ARX Model Research Articles

System Identification of TEG Themostatic System

Thrombelastograph device (TEG) is a measuring instrument of blood viscoelastic properties during coagulation. The measuring temperature of TEG is fixed at 37oC while in some surgery cases, lower temperature surroundings may be adopted. Therefore a new type of TEG with a controllable themostatic system has been designed to mimic various temperature surroundings in surgery. In this paper, a small-sized high accuracy thermostatic system for TEG was designed and its system identification was built to facilitate the development of control strategy. ARX model was supposed to analyze the system identification of the thermostatic system by Matlab System Identification Toolbox. Residual analysis method was adopted to verify the identified model. The results showed that the simulation data of ARX model was consistence with the measured data (matching degree was about 93%). Transfer function of the system can be applied to develop its control strategy.

A linear approach to generalized minimum variance controller design for MIMO nonlinear systems

Designing minimum variance controllers (MVC) for nonlinear systems is confronted with many difficulties. The methods which are able to identify MIMO nonlinear systems are scarce, and linear models are not accurate in modeling nonlinear systems. In this paper, Vector ARX (VARX) models are proposed for designing MVC and generalized minimum variance controller (GMVC) for linear and nonlinear systems, and the accuracy of these models in approximating the nonlinear MIMO system is studied. However, the VARX is a linear model. It is shown that this model can identify some kinds of nonlinear systems with any desired accuracy. Therefore, the controller designed by the VARX is accurate, even for these nonlinear systems. The proposed controller is tested on a both linear system and a nonlinear four-tank benchmark process. In spite of the simplicity of designing GMVCs for the VARX models, the results show that the proposed method is accurate and implementable.

Personalized State-space Modeling of Glucose Dynamics for Type 1 Diabetes Using Continuously Monitored Glucose, Insulin Dose, and Meal Intake

An essential component of any artificial pancreas is on the prediction of blood glucose levels as a function of exogenous and endogenous perturbations such as insulin dose, meal intake, and physical activity and emotional tone under natural living conditions. In this article, we present a new data-driven state-space dynamic model with time-varying coefficients that are used to explicitly quantify the time-varying patient-specific effects of insulin dose and meal intake on blood glucose fluctuations. Using the 3-variate time series of glucose level, insulin dose, and meal intake of an individual type 1 diabetic subject, we apply an extended Kalman filter (EKF) to estimate time-varying coefficients of the patient-specific state-space model. We evaluate our empirical modeling using (1) the FDA-approved UVa/Padova simulator with 30 virtual patients and (2) clinical data of 5 type 1 diabetic patients under natural living conditions. Compared to a forgetting-factor-based recursive ARX model of the same order, the EKF model predictions have higher fit, and significantly better temporal gain and J index and thus are superior in early detection of upward and downward trends in glucose. The EKF based state-space model developed in this article is particularly suitable for model-based state-feedback control designs since the Kalman filter estimates the state variable of the glucose dynamics based on the measured glucose time series. In addition, since the model parameters are estimated in real time, this model is also suitable for adaptive control.

Model Predictive Control of Fractional Order Systems.

This paper provides the model predictive control (MPC) of fractional order systems. The direct method will be used as internal model to predict the future dynamic behavior of the process, which is used to achieve the control law. This method is based on the Grünwald-Letnikov's definition that consists of replacing the noninteger derivation operator of the adopted system representation by a discrete approximation. The performances and the efficiency of this approach are illustrated with practical results on a thermal system and compared to the MPC based on the integer ARX model.

Hourly cooling load forecasting using time-indexed ARX models with two-stage weighted least squares regression

This paper presents a robust hourly cooling-load forecasting method based on time-indexed autoregressive with exogenous inputs (ARX) models, in which the coefficients are estimated through a two-stage weighted least squares regression. The prediction method includes a combination of two separate time-indexed ARX models to improve prediction accuracy of the cooling load over different forecasting periods. The two-stage weighted least-squares regression approach in this study is robust to outliers and suitable for fast and adaptive coefficient estimation. The proposed method is tested on a large-scale central cooling system in an academic institution. The numerical case studies show the proposed prediction method performs better than some ANN and ARX forecasting models for the given test data set.

