Autoregressive Exogenous Model Research Articles

Simultaneous Estimation of Glottal Source Waveforms and Vocal Tract Shapes from Speech Signals Based on ARX-LF Model

Estimating glottal source waveforms and vocal tract shapes is typically done by processing the speech signal using an inverse filter and then fitting the residual signal using the glottal source model. However, due to source-tract interactions, the estimation accuracy is reduced. In this paper, we propose a method to estimate glottal source waveforms and vocal tract shapes simultaneously based on an analysis-by-synthesis approach with a source-filter model constructed of an Auto-Regressive eXogenous (ARX) model and the Liljencrants-Fant (LF) model. Since the optimization of multiple parameters makes simultaneous estimation difficult, we first initialize the glottal source parameters using the inverse filter method, and then simultaneously estimate the accurate parameters of the glottal sources and the vocal tract shapes using an analysis-by-synthesis approach. Experimental results with synthetic and real speech signals showed that the proposed method has higher estimation accuracy than using the inverse filter.

Identification and fault detection in actuator using NN-NARX

In this paper, the use of a Nonlinear Auto Regressive eXogenous Neural Networks model or NN-NARX for identification and fault detection in the actuator of an industrial thermal process is presented. Initially, the techniques of fault detection and diagnosis are exposed; then, emphasis is placed on the models of Artificial Neural Networks for identification and fault detection. Subsequently, the control system of a thermal process used as a case study is described. A monitoring system allows data recording under normal operation conditions for identification using the NN-NARX model. The model is used for residual online generation due to faults that are introduced randomly. Finally, the results of residual generation and evaluation are presented. The designed system is useful for implementation through a hardware device that can be incorporated into the process equipment and support the operator in the presence of failures.

Interval Error Correction Auxiliary Model Based Gradient Iterative Algorithms for Multirate ARX Models

To improve the identification efficiency of the auxiliary model based gradient iterative algorithm, this article derives a couple of interval error correction auxiliary model based gradient iterative (IEC-AM-GI) algorithms for multirate AutoRegressive eXogenous (ARX) models. The unmeasurable outputs between two measured outputs are estimated by two interval error correction auxiliary models. Unlike the AM-GI algorithm, the IEC-AM-GI algorithms can estimate the missing outputs by the auxiliary model and further fine tune through the measurable outputs, which thus are more efficient and accurate than those by only using the auxiliary model. In addition, this article makes a comparison between these two interval error correction auxiliary model methods and through which the optimal interval error correction auxiliary model method for the unmeasurable outputs can be chosen. The effectiveness of the proposed algorithms is demonstrated by the simulation results.

Data-Driven Short-Term Solar Irradiance Forecasting Based on Information of Neighboring Sites

Short-term forecasting of solar irradiance at a targeted site with consideration of its time series and measurements at neighboring sites is studied in this paper. A data-driven framework for forecasting solar irradiance based on fusing spatial and temporal information is proposed. In the framework, data-driven approaches including boosted regression trees (BRT), artificial neural network, support vector machine, and least absolute shrinkage and selection operator are applied to model spatial dependence among solar irradiance time series thereby to generate forecasts of solar irradiance at the targeted site. A comprehensive comparison among data-driven forecasting models is performed using 30-min averaged data of recent two years. Moreover, benchmarking models including scaled persistence model, autoregressive model, and autoregressive exogenous model are employed to further validate the effectiveness of data-driven forecasting models. Computational results of multiple-steps ahead forecasting demonstrate that the BRT model gives the best performance with the lowest normalized root mean squared error of 18.4%, 24.3%, 27.9%, and 30.6% for forecasting horizons of 30, 60, 90, and 120-min, respectively.

Cooling Load Forecasting via Predictive Optimization of a Nonlinear Autoregressive Exogenous (NARX) Neural Network Model

Accurate calculations and predictions of heating and cooling loads in buildings play an important role in the development and implementation of building energy management plans. This study aims to improve the forecasting accuracy of cooling load predictions using an optimized nonlinear autoregressive exogenous (NARX) neural network model. The preprocessing of training data and optimization of parameters were investigated for model optimization. In predictive models of cooling loads, the removal of missing values and the adjustment of structural parameters have been shown to help improve the predictive performance of a neural network model. In this study, preprocessing the training data eliminated missing values for times when the heating, ventilation, and air-conditioning system is not running. Also, the structural and learning parameters were adjusted to optimize the model parameters.

