Autoregressive Exogenous Model Research Articles

Inverse feedforward control of piezoelectric actuators using optimized composite neural network-based Hammerstein model

This paper utilizes the optimized composite neural network (OCNN)-Hammerstein model to directly identify the dynamic inverse hysteresis effect, employing it as a feedforward controller to compensate for the rate-dependent and amplitude-dependent dynamic hysteresis of the piezoelectric actuator. The OCNN-Hammerstein model consists of an optimized composite neural network and an auto-regressive exogenous model in series. The OCNN comprises convolutional neural network layer and radial basis function neural network layer, with its hyperparameters optimized using a modified grey wolf optimizer algorithm. Compared to the existing dynamic Prandtl-Ishlinskii-Hammerstein and dynamic Bouc-Wen-Hammerstein models in the literature, the feedforward controller based on the proposed model in this paper demonstrates superior performance, with an RSME below 0.45 μm and a 74.5% reduction in relative hysteresis at the condition of 300 Hz and maximum amplitude. The feedforward controller exhibits universality across all amplitude ranges and within the 50–300 Hz frequency range, while also providing predictive compensation for dynamic hysteresis at 300–400 Hz. The feedforward controller based on the OCNN-Hammerstein model in this paper provides a crucial methodology for open-loop control of piezoelectric actuators.

A joint optimization strategy for electric vehicles and air conditioning systems with building battery configuration

Building air conditioning systems, electric vehicles and battery energy storage systems all provide substantial flexibility for grid operations. However, the joint optimization strategy involving these three demand response resources in buildings has been infrequently studied. This research proposes a day-ahead optimization strategy to coordinate the joint operation of air conditioning systems and electric vehicles. In this framework, cooling load is predicted using an autoregressive exogenous model, while electric vehicle charging load is predicted through Monte Carlo simulations. An evaluation method is introduced to assess the comprehensive benefits of the demand response strategy, considering thermal comfort, economic efficiency, and grid friendliness. Using an office building in Tianjin, China, as a case study, the results indicate that the joint optimization strategy reduces operational costs by 3.71 % and peak electricity load by 38.62 % compared to the original strategy. Furthermore, it enhances the grid friendliness of the energy system by 42.64 %. The configuration of the battery energy storage system is also explored in conjunction with the optimization strategy to further improve grid friendliness. The impact of economic factors and thermal comfort on the configuration of the battery energy storage system is discussed. In the case study, raising the upper temperature limit by 1 °C can save at least 17.1 % in capacity, while battery energy storage system investment and operational costs can respectively be reduced by 55.04 % and 27.14 % within the thermal comfort range.

Additional fractional gradient descent identification algorithm based on multi-innovation principle for autoregressive exogenous models

This paper proposed the additional fractional gradient descent identification algorithm based on the multi-innovation principle for autoregressive exogenous models. This algorithm incorporates an additional fractional order gradient to the integer order gradient. The two gradients are synchronously used to identify model parameters, thereby accelerating the convergence of the algorithm. Furthermore, to address the limitation of conventional gradient descent algorithms, which only use the information of the current moment to estimate the parameters of the next moment, resulting in low information utilisation, the multi-innovation principle is applied. Specifically, the integer-order gradient and additional fractional-order gradient are expanded into multi-innovation forms, and the parameters of the next moment are simultaneously estimated using multi-innovation matrices, thereby further enhancing the parameter estimation speed and identification accuracy. The convergence of the algorithm is demonstrated, and its effectiveness is verified through simulations and experiments involving the identification of a 3-DOF gyroscope system.

