Autoregressive Exogenous Model Research Articles

Multiple Channel Integration Quality Assessment Method Using NARX

To improve the accuracy of the multiple channel integration quality (MCIQ) evaluation, this paper proposes a comprehensive evaluation method using the nonlinear autoregressive exogenous model (NARX) and constructs an index system. First, the entropy method is used to determine the objective weight of each indicator. The indicators used in this paper are process consistency, information consistency, emotional value, procedural value, service structure transparency, online result value, business relevance, and online purchase intention. Second, an improved gray relational analysis (GRA) algorithm is used to obtain the comprehensive gray relational degree between the above eight indicators’ standard samples and the tested samples. Then, this study uses the dataset preprocessed with the GRA algorithm for training the NARX model. Then, this study uses the trained model to evaluate the quality of multiple channel integration comprehensively. Next, this study uses standardized methods to quantify the evaluation results to provide new ideas and theoretical guidance for teaching traditional retailers to use the advantages of multiple channels to expand their online business. This paper uses 50,000 consecutive samples of a product for 3 months as a dataset in the experimental part. Through the GRA method and the NARX model, the comprehensive gray relational degree between the test sample and the ideal sample is obtained, and the results are quantified. Experiments show that, compared with the GRA method, this paper’s method has a higher degree of fit between the output value and the target value.

Online health diagnosis of lithium-ion batteries based on nonlinear autoregressive neural network

Battery health diagnostics is extremely crucial to guaranty the availability and reliability of the application in which they operate. Data-driven health diagnostics methods, particularly machine learning methods, have gained attention due to their simplicity and accuracy. However, a machine learning method is desired which can cope with the nonlinear behavior of battery cells and yet it avoids high computational complexity to work efficiently in online applications. The accuracy and robustness of machine learning methods strongly depend on the availability of a comprehensive battery degradation dataset that covers a variety of battery aging patterns. While many studies fail to address the aforementioned requirements, this study attempts to address them. Twenty-one nickel manganese cobalt oxide battery cells have been cycled in various operating conditions for more than two years to acquire the data. The partial charging voltage curve is explored to extract the health indicators that describe the health trajectory of the battery. Afterward, a nonlinear autoregressive exogenous (NARX) model is developed to capture the dependency between the health indicators and state of health of battery cells. Finally, the accuracy and robustness of the proposed method are validated. The results demonstrate the ability of NARX to health diagnosis of lithium-ion batteries with a maximum root mean squared error of 0.46 for untrained data. This indicates that the proposed model has high estimation accuracy, low computational complexity, and the ability of battery health estimation regardless of its aging pattern. These features point out the practicability of the proposed technique on online health diagnostics.

A gray-box model for real-time transient temperature predictions in data centers

In response to the need to improve the energy efficiency of data centers (DCs), system designers now incorporate solutions such as continuous performance monitoring, automated diagnostics, and optimal control. While these solutions must ideally be able to predict transient conditions, in particular real time DC temperatures, existing forecasting methods are inadequate because they (1) make restrictive assumptions about system configurations, (2) are extremely time-consuming for real time applications, (3) are accurate only over limited time horizons, (4) fail to accurately model the effects of operating conditions, such as cooling unit operation conditions and server workloads, or (5) ignore important facets of the flow physics and heat transfer that can lead to large prediction errors in extrapolative predictions. To address these deficiencies, we develop a gray-box model that combines machine learning with the thermofluid transport equations relevant for a row-based cooled DC to predict transient temperatures in server CPUs and cold air inlet to the servers. An artificial neural network (ANN) embedded in the gray-box model predicts pressures, which provide inputs for the thermofluid transport equations that predict the spatio-temporal temperature distributions. The model is validated with experimental measurements for different (1) server workload distributions, (2) cooling unit set-point temperatures and (3) the airflow of the cooling units. This gray-box model exhibits superior performance compared to a conventional zonal temperature prediction model and an advanced black-box model that is based on a nonlinear autoregressive exogenous model. An application of the gray-box model involves a case study to detect cooling unit fan failure in a row-based DC cooling system.