Optimization of time‐variable‐parameter model for data‐based soft sensor of industrial debutanizer

SummaryThe enhancement of modern process control methods has caused the popularity of soft sensors in online quality prediction. It is significant to consider the reduction of model complexity, the performance increment, and decrement of input variables in soft sensor design, simultaneously. The aim of this paper is designing and applying a new data‐based soft sensor with minimum input variables for the enhancement of product quality estimation. Time‐varying‐parameter model by employing the Kalman filter and fixed interval smoothing algorithms has been developed to determine the dynamic transfer function and parameters setting based on time. A novel hybrid method with a dynamic autoregressive exogenous variable model and genetic algorithm has been presented for both state identification and parameter prediction. The combinatorial optimization problem has constructed based on a selection of input variables and an evaluation of Akaike information criterion as a fitness function. An industrial debutanizer column has been used for soft sensor performance validation. The result has indicated that the final soft sensor model in comparison to other presented soft sensing methods for this case has less complexity, fewer input variables, more robust and higher predictive performance. Due to fewer input variables, rapid convergence, and low complexity of this model, it can be efficient in industrial processes control, time‐saving, and improvement of quality prediction.

Sequential Monte Carlo Filter for State-of-Charge Estimation of Lithium-Ion Batteries Based on Auto Regressive Exogenous Model

The state of charge (SOC) of lithium-ion batteries (LIBs) is an important evaluation index in battery management system of energy storage systems. However, it is always a challenging task to accurately estimate SOC of LIBs, because of the existence of nonlinear characteristics and significant temperature effects. To improve the SOC estimation accuracy and robustness, a model-based estimation approach for SOC and impedance of LIBs is proposed against uncertain loading profiles and ambient temperatures. First an auto regressive exogenous model for online model order determining and parameters identification is established to monitor parameters variations based on numerical subspace state space system identification method. Second, a sequential Monte Carlo filter is employed to overcome the nonlinear and non-Gaussian error distribution state estimation problems caused by complicated open-circuit voltage characteristics. Finally, evaluation of the adaptability and generality of the proposed method are verified by different LIBs under different operating conditions. Experimental results indicate that the proposed method shows great performance, whose estimation value converges to real SOC within an error of $\pm \text{3}\%$ , and the battery model can simulate battery dynamics robustly with high accuracy.

An Online Virtual Metrology Model With Sample Selection for the Tracking of Dynamic Manufacturing Processes With Slow Drift

Modeling of dynamic manufacturing processes with slow drift using data-driven approaches is challenging because most data-driven models are trained by off-line data. In this paper, we propose to track slow drift of manufacturing processes using an online Bayesian Auto-Regression eXogenous (ARX) model with time-variant parameters. The model parameters are trained off-line and are updated online using Bayes’ rule. To avoid the frequent online model update, a Sample Importance (SI) test is proposed to screen online samples and only the sample that passes SI test is incremented to the VM model. The SI test decides the importance of the sample by collectively considering sample freshness, model prediction error and prediction uncertainty. Furthermore, the SI test is applied to off-line Data Base (DB) and an iteration algorithm is devised for off-line sample selection. The off-line sample selection algorithm can effectively reduce the sample redundancy in off-line DB while maintaining the model performance. To validate the effectiveness of the proposed method, Prognostics and Health Management (PHM) data challenge 2016 dataset is employed to predict material removal rate of chemical-mechanical planarization process. The validation results indicate that the proposed method outperforms existing state-of-art approaches in literature such as Just-in-Time (JIT) and deep learning models.

Regression and classifier of real-time fault data using non-linear autoregressive exogenous model (NARX analysis) and comparing with Python tool

Regression and classifier of real-time fault data using non-linear autoregressive exogenous model (NARX analysis) and comparing with Python tool

Long-Term Glucose Forecasting Using a Physiological Model and Deconvolution of the Continuous Glucose Monitoring Signal.

