ARX Model Research Articles

Analysis and Parametrical Estimation with Real COVID-19 Data of a New Extended SEIR Epidemic Model with Quarantined Individuals

During the recent COVID-19 pandemic, quarantine and testing policies have been of vital importance since the causative agent has been a novel virus and no vaccine was developed at the time. In this work, a new epidemiological deterministic model is proposed, analyzed, and discussed. Such a model includes quarantine periods of people with symptoms that have been tested positive, and it will trigger a trace of their close contact, who will be also tested and put in quarantine if the result is positive. Moreover, how the model parameters affect its stability is analyzed with the basic reproduction number R0. Since the COVID-19 outbreak in Spain (approximately 13/03/2020) until 25/04/2021, different restrictions have been applied. For discussion of a real case study, data have been gathered and used from the Spanish Autonomous Community of Cantabria to estimate the parameters and to see how the restrictions have affected their values. In the parameter estimation process, it has been assumed that the constructed model follows the structure of an ARX model. Finally, by considering that the gathered data are subject to certain errors, the paper discusses how to adequate the model usefulness for its use in fitting and processing data through an estimation mechanism involving the provided daily total and positive performed tests.

Novel Strategy of Adaptive Predictive Control Based on a MIMO-ARX Model

Many industrial processes include MIMO (multiple-input, multiple-output) systems that are difficult to control by standard commercial controllers. This paper describes a MIMO case of a class of SISO-APC (single-input, single-output adaptive predictive controller) based upon an ARX (autoregressive with exogenous variable) model. This class of SISO-APC based on ARX models has been successfully and extensively used in many industrial applications. This approach aims to minimize the barriers between the theory of predictive adaptive control and its application in the industrial environment. The proposed MIMO-APC (MIMO adaptive predictive controller) performance is validated with two simulated processes: a quadrotor drone and the quadruple tank process. In the first experiment the proposed MIMO APC shows ISE-IAE-ITAE performance indices improvements of up to 25%, 25.4% and 38.9%, respectively. For the quadruple tank process the water levels in the lower tanks follow closely the set points, with the exception of a 13% overshoot in tank 1 for the minimum phase behavior response. The controller responses show significant performance improvements when compared with previously published MIMO control strategies.

Identification of microwave heating system with symmetrical octagonal tube cavity using ARX model

As one of the complex technologies in the heating process, microwave heating system has gained attentions in the recent years. A further development of microwave heating control technology becomes necessary considering its superiorities in less energy consumption, volumetric heating ability and satisfying mechanical properties. Several studies on microwave heating system modelling were conducted to encourage the controller design. This work presents the modelling of a microwave heating system using autoregressive with exogenous variables or so-called ARX. The modelling conducted in this research applied the approach of input-output identification method. The generation of input-output datasets for the identification of microwave heating system was carried out in COMSOL simulation environment using symmetrical octagonal tube cavity design with two magnetrons as the inputs and five temperature sensors as the output measurement devices. For the validation and evaluation of the approach, MATLAB identification system toolbox was utilized to find the best ARX model based on the given input-output datasets. The validation test shows that the best ARX model can reach more than 93% in the fit value given all the datasets for all the outputs, while for the evaluation using the perturbed signals from the outside of datasets, the chosen model can obtain 97.35% in the average of the fit value for all the outputs.

Density Estimation in the Regressor Space for Linear and Nonlinear System Identification

In this paper, a new weighting approach for dynamic datasets is introduced. The overall goal of the new method is to improve data-driven model performance. This is achieved by increasing the weight of training data points in areas of the regressor space that are underrepresented in the loss function, while decreasing the weight for overrepresented data points. The method is based on estimating the parameters of a model using weighted error norms, where the weighting is carried out with the inverse values of the kernel density estimated in the regressor space. The performance of the new method is investigated using ARX models as examples in three different cases: when using datasets with different data distributions, datasets with different noise levels, and incorrectly assumed model orders. Additionally, a first attempt of weighted nonlinear system identification is performed. Overall, models weighted by the new method show a significantly improved performance compared to unweighted models while requiring an insignificant amount of additional computational effort.

Experimental performances of nonlinear GPC and discrete–time PID in multivariate process: NARIMAX and ARX models in temperature control of reactive distillation column in synthesis of biodiesel from waste cooking oil

Experimental performances of nonlinear GPC and discrete–time PID in multivariate process: NARIMAX and ARX models in temperature control of reactive distillation column in synthesis of biodiesel from waste cooking oil

Microwave heating control system using genetic algorithm-based PID controller

The superiorities of microwave heating technology have attracted many researchers for further development. Designing a satisfying temperature control system for the microwave system is one of them. To confirm that the controller can work with good system performance, the adjustment of controller parameters is important. Most previous research about microwave control systems did not focus on the tuning problem which is presented in this work. This paper provides the use of a genetic algorithm to adjust the best parameters for a PID controller. A microwave heating system with a single microwave power input and a single output temperature probe which is identified using the ARX model is examined. Evaluation of the proposed controller was conducted in the simulation environment using MATLAB. The result shows that the genetic algorithm can obtain the most optimized parameter for PID controller which can follow a certain heating pattern. The parameters for Kp, Ki, and Kd are 998.94, 79.42, and 79.78, respectively. It can minimize the value of integral absolute error for the given setpoint to 446.11.