Multistep short-term wind speed prediction using nonlinear auto-regressive neural network with exogenous variable selection

Precise wind speed prediction is a key factor in many energy applications, especially when wind energy is integrated with power grids. However, because of the intermittent and nonstationary nature of wind speed, modeling and predicting it is a challenge. In addition, using uncorrelated multivariate variables as exogenous input variables often adversely impacts the performance of prediction models. In this paper, we present a multistep short-term wind speed prediction using multivariate exogenous input variables. We implement different variable selection methods to select the best set of variables that significantly improve the performance of prediction models. We evaluate the performance of eight transfer learning methods, four shallow neural networks (NNs), and the persistence method on predicting the future values of wind speed using ultrashort-term, short-term, and multistep time horizons. We performed the evaluation over two-year high-sampled wind speed data averaged at 10-minute intervals. Results show that Nonlinear Auto-Regressive Exogenous (NARX) model outperformed all other methods, achieving an average mean absolute error (MAE) and root mean square error (RMSE) of 0.2205 and 0.3405 for multistep predictions, respectively. Despite the lower performance of the transfer learning methods (i.e., 0.43 and 0.58 for MAE and RMSE, respectively), it is believed that results could be further improved with a better enhancement of the feature selection and model parameters.

Application of deep neural techniques in predictive modelling for the estimation of Escherichia coli growth rate.

To develop a predictive model for Escherichia coli using deep neural networks. Batch experiments are conducted at different temperatures closer to optimum value (36·5°C, 37°C, 37·5°C, 38°C and 38·5°C) to obtain the growth curves of E .coli K-12. Two primary models namely modified Gompertz and new logistic are chosen. Three secondary models namely Gaussian, nonlinear autoregressive eXogenous (NARX) model and long short-term memory (LSTM) are developed. The novelty in this paper is the development of secondary models using artificial neural network (ANN) and deep network. The performance measures chosen to compare the developed primary and secondary models are correlation coefficient (R2 ), root-mean-square error (RMSE) and accuracy factor (Af ). Results show that modified Gompertz model has better R2 (0·99) and RMSE (0·019) when compared to new logistic model. Also, the deep network model outperforms other secondary models. Based on the primary and novel secondary model, a predictive model (tertiary model) is developed with improved accuracy and is validated. The proposed predictive model exhibit good validation results in terms of RMSE and R2 values and can be applied for determining the growth rate of E. coli at a particular temperature value. The proposed model can be used in food processing industries during enzyme production such as Chymosin, to predict the growth rate of E. coli as a function of temperature. Also, the developed LSTM and NARX models can be used to predict maximum specific growth rate of other microbial strains with proper training.

Forecasting Tourist Visit Using the Vector Autoregressive Exogenous Method (VARX)

Forecasting is an activity to predict what will happen in the future by paying attention to information from the past and the present. A regression model that explains the past movement of the variable itself and also all other variables without distinguishing which endogenous and exogenous variables are called Vector Autoregressive (VAR). But in practice, endogenous variables are supported by exogenous variables. The Vector Autoregressive Exogenous (VARX) model is a development of the VAR with the addition of exogenous variables. The purpose of this study is to form the best model in the VAR method with the addition of an exogenous variable in the form of an effect calendar for forecasting the number of tourists coming to the Special Region of Yogyakarta (DIY). The data used in this study are time series data for 10 years from January 2009 to December 2018 in the form of tourist visit data in the Special Region of Yogyakarta (DIY). The results obtained indicate that the effect calendar variable that affects tourist visitor data in DIY is at Christmas. After being analyzed using MAPE, the best model is the VARX (1.0) model which produces a smaller. So, it can be concluded that the VARX model with the addition of an effects calendar is suitable for predicting tourist visits

A data-driven approach to estimate battery cell temperature using a nonlinear autoregressive exogenous neural network model

