Autoregressive Exogenous Model Research Articles

Modeling and Control of a Phase-Shifted Full-Bridge Converter for a LiFePO4 Battery Charger

A proper charge in an electric vehicle (EV) battery allows it to have a longer useful life and lower maintenance costs. For this purpose, the voltage and current supplied to the battery must be precisely regulated. In this article, the model of a phase-shifted full-bridge (PSFB) converter is obtained. Moreover, a dual control loop was designed to regulate the state of charge of a lithium ferrofosfate (LiFePO4) battery. The autoregressive exogenous (ARX) model is used to model the system. Once the plant model is obtained, it is controlled using a classical controller. A couple of cases are evaluated where the control parameters are modified, and the best approach is selected. From the obtained model, the controller is designed for the proposed cases. The theoretical controller response is compared with the experimental response. The results show a 94% accuracy of the model. In the same way, the result obtained from the controller is accurate in a 96% by comparing it with a simulation. Both the modeling and the control obtained experimentally resemble the results obtained theoretically. The controller manages to respond as expected in all proposed cases.

Theoretical Analysis on Absorption of Carbon Dioxide (CO2) into Solutions of Phenyl Glycidyl Ether (PGE) Using Nonlinear Autoregressive Exogenous Neural Networks.

In this paper, we analyzed the mass transfer model with chemical reactions during the absorption of carbon dioxide (CO) into phenyl glycidyl ether (PGE) solution. The mathematical model of the phenomenon is governed by a coupled nonlinear differential equation that corresponds to the reaction kinetics and diffusion. The system of differential equations is subjected to Dirichlet boundary conditions and a mixed set of Neumann and Dirichlet boundary conditions. Further, to calculate the concentration of CO, PGE, and the flux in terms of reaction rate constants, we adopt the supervised learning strategy of a nonlinear autoregressive exogenous (NARX) neural network model with two activation functions (Log-sigmoid and Hyperbolic tangent). The reference data set for the possible outcomes of different scenarios based on variations in normalized parameters are obtained using the MATLAB solver “pdex4”. The dataset is further interpreted by the Levenberg–Marquardt (LM) backpropagation algorithm for validation, testing, and training. The results obtained by the NARX-LM algorithm are compared with the Adomian decomposition method and residual method. The rapid convergence of solutions, smooth implementation, computational complexity, absolute errors, and statistics of the mean square error further validate the design scheme’s worth and efficiency.

Energy analysis and surrogate modeling for the green methanol production under dynamic operating conditions

Green methanol production, based on intermittent renewable energy sources, requires a more flexible operation mode and close integration with other sections, such as, the electrical grid and electrolysis processes. In this study, methanol synthesis and distillation processes (MSD) for pilot-scale green methanol production (corresponding to 22,236 tons/year) were investigated by dynamic modeling, focusing on energy analysis and dynamic characteristics during load change (LC) operations. The dynamic simulation results with a ramp rate of 50% load / h indicated energy efficiencies of 87.7% (at full-load) and 90.2% (at half-load) for the methanol synthesis process, 86.8% (full-load) and 82.4% (half-load) for the methanol distillation process, and 77.1% (full-load) and 75.4% (half-load) for the MSD process. Relatively small fluctuations were achieved with a ramp time of 1 h for the LC operations. Based on the constructed dynamic model, a surrogate modeling for the MSD process was conducted using the nonlinear autoregressive exogenous model (NARX) model, which exhibited good accuracy with the evaluated performance for the testing data of the root-mean-square error (RMSE) = 3.09 × 10-5, mean absolute error (MAE) = 2.30 × 10-4, and R2 = 1.0. The constructed NARX model can be further integrated with models for other sections of the power-to-methanol process.

