NARX Model Research Articles

Effect of training algorithms in accurate state of charge estimation of lithium ion batteries using NARX model

Effect of training algorithms in accurate state of charge estimation of lithium ion batteries using NARX model

Effect of training algorithms in accurate state of charge estimation of lithium-ion batteries using NARX model

Effect of training algorithms in accurate state of charge estimation of lithium-ion batteries using NARX model

Integrated Identification of the Nonlinear Autoregressive Models With Exogenous Inputs (NARX) for Engineering Systems Design

This brief presents a new framework for the identification of nonlinear autoregressive (AR) models with exogenous inputs (NARX) model for design (NARX-M-for-D), which represents NARX of engineering systems where the model coefficients are represented explicitly as a function of the physical parameters that can be adjusted for the system design. The framework is concerned with identifying a common structure of the NARX model which is shared by all design configurations, and with identifying the nonlinear static maps that link these design parameters with NARX coefficients. The problem of the common structure identification is solved via extended forward orthogonal regression, after which a joint regression problem is formulated to determine the explicit relationships between NARX coefficients and physical parameters for the system. Using sparse regression methods allows simultaneous detection of a compact structure of the NARX model and design parameter maps. The reduced structure improves model generalization in design parameter space which is instrumental for the application of the identified model in the system design. The performance of the framework is evaluated on a benchmark model and on the experimental data from dynamic testing of auxetic foams. An example of evaluating the output frequency response from the identified model demonstrates how the proposed framework can be used to assess dynamical properties of engineered systems in the design process.

A Nonlinear Autoregressive Model with Exogenous Variables for Traffic Flow Forecasting in Smaller Urban Regions

Data-driven forecasting methods have the problems of complex calculations, poor portability and need a large amount of training data, which limits the application of data-driven methods in small cities. This paper proposes a traffic flow forecasting method using a Nonlinear AutoRegressive model with eXogenous variables (NARX model), which uses a dynamic neural network Focused Time-Delay Neural Network (FTDNN) with a Tapped Delay Line (TDL) structure as a nonlinear function. The TDL structure enables the FTDNN to have short-term memory capabilities. At the same time, before the data is input into the FTDNN, the use of trend decomposition or differential calculation on the traffic data sequence can make the NARX model maintain long-term predictive capabilities. Compared with common nonlinear models, the FTDNN has structural advantages. It uses a simple TDL structure without the memory mechanism and the gated structure, which can reduce the parameters of the model and reduce the scale of data. Through the four-day data of Guilin City, the traffic volume forecast for five minutes is verified, and the performance of the NARX model is better than that of the SARIMA model and the Holt-Winters model.

Design assessments of complex systems based on design oriented modelling and uncertainty analysis

In the design of nonlinear complex systems, the output responses of a complex system subject to demanding loading conditions need to be assessed before the system can be used in practice. Current assessment approaches (including physical model based analysis, Finite Element (FE) simulation and similitude experiments) are often time-consuming and problematic. The objective of this study is to develop a novel data-driven approach to predict the output responses, as well as their uncertainties, of a complex system for the aim of design assessment. The results can be used to decide whether redesign of the complex system is required to avoid damage for actual use. To achieve this goal, a novel design-oriented data driven modelling approach has been developed based on the FROLS (Forward Regression Orthogonal Least Squares) algorithm and K-fold cross validation. In this approach, the NARX (Nonlinear AutoRegressive with eXogenous input) model of the system is identified and validated. After that, the Monte Carlo Simulation (MCS) method is applied to quantify the uncertainties of the NARX model coefficients. Subject to specified inputs, the model coefficients’ uncertainties are propagated to the model predicted output responses for design assessments. Finally, the proposed approach is verified by a case study on the design assessment of a Chinese Space Station Scientific Experiment Rack (CSS-SER). The results indicate the efficiency of the proposed approach and its potential to be applied to solve many engineering design problems.

Effect of Rainfall in Predicting Tomato Prices in India: An Application of SARIMAX and NARX Model

Effect of Rainfall in Predicting Tomato Prices in India: An Application of SARIMAX and NARX Model

Cuffless Blood Pressure Estimation During Moderate- and Heavy-Intensity Exercise Using Wearable ECG and PPG.