SYSTEM IDENTIFICATION OF A STEAM DISTILLATION PILOTSCALE USING ARX AND NARX APPROACHES

This paper presents steam temperature models for st eam distillation pilot-scale (SDPS) by comparing Ps eudo Random Binary Sequence (PRBS) versus Multi-Sine (M-Sine) perturba tion signal Both perturbation signals were applied to nonlinear steam distillation system to study the capability of these input signals in exciting nonlinearity of system dynamics. In this work, both linear and nonlinear ARX model structures have been invest igated. Five statistical approaches have been obser ved to evaluate the developed steam temperature models, namely, coefficient of de termination, R 2 ; auto-correlation function, ACF; cross-correlation function, CCF; root mean square error, RMSE; and residual histogra m. The results showed that the nonlinear ARX models are superior as compared to the linear models when M-Sine perturbation appli ed to the steam distillation system. While, PRBS pe rturbation exhibit insufficient to model nonlinear system dynamic

Spatial-Temporal ARX Modeling and Optimization for Polymer Flooding

A new polymer flooding model based on spatial-temporal decomposition and autoregressive model with external input (ARX) (STDARX model) is proposed. Karhunen-Loeve (K-L) decomposition is used to model the two-dimensional state parameters of reservoir (such as water saturation, pressure, and grid concentration). The polymer injection concentration and time coefficient got from the decomposition are taken as the input and output information. After being identified by least square method, the time iterative ARX models of all state variables are obtained, we build the ARX model among pressure, water saturation, grid concentration, and moisture content of production well, and identify it with recursive least-squares (RLS) method. After combining the above two models, we get the STDARX model of polymer flooding. The accuracy is proved by model with four injection wells and nine production wells through data which is obtained from mechanism model. In order to enhance the polymer flooding oil recovery when oil price is changing, iterative dynamic programming (IDP) is applied to optimize the STDARX model, to get the optimal injection of production scheme.

Damage Characterization in Frame Structures using Output-only Modal and Feature-based Techniques

A combined approach involving a modal-based as well as feature-based technique has been proposed for damage characterization in frame structures. In modal-based approach, the modal parameters of a structure are estimated from ambient responses using an output- only system identification technique and subsequently the fundamental mode shape and its derivatives are used for damage characterization purpose. In feature-based approach, autoregressive models with exogenous input (ARX model) are built up using healthy and damaged structural responses and the first ARX model coefficients are used for damage characterization. Simulation studies are carried out on a two-dimensional three-bay twelve- story steel moment-resisting frame to illustrate the applicability of the techniques in identifying damages in beams and columns. Both modal and feature-based approaches are capable of identifying the nature and extent of damages. However, an improvement of the algorithm is desirable for damage quantification and prognosis.

A Realistic Process Example for MIMO MPC based on Autoregressive Models

Advanced controllers such as model predictive control are in use for a wide range of application in the process industry. The potential utilization of such advanced predictive controllers is far from exhausted. One barrier for more widespread implementation is the lack of simple methodologies for advanced control design development which may be used by non experts in control theory. This paper presents and illustrates the use of a simple methodology to design an offset-free MPC based on ARX models. Hence a mechanistic process model is not required. The forced circulation evaporator by Newell and Lee is used to illustrate the offset-free MPC based on ARX models for a nonlinear multivariate process.

Applying Wavelet Decomposition Hydrological Time Series and the Optimization of Model Groups in Flood Forecasting

Applying Wavelet Decomposition Hydrological Time Series and the Optimization of Model Groups in Flood Forecasting This study applies a redundant wavelet transform (WT) and an optimization of model groups to accurately forecast the flood of a watershed. Effective rainfall and direct runoff can be decomposed into detailed signals and an approximation by using a redundant WT. The AutoRegressive model with exogenous Input (ARX), nonlinear ARX (NARX), time-varying ARX, and time-varying NARX models are implemented in parallel at each resolution level, and the optimal model is selected as the forecasting model. The summation of the forecasting results obtained at various resolution levels yields the overall flood forecasting by applying the inverse WT. The first-stage validation results indicate that the optimalforecasting model at each resolution level for six events is timevarying NARX. The second-stage validation results show that the proposed approach is appropriate for modeling the rainfall-runoff process at each resolution level and estimating the overall runoff for small watersheds in Taiwan. The analytic results also confirm that the proposed wavelet-based method outperforms the conventional method, which uses data only at the original resolution level, because of the multi-resolution analysis (MRA) property of the wavelet transform.