Modelling of adsorption of anionic azo dye using Strychnos potatorum Linn seeds (SPS) from aqueous solution with artificial neural network (ANN)

Synthetic dyes used in the textile and paper industries pose a major threat to the environment. In the present research work, the adsorption efficiency of the natural adsorbent Strychnos potatorum Linn (Fam: Loganiaceae) seeds were examined against the reactive orange-M2R dye from aqueous solution by varying the process conditions such as contact time, pH, adsorbent dosage, and initial dye concentration on adsorption of anionic azo dye. This study compares different types of artificial neural networks which are feedforward artificial neural network (FANN) and nonlinear autoregressive exogenous (NARX) model to predict the efficiency of a cost-effective natural adsorbent Strychnos potatorum Linn seeds on removing reactive orange-M2R dye from aqueous solution. Twelve training algorithms of neural network were compared, and the prediction on the adsorption performance of anionic azo dye from aqueous solution using Strychnos potatonum Linn seeds was evaluated by using the root mean squared error (RMSE), mean absolute error (MAE), coefficient of determination (R2), and accuracy. For FANN model, Levenberg-Marquardt (LM) backpropagation with 19 hidden neurons was selected as the optimum FANN model, with R2 of 0.994 and accuracy of 87.20%, 98.21%, and 66.60% for training, testing, and validation datasets, respectively. For NARX model, LM with 8 hidden neurons was selected as the most suitable training algorithm, with R2 value of more than 0.99 and accuracy of 88.00%, 90.91%, and 75.00% for training, testing, and validation datasets, respectively. NARX model accurately predicted the adsorption of anionic azo dye from aqueous solution using Strychnos potatonum Linn seeds with better performance than FANN model.

Data-driven fault tolerant predictive control for temperature regulation in data center with rack-based cooling architecture

Recently increasing amount of data centers (DCs) have been constructed for the development of information and communications technology (ICT). Meanwhile, more energy consumption is required to support the operation of DCs, where nearly thirty percent of the consumption is used for cooling system. Therefore, this paper studies an efficient cooling architecture named rack mountable cooling unit (RMCU) for DCs, and provides a novel data-driven fault tolerant predictive controller to regulate the temperature accordingly. In order to circumvent the complicated physics modeling in DC, a data-driven modeling method is developed. In this method, multiple local linear models in form of auto-regressive exogenous (ARX) model are selected to describe the strongly nonlinear system. Besides, the multiple sub-models are identified through partial least square (PLS) and corresponding training data is partitioned by fuzzy c-means (FCM). Then, on the basis of developed data-driven model, a predictive controller considering actuator faults is designed to manage the temperature in DC. Finally, real experimental results are presented and demonstrate the superior performance of our proposed controller.

Prediction Model of the Mechanical Behavior of a Fuel Cell Stack under Strengthened Road Vibrating Conditions

In this paper, a data-oriented model has been presented by nonlinear autoregressive exogenous model (NARX) neural network, which aims at predicting the mechanical behavior of a fuel cell stack for vehicle under the real-life operational conditions. A 300-hour vibration test with reproduction of SVP road spectrum was completed on a Multi-Axial Simulation Table. At the same time, data acquisition of drive displacement and acceleration response on stack was carried out in every 50 hours. All data collected were used to train and evaluate the model based on NARX. Result shows that the prediction model built is of good precision and consistent with the actual situation.

Volatility Analysis and Visualization of Climate Data Based on Wavelets

In this article, we analyze the real meteorological data recorded by Wenzhou Meteorological Bureau from 1951 to 1997. The data has not been used elsewhere and is available at Meteorological Station Wenzhou (ID: CHM00058659) at https://geographic.org/global_weather/china. We perform the time series volatility analysis including ARMA, ARIMA, ARCH-LM, PARCH, SARMA and Morlet wavelet analysis and use the Mann-Kendall (M-K) test to analyze both the trend and mutation defined by statistics sequence. In addition, a Morete wavelet time-frequency model is established to show that both the precipitation and temperature have a very important 12-month cycle and the precipitation is also very unstable. We then employ the STL, coif1 decompositions and NAR model to capture both the volatility and Heteroscedasticity in the data. In addition, the performance of the fitted model has been proven to be satisfactory on actual climate data with the small Mean Square Error (MSE), Root-Mean-Squarred Error (RMSE), and coefficient of determination. Finally, monthly average temperature is added as an exogenous (covariate) variable and a nonlinear autoregressive exogenous model is employed to improve the performance of the model. Our results show that the performance of NARX model is more accurate and stable with better mean square error.