(1) Objective: Blood glucose forecasting in type 1 diabetes (T1D) management is a maturing field with numerous algorithms being published and a few of them having reached the commercialisation stage. However, accurate long-term glucose predictions (e.g., >60 min), which are usually needed in applications such as precision insulin dosing (e.g., an artificial pancreas), still remain a challenge. In this paper, we present a novel glucose forecasting algorithm that is well-suited for long-term prediction horizons. The proposed algorithm is currently being used as the core component of a modular safety system for an insulin dose recommender developed within the EU-funded PEPPER (Patient Empowerment through Predictive PERsonalised decision support) project. (2) Methods: The proposed blood glucose forecasting algorithm is based on a compartmental composite model of glucose–insulin dynamics, which uses a deconvolution technique applied to the continuous glucose monitoring (CGM) signal for state estimation. In addition to commonly employed inputs by glucose forecasting methods (i.e., CGM data, insulin, carbohydrates), the proposed algorithm allows the optional input of meal absorption information to enhance prediction accuracy. Clinical data corresponding to 10 adult subjects with T1D were used for evaluation purposes. In addition, in silico data obtained with a modified version of the UVa-Padova simulator was used to further evaluate the impact of accounting for meal absorption information on prediction accuracy. Finally, a comparison with two well-established glucose forecasting algorithms, the autoregressive exogenous (ARX) model and the latent variable-based statistical (LVX) model, was carried out. (3) Results: For prediction horizons beyond 60 min, the performance of the proposed physiological model-based (PM) algorithm is superior to that of the LVX and ARX algorithms. When comparing the performance of PM against the secondly ranked method (ARX) on a 120 min prediction horizon, the percentage improvement on prediction accuracy measured with the root mean square error, A-region of error grid analysis (EGA), and hypoglycaemia prediction calculated by the Matthews correlation coefficient, was , , and , respectively. Although showing a trend towards improvement, the addition of meal absorption information did not provide clinically significant improvements. (4) Conclusion: The proposed glucose forecasting algorithm is potentially well-suited for T1D management applications which require long-term glucose predictions.

A randomized two-stage iterative method for switched nonlinear systems identification

This paper addresses the identification of discrete time switched nonlinear systems, which are collections of discrete time nonlinear continuous systems (modes) indexed by a finite-valued variable defining the current mode. In particular, we consider the class of Switched Nonlinear AutoRegressive eXogenous (Switched NARX, or SNARX) models, where the continuous dynamics are represented by NARX models. Given a set of input–output data, the identification of a SNARX model for the underlying system involves the simultaneous identification of the mode sequence and of the NARX model associated to each mode, configuring a mixed integer non-convex optimization problem, hardly solvable in practice due to the large combinatorial complexity. In this paper, we propose a black-box iterative identification method, where each iteration is characterized by two stages. In the first stage the identification problem is addressed assuming that mode switchings can occur only at predefined time instants, while in the second one the candidate mode switching locations are refined. This strategy allows to significantly reduce the combinatorial complexity of the problem, thus allowing an efficient solution of the optimization problem. The combinatorial optimization is addressed using a randomized method, whereby the sample-mode map and the SNARX model structure are characterized by a probability distribution, which is progressively tuned via a sample-and-evaluate strategy, until convergence to a limit distribution concentrated on the best SNARX model of the system generating the observed data.

Multimodel Approach to Robust Identification of Multiple-Input Single-Output Nonlinear Time-Delay Systems

The robust multimodel solution for multiple-input single-output nonlinear time-delay systems identification with polluted outputs is derived in this article. First, all the local autoregressive exogenous models are preidentified at the working points; then, the global system model is built by interpolating the local models with a smoothing strategy. The outliers and input time-delays which often increase the nonideality of process data are both considered. To cope with the outliers, the Laplace distribution is reutilized to describe the output measurement process and the negative impact resulted from each outlier imposed on parameter estimation can be suppressed through automatically assigned small weight. The parameter estimation procedure is realized with the expectation–maximization algorithm and the joint posterior probability of all input delays is also maximized to calculate the unknown input time-delays. With the verifications on a numerical example and the continuous fermentation process, the validity of the proposed approach is proved.