Control-Relevant Adaptive Personalized Modeling From Limited Clinical Data for Precise Warfarin Management.

Warfarin is a challenging drug to administer due to the narrow therapeutic index of the International Normalized Ratio (INR), the inter- and intra-variability of patients, limited clinical data, genetics, and the effects of other medications. Goal: To predict the optimal warfarin dosage in the presence of the aforementioned challenges, we present an adaptive individualized modeling framework based on model (In)validation and semi-blind robust system identification. The model (In)validation technique adapts the identified individualized patient model according to the change in the patient's status to ensure the model's suitability for prediction and controller design. Results: To implement the proposed adaptive modeling framework, the clinical data of warfarin-INR of forty-four patients has been collected at the Robley Rex Veterans Administration Medical Center, Louisville. The proposed algorithm is compared with recursive ARX and ARMAX model identification methods. The results of identified models using one-step-ahead prediction and minimum mean squared analysis (MMSE) show that the proposed framework effectively predicts the warfarin dosage to keep the INR values within the desired range and adapt the individualized patient model to exhibit the true status of the patient throughout treatment. Conclusion: This paper proposes an adaptive personalized patient modeling framework from limited patientspecific clinical data. It is shown by rigorous simulations that the proposed framework can accurately predict a patient's doseresponse characteristics and it can alert the clinician whenever identified models are no longer suitable for prediction and adapt the model to the current status of the patient to reduce the prediction error.

Multitask Maximum Likelihood Identification for ARX Model With Multisensor

Multitask Maximum Likelihood Identification for ARX Model With Multisensor

Model Identification and Control of Evapotranspiration for Irrigation Water Optimization

Water conservation starts from rationalizing irrigation, as it is the largest consumer of this vital source. Following the critical and urgent nature of this issue, several works have been proposed. The idea of most researchers is to develop irrigation management systems to meet the water needs of plants with optimal use of this resource. In fact, irrigation water requirement is only the amount of water that must be applied to compensate the evapotranspiration loss. Penman-Monteith equation is the most common formula to evaluate reference evapotranspiration, but it requires many factors that cannot be available in many cases. This leads to a trend towards behavior model estimation. System identification with control is one of the most promising applications in this axis. The idea behind this proposal depends on three stages: First, the estimation of reference evapotranspiration (ET0) by a linear ARX model, where temperature, relative humidity, insolation duration and wind speed are used as inputs, and ET0 estimated by Penman-Monteith equation as output. The results show that the values estimated by this method were in good agreement with the measured data. The second part of this paper is to manage the quantity of water. For this purpose, two controllers are used for testing, lead-lag and PID. To adjust the first controller and optimize the choice of its parameters, Nelder-Mead algorithm is used. In the last part, a comparative study is done between the two used controllers.

Identification of an ARX model with impulse noise using a variable step size information gradient algorithm based on the kurtosis and minimum Renyi error entropy

AbstractARX model is an autoregressive model with exogenous terms. Because of its simplicity and easy parameterization, the ARX model has been widely used in various applications. However, most reports on ARX identification are about Gaussian noise or white noise environment. In many practical industrial applications, impulse noise widely exists. For systems contaminated by this noise, the performance of the mean square error algorithm will deteriorate. To get more accurate results, a variable step size stochastic information gradient algorithm is proposed. The algorithm is based on the Renyi square error entropy and introduces a fourth‐order statistic of the error–kurtosis–into the variable step size, which not only effectively suppresses the impulse noise, but also accelerates the convergence speed. At the same time, a simple method of determining the maximum step size is given. The computational cost and the convergence are also analyzed. Numerical experiments and case study show that for the ARX model disturbed by impulse noise, the proposed algorithm can obtain high‐precision parameter estimates with fast convergence speed.

Artificial Neural Networks Models Based on ARX and State Space Forms and Adaptive Control PID/LQR of Systems Based on Peltier Cells

To improve the performance of a thermal plant based on Peltier cell actuators, an online parametric estimation via artificial neural networks and adaptive controller is presented. The control actions are based on adaptive digital controller and an adaptive quadratic linear regulator approaches. The Artificial neural networks topology is based on ARX and NARX models, and its training algorithms, such as accelerated backpropagation and recursive least square. The Control strategies are design-oriented to adaptive digital PID controller and quadratic linear regulator framework. The proposal is evaluated on temperature control of an object that is inside of a chamber.