Identification of switched gated recurrent unit neural networks with a generalized Gaussian distribution

Due to the limitations of the model itself, the performance of switched autoregressive exogenous (SARX) models will face potential threats when modeling nonlinear hybrid dynamic systems. To address this problem, a robust identification approach of the switched gated recurrent unit (SGRU) model is developed in this paper. Firstly, all submodels of the SARX model are replaced by gated recurrent unit neural networks. The obtained SGRU model has stronger nonlinear fitting ability than the SARX model. Secondly, this paper departs from the conventional Gaussian distribution assumption for noise, opting instead for a generalized Gaussian distribution. This enables the proposed model to achieve stable prediction performance under the influence of different noises. Notably, no prior assumptions are imposed on the knowledge of operating modes in the proposed switched model. Therefore, the EM algorithm is used to solve the problem of parameter estimation with hidden variables in this paper. Finally, two simulation experiments are performed. By comparing the nonlinear fitting ability of the SGRU model with the SARX model and the prediction performance of the SGRU model under different noise distributions, the effectiveness of the proposed approach is verified.

A gazelle optimization expedition for key term separated fractional nonlinear systems with application to electrically stimulated muscle modeling

Various real-time processes are effectively represented with a fractional nonlinear autoregressive exogenous (F-NARX) model where estimation of model parameters is considered as an essential task. In this study, a population-based gazelle optimization algorithm (GOA) inspired by the evolutionary characteristics of gazelle's is exploited for the parameter estimation of the key term-separated F-NARX system. The Grünwald-Letnikov derivative, a fractional order calculus operator is integrated to develop the F-NARX system from a conventional non-linear autoregressive system. The mean square error-based merit function is developed and the effectiveness of the GOA for the F-NARX system is analyzed in terms of speedy convergence, estimation accuracy, complexity and robustness for different noise scenarios. The extendibility of the GOA is assessed through the estimation of stiff parameters of the electrically stimulated muscle model (ESMM) required for rehabilitation of paralyzed muscles. The efficacy of the GOA is endorsed through Wilcoxon signed rank statistical test in comparison with recent counterparts of Runge Kutta optimization algorithm, Whale optimization algorithm, and Harris Hawks optimization algorithm.

Comprehensive compensation of dynamic hysteresis and creep for piezoelectric actuator

This paper addresses the modeling of dynamic hysteresis and creep in piezoelectric actuators, and employs feedforward open-loop control based on inverse models to compensate for hysteresis and creep phenomena. The comprehensive model consists of quasi-dynamic and dynamic components. The quasi-dynamic model combines the quasi-dynamic Prandtl–Ishlinskii (PI) model with an PI-based linear time-invariant model, while the dynamic part utilizes the auto-regressive exogenous model. The model accurately describes creep and dynamic hysteresis with modeling errors of less than 0.01 μm and 0.14 μm, respectively. The inversion of the comprehensive model has been proven to exhibit unique convergence. Under inverse feedforward control, the improvement in dynamic hysteresis and hysteresis with creep can be achieved at 94% and 83%, respectively. The comprehensive model proposed in this paper accurately describes the dynamic hysteresis and creep phenomena in piezoelectric actuators and realizes open-loop compensation control, achieving precise actuation of piezoelectric actuators.

Physically based vs. data-driven models for streamflow and reservoir volume prediction at a data-scarce semi-arid basin

Physically based or data-driven models can be used for understanding basinwide hydrological processes and creating predictions for future conditions. Physically based models use physical laws and principles to represent hydrological processes. In contrast, data-driven models focus on input–output relationships. Although both approaches have found applications in hydrology, studies that compare these approaches are still limited for data-scarce, semi-arid basins with altered hydrological regimes. This study aims to compare the performances of a physically based model (Soil and Water Assessment Tool (SWAT)) and a data-driven model (Nonlinear AutoRegressive eXogenous model (NARX)) for reservoir volume and streamflow prediction in a data-scarce semi-arid region. The study was conducted in the Tersakan Basin, a semi-arid agricultural basin in Türkiye, where the basin hydrology was significantly altered due to reservoirs (Ladik and Yedikir Reservoir) constructed for irrigation purposes. The models were calibrated and validated for streamflow and reservoir volumes. The results show that (1) NARX performed better in the prediction of water volumes of Ladik and Yedikir Reservoirs and streamflow at the basin outlet than SWAT (2). The SWAT and NARX models both provided the best performance when predicting water volumes at the Ladik reservoir. Both models provided the second best performance during the prediction of water volumes at the Yedikir reservoir. The model performances were the lowest for prediction of streamflow at the basin outlet (3). Comparison of physically based and data-driven models is challenging due to their different characteristics and input data requirements. In this study, the data-driven model provided higher performance than the physically based model. However, input data used for establishing the physically based model had several uncertainties, which may be responsible for the lower performance. Data-driven models can provide alternatives to physically-based models under data-scarce conditions.

