NARX Model Research Articles

Mobility Prediction of Off-Road Ground Vehicles Using a Dynamic Ensemble of NARX Models

Abstract Mobility prediction of off-road autonomous ground vehicles (AGV) in uncertain environments is essential for their model-based mission planning, especially in the early design stage. While surrogate modeling methods have been developed to overcome the computational challenge in simulation-based mobility prediction, it is very challenging for a single surrogate model to accurately capture the complicated vehicle dynamics. With a focus on vertical acceleration of an AGV under off-road conditions, this article proposes a surrogate modeling approach for AGV mobility prediction using a dynamic ensemble of nonlinear autoregressive models with exogenous inputs (NARX) over time. Synthetic vehicle mobility data of an AGV are first collected using a limited number of high-fidelity simulations. The data are then partitioned into different segments using a variational Gaussian mixture model to represent different vehicle dynamic behaviors. Based on the partitioned data, multiple surrogate models are constructed under the NARX framework with different numbers of lags. The NARX models are then assembled together dynamically over time to predict the mobility of the AGV under new conditions. A case study demonstrates the advantages of the proposed method over the classical NARX models for AGV mobility prediction.

Analyzing Efficacy and Safety of Anti-Fungal Blue Light Therapy via Kernel-Based Modeling the Reactive Oxygen Species Induced by Light.

The goal of this study is to investigate the efficacy, safety, and mechanism of ABL for inactivating Candida albicans (C. albicans), and to determine the best wavelength for treating candida infected disease, by experimental measurements and dynamic modeling. The changes in reactive oxygen species (ROS) in C. albicans and human host cells under the irradiation of 385, 405, and 415 nm wavelengths light with irradiance of 50 mW/cm2 were measured. Moreover, a kernel-based nonlinear dynamic model, i.e., nonlinear autoregressive with exogenous inputs (NARX), was developed and applied to predict the concentration of light-induced ROS, whose kernels were selected by a newly developed algorithm based on particle swarm optimization (PSO). The ROS concentration was increased respectively about 10-12 times in C. albicans and about 3-6 times in human epithelial cells by the ABL treatment with the same fluence of 90 J/cm2. The NARX models were respectively fitted to the data from the experiments on both types of cells. Besides, four different kernel functions, including Gaussian, Laplace, linear and polynomial kernels, were compared in their fitting accuracies. The errors with the Laplace kernel turned out to be only 0.2704 and 0.0593, as respectively fitted to the experimental data of the C. albicans and human host cells. The results demonstrated the effectiveness of the NARX modeling approach, and revealed that the 415 nm light was more effective as an anti-fungal treatment with less damage to the host cells than the 405 or 385 nm light. The kernel-based NARX model identification algorithm offers opportunities for determining the effective and safe light dosages in treating various fungal infection diseases.

Aero-engine on-board model based on big Quick Access Recorder data

With the development of the Full Authority Digital Engine Controller (FADEC) technology, the aero-engine on-board model is widely used in Engine Health Management (EHM) and control. Due to the FADEC’s limited computational capability and storage capacity, the model should not be very intricate; consequently, the interpolation model is widely utilized. Although the interpolation model’s low precision precludes further development of on-board models for EHM and control. To address the trade-off between precision and complexity, a novel on-board modeling method is proposed based on the Nonlinear Autoregressive with Exogenous Inputs Backpropagation neural network (NARX-BPNN) trained using the mini-batch Levenberg–Marquardt (LM) algorithm on large Quick Access Recorder (QAR) data. The NARX model’s features and time delay are chosen by referring to the line interpolation model, which gives interpretability for feature selection. The combination of a shallow neural network and big data training can guarantee the on-board model’s real-time and storage requirements, as well as its generalizability. The mini-batch LM method can avoid both the local optimum problem in the shallow neural network and the storage difficulty associated with massive data while still achieving a rapid convergence rate due to the LM algorithm’s global view. The NARX-BPNN models are compared to an existing line interpolation model using 100 different aero-engines' QAR data. The results reveal that accuracy may be increased by approximately 30% while maintaining superior dynamic performance and anti-noise capacity compared to the line interpolation approach.