Transient detection of either maldistribution or flowrate change in a counter current plate-fin heat exchanger using an ARX model

Parametric models of ARX structure express the relationship between an input u(t) and one output yarx(t). The purpose of the study is first to identify such a transient model through temperature measurements in a calibration experiment. It relates the output, that is the temperature response at the outlet of each of the two fluids that flow inside the heat exchanger, to the temperature increase at the inlet of the hot fluid, considered as a transient thermal input. This model is validated in a different experiment and transient perturbation experiments are run with maldistribution or flowrate changes. They are processed in order to detect such structural changes with respect to the calibrated model and to get the steady state characteristics, transmittances and effectivenesses, of the exchanger. The advantages and drawbacks of this non-destructive technique, which does not rely on any heat transfer correlation, are detailed and discussed.

Symposium Title: Construction and Validation of an Event-Related Potential Platform

A model predictive control (MPC) system based on latent variables (LV) model generated by using partial least squares (PLS) method is developed. The difference in the performance of MPCs that use recursively updated LV models based on autoregressive time series modeling (with exogenous inputs - ARX) and PLS is studied. The effect of signal noise on MPC performance is also investigated for both types of models. MPC performance is evaluated by regulating the blood glucose concentration (BGC) of people with Type 1 diabetes mellitus (T1DM) in simulation studies. Signal noise in glucose concentration sensor data, delays caused by insulin absorption and action, and disturbances caused by consumption of meals make the regulation of BGC difficult. The proposed controller is evaluated with 10 in-silico adult subjects of the UVa/Padova simulator with different levels of signal noise. The results illustrate the effectiveness of the MPC based on LV model. The average time for BGC in the safe range (70-180 mg/dL) for the LV-based MPC is 83.23% compared to 79.68% for the MPC based on ARX model when intravenous BGC values are used. The average time in safe range decreases to 76.04% and 71.92%, respectively, when using the generic CGM sensor of the simulator. It is reduced further to 71.93% and 67.20% when additional noise is added to CGM readings.

Rainfall-Runoff Models with Fractional Derivatives Applied to Kurau River Basin, Perak, Malaysia

Kurau River Basin (KRB), which covers an area of 322 km2 and is the main drainage artery pouring into Bukit Merah Reservoir (BMR), is located in Perak State of Malaysia. The study of rainfall-runoff processes in KRB is important because BMR plays a vital role in rice production, flood control, ecosystems, and tourism in the region. This study proposes a new approach to rainfall-runoff modeling based on the fractional calculus. A dataset of daily rainfall and streamflow has been acquired. Then, the standard linear autoregressive with exogenous input (ARX) model is identified from the dataset in the sense of least square error. We consider the ARX model as a discretized differential equation with fractional orders. Such a model with fractional derivatives is versatile to represent hysteresis, which is intrinsically linked to the real runoff processes in tropical catchment basins like KRB.

Identification of the ARX Model with Random Impulse Noise Based on Forgetting Factor Multi-error Information Entropy.

Entropy has been widely applied in system identification in the last decade. In this paper, a novel stochastic gradient algorithm based on minimum Shannon entropy is proposed. Though needing less computation than the mean square error algorithm, the traditional stochastic gradient algorithm converges relatively slowly. To make the convergence faster, a multi-error method and a forgetting factor are integrated into the algorithm. The scalar error is replaced by a vector error with stacked errors. Further, a simple step size method is proposed and a forgetting factor is adopted to adjust the step size. The proposed algorithm is utilized to estimate the parameters of an ARX model with random impulse noise. Several numerical solutions and case study indicate that the proposed algorithm can obtain more accurate estimates than the traditional gradient algorithm and has a faster convergence speed.

Online unsupervised detection of structural changes using train–induced dynamic responses

This paper exploits unsupervised data-driven structural health monitoring (SHM) in order to propose a continuous online procedure for damage detection based on train-induced dynamic bridge responses, taking advantage of the large-magnitude loading for enhancing sensitivity to small-scale structural changes. While such large responses induced by trains might create more damage-sensitive information in the measured response, it also amplifies the effects on those measurements from the environment. Thus, one of the biggest contributions herein is a methodology that exploits the large bridge responses induced by train passage while rejecting the confounding influences of the environment in such a way that false positive detections are mitigated. Furthermore, this research work introduces an adaptable confidence decision threshold that further improves damage detection over time. To ensure an online continuous assessment, a hybrid combination of autoregressive exogenous input (ARX) models, principal components analysis (PCA), and clustering algorithms was sequentially applied to the monitoring data, in a moving window process. A comparison between the performance obtained from autoregressive (AR) and ARX models as feature extractors was conducted, and it was concluded that ARX models lead to increased sensitivity to damage due to their ability to capture cross information between the sensors. The PCA proved its importance and effectiveness in removing observable changes induced by variations in train speed or temperature without the need to measure them, and the clustering methods allowed for an automatic classification of the damage-sensitive features. Since it was not possible to introduce damage to the bridge, several structural conditions were simulated with a highly reliable digital twin of the Sado Bridge, tuned with experimental data acquired from a SHM system installed on site, in order to test and validate the efficiency of the proposed procedure. The strategy proved to be robust when detecting a comprehensive set of damage scenarios with a false detection incidence of 2%. Moreover, it showed sensitivity to smaller damage levels (earlier in life), even when it consists of small stiffness reductions that do not impair structural safety and are imperceptible in the original signals.