Abstract Battery cell temperature is a key parameter in battery life degradation, safety, and dynamic performance. Intense charging-discharging operations and high-ambient temperatures escalate battery cell temperature, which in turn accelerates its degradation. Therefore, accurate battery cell temperature estimation can play a significant role in ensuring the optimal operation of a battery energy storage system (BESS). In order to estimate battery cell temperature as accurate as possible, use of non-linear models is imperative due to the non-linear nature of the battery operation. This paper proposes a data-driven model based on a Non-linear Autoregressive Exogenous (NARX) neural network to estimate battery cell temperatures in a utility-scale BESS, considering strongly-correlated independent variables, e.g., charging-discharging current and ambient temperature. Due to different temperature and weather characteristics in each season, seasonal NARX models have also been derived and compared with the universal one. The proposed models’ performance has been verified using the field data collected from a grid-connected BESS within a PV plant. The simulation results show high accuracy of the proposed model compared to the measured data for both seasonal and universal models without considering the complexity of the large-scale battery and container thermal dynamics. In particular, in more than 95% of the time, the estimated values yield root mean squared errors (RMSE) below 1 ∘C in different conditions, which confirms the validity and accuracy of the proposed model. Moreover, seasonal models show better performance with 18% to 50% less RMSE on average (for 1 h to 24 h forward estimation) compared to the universal model.

An Accurate State of Charge Estimation Method for Lithium Iron Phosphate Battery Using a Combination of an Unscented Kalman Filter and a Particle Filter

An accurate state of charge (SOC) estimation of the battery is one of the most important techniques in battery-based power systems, such as electric vehicles (EVs) and energy storage systems (ESSs). The Kalman filter is a preferred algorithm in estimating the SOC of the battery due to the capability of including the time-varying coefficients in the model and its superior performance in the SOC estimation. However, since its performance highly depends on the measurement noise (MN) and process noise (PN) values, it is difficult to obtain highly accurate estimation results with the battery having a flat plateau OCV (open-circuit voltage) area in the SOC-OCV curve, such as the Lithium iron phosphate battery. In this paper, a new integrated estimation method is proposed by combining an unscented Kalman filter and a particle filter (UKF-PF) to estimate the SOC of the Lithium iron phosphate battery. The equivalent circuit of the battery used is composed of a series resistor and two R-C parallel circuits. Then, it is modeled by a second-order autoregressive exogenous (ARX) model, and the parameters are identified by using the recursive least square (RLS) identification method. The validity of the proposed algorithm is verified by comparing the experimental results obtained with the proposed method and the conventional methods.

Robust identification of linear ARX models with recursive EM algorithm based on Student’s t-distribution

This paper considers the robust identification issue of linear systems represented by autoregressive exogenous models using the recursive expectation-maximization (EM) algorithm. In this paper, a recursive Q-function is formulated based on the maximum likelihood principle. Meanwhile, the outliers that frequently appear in practical processes are accommodated with the Student’s t-distribution. The parameter vector, variance of noise, and the degree of freedom are recursively estimated. Finally, a numerical example, as well as a simulated continuous stirred tank reactor (CSTR) system, is performed to verify the effectiveness of the proposed recursive EM algorithm.

Projection-based and neural-net reduced order model for nonlinear Navier–Stokes equations

This paper presents complete steps for the construction and solution algorithm for a projection-based reduced order model coupled with an artificial neural net model. The reduced model is constructed based on the Galerkin projection of the equations governing the physical processes on reduced subspaces obtained by the Proper Orthogonal Decomposition method. The projection is done using numerical discretisation schemes implemented in the commonly used OpenFOAMⓇ platform. The neural net model is trained using the Nonlinear AutoRegressive eXogenous model network (NARX) architecture. The reduced order models are demonstrated for true predictions of incompressible flows at low Reynolds numbers driven by various boundary conditions. Compared with the full CFD simulations, this model shows excellent agreement while only requiring a fraction of the computational resources.

Self-similar segmentation and multifractality of post-stack seismic data

Layering detection is an important step in petroleum engineering. Time series of post-stack seismic data and wire-line log data belong to subsurface layering. They exhibit multifractal properties with complex patterns because of the heterogeneity and different genetic properties in the earth layers. In a multifractal configuration, any piece of a series has a distinct Hurst exponent that reflects its nature and can be used for zone detection. Time series are post-stack seismic traces and wire-line log data near the well-bores. Self-similar Autoregressive Exogenous (SAE) model is a modified method which can place self-similar post-stack seismic and wire-line log segments across layers with the same lithology. The results satisfy the capability of layering identification from seismic data by SAE model.