Online voltage prediction using gaussian process regression for fault-tolerant photovoltaic standalone applications

This paper presents a fault detection system for photovoltaic standalone applications based on Gaussian Process Regression (GPR). The installation is a communication repeater from the Confederación Hidrográfica del Ebro (CHE), public institution which manages the hydrographic system of Aragón, Spain. Therefore, fault-tolerance is a mandatory requirement, complex to fulfill since it depends on the meteorology, the state of the batteries and the power demand. To solve it, we propose an online voltage prediction solution where GPR is applied in a real and large dataset of two years to predict the behavior of the installation up to 48 hour. The dataset captures electrical and thermal measures of the lead-acid batteries which sustain the installation. In particular, the crucial aspect to avoid failures is to determine the voltage at the end of the night, so different GPR methods are studied. Firstly, the photovoltaic standalone installation is described, along with the dataset. Then, there is an overview of GPR, emphasizing in the key aspects to deal with real and large datasets. Besides, three online recursive multistep GPR model alternatives are tailored, justifying the selection of the hyperparameters: Regular GPR, Sparse GPR and Multiple Experts (ME) GPR. An exhaustive assessment is performed, validating the results with those obtained by Long Short-Term Memory (LSTM) and Nonlinear Autoregressive Exogenous Model (NARX) networks. A maximum error of 127 mV and 308 mV at the end of the night with Sparse and ME, respectively, corroborates GPR as a promising tool.

Localized health monitoring for seismic resilience quantification and safety evaluation of smart structures

Natural hazards such as earthquakes, hurricanes, and floods cause billions of dollars of economic loss and claim thousands of lives every year. Researchers have proposed various tools and techniques to evaluate, manage, and mitigate seismic risk and improve resilience. Nonetheless, given the uncertainties involved, accurate system assessment requires real-time data on structural health and performance which can be attained through structural health monitoring (SHM) systems. This paper integrates component-based resilience quantification methods and SHM techniques to present a new probabilistic framework for seismic structural system evaluation and decision analysis. A trilateral framework is introduced which (1) uses the data obtained from a localized wireless sensor network to detect and locate damage, (2) develops component-based functionality curves to quantify the seismic resilience of the structure, and (3) makes post-quake rapid decisions based on a multi-criteria safety evaluation method. A nonlinear autoregressive exogenous (ARX) model is used to identify structural response and a statistical damage-sensitive coefficient is used to detect, locate, and measure damage in the system. Minor damages due to corrosion and major damages due to past extreme events are studied in the functionality analysis. Two groups of archetype building structures located in a high seismic region are studied, namely steel diagrid and special reinforced concrete structures. The results show that maximum absolute floor acceleration is the most accurate demand parameter for locating damage whereas maximum floor displacement and interstory drift ratio can effectively detect and measure damages.

Defect detection in guided wave signals using nonlinear autoregressive exogenous method

To perform long-term structural health monitoring, a method based on a nonlinear autoregressive exogenous network is used to learn the features present in signals acquired from a pristine structure. When a subsequent measured signal is input to the trained nonlinear autoregressive exogenous network, the output is a prediction of the equivalent signal from a pristine structure. The residual when the pristine predicted signal is subtracted from the measured signal is used for defect detection and localization. A methodology of how to train, test and assess a nonlinear autoregressive exogenous network for guided wave signals is introduced and applied to experimental data obtained over a period of 8 years from a sparse array of guided wave sensors deployed on a steel storage tank. A separate nonlinear autoregressive exogenous model is trained for each sensor pair in the array using data captured in 2012. The method is first tested using data from a single pair of sensors. Defect signals are synthesized by superposing simulated responses from defects onto later experimental signals obtained from the real structure. The test results for the nonlinear autoregressive exogenous method show better detection performance than those from the optimal baseline selection method, in terms of receiver operating characteristic curves. The detection performance of the nonlinear autoregressive exogenous method is further assessed on signals from the whole sensor array, again with simulated defect responses superposed. It is shown that good detection and localization performance can be achieved by combining the nonlinear autoregressive exogenous residual signals from different sensor pairs. The nonlinear autoregressive exogenous method is tested on experimental data acquired at intervals over the following 7 years as the condition of the tank naturally degrades. Indications from localized corrosion are observed. Finally, an artificial localized anomaly is added to the tank and is visible at the correct location in the image formed using the nonlinear autoregressive exogenous method.