Application of Rainfall-Runoff Simulation Based on the NARX Dynamic Neural Network Model

The research into rainfall-runoff plays a very important role in water resource management. However, runoff simulation is a challenging task due to its complex formation mechanism, time-varying characteristics and nonlinear hydrological dynamic process. In this study, a nonlinear autoregressive model with exogenous input (NARX) is used to simulate the runoff in the Linyi watershed located in the northeastern part of the Huaihe river basin. In order to better evaluate the performance of NARX, a distributed hydrological model, TOPX, is used to simulate the discharge as a reference, and runoff classification by cluster analysis is used to further improve the accuracy of runoff simulation. Based on the four statistics indexes of the Nash–Sutcliffe efficiency (NSE), correlation coefficient (CC), root mean square error (RMSE) and mean relative bias (Bias), the NARX model is capable of simulating the rainfall-runoff dynamic process satisfactorily, although there is a little underestimation of the peak flow. After runoff classification, underestimation has been improved, and discharge simulation driven by NARX based on runoff classification (C-NARX) is well consistent with the observation. It is feasible to take it as a promising method, which also can be seen as a good reference and replacement for the current rainfall-runoff simulation.

Forecasting groundwater level of karst aquifer in a large mining area using partial mutual information and NARX hybrid model

Predicting the groundwater level of karst aquifers in North China Coalfield is essential for early warning of mine water hazards and regional water resources management. However, the dynamic changes of strata structure and hydrogeological parameters driven by coal mining activity cause challenges to the process-oriented groundwater model. In order to achieve accurate prediction of groundwater level in large mining areas, this study was the first to use the data-driven Nonlinear Autoregressive with External Input (NARX) model to predict the groundwater level of six karst aquifer observation wells in Pingshuo Mining Area. Three variable input scenarios were set up, solely considering meteorological factors, anthropogenic disturbance factors, and considering both meteorological and anthropogenic disturbance factors. The novel partial mutual information (PMI) screening algorithm was adopted to determine optimized input variables in each scenario. The input and feedback delay coefficients of NARX model were determined by using Seasonal-trend Decomposition Procedure Based on Loess (STL) algorithm and auto- and cross-correlation functions. The results showed that PMI algorithm can effectively screen out the optimal input variables for predicting groundwater level, the NSE coefficients of the PMI-NARX models under the three scenarios were 38.81%, 4.26% and 41.46% higher than those of the corresponding control experiments, respectively. In addition, the prediction performance of the PMI-NARX built on the basis of meteorological factors is poor (NSE <0.63). However, in scenarios which solely use anthropogenic disturbance factors and both use meteorological and anthropogenic disturbance factors, the PMI-NARX coupling models exhibit good prediction performance (NSE and R2 are all greater than 0.8). Especially under solely considering anthropogenic disturbance factors scenario, the model still exhibited good prediction accuracy with a negligible number of input variables. The results can provide technical and theoretical support for the prediction of groundwater level in other mining areas.

Reconstruction and prediction of state variables in distillation/absorption processes under off-design and limited measurement conditions

Distillation and absorption processes are characterized by a large number of state variables. In order to reconstruct and predict these state variables under off-design and limited measurement conditions, this paper combines the proper orthogonal decomposition (POD) method with the nonlinear autoregressive with exogenous input (NARX) data-driven model. The POD method can reduce the full-order variables to a small number of fundamental modes and temporal coefficients. The NARX model is used to predict the temporal coefficients in POD. After correcting the temporal coefficients by limited measurements, the reconstruction error of the state variables for the absorption case can be reduced to within 7%. The novel method proposed in this paper can still effectively predict the state variables in the absorption or distillation case without going through the POD step for updating and the NARX step for retraining even under off-design conditions.