Identification of the Flip Folder Folding Machine Using Artificial Neuro Network Method with NARX (Nonlinear Auto Regressive Exogenous) Structure

Folding machine is a tool that is needed in the small and medium scale laundry industry that has a goal for the efficiency of production time. The flip folder is the main component of this tool, which functions to fold the clothes by moving to form a certain deflection angle where the movement process is controlled by the controller. The system modeling process is the first step to study the characteristics of the system. In a dynamic system, the form of linear modeling is approved difficult to obtain a model that represents the actual physical model. Selecting the structure of the NARX (Nonlinear Autoregressive eXogenous) model was chosen to obtain the dynamic nature of the system. An estimation method to obtain parameter values from the system used Artificial Neural Networks (ANN), which is a trading scheme to be able to predict the output of a system that uses input data and output. Based on the offline assessment process using measurement data obtained by the NARX ANN model on the variation of the number of layers in 30 with a value of MSE 0,38641.

Identification of the Flip Folder Folding Machine Using Artificial Neuro Network Method with NARX (Nonlinear Auto Regressive Exogenous) Structure

Folding machine is a tool that is needed in the small and medium scale laundy industry that has a goal for the efficiency of production time. Flip folder is the main component of this tool which functions to fold the clothes by moving to form a certain deflection angle where the movement process is controlled by the controller. The system modeling process is the first step to study the characteristics of the system. In a dynamic system the form of linear modeling is approved difficult to obtain a model that represents the actual physical model. Selecting the structure of the NARX (Nonlinear Autoregressive eXogenous) model was chosen to obtain the dynamic nature of the system. As an estimation method to obtain parameter values from the system used Artificial Neural Networks (ANN) which is a trading scheme to be able to predict the output of a system that uses input data and output. Based on the offline assessment process using measurement data obtained by the NARX ANN model on the variation of the number of layers in 30 with a value of MSE 0, 38641.

INVESTIGATION OF INTRINSIC DYNAMIC CHARACTERISTICS IN AN OSCILLATING HEAT PIPE

Conjugate heat transfer devices based on oscillating phenomenon allow thermal instability to play a crucial role in thermal management. This study proposed and tested a hollow cylindrical oscillating heat pipe (OHP) for managing waste heat sources. Deionized water was filled as a working medium at ratios of 10%-90%. Experiments were conducted with heat inputs 10-120 W; the performance was dependent on the features of self-sustained oscillations. Dry-out was found only under low filling conditions, and this operating fault can be avoided by increasing the working medium. A medium level of approximately 50% is optimal. The intrinsic thermal instability related to the performance of an oscillating thermal design has attracted considerable academic interest. Simplifications and assumptions of traditional modeling approaches render them unsuitable for probing the dynamic characteristics of such thermal designs. A nonlinear autoregressive exogenous (NARX) modeling based on machine learning techniques was introduced to identify the causality of the heat transfer mechanism of the OHP. The discrete models estimated using the NARX modeling accurately simulated OHP dynamics, which were further revealed through spectrum analysis. Energy excitation, shown as frequency resonances, was distinctly related to OHP performance.

Identification of Slow-Rate Integrated Measurement Systems Using Expectation–Maximization Algorithm

Despite the fact that slow-rate integrated measurement (SRTM), a gradual accumulation of material during a period of time, is a well-known method of sampling in industrial systems, especially chemical processes, the problem of the identification of SRTM systems has not been addressed so far. In this regard, system identification of the processes having SRTM will be presented in this work. By selecting finite impulse response (FIR) and autoregressive exogenous (ARX) models for the systems, parameters of them will be accurately estimated in the framework of the expectation-maximization (EM) algorithm. For this purpose, the instantaneous values of the output at the fast-rate sampling time are assumed to be latent variables. Applying the EM algorithm leads to some high-dimensional integrals, for which Monte Carlo simulation is adopted. The effectiveness of the proposed method is illustrated by both a simulation study and implementation on a laboratory-scale pH neutralization pilot plant.

Snowmelt-Driven Streamflow Prediction Using Machine Learning Techniques (LSTM, NARX, GPR, and SVR)

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.