To develop and evaluate an accurate method for cuffless blood pressure (BP) estimation during moderate- and heavy-intensity exercise. Twelve participants performed three cycling exercises: a ramp-incremental exercise to exhaustion, and moderate and heavy pseudorandom binary sequence exercises on an electronically braked cycle ergometer over the course of 21 minutes. Subject-specific and population-based nonlinear autoregressive models with exogenous inputs (NARX) were compared with feedforward artificial neural network (ANN) models and pulse arrival time (PAT) models. Population-based NARX models, (applying leave-one-subject-out cross-validation), performed better than the other models and showed good capability for estimating large changes in mean arterial pressure (MAP). The models were unable to track consistent decreases in BP during prolonged exercise caused by reduction in peripheral vascular resistance, since this information is apparently not encoded in the employed proxy physiological signals (electrocardiography and forehead PPG) used for BP estimation. Nevertheless, the population-based NARX model had an error standard deviation of 11.0 mmHg during the entire exercise window, which improved to 9.0 mmHg when the model was periodically calibrated every 7 minutes. Population-based NARX models can estimate BP during moderate- and heavy-intensity exercise but need periodic calibration to account for the change in vascular resistance during exertion. MAP can be continuously tracked during exercise using only wearable sensors, making monitoring exercise physiology more convenient and accessible.

Approximation and Analysis of Natural Data Based on NARX Neural Networks Involving Wavelet Filtering

Recurrent neural network (RNN) models continue the theory of the autoregression integrated moving average (ARIMA) model class. In this paper, we consider the architecture of the RNN with embedded memory—«Process of Nonlinear Autoregressive Exogenous Model» (NARX). Though it is known that NN is a universal approximator, certain difficulties and restrictions in different NN applications are still topical and call for new approaches and methods. In particular, it is difficult for an NN to model noisy and significantly nonstationary time series. The paper suggests optimizing the modeling process for a complicated-structure time series by NARX networks involving wavelet filtering. The developed procedure of wavelet filtering includes the application of the construction of wavelet packets and stochastic thresholds. A method to estimate the thresholds to obtain a solution with a defined confidence level is also developed. We introduce the algorithm of wavelet filtering. It is shown that the proposed wavelet filtering makes it possible to obtain a more accurate NARX model and improves the efficiency of the forecasting process for a natural time series of a complicated structure. Compared to ARIMA, the suggested method allows us to obtain a more adequate model of a nonstationary time series of complex nonlinear structure. The advantage of the method, compared to RNN, is the higher quality of data approximation for smaller computation efforts at the stages of network training and functioning that provides the solution to the problem of long-term dependencies. Moreover, we develop a scheme of approach realization for the task of data modeling based on NARX and anomaly detection. The necessity of anomaly detection arises in different application areas. Anomaly detection is of particular relevance in the problems of geophysical monitoring and requires method accuracy and efficiency. The effectiveness of the suggested method is illustrated in the example of processing of ionospheric parameter time series. We also present the results for the problem of ionospheric anomaly detection. The approach can be applied in space weather forecasting to predict ionospheric parameters and to detect ionospheric anomalies.