Trend Analysis of Water Inflow Into the Dam Reservoirs Under Future Conditions Predicted By Dynamic NAR and NARX Models

Trend Analysis of Water Inflow Into the Dam Reservoirs Under Future Conditions Predicted By Dynamic NAR and NARX Models

Estimating the incidence of spontaneous breathing effort of mechanically ventilated patients using a non-linear auto regressive (NARX) model

Background and objectiveMechanical ventilation (MV) provides breathing support for acute respiratory distress syndrome (ARDS) patients in the intensive care unit, but is difficult to optimize. Too much, or too little of pressure or volume support can cause further ventilator-induced lung injury, increasing length of MV, cost and mortality. Patient-specific respiratory mechanics can help optimize MV settings. However, model-based estimation of respiratory mechanics is less accurate when patient exhibit un-modeled spontaneous breathing (SB) efforts on top of ventilator support. This study aims to estimate and quantify SB efforts by reconstructing the unaltered passive mechanics airway pressure using NARX model. MethodsNon-linear autoregressive (NARX) model is used to reconstruct missing airway pressure due to the presence of spontaneous breathing effort in mv patients. Then, the incidence of SB patients is estimated. The study uses a total of 10,000 breathing cycles collected from 10 ARDS patients from IIUM Hospital in Kuantan, Malaysia. In this study, there are 2 different ratios of training and validating methods. Firstly, the initial ratio used is 60:40 which indicates 600 breath cycles for training and remaining 400 breath cycles used for testing. Then, the ratio is varied using 70:30 ratio for training and testing data. Results and discussionThe mean residual error between original airway pressure and reconstructed airway pressure is denoted as the magnitude of effort. The median and interquartile range of mean residual error for both ratio are 0.0557 [0.0230 - 0.0874] and 0.0534 [0.0219 - 0.0870] respectively for all patients. The results also show that Patient 2 has the highest percentage of SB incidence and Patient 10 with the lowest percentage of SB incidence which proved that NARX model is able to perform for both higher incidence of SB effort or when there is a lack of SB effort. ConclusionThis model is able to produce the SB incidence rate based on 10% threshold. Hence, the proposed NARX model is potentially useful to estimate and identify patient-specific SB effort, which has the potential to further assist clinical decisions and optimize MV settings.

ESTIMATION OF KNEE JOINT TORQUE DURING SIT–STAND MOVEMENT BASED ON sEMG SIGNALS USING NEURAL NETWORKS

The estimation of knee joint torque is important for the development of powered exoskeletons to achieve ideal gait characteristics. In this study, we proposed three different models to predict the required torque for performing sit-to-stand (STS) and back-to-sit (BTS) movements. The surface electromyography (sEMG) signals were extracted from the biceps femoris and rectus femoris muscles during STS and BTS movements. The time-domain features selected as input to the models for torque prediction are integrated EMG (iEMG), root mean square (RMS), and mean absolute value (MAV). Two-way ANOVA analysis identifies the significance of NN models and EMG features of the muscles in predicting the knee joint torque requirement. The artificial neural network models selected for prediction are the feed-forward back-propagation algorithm, ANFIS, and NARX. The theoretical value of knee joint torque calculated using the Lagrange method was compared with the torque output for each model based on root mean square error (RMSE). The desired torque predicted using the NARX model confirms to have the least average error ([Formula: see text][Formula: see text]Nm), which indicates that NARX can estimate knee joint torque more accurately from sEMG than other models.

