine nonlinear model. The experimental results validate the efficiency of ASVM in identification and control of discrete-time nonlinear systems.
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Wotzka, Daria, Grażyna Suchacka, Paweł Frącz, Łukasz Mach, Marzena Stec, and Joachim Foltys. "Analysis of the Housing Market Dynamics Using NARX Neural Network." Anwendungen und Konzepte der Wirtschaftsinformatik, no. 19 (August 10, 2024): 7. http://dx.doi.org/10.26034/lu.akwi.2024.5947.

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This study employs a Nonlinear Autoregressive with eXogenous inputs (NARX) neural network to model the dynamics of the housing construction market in Poland, with a distinction made between segments of developers and individual investors. The dataset under analysis contains the 19-year data corresponding to the numbers of housing units approved for construction, under construction, and completed. The NARX model was calibrated thoroughly to suit unique characteristics of the data, with an emphasis put on the hidden layer size and delay parameters, to capture the estate market's nonlinear trends. Results show a very high efficiency of NARX models and highlight distinct patterns and dynamics in the housing completion, construction starts, and permit issuance between the two market segments. These variations are vital for understanding the distinct forces and trends shaping the developers’ and individual investors’ markets in the Polish housing sector. Findings of the analysis provide valuable insight into the nanced functioning of these market segments.
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Fuselero, AL Diego Pega, Hannah Mae San Agustin Portus, and Bonifacio Tobias Doma Jr. "Daily Solar Radiation Forecasting based on a Hybrid NARX-GRU Network in Dumaguete, Philippines." International Journal of Renewable Energy Development 11, no. 3 (2022): 839–50. http://dx.doi.org/10.14710/ijred.2022.44755.

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In recent years, solar radiation forecasting has become highly important worldwide as solar energy increases its contribution to electricity grids. However, due to the intermittent nature of solar radiation caused by meteorological parameters, forecasting errors arise, and fluctuations in the power output of photovoltaic (PV) systems become a severe issue. This paper aims to introduce a forecasting hybrid model of daily global solar radiation time series. Meteorological data and solar radiation samples from Dumaguete, Philippines, are used to assess the forecasting accuracy of the proposed nonlinear autoregressive network with exogenous inputs (NARX) – gated recurrent unit (GRU) hybrid model. Four different models were trained using the meteorological and solar radiation data, which are the Optimizable Gaussian Process Regression (GPR), Nonlinear Autoregressive Network (NAR), NARX, and the proposed Hybrid NARX-GRU Network. Results show that the hybrid NARX-GRU model has a root mean square error (RMSE) of ~0.05 and a training time of 33 seconds. The proposed hybrid model has better forecasting performance compared to the three models which obtained RMSE values of 27.741, 39.82, and 28.92, for the GPR, NAR, and NARX, respectively. The simulation results demonstrate that the NARX-GRU model significantly outperforms the regression and single models in terms of statistical metrics and training efficiency. Furthermore, this study shows that the hybridized NARX-GRU model is able to provide an effective estimation for daily global solar radiation, which is important in the operation of PV plants in the country, specifically for unit commitment purposes
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Chao, K. M., K. I. Hoi, K. V. Yuen, and K. M. Mok. "Adaptive Modelling of the Daily Behavior of the Boundary Layer Ozone in Macau." ISRN Meteorology 2012 (July 8, 2012): 1–7. http://dx.doi.org/10.5402/2012/434176.

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The present study aims to develop an efficient dynamic statistical model to describe the daily behavior of boundary layer ozone in Macau. Four types of Kalman-filter-based models were proposed and applied to model the daily maximum of the 8 hr averaged ozone concentrations within a decade (2000–2009). First, the boundary layer ozone was modelled with the time-varying autoregressive model of order p, TVAR(p), which is a pure time series model hindcasting the ozone concentration by a weighted sum of the ozone histories of the previous p days. Then, it was modelled with the time-varying autoregressive model with linear exogenous input, TVAREX-Lin, which combines the TVAR model and the exogenous input of key meteorological variables in a linear fashion. Next, the nonlinear TVAREX model (TVAREX-NLin) which assumes the nonlinear influence of individual meteorological variable on ozone was adopted. Finally, a semiempirical TVAREX model (TVAREX-O3) was proposed to address the coastal nature of Macau and the interaction between the input variables. It was found that the proposed TVAREX-O3 model was the most efficient one among the model candidates in terms of the general modelling performance and the capability of modelling the episode situation.
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Astatkie, T. "Absolute and relative measures for evaluating the forecasting performance of time series models for daily streamflows." Hydrology Research 37, no. 3 (2006): 205–15. http://dx.doi.org/10.2166/nh.2006.008.

