Autoregressive Exogenous Model Research Articles

Comprehensive compensation of dynamic hysteresis and creep for piezoelectric actuator

Abstract 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 model with an Prandtl-Ishlinskii-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.

Estimating lags in a kraft mill

Abstract 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 in the 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%.

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.

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.

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

Online Detection and Fuzzy Clustering of Anomalies in Non-Stationary Time Series

We consider the challenge of detecting and clustering point and collective anomalies in streaming data that exhibit significant nonlinearities and seasonal structures. The challenge is motivated by detecting problems in a communications network, where we can measure the throughput of nodes, and wish to rapidly detect anomalous traffic behaviour. Our approach is to train a neural network-based nonlinear autoregressive exogenous model on initial training data, then to use the sequential collective and point anomaly framework to identify anomalies in the residuals generated by comparing one-step-ahead predictions of the fitted model with the observations, and finally, we cluster the detected anomalies with fuzzy c-means clustering using empirical cumulative distribution functions. The autoregressive model is sufficiently general and robust such that it provides the nearly (locally) stationary residuals required by the anomaly detection procedure. The combined methods are successfully implemented to create an adaptive, robust, computational framework that can be used to cluster point and collective anomalies in streaming data. We validate the method on both data from the core of the UK’s national communications network and the multivariate Skoltech anomaly benchmark and find that the proposed method succeeds in dealing with different forms of anomalies within the nonlinear signals and outperforms conventional methods for anomaly detection and clustering.

Uncertainty Evaluation of a Gas Turbine Model Based on a Nonlinear Autoregressive Exogenous Model and Monte Carlo Dropout.

Gas turbines are thermoelectric plants with various applications, such as large-scale electricity production, petrochemical industry, and steam generation. In order to optimize the operation of a gas turbine, it is necessary to develop system identification models that allow for the development of studies and analyses to increase the system's reliability. Current strategies for modeling complex and non-linear systems can be based on artificial intelligence techniques, using autoregressive neural networks of the NARX and LSTM type. In this context, this work aims to develop a model of a gas turbine capable of estimating the rotation speed of the turbine and simultaneously estimating the uncertainty associated with the estimation. These methodologies are based on artificial neural networks and the Monte Carlo dropout simulation method. The results were obtained from experimental data from a 215 MW gas turbine, getting the best model with a MAPE of 0.02% and an uncertainty associated with the turbine rotation speed of 2.2 RPM.

Machine Learning-Based Indoor Relative Humidity and CO2 Identification Using a Piecewise Autoregressive Exogenous Model: A Cob Prototype Study

The population of developed nations spends a significant amount of time indoors, and the implications of poor indoor air quality (IAQ) on human health are substantial. Many premature deaths attributed to exposure to indoor air pollutants result from diseases exacerbated by poor indoor air. CO2, one of these pollutants, is the most prevalent and often serves as an indicator of IAQ. Indoor CO2 concentrations can be significantly higher than outdoor levels due to human respiration and activity. The primary objective of this research was to numerically investigate the indoor relative humidity and CO2 in cob buildings through the CobBauge prototype, particularly during the first months following the building delivery. Both in situ experimental studies and numerical predictions using an artificial neural network were conducted for this purpose. The study presented the use of a piecewise autoregressive exogenous model (PWARX) for indoor relative humidity (RH) and CO2 content in a building constructed with a double walling system consisting of cob and light earth. The model was validated using experimental data collected over a 27-day period, during which indoor RH and CO2 levels were measured alongside external conditions. The results indicate that the PWARX model accurately predicted RH levels and categorized them into distinct states based on moisture content within materials and external conditions. However, while the model accurately predicted indoor CO2 levels, it faced challenges in finely classifying them due to the complex interplay of factors influencing CO2 levels in indoor environments.