Short-Term Forecasting of Energy Production for a Photovoltaic System Using a NARX-CVM Hybrid Model

In this paper, a methodology for short-term forecasting of power generated by a photovoltaic module is reported. The method incorporates a nonlinear autoregressive with exogenous inputs (NARX) fed by the solar radiation and temperature times series, as well as an estimation of power time series obtained by implementing an ideal single diode model. This synthetic time series was validated against an actual photovoltaic module. The NARX model has been implemented in conjunction with the corrective vector multiplier (CVM) technique, which uses solar radiation under clear sky conditions to adjust the forecasting results. In addition, collinearity and the Granger causality tests were used to choose the input variables. The forecasting horizon was 24-h-ahead. The hybrid NARX-CVM model was compared to a nonlinear autoregressive neural network and persistence model using the typic forecasting error measures such as the mean bias error, mean squared error, root mean squared error and forecast skill. The results showed that the forecasting skills of the hybrid model are about 34% against the NAR model and about 42% against the Persistence model. The model was validated by blind forecasting. The results demonstrated evidence of the quality of the conformed forecasting model and the convenience of its implementation and building.

Frequency Sweep Modeling Method for the Rotor-Bearing System in Time Domain Based on Data-Driven Model

In practice, the modeling and analysis of nonlinear rotor-bearing systems are difficult due to the nonlinearity and complexity. In the previous studies, finite element simulation and mathematical modeling methods are mostly adopted to conduct the analysis. However, due to the time-consuming problem in finite element simulation and the lack of sufficient prior knowledge in mathematical modeling, the traditional method is difficult to establish the representation model. In order to overcome this issue, in this study, a data-driven model referred to as the NARX (Nonlinear Auto-Regressive with exogenous inputs) model is introduced to conduct the modeling and analysis of the rotor-bearing system. The identification of the NARX model requires random excitation as the system input, while the input signal of the rotor system is harmonics. Therefore, a time-domain frequency sweep modeling method is proposed in this paper by introducing the rotating speed into the coefficients function expression of the NARX model, the system output can be predicted according to the given speed. Moreover, the representation model of the rotor-bearing system obtained by using the proposed method is validated under different rotating speeds, the results show the applicability of the proposed modeling approach. Finally, an experimental case of the rotor-bearing test rig is demonstrated to show the application in practice. Both the numerical and experimental studies illustrate the applicability of the proposed modeling method, which provides a reliable model for dynamic analysis and fault diagnosis of the rotor-bearing system.

Research on data‐driven model for soft sensing of natural gas production system

AbstractIn view of the problems of high cost and low reliability in obtaining operation information such as flow rate and pressure of offshore natural gas production system, research on soft sensing is carried out, and a dynamic data‐driven model bank is established, in purpose of estimating single‐well flow rate and wellhead pressure, providing convenience tool for online monitoring and system safety analysis. Combining dynamic and steady‐state samples, introducing black‐box identification techniques including orthogonal least square regression and deep learning along with parameter correction techniques such as bi‐objective least square algorithm and transfer learning, a series of nonlinear auto‐regressive models with exogenous inputs (NARX) are built, consisting of black‐box and gray‐box polynomial NARX (Poly‐NARX) models as well as deep neural network NARX (DNN‐NARX) models, approximately describing the dynamic performance of gas production well. Through realistic operation data, the simulation results of Poly‐NARX, DNN‐NARX, and multiple‐layer‐perception‐NARX models are compared. It is observed that gray‐box DNN‐NARX model shows the best performance with advantages of higher global applicability, better approximation ability, and stronger generalization ability. Proposed model bank is of high expansibility and engineering applicability for soft sensing problems in the petroleum industry, laying the ground work for building smart oil and gas field.

Empirical Analysis for Stock Price Prediction Using NARX Model with Exogenous Technical Indicators.

Stock price prediction is one of the major challenges for investors who participate in the stock markets. Therefore, different methods have been explored by practitioners and academicians to predict stock price movement. Artificial intelligence models are one of the methods that attracted many researchers in the field of financial prediction in the stock market. This study investigates the prediction of the daily stock prices for Commerce International Merchant Bankers (CIMB) using technical indicators in a NARX neural network model. The methodology employs comprehensive parameter trails for different combinations of input variables and different neural network designs. The study seeks to investigate the optimal artificial neural networks (ANN) parameters and settings that enhance the performance of the NARX model. Therefore, extensive parameter trails were studied for various combinations of input variables and NARX neural network configurations. The proposed model is further enhanced by preprocessing and optimising the NARX model's input and output parameers. The prediction performance is assessed based on the mean squared error (MSE), R-squared, and hit rate. The performance of the proposed model is compared with other models, and it is shown that the utilisation of technical indicators with the NARX neural network improves the accuracy of one-step-ahead prediction for CIMB stock in Malaysia. The performance of the proposed model is further improved by optimising the input data and neural network parameters. The improved prediction of stock prices could help investors increase their returns from investment in stock markets.