Analysis of hourly cooling load prediction accuracy with data-mining approaches on different training time scales

Data-mining approaches for improving building cooling load predictions are presented and analyzed on different training time scales (T-1 to T-6) in this paper. Multiple linear regression (MLR), auto regression (AR), autoregressive exogenous (ARX) model, multiple nonlinear regression (MNR), and a back propagation neural network (BP). In this study, a real case in Guangzhou was examined to verify the performance of the prediction models on different time scales using measured cooling load and weather data. Based on the sensitivity analysis, the variable with largest sensitivity is selected as the input to the proposed MNR model, which can ensure prediction accuracy while increasing prediction speed. The case study shows that the prediction from the MNR model is comparable to or better than that from the BP model on different training time scales. The results also show that the MNR model could provide satisfactory prediction accuracy with less data (e.g., 3 d of weather and historical load data), while the BP model requires at least one month of training data to provide the same prediction accuracy. An analysis of the prediction performance results shows that the prediction accuracy from the regression models will decrease and the prediction accuracy from the BP model gradually increases as the training time scale increases. Surprisingly, the prediction accuracy with the MNR model is superior to that from the BP model with T-1 to T-4 training time scales. Finally, it is shown that the MNR model with the limited variable as inputs provides higher prediction accuracy than four other models with training time scales T-1 to T-4. The MNR model requires less training data, simpler hardware, and low computational complexity, making it preferable for quick on-site load prediction.

Data-Driven Modeling and UFIR-Based Outlet NO$_{x}$ Estimation for Diesel-Engine SCR Systems

An accurate and efficient model for selective catalytic reduction (SCR) systems plays an important role in diagnosis and control of diesel-engine after-treatment systems. In this paper, we investigate the data-driven modeling of SCR systems and outlet NO $_{x}$ concentration estimation based on the developed data-driven model and the algorithm of unbiased finite impulse response (UFIR) filtering. The structure used for the data-driven model is an autoregressive exogenous (ARX) model and the method of partial least square is utilized to identify the parameters of the corresponding ARX model. Moreover, the approach of fuzzy c-means is employed to partition the data and derive multiple local linear models with a better performance on approximating the system nonlinearities. Finally, the algorithm of UFIR filtering is adopted to estimate the outlet NO $_{x}$ concentration due to its strong robustness without the statistics of process and measurement noises. The performance of proposed approaches on SCR systems is validated with simulations based on experimental data. In addition, comparisons show the improvement of the adopted algorithm on the estimation accuracy.

Development of a Soft Sensor for Indirect Temperature Measurement in a Coffee Machine

In control processes, sometimes it would be necessary to know variables at locations that are barely accessible. In such cases, soft sensors (also known as “virtual sensors”) could really help. In fact, they are powerful instruments for the indirect measure of quantities that would not be measurable, if not with the installation of physical sensors that could perturbate the normal working conditions of the system under test. In this paper, the authors describe an approach to indirectly measure temperature values in a brew group of a professional coffee machine. A finite element (FE) model simulating both the fluid dynamics and the thermal distribution on the group was developed and validated by dedicated experimental tests. The FE model was then exploited to feed an autoregressive exogenous model [autoregressive with eXogenous input (ARX) model] linking the temperature in the boiler (i.e., a quantity ordinarily assessed in the coffee machine) and the one near the water output, where otherwise a hardware sensor would compromise the correct coffee brewing process and the safety/quality of the brewed coffee. The obtained data-driven soft sensor can help to improve the control unit architecture of the coffee machine.

Effect of Sensors Sensitivity on Lithium-Ion Battery Modeled Parameters and State of Charge: A Comparative Study

The accurate estimation of the state of charge (SOC) is usually acknowledged as one of the essential features in designing of battery management system (BMS) for the lithium-ion batteries (LIBs) in electric vehicles (EVs). A suitable battery model is a prerequisite for correct SOC measurement. In this work, the first and second order RC autoregressive exogenous (ARX) battery models are adopted to check the influence of voltage and current transducer measurement uncertainty. The Lagrange multiplier method is used to estimate the battery parameters. The sensitivity analysis is performed under the following conditions: Current sensor precision of ±5 mA, ±50 mA, ±100 mA, and ±500 mA and voltage sensor precision of ±1 mV, ±2.5 mV, ±5 mV, and ±10mV. The comparative analysis of both models under the perturbed environment has been carried out. The effects of the sensor’s sensitivity on the different battery structures and complexity are also analyzed. Results shows that the voltage and current sensor sensitivity has a significant influence on SOC estimation. This research outcome assists the researcher in selecting the optimal value of sensor accuracy to accurately estimate the SOC of the LIB.