Inverse ARX (IARX) method for boundary specification in heat conduction problems

Heat conduction problems are usually solved either with analytical or numerical simulations, or with a reduced model using system identification. The use of polynomial models, often used in automation theory, gained the attention of the thermal community in the last decades to elaborate these reduced models because of their simplicity and performance to characterize an invariable system. They allow, for example, estimating a local temperature with a known input heat source. However, using polynomial models (or identified systems) in inverse conduction problems is not straightforward, usually requiring either a second inversion step. In this paper, we present a novel inverse technique based on the polynomial model ARX (autoregressive with exogenous input) that allows the estimation of an unknown input (like an imposed heat flux on a boundary) using a known output (temperature measurement). This new method, named inverse ARX or IARX, only requires a calibration step as a regular polynomial model and, then, it can estimate the input by a direct calculation with the identified parameters. The difference between IARX and ARX is the presence of future exogenous parameters, which were deduced using the initial discrete form of the ARX model. We present herein a numerical example using IARX of a 1D heat conduction simulation and IARX succeeded to estimate the input heat flux, even with high discontinuities and high measurement noises. Finally, we compare the proposed method with the classical Beck’s function specification method. IARX presented advantages like having no restriction for the number of future terms used in the model and performing the calculation 45% faster and with much less memory space consumption than with Beck’s method.

Damage diagnosis of high-rise buildings under variable ambient conditions using subdomain approach

Tall structures, during their service lifetime, face many scenarios and are often prone to damages. Generally, static or dynamic measurements from the entire structure are used while formulating the Structural Health Monitoring (SHM) techniques for damage diagnosis. In this paper, an output-only damage diagnostic technique using the decentralized concept (subdomain-based) for high-rise buildings, employing the Vector form of the Autoregressive with exogenous input (VARX) model is developed. Vector version of the ARX model is preferred, as the vector models are more effective in detecting/localising the damage, when compared to the scalar models, due to their capability to predict the signals from a group of sensors per trial. In this work, the dynamic equation of motion associated with a building model is recast into the form of the VARX model, aiding to the decentralised damage diagnostic algorithm. New damage indices have been proposed to handle the inevitable confounding factors like environmental and operational variabilities (EoV), apart from measurement noise, to avoid false-positive alarms. The effectiveness of the proposed subdomain based damage diagnostic technique and its robustness to environmental/operational variabilities and measurement noise, are illustrated using the synthetic time-history responses of a 25-storey framed structure and the responses from a ten-storey experimental steel framed structure.

Data-Driven Modeling of a Pilot Plant Batch Reactor and Validation of a Nonlinear Model Predictive Controller for Dynamic Temperature Profile Tracking.

Batch process plays a very crucial and important role in process industries. The increased operational flexibility and trend toward high-quality, low-volume chemical production has put more emphasis on batch processing. In this work, nonlinearities associated with the batch reactor process have been studied. ARX and NARX models have been identified using open-loop data obtained from the pilot plant batch reactor. The performance of the batch reactor with conventional linear controllers results in aggressive manipulated variable action and larger energy consumption due to its inherent nonlinearity. This issue has been addressed in the proposed work by identifying the nonlinear model and designing a nonlinear model predictive controller for a pilot plant batch reactor. The implementation of the proposed method has resulted in smooth response of the manipulated variable as well as reactor temperature on both simulation and real-time experimentation.

Offset-free ARX-based adaptive model predictive control applied to a nonlinear process

An adaptive steady state constrained autoregressive with extra input (SSARX) model is developed and embedded into a model predictive control (MPC) framework to regulate a nonlinear process for setpoint tracking. The resulting linear MPC can minimize the deviation of output from the setpoint along the entire prediction horizon and finally achieve zero-offset control even with model mismatch. Our contributions lie in three aspects: First, we develop a steady state constrained ARX model identification method. Second, we design an information matrix based index for model re-identification using online closed-loop data. Third, when steady state input values are unknown, our algorithm can adaptively adjust parameters in the objective function and model to track the setpoint crossing a wide range of operating conditions. A fermenter control problem is studied to demonstrate the effectiveness of the proposed approach.