Groundwater Level Forecasting in the Jakarta Groundwater Basin

Groundwater is an important source of fresh water worldwide. Jakarta, the capital city of the Republic of Indonesia, is a large city with a population of more than 10 million and the center of the country’s economy and urban development. However, Jakarta has many challenges related to groundwater management. Changes in well GWL serve as a direct indicator of the effects of groundwater evolution, and GWL time series usually contain important information about aquifer dynamics. Therefore, water managers and engineers must model and predict GWL, identify and measure groundwater resources, and maintain a balance between supply and demand. Measuring and analyzing the groundwater table (GWL) of an aquifer are an important and valuable activity in the management of groundwater resources, and information on GWL variability can be used to determine groundwater availability. Accurate and reliable groundwater level estimation is very important because it provides important information about the quantitative groundwater status of an aquifer. The main advantage of AI models is their ability to reproduce nonlinear and complex processes without a full understanding of the underlying physics. As a result, the use of AI techniques in GWL modeling continues to grow, attracting the attention of scientists around the world. Using a nonlinear autoregressive network with extrinsic input (NARX) with a timestep of 14 days, this study is aimed at predicting the volatility of Jakarta’s GWL. Based on the research results, both JKT-01 and JKT-03 show a linear downward trend. On the other hand, JKT-02 and JKT-04 show a stable linear trend. GWL increases the linear trend of JKT-05. Variable results are generated by model performance. Model performance ( R ) varied between 0.2 and 0.9 during the training phase and between 0.2 and 0.9 during the validation phase. The overall performance of the model varies from 0.3 to 0.9. The diverse lithology and high pumping capacity in Jakarta are the reasons for the different modeling results. Forecasts for 14 days (14 timesteps) show that GWL remains constant at certain well locations, while GWL decreases at other locations. This is a consideration that stakeholders can consider to reduce the small effect of the daily GWL pattern as a result of NARX modeling.

Artificial neural network-based model predictive control for optimal operating conditions in proton exchange membrane fuel cells

In the large-scale commercialization of proton exchange membrane fuel cells (PEMFC), efficient control of the dynamic operation requires the consideration of complex nonlinearities in current, temperature, pressure, and membrane hydration. In this study, an artificial neural network (ANN) model was developed and integrated with model predictive control (MPC) to provide optimal conditions for operating the PEMFC system under different current load changes. For this purpose, after modeling a 1.2 kW PEMFC in a MATLAB/Simulink environment, the accuracy of the model was validated within a maximum relative error of 2.30% compared to the experimental data. Next, the power production, temperature, and internal relative humidity of the model were extracted under all feasible operating conditions. The extracted data were used to train the nonlinear autoregressive network with exogenous inputs (NARX), and hyperparameters of neural networks were selected through Bayesian optimization. The NARX model trained with optimal parameters had a mean square error (MSE) of 2.14 × 10−4 and was integrated into the MPC to obtain neural network model predictive control (NNMPC). The developed NNMPC provides the optimal operating temperature and pressure for the PEMFC model at 10-s intervals through iterative simulation of the NARX under Bayesian optimization. To verify the performance of the control system, the developed NNMPC and fixed-setpoint scenario were compared. Each control scenario consisted of three current load profiles: low, medium, and high current. The NNMPC yielded improved system power by maintaining the optimal stack temperature, cathode pressure and membrane hydration for current changes at a low computational cost. The optimized power of the PEMFC system showed an average increase of 10.9% compared to fixed-setpoint condition.

Investigation and Experimental Validation of Kriging-NARX Modeling for Real-Time Hybrid Simulation

ABSTRACT This study proposes the use of nonlinear autoregressive with exogenous input (NARX) to emulate dynamic behavior of analytical substructures in real-time hybrid simulation (RTHS). The training of the NARX model can be conducted numerically, and its implementation presents a good representation of structural dynamics with minimum computational demands on the RTHS equipment. A Kriging metamodel is further introduced to surrogate the NARX model coefficients to account for ground motion uncertainties. RTHS of a single-degree-of-freedom (SDOF) structure with a self-centering viscous damper are conducted as proof of concept to experimentally demonstrate the effectiveness of proposed Kriging-NARX metamodeling approach.

A Hybrid Model for Electricity Demand Forecast Using Improved Ensemble Empirical Mode Decomposition and Recurrent Neural Networks with ERA5 Climate Variables

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.

Data‐driven nonlinear autoregressive with external input model‐based compensation for real‐time testing

Actuator control plays an important role for real-time testing based experimental techniques such as real-time hybrid simulation (RTHS). Accurate modeling of actuator dynamics can be challenging due to the complexity and nonlinearity of the servo-hydraulic system. In this study, nonlinear autoregressive with external input (NARX) modeling is introduced to emulate the servo-hydraulic dynamics. The command and measured displacements of the actuator are used as input and output of the NARX model. The coefficients of the NARX model of different orders are determined online through ordinary least square regression in a real-time manner. Data weight is further proposed to account for most recent variation in command and measured displacements. Real-time tests with predefined random and chirp signals are conducted to evaluate the performance of proposed NARX model-based compensation of different orders, window length, and data weight. The efficacy and robustness of proposed NARX model-based compensation are further verified through computational simulation of a RTHS benchmark model. Both numerical simulation and laboratory experiments demonstrate that the proposed method enables effective negation of servo-hydraulic dynamics for real-time testing.