On the relationship between oil and gas markets: a new forecasting framework based on a machine learning approach

Owing to the uncertainty around the coupling and decoupling of oil and gas prices, this study re-examines the relationship between oil and gas markets by modeling the price of one energy source based on the price of the other, both linearly and nonlinearly. We present an autoregressive exogenous model and three nonlinear frameworks with different patterns of asymmetry. Based on daily data from January 7, 1997, to December 29, 2017, our analysis reaches two main findings. First, the nonlinear frameworks outperform the linear model (i.e., the autoregressive exogenous model) in modeling the relationship between oil and gas prices. Second, the nature of asymmetry varies based on market direction. We show that when oil prices exhibit an extreme movement (i.e., beyond a threshold value in absolute value), gas prices react nonlinearly, and that there is no relationship otherwise. Our results are robust for other frequencies, mainly weekly and monthly. These findings explain the conflicting results in the literature on the complex relationship between these markets. The results might serve investors in term of hedging, portfolio diversification, and asset allocation as we show that in the calm period, there is no relationship between oil and gas prices; however, the interaction between markets is more pronounced during periods of extreme movement. Similarly, policymakers’ awareness of the nonlinear dynamic under extreme movements could inform the regulation policy and/or adjustment in case oil (gas) prices increase or decrease.

Simulation and modeling of two-level DC/DC boost converter using ARX, ARMAX, and OE model structures

<span>This paper presents simulation and modeling of two-level DC/DC boost converter using system identification technique. The main objective is to identify the unknown mathematical model from designated converter that has 2 modes of operation. Signals from the converter were processed based on the impulse response from input and output voltages, which were in time domain data. Auto Regressive with eXogenous (ARX), Auto Regressive Moving Average with eXogenous (ARMAX), and Output-Error (OE) model structure techniques had been employed to generate a model from the converter, whose validation was based on coefficient of determination (R<sup>2</sup>) or best fits criterion. The result shows that the ARX model structure produced the best model with 94.03%, compared to ARMAX and OE with 93.70% and 92.25% respectively. In terms of stability for open-loop analysis, the ARX model structure gave the most stable system.</span>

Comparative study of lithium‐ion battery open‐circuit‐voltage online estimation methods

As an important property and distinct characteristic of different lithium-ion batteries, open-circuit-voltage (OCV) online estimation can provide useful information for battery monitoring and fault diagnosis. However, studies dedicated to battery OCV estimation are not as much as the research efforts on state-of-charge determination and parameter identification such as capacity and resistance. Hence, a general discussion for selecting the battery OCV estimation algorithm is proposed in this study. To this end, modelling process of extended state-space model and autoregressive exogenous model is presented in detail. Four estimation algorithms, namely, Luenberger observer, Kalman filter, recursive least-square with forgetting factor and recursive least-square with variable forgetting factor are selected and compared in terms of estimation accuracy, computational cost, parameter tuning and robustness to parameter variations. Based on real battery cell parameters and environmental conditions, simulation results have shown that even if they are less robust to model uncertainty, observer-based methods exhibit better estimation performances than regression-based ones.

Comparison of static MLP and dynamic NARX neural networks for forecasting of atmospheric PM10 and SO2 concentrations in an industrial site of Turkey

This study aims to compare performances of two static and one dynamic neural networks used for prediction of hourly ambient air quality concentrations in an industrial site of Turkey. Two air pollutants (PM10 and SO2) and three meteorological parameters (ambient air temperature, relative humidity, and wind speed) were used as input variables. The predictions of the dynamic nonlinear autoregressive exogenous (NARX) model were compared with the predictions of the static multilayer perceptron (MLP) neural network model. The results showed that the predictions of the NARX neural network were obviously better than the predictions of MLP networks. The coefficient of determination (R2), index of agreement and efficiency between the observed and predicted air pollutant concentrations by the NARX model were 0.9773, 0.994, and 0.977 for PM10, respectively while the same parameters were 0.9984, ≈1, and ≈1 for SO2. The MBEs (mean bias errors) were also approximately zero for both pollutants that indicate the adequacy of the model. The values of RMSE (root mean squared error) were also fractional as 0.0191 and 0.0087 for both pollutants. The NARX model predicted SO2 concentrations better than PM10 concentrations. In comparison with MLP network structures, NARX network exhibits faster convergence. The model suggested in this study could be used to support and improve air quality management practices.