Adaptive accelerated proximal gradient algorithm for auto-regressive exogenous models with outliers

This study introduces an enhanced recursive least-squares algorithm that applies the adaptive accelerated proximal gradient method to identify Auto-Regressive Exogenous models with output outliers. First, the outlier problem was converted into a robust principal component analysis problem. The adaptive accelerated proximal gradient method is then introduced to recover the information matrix, and the recursive least squares algorithm is applied to estimate the model parameters. Furthermore, we demonstrated that the parameter estimation is unbiased and that the parameter estimation error converges to zero under persistent excitation. A series of bench tests consistently highlighted the practicality and effectiveness of the proposed algorithm.

Estimating lags in a kraft mill.

In pulp mills, lags obscure the effect of upstream operations on downstream measurements. Here, we estimate lags in a Canadian pulp mill using autoregressive exogenous (ARX) models. First, we show that ARX models can approximate lags in a process simulation that resembles the liquor storage tanks in pulp mills, a major source of lag inthe kraft recovery cycle. Then, we use ARX models to estimate the lagged effect of a change in species pulped on as-fired liquor heating value, viscosity, and boiling point rise. Additionally, we compare the predictions of the ARX models to autoregressive (AR) models and a persistence model. The estimated lags between a change in species and heating value (49 h) and boiling point rise (41 h) agree with a detailed simulation of the mill and are close to estimated hydraulic residence times, suggesting that the liquor tanks exhibit imperfect mixing. A lagged effect of species change on viscosity could not be identified. ARX and AR models produce similar predictions that are slightly better than those of a persistence model. Finally, we show that process measurements upstream of units characterized by large residence times will likely provide little benefit to prediction accuracy.

Spatial Weight Matrix Comparison of SAR-X Model using Casetti Approach

The Spatial Autoregressive Exogenous (SAR-X) model with the Casetti approach is used to describe the influence of location and exogenous variables in the description and prediction of spatial observations, namely, people's habits and behavior towards culture in Java Island. The SAR-X model with the Casetti approach is characterized by a spatial weight matrix that describes the coordinates of the region at each location. The spatial weight matrix is determined outside the model. This study examines the spatial weight matrix determined based on rook contiguity, bishop contiguity, queen contiguity, inverse distance and inverse distance squared, and compares the application of the spatial weight matrix to the SAR-X model with the Casetti approach for the description and prediction of people's habits and behavior towards culture in Java Island. The description and prediction results obtained are measured using the Root Mean Square Error (RMSE) value. The results of data processing show that the best spatial weight matrix in the SAR-X model with the Casetti approach to community habits and behavior in Java Island is the inverse distance squared spatial weight matrix, supported by the calculation of the minimum RMSE value and the coefficient of determination above 60%.

Using nonlinear auto-regressive with exogenous input neural network (NNARX) in blood glucose prediction

BackgroundPredicting of future blood glucose (BG) concentration is important for diabetes control. Many automatic BG monitoring or controlling systems use BG predictors. The accuracy of the prediction for long prediction time is a major factor affecting the performance of the control system. The predicted BG can be used for glycemia management in the form of early hypoglycemic/hyperglycemic alarms or adjusting insulin injections. Recent developments in continuous glucose monitoring (CGM) devices open new opportunities for glycemia management of diabetic patients. Many of those systems need prediction for long prediction horizons to avoid going through hypo or hyperglycemia.MethodsIn this article a nonlinear autoregressive exogenous input neural network (NNARX) is proposed to predict the glucose concentration for longer prediction horizons (PHs) than that was obtained previously with an established recurrent neural network (RNN). The proposed NNARX is a modified version from our previously published RNN with different initialization and building technique but has the same architecture. The modification is based on starting with building nonlinear autoregressive exogenous input model using MATLAB and train it, then close the loop to get NNARX network.ResultsThe results of using the proposed NNARX indicate that the proposed NNARX is better in prediction and stability than unmodified RNN as PH becomes higher than 45 minutes.ConclusionsModification in RNN building extends the ability of the prediction till 100 minutes. It performs statistically significant improvements in the FIT and RMSE values for 100 minutes prediction. It also decreases root mean squared error (RMSE) for both 45 and 60 minutes of prediction.