Online Rotor Systems Condition Monitoring Using Nonlinear Output Frequency Response Functions Under Harmonic Excitations

Operation conditions such as rub-impact and misalignment usually accumulate and can eventually induce severe faults in rotor systems. These abnormal conditions often make rotor systems behave nonlinearly. Consequently, nonlinear signal and systems analyses have been applied to address rotor system condition monitoring and fault diagnosis problems. Nonlinear frequency response functions (NOFRFs) are a concept proposed to extend the well-known concept of frequency response function to the nonlinear case, and have recently been exploited to solve problems with signal analysis based rotor system condition monitoring and fault diagnosis. However, existing NOFRFs based analyses require conducting offline experiments on rotor systems. This cannot satisfy the industrial need of continuous monitoring of rotor system operational conditions, which is important for online fault diagnosis. In order to resolve this problem, the present article proposes a novel approach that performs the rotor system condition monitoring using the NOFRFs determined directly from the rotor system online operational data which are inherently harmonics. This approach involves the identification of a data-driven NARX (nonlinear auto regressive with eXegenous input) model of rotor systems from harmonic excitations and corresponding responses, evaluation of rotor system NOFRFs using the identified NARX model, and the use of evaluated NOFRFs for rotor system operational condition monitoring and fault diagnosis. The approach, for the first time, enables the NOFRFs to be applied to perform online monitoring of rotor systems. Experimental studies have been conducted to verify the effectiveness and potential applications of the proposed approach as well as its advantages over commonly used signal analysis based techniques.

HOW MACHINE LEARNING ALGORITHMS ARE USED IN METEOROLOGICAL DATA CLASSIFICATION: A COMPARATIVE APPROACH BETWEEN DT, LMT, M5-MT, GRADIENT BOOSTING AND GWLM-NARX MODELS

Rainfall prediction is one of the most challenging task faced by researchers over the years. Many machine learning and AI based algorithms have been implemented on different datasets for better prediction purposes, but there is not a single solution which perfectly predicts the rainfall. Accurate prediction still remains a question to researchers. We offer a machine learning-based comparison evaluation of rainfall models for Kashmir province. Both local geographic features and the time horizon has influence on weather forecasting. Decision trees, Logistic Model Trees (LMT), and M5 model trees are examples of predictive models based on algorithms. GWLM-NARX, Gradient Boosting, and other techniques were investigated. Weather predictors measured from three major meteorological stations in the Kashmir area of the UT of J&K, India, were utilized in the models. We compared the proposed models based on their accuracy, kappa, interpretability, and other statistics, as well as the significance of the predictors utilized. On the original dataset, the DT model delivers an accuracy of 80.12 percent, followed by the LMT and Gradient boosting models, which produce accuracy of 87.23 percent and 87.51 percent, respectively. Furthermore, when continuous data was used in the M5-MT and GWLM-NARX models, the NARX model performed better, with mean squared error (MSE) and regression value (R) predictions of 3.12 percent and 0.9899 percent in training, 0.144 percent and 0.9936 percent in validation, and 0.311 percent and 0.9988 percent in testing.

Sugarcane Yield Estimation of Yamunanagar and Panipat District of Haryana Using NARX Model

Uncontrollable factors that affect yield variability include seasonal and intra seasonal weather variations. The degree to which meteorological factors affect agricultural productivity depends not only on their quantity but also on how they are distributed throughout the crop season. Therefore, while estimating the dynamic behavior of agricultural production, it should be able to take advantage from both historical data on crop yield and the impact of different external environmental driving forces. In this study, Yamunanagar and Panipat districts of Haryana's sugarcane yield have been attempted to be estimated using NARX (Nonlinear Autoregressive Model with Exogenous Input) models. The NARX model with one hidden neuron and arf13, and the NARX model with two hidden neuron and tmx13 selected as best model for Yamunanagar and Panipat districts respectively with smaller values of percent relative deviation (RD (%)), mean absolute percentage error (MAPE) and root mean squared error (RMSE).