Carbon dioxide reforming of methane over Ni-based catalysts: Modeling the effect of process parameters on greenhouse gasses conversion using supervised machine learning algorithms

This study aims to model the effect of process parameters on the conversion of carbon dioxide (CO2) and methane (CH4) during reforming reaction over Nickel (Ni) catalysts. Various supervised machine learning algorithms were employed for the model development. To determine the best model, different configurations of the multilayer perceptron (MLP) and nonlinear auto-regressive exogenous (NARX) neural network models and their performances were evaluated. The performance of the various models was tested through their ability to predict the conversion of the CO2 and CH4. The best MLP network configurations of 5–15–2, 5–4–2, and 5–7–2 were obtained for the Levenberg-Marquardt-, the Bayesian Regularization-, and the Scaled conjugate gradient-trained MLP, respectively. While optimized NARX neural network configurations of 5–18–2, 5–13–2, and 5–8–2 were obtained for the Levenberg-Marquardt, Bayesian Regularization, and the Scaled conjugate gradient training algorithms, respectively. The Bayesian Regularization trained NARX with a coefficient of determination (R2) of 0.998 and MSE of 3.24×10–9 displayed the best performance with an accurate prediction of the thermo-catalytic conversion of CH4 and CO2. The sensitivity analysis revealed that the predicted CH4 and CO2 conversion were influenced in the order of reaction temperature > reduction temperature > calcination temperature > time on stream > Ni loading.

Fatigue level detection using multivariate autoregressive exogenous nonlinear modeling based on driver body pressure distribution

Prolonged driving causes symptoms of fatigue in drivers and changes their physical condition during driving. The purpose of this paper is to use a force measurement system located in the driver’s seat by force-sensitive resistance pressure sensors in order to record the received information to predict fatigue by learning regression-based models. This system is designed with 16 FSR (Force Sensing Resistor) sensors mounted on the seat and its backrest that records the driver’s body’s data, based on the force exerted by the driver on the seat in standard mode and during driving at various times. Fatigue level prediction is based on the trained nonlinear autoregressive exogenous model. In this procedure, models based on multivariate regression are first trained, and then correctness is checked. In this paper, the fatigue index is divided into five parts from 0 to 100 included fully conscious, slightly tired, moderately tired, very tired, and extremely tired, so the criterion for diagnosis is crossing the 75% of fatigue index and entering the extremely tired range. The results show that nonlinear models based on exogenous autoregressive have better performance than the linear mode, and even in the nonlinear model of NARX neural network, the fatigue of one step ahead is well predictable. A flopped state will be predictable when the body is immersed in the seat due to fatigue, so is far from the standard sitting position and will be in the extremely tired warning range.

Prediction of spring flows using nonlinear autoregressive exogenous (NARX) neural network models.

In the Mediterranean area, climate changes have led to long and frequent droughts with a drop in groundwater resources. An accurate prediction of the spring discharge is an essential task for the proper management of the groundwater resources and for the sustainable development of large areas of the Mediterranean basin. This study shows an unprecedented application of non-linear AutoRegressive with eXogenous inputs (NARX) neural networks to the prediction of spring flows. In particular, discharge prediction models were developed for 9 monitored springs located in the Umbria region, along the carbonate ridge of the Umbria-Marche Apennines. In the modeling, the precipitation was also considered as an exogenous input parameter. Good performances were achieved for all the springs and for both short-term and long-term predictions, passing from a lag time equal to 1month (R2 = 0.9012-0.9842, RAE = 0.0933-0.2557) to 12months (R2 = 0.9005-0.9838, RAE = 0.0963-0.2409). The forecasting sensitivity to changes in the temporal resolution, passing from weekly to monthly, was also assessed. The good results achieved recommend the use of the NARX network for spring discharge prediction in other areas characterized by karst aquifers.