Modeling, experimental investigation and real-time control of active water cooling system for photovoltaic module

ABSTRACT Photovoltaic (PV) cells are integral in harnessing solar energy, yet their performance is hindered by excessive heat generation, impacting efficiency and sustainability. Addressing the challenge of efficiency loss in photovoltaic (PV) cells due to overheating, this study focuses on optimizing active water cooling control for PV modules. The aim is to develop a dynamic, sustainable model and integrate a PID controller tuned by Sine Cosine Algorithm (SCA), targeting optimal operating temperatures. This study introduces a dynamic model and a closed-loop control system to manage PV cell temperature, investigating the correlation between water flow and temperature regulation. Experimental data is gathered using a pseudo-random binary sequence (PRBS) as an excitation signal, forming the foundation of an Auto Regressive eXogenous (ARX) model. The closed-loop system incorporates a PID controller and tuned using the Sine Cosine Algorithm (SCA) to optimize performance. The resulting model is rigorously validated through experimental investigation, demonstrating its precision in capturing the system’s dynamics. Moreover, the implementation of a controller-based cooling system substantiates the model’s practical efficacy. The research demonstrates significant improvements when implementing a controller-based water-cooling system for photovoltaic (PV) modules. Compared to the baseline scenario without cooling, the system achieves a 34.5% reduction in average PV temperature (from 59.2°C to 38.9°C) and a 9.46% increase in average power output (from 196.7W to 215.3W). Moreover, this system utilizes only 248.8 liters of water, marking a substantial 64% decrease in water consumption compared to traditional free-flow cooling methods, which use 790.9 liters. The research demonstrates that the controller-based cooling approach is a sustainable option, delivering power output comparable to the free-flow method, yet significantly lowering water consumption. This research signifies a turning point for sustainability, offering an efficient and water-conscious approach for enhancing PV system performance, a crucial step toward a greener and more environmentally responsible energy future.

Predicting the Torque Demand of a Battery Electric Vehicle for Real-World Driving Maneuvers Using the NARX Technique

An identification technique is proposed to create a relation between the accelerator pedal position and the corresponding driving moment. This step is beneficial to replace the complex physical model of the vehicle control unit, especially when the sufficient information needed to model certain functionalities of the vehicle control unit are unavailable. We utilized the nonlinear autoregressive exogenous model to regenerate the electric motor torque demand, given the accelerator pedal position, the motor’s angular speed, and the vehicle’s speed. This model proved to be extremely efficient in representing this highly complex relationship. The data employed for the identification process were chosen from an actual three-dimensional route with sudden changes of a dynamic nature in the driving mode, different speed limits, and elevations, as an attempt to thoroughly cover the driving moment scope based on the alternation of the given inputs. Analyzing the selected route data points showed the widespread coverage of the motor’s operational scope compared to a standard driving cycle. The training outcome revealed that linear modeling is inadequate for identifying the targeted system, and has a substantial estimation error. Adding the nonlinearity feature to the model led to an exceptionally high accuracy for the estimation and validation datasets. The main finding of this work is that the combined model from the nonlinear autoregressive exogenous and the sigmoid network enables the accurate modeling of highly nonlinear dynamic systems. Accordingly, the maximum absolute estimation error for the motor’s moment was less than 10 Nm during the real-world driving maneuver. The highest errors are found around the maximum motor’s moment. Finally, the model is validated with measurements from an actual field test maneuver. The identified model predicted the driving moment with a correlation of 0.994.