Adaptive non-linear soft sensor for quality monitoring in refineries using Just-in-Time Learning—Generalized regression neural network approach

Real time estimation of target quality variables using soft sensor relevant to time varying process conditions will be a significant step forward in effective implementation of Industry 4.0. Generalized Regression neural network (GRNN) has been used as a steady state quality monitoring soft sensor with reasonable estimation accuracy. However, the accurate prediction capability of GRNN has rarely been explored in a time varying environment. This article reports design of adaptive soft sensor using GRNN as a local model in Just-in-Time learning (JITL-GRNN) framework. The JITL-GRNN adaptive soft sensing technique is further investigated in various dimensions such as, the effect of different similarity index criteria and relevant dataset size on model prediction accuracy and model computation time. Performance of the proposed JITL-GRNN soft sensor is investigated by assessing its prediction accuracy on two benchmark industrial datasets. In addition, dynamic Non-linear autoregressive with exogenous inputs (NARX) neural network model is also developed and the performance of NARX model was compared with the proposed JITL-GRNN model. Results show that the JITL-GRNN adaptive soft sensor has at par or better prediction capability than the NARX model and many other models reported in literature.

Electricity demand prediction for sustainable development in Cambodia using recurrent neural networks with ERA5 reanalysis climate variables

Sustainable energy development plays a prominent role in energy planning to maintain natural resources and mitigate the usage of fossil fuels. The atmospheric factor is one of the main influencing factors that changed the electricity consumption’s behavior due to global warming. In this study, the recurrent neural network (RNN) models were developed to examine the effects of 66 climate variables, collected from the European Center for Medium-Range Weather Forecast (ECMWF) ERA5 reanalysis, on power demand in Cambodia. The statistically significant climate variables were filtered by considering the cross-correlation between power demand and each climate variable. Moreover, the wide range of feedback delays was computed from the power demand dataset and was defined using the 95% confidence intervals. The comparison between a nonlinear autoregressive neural network with exogenous inputs (NARX) using historical power demand with the correlated climate variables and a nonlinear autoregressive neural network (NAR) using only historical power demand dataset was made. The various benchmarked models were evaluated and compared for their performances using statistical indices such as normalized root-mean-square error (NMSE) and coefficient of determination (R2). The results showed the NARX model could perform better than the NAR model for predicting electricity demand time-series.

Application of Nonlinear Time Series and Machine Learning Algorithms for Forecasting Groundwater Flooding in a Lowland Karst Area

AbstractIn karst limestone areas interactions between ground and surface waters can be frequent, particularly in low lying areas, linked to the unique hydrogeological dynamics of that bedrock aquifer. In extreme hydrological conditions, however, this can lead to wide‐spread, long‐duration flooding, resulting in significant cost and disruption. This study develops and compares a nonlinear time‐series analysis based nonlinear autoregressive model with exogenous variables (NARX), machine learning based near support vector regression as well as a linear time‐series ARX model in terms of their performance to predict groundwater flooding in a lowland karst area of Ireland. The models have been developed upon the results of several years of field data collected in the area, as well as the outputs of a highly calibrated semi‐distributed hydraulic/hydrological model of the karst network. The prediction of total flooding volume indicates that the performances of all the models are similarly accurate up to 10 days into the future. A NARX model taking inputs of the past 5 days' flood volume; rainfall data and tidal amplitude data across the past 4 days, showed the best flood forecasting performance up to 30 days into the future. Existing real‐time telemetric monitoring of water level data at two points in the catchment can be fed into the model to provide an early warning flood warning tool. The model also predicts freshwater discharge from the inter‐tidal spring into the Atlantic Ocean which hitherto had not been possible to monitor.