Modal identification using bandpass filters based on an ARX model of transient response

The interarea modes of a power system can be identified from a transient response in the frequency data of the phasor measurement units during a power system event. An effective impulse response of the modes can be obtained from the transient response, which contains measurement noise. In this paper, a modal identification method that is insensitive to the measurement noise is proposed using an autoregressive exogenous (ARX) model and bandpass filters. To remove the noise, the effective impulse response is filtered through a combined system of bandpass filters with narrow bandwidths centered on the oscillation frequencies of each mode. Modal identification is fulfilled by estimating the coefficients of the ARX model from the filtered impulse response. The identification accuracy of the proposed method is compared with that of the Prony method with singular value decomposition and discrete Fourier transform method. First, the identification accuracy of the three methods is investigated through simulations on modal spacing and measurement noise. Next, an IEEE 39-bus system is simulated to compare the identification accuracy of the three methods. Finally, the feasibility of the proposed method is demonstrated by identifying interarea modes of power systems in North America from transient responses of their frequency data.

Design of Nonlinear Autoregressive Exogenous Model Based Intelligence Computing for Efficient State Estimation of Underwater Passive Target.

In this study, an intelligent computing paradigm built on a nonlinear autoregressive exogenous (NARX) feedback neural network model with the strength of deep learning is presented for accurate state estimation of an underwater passive target. In underwater scenarios, real-time motion parameters of passive objects are usually extracted with nonlinear filtering techniques. In filtering algorithms, nonlinear passive measurements are associated with linear kinetics of the target, governing by state space methodology. To improve tracking accuracy, effective feature estimation and minimizing position error of dynamic passive objects, the strength of NARX based supervised learning is exploited. Dynamic artificial neural networks, which contain tapped delay lines, are suitable for predicting the future state of the underwater passive object. Neural networks-based intelligence computing is effectively applied for estimating the real-time actual state of a passive moving object, which follows a semi-curved path. Performance analysis of NARX based neural networks is evaluated for six different scenarios of standard deviation of white Gaussian measurement noise by following bearings only tracking phenomena. Root mean square error between estimated and real position of the passive target in rectangular coordinates is computed for evaluating the worth of the proposed NARX feedback neural network scheme. The Monte Carlo simulations are conducted and the results certify the capability of the intelligence computing over conventional nonlinear filtering algorithms such as spherical radial cubature Kalman filter and unscented Kalman filter for given state estimation model.

An inquiry into the capabilities of baseline building energy modelling approaches to estimate energy savings

While baseline energy modelling approaches for buildings are progressing to meet the demand for measurement and verification (M&V) of savings of an energy performance contract, more robust and insightful modelling approaches are needed. This study compares four baseline modelling approaches (e.g., change point, nonlinear autoregressive exogenous models (NARX), Gaussian process, and ensembles of trees) in terms of predictive accuracy and operational insights. The approaches were selected based on preliminary study and employed on pre- and post-intervention data gathered from twelve commercial buildings in Ottawa, Canada. Changes in the post-intervention energy use were estimated by comparing the predicted data with measured data for the individual buildings. The known primary intervention in these buildings was implementing commercially available smart building technologies that identify and address operational suboptimalities. A deeper analysis of one building’s automation system data indicates that energy savings were largely due to simple corrective actions such as eliminating the concurrent operation of heating and cooling coils of an air handling unit. The results show that saving estimates are largely affected by the choice of baseline energy modelling approach. NARX outperformed all other modelling approaches regarding accuracy and data fitting capability. On the contrary, the change point modelling approach offered insights into the operational performance of the buildings.

Synergistic bridge modal analysis using frequency domain decomposition, observer Kalman filter identification, stochastic subspace identification, system realization using information matrix, and autoregressive exogenous model