ARX modeling of nuclear power dynamic characteristics with reactivity disturbance based on dynamics mechanism

ARX modeling of nuclear power dynamic characteristics with reactivity disturbance based on dynamics mechanism

Blind Identification via Lifting

Blind system identification is known to be an ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements. We phrase this as a constrained rank minimization problem and present a relaxed convex formulation to approximate its solution. To make the problem well posed we assume that the sought input lies in some known linear subspace.

시스템 식별기법을 활용한 파압과 해수면 모델링

A System Identification method to develop parametric models linking free surface elevation and wave pressure is presented and two models are built allowing for either wave pressure or free surface elevation simulation. Linear, time invariant model structures with static nonlinearities are assumed and solutions are sought in a form of autoregressive model with extra input (ARX). An arbitrary chosen free-surface elevation and wave pressure dataset is used for estimation of the models, which are subsequently verified against datasets with similar pressure gauge depth but different free-surface elevation spectra due to different meteorological conditions. It is shown that freesurface simulation using System Identification methods can perform better than traditional linear transfer function derived from linear wave theory (LTF), while wave pressure simulation quality using presented methods is generally similar to that obtained with corrected LTF. 핵심용어: system identification, wind waves, free surface elevation, sea wave pressure, autoregressive model, ARX model, linear transfer function, wind wave spectrum, free surface records, pressure records, ì‹œìŠ¤í œ 식별법, 풍파, 해수면, í•´ì €íŒŒì••, 자기회기모형, ARX 모형, ì„ í˜•ì „ì†¡í•¨ìˆ˜, 풍파스펙트럼, 해수면 시계열자료, 파압 시계열자료

Comparison of ARX and ARMAX models for thermoelectric refrigerator

System identification is a procedure to characterize the dynamic behavior of a system, a system component based on measured data. This paper presents a study of the modeling and parameter identification of a refrigerator process by using the mathematical black-box modeling technique- ARX and ARMAX structure. A general ARX and ARMAX structure has been constructed for usual thermoelectric refrigerator systems and the Recursive Least Square (RLS) process is used for model parameters identification. The capabilities of the model constructed compared with that of ARX and ARMAX model. Several compositions of ARX and ARMAX orders and forgetting factor are analyzed for thermoelectric air-conditioning model to examine the optimal adjustments that improve their efficiency of PID controller.

Parametric time‐domain identification of multiple‐input systems using decoupled output signals

SUMMARYCivil engineering structures are often subjected to multidirectional actions such as earthquake ground motion, which lead to complex structural responses. The contributions from the latter multidirectional actions to the response are highly coupled, leading to a MIMO system identification problem. Compared with single‐input, multiple‐output (SIMO) system identification, MIMO problems are more computationally complex and error prone. In this paper, a new system identification strategy is proposed for civil engineering structures with multiple inputs that induce strong coupling in the response. The proposed solution comprises converting the MIMO problem into separate SIMO problems, decoupling the outputs by extracting the contribution from the respective input signals to the outputs. To this end, a QR factorization‐based decoupling method is employed, and its performance is examined. Three factors, which affect the accuracy of the decoupling result, including memory length, input correlation, and system damping, are investigated. Additionally, a system identification method that combines the autoregressive model with exogenous input (ARX) and the Eigensystem Realization Algorithm (ERA) is proposed. The associated extended modal amplitude coherence and modal phase collinearity are used to delineate the structural and noise modes in the fitted ARX model. The efficacy of the ARX‐ERA method is then demonstrated through identification of the modal properties of a highway overcrossing bridge. Copyright © 2013 John Wiley & Sons, Ltd.

A modeling and control approach to magnetic levitation system based on state-dependent ARX model

Magnetic levitation (Maglev) systems are usually strongly nonlinear, open-loop unstable and fast responding. In order to control the position of the steel ball in a Maglev system, a data-driven modeling approach and control strategy is presented in this paper. A state-dependent AutoRegressive with eXogenous input (SD-ARX) model is built to represent the dynamic behavior between the current of electromagnetic coil and the position of the ball. State-dependent functional coefficients of the SD-ARX model are approximated by Gaussian radial basis function (RBF) neural networks. The model parameters are identified offline by applying the structured nonlinear parameter optimization method (SNPOM). Based on the model, a predictive controller is designed to stabilize the magnetic levitation ball to a given position or to make it track a desired trajectory. The real-time control results of the proposed approach and the comparisons with other two approaches are given, which demonstrate that the modeling and control method presented in this paper are very effective and superior in controlling the fast-responding, strongly nonlinear and open-loop unstable system. This paper gives the real experimental evidence that the RBF-ARX model is capable of not only globally, but also locally capturing and quantifying a nonlinear and fast-response system's behavior, and the model-based predictive control strategy is able to work quite well in a wide working-range of the nonlinear system.