Defect detection and localisation using guided wave images from array data processed by nonlinear autoregressive exogenous model and Gamma statistical operator

Guided wave structural health monitoring (GWSHM) systems, using the delay-and-sum imaging algorithm, are an efficient solution to detect and localise defects in industrial structures. However, the image artifacts caused by either imperfect detection or sensor lay-out limitations make it difficult to identify and locate defects accurately. In order to enhance the performance of defect detection and localisation in GWSHM systems, this paper proposes a three-step procedure for post-processing guided wave signals prior to image formation. In the first step, the signals are processed using the nonlinear autoregressive exogenous model to suppress noise from benign features. The second step calculates the probability of defect presence based on the rescaled Gamma cumulative distribution function. This probabilistic threshold is then determined from the quantile mapping. Finally, a guide wave image is formed using the delay-and-sum imaging algorithm. The experimental validation was performed to inspect a 6 mm-diameter through-thickness circular hole on an aluminium plate and the defects were further scaled as simulated datasets to test its detectability under various amplitudes. In the second procedure step, the detection and localisation performance of the proposed procedure was compared with that of using the signal difference coefficient and the Rayleigh maximum likelihood estimator. It is shown that the proposed procedure can enhance the contrast between damaged and undamaged regions, providing more reliable and accurate guided wave images.

Performance analysis of a robust MF-PTC strategy for induction motor drive

The load model-based conventional predictive torque control (PTC) strategy performs as a high-performance controller at transient and steady-state conditions. However, its performance is poor on the issue of parameters variation. A robust model-free PTC (MF-PTC) strategy has been proposed in this paper to overcome the aforementioned drawback. An auto-regressive exogenous (ARX) model instead of a load model has been used to establish a model-free controller. This model is usually formed based on their input-output transfer function. A recursive least square algorithm has been employed to estimate the unknown parameters of the ARX model. Then, an observable canonical state-space model uses those estimated parameters to achieve an accurate prediction of the control variables. The performance of the proposed scheme can be affected by the variation of resistance. A resistance estimator based on the model reference adaptive system observer has been applied to improve the robustness of the system against variation of the stator and rotor resistance, and inductance measurement uncertainty. Simulation results show that the proposed MF-PTC scheme is robust against parameters uncertainty and works well at transient and steady-state conditions.

Implementation of ARM STM32F4 microcontroller for speed control of BLDC motor based on bat algorithm

Brushless direct current (BLDC) motor speed performance is an essential component that must be considered in the electric vehicle drive system. This research aims to obtain the transfer function from the mathematical modeling of the BLDC motor and optimization of the BLDC motor so that a high transient response is received. The method used in this study is to identify system parameters and then model them using the structure of the autoregressive exogenous (ARX) polynomial model. Meanwhile, to get a high transient response performance, optimization is done with a hybrid intelligent controller. The experimental findings indicate that the optimization process utilizing the bat method yielded the most favorable transient response. The resulting values for the proportional gain (Kp), integral gain (Ki), and derivative gain (Kd) were determined to be 31.2685, 7.7375, and -1.1934, respectively. In the current investigation, the minimum frequency value is 6381934.619. Also determined are the transient response characteristics, which include a rise time of 0.289 seconds, a settling time of 10.9 seconds, an overshoot of 3.4%, and a peak time of 1.04 seconds. Furthermore, the closed-loop system demonstrates stable behavior in terms of stability.

Active flow control for bluff body drag reduction using reinforcement learning with partial measurements