The Nesterov accelerated gradient algorithm for Auto-Regressive Exogenous models with random lost measurements: Interpolation method and auxiliary model method

For ARX models with random lost measurements, this article proposes an interpolation and auxiliary model based Nesterov accelerated gradient algorithm. This algorithm utilizes the interpolation and auxiliary model methods to fill in lost measurements. The parameters are estimated with better accuracy based on the interpolated input and predicted output data. Two simulation examples are presented to verify the effective of the proposed algorithm.

An Efficient Dynamic Auto-Regressive CCA for Time Series Imputation With Irregular Sampling

System dynamics are inevitable in industrial processes due to factors such as ambient disturbances and controller tuning. Accurate modeling of these dynamics are of key importance for subsequent process analysis and anomaly detection, and dynamic latent variable methods are widely adopted since they retain good interpretability. However, only dynamic cross-correlations are modeled in existing methods, leaving a large portion of quality information unexploited. In this work, an efficient dynamic auto-regressive canonical correlation analysis (EDACCA) method is proposed with a modified auto-regressive exogenous model to extract dynamics in both auto-correlations and cross-correlations. The flexibility and efficiency of EDACCA are improved with the design of weighting parameters and the economic singular value decomposition. EDACCA is further adapted for multi-step ahead (MS) prediction and missing data imputation. Two industrial processes are employed to evaluate the prediction performance and imputation performance of EDACCA. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Different sampling rates are usually set for process and quality variables in industrial processes, which leads to less quality samples. Meanwhile, system dynamics are not fully exploited for dynamic predictive modeling in most existing algorithms. The focus of this study is to develop a customized data imputation method for different data volume of process and quality data. An efficient dynamic auto-regressive canonical correlation analysis (EDACCA) is designed to extract temporal relations between process and quality variables, which is also adapted for multi-step-ahead prediction purpose. An EDACCA based data imputation method is also proposed to impute incomplete data caused by irregular sampling rates.

Model Predictive Control in buildings with thermal and visual comfort constraints

Model Predictive Control can cope with conflicting control objectives in building energy managements. In terms of user satisfaction, visual comfort has been proven in several studies to be a crucial factor, however thermal comfort is typically considered the only important aspect. Besides human well-being, visual comfort strongly impacts the productivity of the occupants in offices. Therefore, from an economic point of view, it is essential to include visual comfort in Model Predictive Control for buildings. In this paper semi-linear support vector machine is applied to learn suitable models for visual comfort measured by Daylight Glare Probability. The resulting model is incorporated into a Model Predictive Control framework, together with an autoregressive exogenous model accounting for the thermal dynamics of the building. The approach is validated through an extensive numerical case study, and the benefits of including visual comfort and blind control in the Model Predictive Control problem are evaluated. We observe that the proposed Model Predictive Control scheme ensures both the thermal and visual comfort constraints at the expense of 2.2% to 7.2% higher energy consumption compared to the benchmark Model Predictive Control configuration, which considers only the thermal comfort constraints.

Parameters estimation for the Hammerstein‐Wiener models with colored noise based on hybrid signals

SummaryA three‐stage estimation approach of the Hammerstein‐Wiener model with colored noise using hybrid signals is considered in this article. The Hammerstein‐Wiener model where a linear dynamic block is embedded between two static nonlinear elements, in which two nonlinear elements represented by two independent neural fuzzy models and a linear element represented by autoregressive exogenous model. The designed hybrid signals that consist of separable signals and random signals are devoted to estimating independently. First, the characteristics of separable signals in the action of the static nonlinear element are analyzed, then the output nonlinear element parameters are estimated utilizing two groups of separable signals with a multiple. Moreover, least squares based on correlation analysis method is applied to estimate linear element using one set of separable signals, which handles the interference of colored process noise. Finally, the recursive extended least squares algorithm is derived to estimate the input nonlinear element and the autoregressive moving average noise model, which improves parameters estimation accuracy owing to estimating colored noise model parameters in recursive estimate process. The feasibility of the presented estimation technique is demonstrated by an illustrative simulation example and a practical nonlinear process.