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Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) are widely used measures for evaluating the forecasting performance of time series models. Although these absolute measures can be used to compare the performance of competing models, one needs a reference to judge the goodness of the forecasts. In this paper, two relative measures, coefficient of efficiency (E) and index of agreement (d), and their modified versions (EM, EMP, dM and dMP) with desired values of closer to one are presented. These measures are illustrated by comparing the modeling ability and validation forecasting performance of a Nonlinear Additive Autoregressive with Exogenous variables (NAARX), Nested Threshold Autoregressive (NeTAR), and Multiple Nonlinear Inputs Transfer Function (MNITF) models developed for the Jökulsá eystri daily streamflow data. The results suggest that NeTAR describes the system best, and gives better 1- and 2-day ahead validation forecasts. MNITF gives better forecasts for 3-day ahead, and NeTAR and NAARX give comparable performance for 4- and 5-day ahead forecasting. The values of E and d were larger than those of the modified versions, giving a false sense of model performance, and unlike the modified versions, they decreased as forecast lead times increased. Differences among the values of these six relative measures can reveal the sensitiveness of competing models to outliers, and their potential for long-term forecasting. Accordingly, NeTAR was the least sensitive to outliers and NAARX was the most sensitive, with MNITF in between; and NAARX showed the most potential for long-term streamflow forecasting.
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48

Patanè, Luca, Francesca Sapuppo, and Maria Gabriella Xibilia. "Soft Sensors for Industrial Processes Using Multi-Step-Ahead Hankel Dynamic Mode Decomposition with Control." Electronics 13, no. 15 (2024): 3047. http://dx.doi.org/10.3390/electronics13153047.

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In this paper, a novel data-driven approach for the development of soft sensors (SSs) for multi-step-ahead prediction of industrial process variables is proposed. This method is based on the recent developments in Koopman operator theory and dynamic mode decomposition (DMD). It is derived from Hankel DMD with control (HDMDc) to deal with highly nonlinear dynamics using augmented linear models, exploiting input and output regressors. The proposed multi-step-ahead HDMDc (MSA-HDMDc) is designed to perform multi-step prediction and capture complex dynamics with a linear approximation for a highly nonlinear system. This enables the construction of SSs capable of estimating the output of a process over a long period of time and/or using the developed SSs for model predictive control purposes. Hyperparameter tuning and model order reduction are specifically designed to perform multi-step-ahead predictions. Two real-world case studies consisting of a sulfur recovery unit and a debutanizer column, which are widely used as benchmarks in the SS field, are used to validate the proposed methodology. Data covering multiple system operating points are used for identification. The proposed MSA-HDMDc outperforms currently adopted methods in the SSs domain, such as autoregressive models with exogenous inputs and finite impulse response models, and proves to be robust to the variability of systems operating points.
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49

Thapa, Samit, Zebin Zhao, Bo Li, et al. "Snowmelt-Driven Streamflow Prediction Using Machine Learning Techniques (LSTM, NARX, GPR, and SVR)." Water 12, no. 6 (2020): 1734. http://dx.doi.org/10.3390/w12061734.

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Although machine learning (ML) techniques are increasingly popular in water resource studies, they are not extensively utilized in modeling snowmelt. In this study, we developed a model based on a deep learning long short-term memory (LSTM) for snowmelt-driven discharge modeling in a Himalayan basin. For comparison, we developed the nonlinear autoregressive exogenous model (NARX), Gaussian process regression (GPR), and support vector regression (SVR) models. The snow area derived from moderate resolution imaging spectroradiometer (MODIS) snow images along with remotely sensed meteorological products were utilized as inputs to the models. The Gamma test was conducted to determine the appropriate input combination for the models. The shallow LSTM model with a hidden layer achieved superior results than the deeper LSTM models with multiple hidden layers. Out of seven optimizers tested, Adamax proved to be the aptest optimizer for this study. The evaluation of the ML models was done by the coefficient of determination (R2), mean absolute error (MAE), modified Kling–Gupta efficiency (KGE’), Nash–Sutcliffe efficiency (NSE), and root-mean-squared error (RMSE). The LSTM model (KGE’ = 0.99) enriched with snow cover input achieved the best results followed by NARX (KGE’ = 0.974), GPR (KGE’ = 0.95), and SVR (KGE’ = 0.949), respectively. The outcome of this study proves the applicability of the ML models, especially the LSTM model, in predicting snowmelt driven discharge in the data-scant mountainous watersheds.
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50

Di Nunno, Fabio, Giovanni de Marinis, Rudy Gargano, and Francesco Granata. "Tide Prediction in the Venice Lagoon Using Nonlinear Autoregressive Exogenous (NARX) Neural Network." Water 13, no. 9 (2021): 1173. http://dx.doi.org/10.3390/w13091173.

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In the Venice Lagoon some of the highest tides in the Mediterranean occur, which have influenced the evolution of the city of Venice and the surrounding lagoon for centuries. The forecast of “high waters” in the lagoon has always been a matter of considerable practical interest. In this study, tide prediction models were developed for the entire lagoon based on Nonlinear Autoregressive Exogenous (NARX) neural networks. The NARX-based model development was performed in two different stages. The first stage was the training and testing of the NARX network, performed on data collected in a given time interval at the tide gauge of Punta della Salute, at the end of Canal Grande. The second stage consisted of a comprehensive validation of the model in the entire Venice Lagoon, with a detailed analysis of data from three measuring stations located in points of the lagoon with different characteristics. Good predictions were achieved regardless of whether the meteorological parameters were considered among input parameters, even with considerable time advance. Furthermore, the forecasting model based on NARX has proved capable of predicting even exceptional high tides. The proposed model could be a useful support tool for the management of the MOSE system, which will protect Venice from high waters.
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