Active flow control for drag reduction with reinforcement learning (RL) is performed in the wake of a two-dimensional square bluff body at laminar regimes with vortex shedding. Controllers parametrised by neural networks are trained to drive two blowing and suction jets that manipulate the unsteady flow. The RL with full observability (sensors in the wake) discovers successfully a control policy that reduces the drag by suppressing the vortex shedding in the wake. However, a non-negligible performance degradation ( $\sim$ 50 % less drag reduction) is observed when the controller is trained with partial measurements (sensors on the body). To mitigate this effect, we propose an energy-efficient, dynamic, maximum entropy RL control scheme. First, an energy-efficiency-based reward function is proposed to optimise the energy consumption of the controller while maximising drag reduction. Second, the controller is trained with an augmented state consisting of both current and past measurements and actions, which can be formulated as a nonlinear autoregressive exogenous model, to alleviate the partial observability problem. Third, maximum entropy RL algorithms (soft actor critic and truncated quantile critics) that promote exploration and exploitation in a sample-efficient way are used, and discover near-optimal policies in the challenging case of partial measurements. Stabilisation of the vortex shedding is achieved in the near wake using only surface pressure measurements on the rear of the body, resulting in drag reduction similar to that in the case with wake sensors. The proposed approach opens new avenues for dynamic flow control using partial measurements for realistic configurations.

Online neuro-fuzzy model learning of dynamic systems with measurement noise

Model identification of nonlinear time varying dynamic systems is challenging because the system behaviours may vary significantly in different operational conditions. If the changes are insufficiently captured by training data, the trained model is unable to capture the system response well when the operational condition changes. The model performance may also be deteriorated in real-time implementation due to the noise in sensors or the environment. This paper presents a self-adaptive Neuro-Fuzzy (NF) modelling framework to address these challenges. The NF model, trained offline based on experimental data, combines the Auto-Regressive with eXogenous (ARX) models and Gaussian activation functions to capture the nonlinear system behaviours. During online implementation, the ARX model parameters are updated using new data through a recursive generalised least squares method, which embeds a noise model to eliminate effects of the noise. The online updating algorithm has a provable convergence guarantee and enables the proposed NF model to adapt to changes in system behaviours automatically. Efficacy of the algorithm is verified through two numerical examples and an experiment on a commercial automotive engine.

Nonlinear multi independent variables in quantifying river bank erosion using Neural Network AutoRegressive eXogenous (NNARX) model

This study proposed a novel application of Neural Network AutoRegressive eXogenous (NNARX) model in predicting nonlinear behaviour of riverbank erosion rates which is difficult to be achieved with good accuracy using conventional approaches. This model can estimate complex river bank erosion rates with flow variations. The NNARX model analysed to a set of primary data, 60% (203 data for training) and 40% (135 data for testing), which were collected from Sg. Bernam, Malaysia. A set of nondimensional parameters, known as functional relationship, used as an input to the NNARX model has been established using the method of repeating variables. The One-Step-Ahead time series prediction plots are used to assess the accuracy of all developed models. Model no. 6 (5 independent variables with 10 hidden layers) gives good predictive performance, supported by the graphical analysis with discrepancy ratio of 94% and 90% for training and testing datasets. This finding is consistent with model accuracy result, where Model no. 6 achieved R2 of 0.932 and 0.788 for training and testing datasets, respectively. Result shows that bank erosion is maximized when the near-bank velocity between 0.2 and 0.5 m/s, and the riverbank erosion is between 1.5 and 1.8 m/year. On the other hand, higher velocities ranging from 0.8 to 1.3 m/s induces erosion at a rate between 0.1 and 0.4 m/year. Sensitivity analysis shows that the highest accuracy of 91% is given by the ratio of shear velocity to near-bank velocity followed by boundary shear stress to near-bank velocity ratio (88.5%) and critical shear stress to near-bank velocity ratio (88.2%). It is concluded that the developed model has accurately predicted non-linear behaviour of riverbank erosion rates with flow variations. The study's findings provide valuable insights in advanced simulations and predictions of channel migration, encompassing both lateral and vertical movements, the repercussions on the adjacent river corridor, assessing the extent of land degradation and in formulating plans for effective riverbank protection and management measures.

A Dynamic Nonlinear Autoregressive Exogenous Model to Analyze the Impact of Mobility during COVID-19 Pandemic on the Electricity Consumption Prediction in Jordan

A Dynamic Nonlinear Autoregressive Exogenous Model to Analyze the Impact of Mobility during COVID-19 Pandemic on the Electricity Consumption Prediction in Jordan