ARX Model Research Articles

CRONE Toolbox for system identification using fractional differentiation models

This paper presents the latest developments for the continuous-time system identification toolbox with fractional models (or fractional order systems): the CRONE toolbox. This toolbox is to be run with Matlab which includes time-domain identification algorithms for estimating continuous-time models directly from sampled data. The originality of the implemented algorithms is that they allow either fixing fractional differentiation orders or estimating them along with transfer function coefficients. One of the main issues when dealing with fractional models is their time-domain simulation. Three different time-domain simulation methods can be used independently from system identification methods. Output Error (OE), state variable filters (SVF) and (optimal) instrumental variables (IV) methods for ARX and OE models are provided to the end-user. The object oriented programming of the toolbox allows overloading standard script names. As a consequence, an end-user familiar with standardMatlab operators and scripts can use straightforwardly the CRONE toolbox.

Quasilinear Extreme Learning Machine Model Based Internal Model Control for Nonlinear Process

A new strategy for internal model control (IMC) is proposed using a regression algorithm of quasilinear model with extreme learning machine (QL-ELM). Aimed at the chemical process with nonlinearity, the learning process of the internal model and inverse model is derived. The proposed QL-ELM is constructed as a linear ARX model with a complicated nonlinear coefficient. It shows some good approximation ability and fast convergence. The complicated coefficients are separated into two parts. The linear part is determined by recursive least square (RLS), while the nonlinear part is identified through extreme learning machine. The parameters of linear part and the output weights of ELM are estimated iteratively. The proposed internal model control is applied to CSTR process. The effectiveness and accuracy of the proposed method are extensively verified through numerical results.

Design and Experimental Tests of an LPV Power System Stabilizer on a 10kVA Small-scale Generating Unit

In this paper, the application of linear parameter-varying (LPV) identification and control methods for designing and performance evaluation of an adaptive power system stabilizer (PSS) is presented. The target control objective is to improve the damping of the dominant electromechanical oscillating mode in the power system. The performance of the LPV PSS controller has been assessed by means of experimental tests carried out on 10 kVA small-scale power system. For design purposes, an LPV ARX model was estimated from experimental tests, for a wide range of operating conditions. The LPV controller was tuned via an optimization problem, in the form of a Parameterized Linear Matrix Inequality (PLMI). The solution was obtained through a sum-of-squares relaxation. Both the LPV model and the LPV-PSS have an explicit dependency on system scheduling variables, namely the active and reactive powers measurements. Therefore, the LPV-PSS was designed to ensure stability and performance for a wide range of operating conditions, an objective usually difficult to obtain by using fixed parameter controllers.

Predicting Electricity Pool Prices Using Hidden Markov Models

In this paper, Alberta electricity spot market or Power Pool pricing is studied and the pool price is modeled through a hidden Markov model and multiple local ARX models. By selecting and preprocessing the exogenous factors (e.g. the price forecast from Alberta Electric System Operator (AESO), demand forecast and so forth), a one-hour ahead prediction model for pool price is formulated with parameters being estimated from the real data. Validation results show that this approach can improve the price forecasting and in particular, for high pool prices.

Regularization Features in the System Identification Toolbox

Regularization is a well known technique in estimation methodology. Its usefulness to assure well conditioned calculations and to handle reliable prior information about partly known parameters is a classical theme in statistics. Recently some deeper understanding about the advantages for general estimation and identification methods has been found and discussed. This is often done using the term "kernel methods". It has some links to machine learning and statistical function learning as well as to reproducing kernel Hilbert spaces. But algorithmically, it is all a question of regularization with an appropriate (quadratic norm) regularization matrix. Regularization was introduced into the MATLAB System Identification Toolbox in the 2013a version. It is a general option for all linear and nonlinear model estimation. Several specialized commands for estimation impulse responses (impulseest), tuning of kernels for ARX models (arxRegul), and general linear state space models with regularization (ssregest) have also been implemented. The paper describes and illustrates the used of these new features in the toolbox.

Weighted Stochastic Gradient Identification Algorithms for ARX models

In this paper, weighted stochastic gradient (WSG) algorithms for ARX models are proposed by modifying the standard stochastic gradient identification algorithms. In the proposed algorithms, the correction term is a weighted term of the correction terms of the standard SG algorithm in the current and last recursive steps. In addition, a latest estimation based WSG (LE-WSG) algorithm is also established. The convergence performance of the proposed LE-WSG algorithm is then analyzed. It is shown by a numerical example that both the WSG and LE-WSG algorithms can possess faster convergence speed and higher convergence precision compared with the standard SG algorithms if the weighting factor is appropriately chosen.

Intelligent control model and its simulation of flue temperature in coke oven

In this paper, one-variable linear regression mathematical model of top of regenerator temperature and flue temperature in machine side is built using the linear regress theory. The parameters of ARX model is determined by identification method of least square method and the mathematical model of flue temperature control is established. Applying the basis cascade control theory, system adopts flue temperature and coal flue gas flow as controlled parameters of host circuit and subsidiary circuit respectively. The compound Fuzzy-PID control strategy is presented combined with the characteristics of temperature system after analyzing the conventional PID control algorithm and fuzzy control algorithm. Using step signal and periodic signal to simulate the conventional PID and compound Fuzzy-PID algorithm, the result has indicated: Compound Fuzzy PID control algorithm combines with the advantages of fuzzy control and PID control algorithm, including fast response speed and strong anti-interference ability. When external conditions change, the fuzzy PID compound control can show the strong adaptability and robustness which effectively improve the stability of the control system.