Modal Identification of Structures from Seismic Response Data via Amplitude-Dependent Time Series Model

The present work develops a novel procedure of establishing a amplitude-dependent time series model for a nonlinear system and estimating the instantaneous modal parameters of the system from the dynamical responses. The undetermined coefficient in a amplitude-dependent autoregressive with exogenous input (amplitude-dependent ARX) model are assumed as function s of amplitude and are expanded by shape functions constructing by moving least-squares with polynomial basis functions. The amplitude of dynamical responses could be obtained by Hilbert transform. The instantaneous modal parameters of the system are directly estimated from the coefficient in the amplitude-dependent ARX model. Finally, the proposed approach is applied to process measured data for a frame specimen subjected to a series of base excitations in shaking table tests. The specimen was damaged during testing. The identified modal parameters are consistent with observed physical phenomena.

Adaptive Predictive Control using GOBF-ARX Models: An Experimental Case Study

Industrial applications of model predictive control rely mostly on linear empirical models obtained by employing time series analysis approaches. These models can quickly become obsolete and require maintenance when the operating conditions become significantly different from the design conditions. The need to generate good predictions in the face of changing operating conditions and / or plant characteristics can be fulfilled through updating the linear model parameters online. This work is aimed at the development of adaptive MPC (AMPC) scheme based on ARX models, which are parameterized using generalized orthonormal basis filters (GOBF). The proposed model structure, in addition to capturing the dynamics with respect to the manipulated inputs, facilitates modeling of stationary as well as non-stationary components of the unmeasured disturbances. The feasibility of using the proposed AMPC scheme is established by conducting experimental studies on a benchmark Heater-Mixer setup.

Identification of the Feedforward Component in Manual Control With Predictable Target Signals

In the manual control of a dynamic system, the human controller (HC) often follows a visible and predictable reference path. Compared with a purely feedback control strategy, performance can be improved by making use of this knowledge of the reference. The operator could effectively introduce feedforward control in conjunction with a feedback path to compensate for errors, as hypothesized in literature. However, feedforward behavior has never been identified from experimental data, nor have the hypothesized models been validated. This paper investigates human control behavior in pursuit tracking of a predictable reference signal while being perturbed by a quasi-random multisine disturbance signal. An experiment was done in which the relative strength of the target and disturbance signals were systematically varied. The anticipated changes in control behavior were studied by means of an ARX model analysis and by fitting three parametric HC models: two different feedback models and a combined feedforward and feedback model. The ARX analysis shows that the experiment participants employed control action on both the error and the target signal. The control action on the target was similar to the inverse of the system dynamics. Model fits show that this behavior can be modeled best by the combined feedforward and feedback model.

Hammerstein identification of supercharged boiler superheated steam pressure using Laguerre-Fuzzy model

System identification plays an important role in many fields of science and engineering. This paper deals with a new nonlinear identification method fit for supercharged boiler superheated steam pressure. The superheated steam pressure is influenced by fuel and superheated steam flow, whereas traditional identification methods always omit the influence of superheated steam flow, and receive limited identification precision due to the uncertain time delay and strong nonlinearity. Taking into account that Laguerre filters can approximate linear systems (even with time delay) with a model order lower than ARX model and fuzzy identification from measured data is effective enough to approximate uncertain nonlinear systems, Laguerre filters and fuzzy model are firstly combined into Hammerstein structure to construct Laguerre-Fuzzy Hammerstein model. The defined model is a two inputs single output model which considers both of the two nonlinear variables and can avoids the decrease of identification precision resulted by uncertain time delay. The proposed model is applied in the nonlinear identification of supercharged boiler superheated steam pressure. Simulation results show that the Laguerre-Fuzzy Hammerstein model can trace the process nonlinearity precisely and has higher prediction accuracy than ARX model and basic Hammerstein model with a lower model order. Moreover, Laguerre-Fuzzy Hammerstein model improves the computation efficiency and system stability greatly.