A new hybrid models based on the neural network and discrete wavelet transform to identify the CHIMERE model limitation.

A greater understanding of ozone damage to the environment and health led to an increased demand for accurate predictions. This study provides two new accurate hybrid models of ozone prediction. The first one (CHIMERE-NARX) is based on a NARX model as a post-processing of the CHIMERE model. In the second (CHIMERE-NARX-DWT), a discrete wavelet transform (DWT) has been added. Our models were built and validated using ozone measurements from the Mediouna station in Casablanca, Morocco, from February 1st to March 27th, 2021. The results highlighted the CHIMERE model limitations, such as wind speed overestimation and insufficient emission data. The first hybrid successfully increased the correlation coefficient from 88 to 93% and reduced RMSE from 23.99 μg/m3 to -3.54 μg/m3, overcoming CHIMERE limitations to some extent, especially during nighttime. A second hybrid addressed the first hybrid limitation, such as using ozone as a single input. This hybrid successfully balanced the weight of NARX at night against the day, increasing the correlation coefficient to 98% and decreasing RMSE to -0.02 μg/m3. This study presents a new generation of post-processing based on deterministic model processes, with the possibility of training them with minimum input data, which can be applied to other models using various pollutants.

Improvement of LSTM-Based Forecasting with NARX Model through Use of an Evolutionary Algorithm

The reported work aims to improve the performance of LSTM-based (Long Short-Term Memory) forecasting algorithms in cases of NARX (Nonlinear Autoregressive with eXogenous input) models by using evolutionary search. The proposed approach, ES-LSTM, combines a two-membered ES local search procedure (2MES) with an ADAM optimizer to train more accurate LSTMs. The accuracy is measured from both error and trend prediction points of view. The method first computes the learnable parameters of an LSTM, using a subset of the training data, and applies a modified version of 2MES optimization to tune them. In the second stage, all available training data are used to update the LSTM’s weight parameters. The performance of the resulting algorithm is assessed versus the accuracy of a standard trained LSTM in the case of multiple financial time series. The tests are conducted on both training and test data, respectively. The experimental results show a significant improvement in the forecasting of the direction of change without damaging the error measurements. All quality measures are better than in the case of the standard algorithm, while error measures are insignificantly higher or, in some cases, even better. Together with theoretical consideration, this proves that the new method outperforms the standard one.

Real-Time Hybrid Simulation with Polynomial Chaos NARX Modeling for Seismic Response Evaluation of Structures Subjected to Stochastic Ground Motions

Real-Time Hybrid Simulation with Polynomial Chaos NARX Modeling for Seismic Response Evaluation of Structures Subjected to Stochastic Ground Motions

Identification Approach for Nonlinear MIMO Dynamics of Closed-Loop Active Magnetic Bearing System

A systematic identification approach for the rotor/radial active magnetic bearing (rotor/RAMB) system is presented in this study. First, the system identification of the controller of commercial TMP is undertaken, and the corresponding linear dynamic models are constructed. To perfectly excite the nonlinearities of the rotor/RAMB system, a parallel amplitude-modulated pseudo-random binary sequence (PAPRBS) generator, which possesses the merits of no correlation among the perturbation signals, is employed. The dynamics of the rotor/RAMB system is identified with a Hammerstein–Wiener model. To reduce the difficulty of the identified two nonlinear blocks, the output nonlinear characteristics are estimated prior to the recursive process. Two conventional nonlinear model structures, i.e., NARX and NARMAX, are employed for comparison to verify the effectiveness of the identified Hammerstein–Wiener model. The averaged fit values of the Hammerstein–Wiener model, NARX model, and NARMAX model are 93.25%, 88.36%, and 76.91%, respectively.