This paper presents multiple system identification of large-scale bridge structures proposing the combined usage of different modal parameter findings, namely from Frequency Domain Decomposition, Observer Kalman Filter Identification/Eigensystem Realization Algorithm, Combined Deterministic Stochastic Subspace Identification, System Realization Using Information Matrix, and Autoregressive Exogenous Model. A method-centric democratic ranking approach visualizes and quantifies the harmony among different system identification methods in terms of modal parameters, then ranks them based on the correlation among each other, and consequently complies with the highest rank modal parameter outputs. The synergistic scheme is applied on a numerical beam and two bridge structures including one healthy and another subjected to progressive damage. Looking at the top-rank selections, one can see that outlier identification results from a population of modal parameters can intuitively become extinct. The collaboration among methods is dependent on the chosen methods; therefore, method selection relies on care and fair representation of the identification features. Lack of agreement between methods can indicate low confidence in the outranking method and is quantified by median absolute deviation. Nevertheless, the majority of the algorithm population agrees on specific results, which are valuable to produce state knowledge despite low signal to noise ratio, especially without the presence of a reference. Thus, the collaborative usage of multiple methods in a systematic and ranking-based manner reduces significant error and outlier possibilities in modal identification due to algorithm-related issues, which is the novel contribution of this study.

Feasibility of Black-Box Time Domain Modeling of Single-Phase Photovoltaic Inverters Using Artificial Neural Networks

This paper introduces a new black-box approach for time domain modeling of commercially available single-phase photovoltaic (PV) inverters in low voltage networks. An artificial neural network is used as a nonlinear autoregressive exogenous model to represent the steady state behavior as well as dynamic changes of the PV inverter in the frequency range up to 2 kHz. The data for the training and the validation are generated by laboratory measurements of a commercially available inverter for low power applications, i.e., 4.6 kW. The state of the art modeling approaches are explained and the constraints are addressed. The appropriate set of data for training is proposed and the results show the suitability of the trained network as a black-box model in time domain. Such models are required, i.e., for dynamic simulations since they are able to represent the transition between two steady states, which is not possible with classical frequency-domain models (i.e., Norton models). The demonstrated results show that the trained model is able to represent the transition between two steady states and furthermore reflect the frequency coupling characteristic of the grid-side current.

Prediction of temperature distribution around fusion zone in fiber dissimilar laser welding of AISI 304 and AISI 420: A wavelet network nonlinear ARX model

This paper has proposed a parameter estimation method for a laser welding process inherently highly nonlinear as a result of the highly nonlinear inputs and outputs of the system. Hence, a nonlinear system identification method was developed for the laser welding process using the wavelet network nonlinear autoregressive exogenous (ARX) model. The advantage of ARX over the standard nonlinear models is that it not only considers the delayed input and output regressors but also uses nonlinear functions for mapping, thus making ARX a better candidate for the prediction of nonlinear behaviors. In total, nine available datasets for the training and test phases at pulse durations, pulse frequencies, focal lengths, currents, and welding speeds were considered. Five inputs including pulse duration, pulse frequency, focal length, current and welding speed, and temperature as one output were considered. The first eight datasets were utilized for the training phase and one was used for the testing phase. The results showed that the ARX model had an acceptable performance in training and test phases, and it was capable of identifying the nonlinear and time-variant phenomenon of the laser welding process examined in this paper. For instance, most fitness values for austenitic and ferritic steel samples in the training time histories were 97.13 and 97.95, respectively.

Anomaly Detection Based on Multidimensional Data Processing for Protecting Vital Devices in 6G-Enabled Massive IIoT

As a result of the increasing deployment of Industrial-Internet-of-Things (IIoT) architectures, large volumes of multidimensional data are continuously generated. An important issue with these data is that higher dimensionality increases the degree of fragmentation. Furthermore, data sets collected by IIoT nodes often display outliers, which are usually caused by anomalous events or errors. These outliers contain considerable valuable information, which prevent the normal operation of the system. Thus, methodologies are able to quantify the obtained information to protect the high priority IIoT nodes, are crucial. This study aims at developing such a method driven by sixth-generation (6G) networks. The proposed algorithm uses a multidimensional data relationship diagram to characterize the spatiotemporal correlations among heterogeneous data. Then, an autoregressive exogenous model is used to eliminate the effects of noise on sensor data, and to help in detecting anomalies. Finally, the algorithm produces a Cumulative Coefficient of Value (CCoV), to identify high-value sensing devices and enable massive Internet of Things (IoT) with 6G-using the characteristic patterns hidden within the data. The experimental results demonstrate that the proposed method can effectively handle the effects of the ubiquitous interference noise in complex industrial environments. Moreover, the method yields effective anomaly detection and compensates for some of the shortcomings in traditional methods.