Identification of industrial air compression system using neural network

The existence of random variable in any industrial process is basically unavoidable. It occasionally creates nonlinearity behavior of a system and makes predictive control complicated. Such a random behavior must not be ignored as it may indicate any unknown event occurring during the process. System identification is an approach to construct the mathematical model of a dynamical system using the instrumentation signal of input and output of the system. This study performs system identification by using the NARX model as a base model with the nonlinear functions of a neural network for an industrial air compression system. The identification undergoes a series of analysis (number of neuron, delay and data division) to determine the most suitable NARX-NN model architecture configuration before coming up with a final model. Finally, the validation of model’s predictive performance is carried out through several analyses, namely, mean square error and regression value. The predicted data are compared to the industrial data to verify its accuracy which shows that the final model had successfully ruled out the suspicious random event data.

A Water Consumption Forecasting Model by Using a Nonlinear Autoregressive Network with Exogenous Inputs Based on Rough Attributes

Scientific prediction of water consumption is beneficial for the management of water resources. In practice, many factors affect water consumption, and the various impact mechanisms are complex and uncertain. Meanwhile, the water consumption time series has a nonlinear dynamic feature. Therefore, this paper proposes a nonlinear autoregressive model with an exogenous input (NARX) neural network model based on rough set (RS) theory. First, the RS theory was used to analyze the importance of each attribute in water consumption. Then, the main influencing factor was selected as the input of the NARX neural network model, which was applied to predict water consumption. The proposed model is proved to give better results of a single NARX model and a back propagation neural network. The experimental results indicate that the proposed model has higher prediction accuracy in terms of the mean absolute error, mean absolute percentage error and root mean square error.

Nonlinear Model Predictive Control of Post-combustion CO2 Capture Process for Flexible Operation

A large amount of energy requirement for solvent regeneration is a major barrier to the widespread adoption of amine-based post-combustion CO2 capture (PCC). Flexible operation is one of the ways to lower the energy penalty by responding to changes in economic factors like the energy price. However, for effective implementation of flexible operation strategies, it is necessary to identify the most economic operating condition under various potential scenarios and to establish an appropriate control strategy to operate the process. As flexible operation will inherently involve a large operating envelope, we investigate the use of nonlinear model predictive control (NMPC) technology. To circumvent the problem of solving a large-scale nonlinear programming problem online, a simpler NARX model is identified and used. With the NARX model, an offset-free NMPC is designed and simulated under various dynamic scenarios. The developed NARX-based NMPC shows satisfactory control performance, stabilizing the CO2 capture rate faster than LMPC by 60-100 min.

Improved Time Synchronous Averaging and Its Application in Data-Driven Rotor Fault Diagnosis

During the assembly and operation of rolling bearings, the inner ring and outer ring are prone to misalignment, which will cause eccentric wear and seriously affects the performance and service life of the bearing. In this paper, the NARX (Nonlinear Auto-Regressive with exogenous inputs) model of a bearing-rotor system is established to evaluate the severity of eccentric wear. Effective data preprocessing is a prerequisite for accurately establishing a NARX model. Considering no large fluctuations in rotational speed and load, and strong autocorrelation of vibration signal, an improved TSA (Time Synchronous Averaging) is proposed, which is combined with the Pearson correlation function. This method can effectively determine the number of time delay points, automatically compensate the phase, and avoid the accumulation of phase errors. In the absence of a tachometer, compared to conventional TSA, the method proposed can reduce the attenuation of high-frequency components and avoid distortion of vibration signals. Finally, the diagnosis approach combined with the improved TSA is determined and verified by the experiment. The improved TSA and data-driven fault diagnosis method proposed in this paper provide a theoretical reference for assembly performance detection and operation state monitoring of the bearing-rotor system.