The System Science Development of Local Time‐Dependent 40‐keV Electron Flux Models for Geostationary Orbit

AbstractAt geosynchronous Earth orbit, the radiation belt/ring current electron fluxes with energies up to several hundred kiloelectron volts can vary widely in magnetic local time (MLT). This study aims to develop Nonlinear AutoRegressive eXogenous models using system science techniques, which account for the spatial variation in MLT. This is difficult for system science techniques, since there is sparse data availability of the electron fluxes at different MLT. To solve this problem, the data are binned from Geostationary Operational Environmental Satellites (GOES) 13, 14, and 15 by MLT, and a separate Nonlinear AutoRegressive eXogenous model is deduced for each bin using solar wind variables as the inputs to the model. These models are then conjugated into one spatiotemporal forecast. The model performance statistics for each model varies in MLT with a prediction efficiency between 47% and 75% and a correlation coefficient between 51.3% and 78.9% for the period from 1 March 2013 to 31 December 2017.

Identification and control of nonlinear systems using PieceWise Auto-Regressive eXogenous models

In this paper, we consider the problems of nonlinear system representation and control. In fact, we propose a solution based on PieceWise Auto-Regressive eXogenous (PWARX) models since these models are able to approximate any nonlinear behaviour with arbitrary precision. Moreover, the identification and control approaches of linear systems can be extended to these models because the parameters of each sub-model are linearly related to the output. The proposed solution is based on two steps. The first allows to represent the nonlinear system by a PWARX model using the identification approach. The second consists in designing a controller for each sub-model using the pole placement strategy. Simulation and experimental results are presented to illustrate the performance of the proposed approach.

Neural Network Approach to Forecast Hourly Intense Rainfall Using GNSS Precipitable Water Vapor and Meteorological Sensors

This work presents a methodology for the short-term forecast of intense rainfall based on a neural network and the integration of Global Navigation and Positioning System (GNSS) and meteorological data. Precipitable water vapor (PWV) derived from GNSS is combined with surface pressure, surface temperature and relative humidity obtained continuously from a ground-based meteorological station. Five years of GNSS data from one station in Lisbon, Portugal, are processed. Data for precipitation forecast are also collected from the meteorological station. Spaceborne Spinning Enhanced Visible and Infrared Imager (SEVIRI) data of cloud top measurements are also gathered, providing collocated information on an hourly basis. In previous studies it was found that the time-varying PWV is correlated with rainfall and can be used to detected heavy rain. However, a significant number of false positives were found, meaning that the evolution of PWV does not contain enough information to infer future rain. In this work, a nonlinear autoregressive exogenous neural network model (NARX) is used to process the GNSS and meteorological data to forecast the hourly precipitation. The proposed methodology improves the detection of intense rainfall events and reduces the number of false positives, with a good classification score varying from 63% up to 72% and a false positive rate of 36% down to 21%, for the tested years in the dataset. A score of 64% for intense rain events classification with 22% false positive rate is obtained for the most recent years. The method also achieves an almost 100% hit rate for the rain vs no rain detection, with close to no false alarms.

A novel adaptive model predictive controller for load frequency control of power systems integrated with DFIG wind turbines

With the rapid growth of renewable energy resources, wind energy system is getting more interest everywhere throughout the world. However, its extensive use in power systems prompts many power system dynamics and stability problems. Load variation and anomalous operating conditions prompt inconsistencies in frequency and planned power trades. These inconsistencies should be remedied by load frequency control. This paper introduces a novel frequency control system utilizing a mix of adaptive model predictive controller (AMPC) and recursive polynomial model estimator (RPME) integrated with double fed induction generator wind turbines. Inside each control duration, the RPME is identifying a discrete-time online autoregressive exogenous model. The latter is used through the AMPC to update the interior plant model in order to achieve a successful nonlinear control. The performance of the proposed system has been verified and contrasted with the conventional MPC system through a computer simulation-based MATLAB/SIMULINK. The simulation results demonstrated the superiority of the proposed system as for the conventional MPC system.