Dynamic modeling for thermal error in motorized spindles

This paper proposes a new modeling methodology to predict thermal error in motorized spindles. The dynamic model predicts thermal errors that are caused by deformation in the motorized spindle structure due to heat flow from internal sources. These thermally induced errors become more serious and dominate the total error when it comes to high speed and high precision. If these thermal errors can be predicted, they can be compensated in real time. In this paper, a new thermal errors model (ARX model) is presented which capitalizes on the notion that the motorized spindle thermoelastic system has very complicated dynamics. Furthermore, the selection principle of temperature key points, which are indispensable for building a robust thermal error model, is provided using the thermal error sensitivity technology. At last, an experiment on the thermal error in a motorized spindle is conducted to verify the effectiveness of the ARX model, the experimental results show that above 80 % of axial thermal errors are predicted for a variety of motorized spindle cycles and the dynamic model has good accuracy and robustness.

Story-wise system identification of actual shear building using ambient vibration data and ARX model

A sophisticated story-wise stiffness identification method for a shear building structure is applied to the case where the shear building is subjected to an actual micro-tremor. While the building responses to earthquake ground motions are necessary in the previous method, it is shown that micro-tremors can be used for identification within the same framework. This enhances the extended usability and practicality of the previously proposed identification method. The difficulty arising in the limit manipulation at zero frequency in the previous method is overcome by introducing an ARX model. The weakness of small SN ratios in the low frequency range is avoided by using the ARX model together with filtering and introducing new constraints on the ARX parameters.

Story-wise system identification of actual shear building using ambient vibration data and ARX model

A sophisticated story-wise stiffness identification method for a shear building structure is applied to the case where the shear building is subjected to an actual micro-tremor. While the building responses to earthquake ground motions are necessary in the previous method, it is shown that micro-tremors can be used for identification within the same framework. This enhances the extended usability and practicality of the previously proposed identification method. The difficulty arising in the limit manipulation at zero frequency in the previous method is overcome by introducing an ARX model. The weakness of small SN ratios in the low frequency range is avoided by using the ARX model together with filtering and introducing new constraints on the ARX parameters.

A Method of Order Determination for ARX and ARMA Models Based on Nonnegative Garrote

Classical order determination methods of ARX and ARMA models suffer from the drawbacks of computationally infeasible and poor stability. To solve these problems, order determination using nonnegative garrote (NNG) method is proposed. By analyzing the properties of ARX and ARMA models, a modification of original NNG method is made to fit the dynamical system identification problem. Furthermore, the solution algorithm of proposed method is presented. Simulations show the validation of proposed method, which has better stability than classical information based criteria methods.

Time Delay Measurement Compensation in Harmonic State Estimation

The proliferation of power electronics equipments generates harmonics distortion problem. Harmonics have many effects to the power system grid and the main limitation of harmonics is heating of power system devices. To monitor and mitigate the harmonics, the source location and the level of harmonics should be known. However, harmonic measurements are costly and is not practical to put harmonic measurement in each location in the grid. Hence, harmonic state estimation is needed. The most common method in harmonic state estimation is singular value decomposition (SVD). A time delay of the measurements can affect the SVD performance, therfore,this paper presents a prediction method based on ARX model and modified normalized least mean square to compensate the time delay measurements. The result shows better performance of the proposed method as compared to least mean square.

Optimal Kernel and Wavelet Coefficients to Support Vector Regression Model and Wavelet Neural Network for Time Series Rainfall Prediction

Rainfall prediction is an active topic recently since people want to make decisions about crop and irrigation cycles to understand weather and climate patterns. Due to need of predicting this natural phenomenon, various research works has been carried out previously with different type of techniques using historical data. In this paper, a hybrid model based on support vector regression (SVR) model and wavelet neural network (WNN) for rainfall prediction is proposed. In hybridized SVR-WNN, optimal kernel and wavelet coefficients are generated using hybrid algorithm. Here, artificial bee colony (ABC) and genetic algorithm (GA) are hybridized and used to this purpose. These optimal kernel functions and wavelet coefficients are supplied to hybrid model to predict the rainfall. In hybrid model, wavelet neural network with ARX modeling and support vector regression (SVR) model is effectively hybridized to time series rainfall prediction. The performance of the hybrid model is analyzed with the help of real datasets taken from Assam, Chhattisgarh, East Rajasthan, Gangetic West Bengal, Gujarath, Haryana, Telangana, Rajalaseema regions. From the results, it can be concluded that proposed rainfall prediction model have shown the MAPE performance of 20, the RMSE performance of 2, MAD performance of 12, but existing model show the MAPE performance of 61, the RMSE performance of 3, MAD performance of 27 for Telangana dataset.

Detection of Model Parameter Mismatch Using Simplified Partial Correlation Analysis for Closed-Loop System

Partial correlation analysis is used in detecting the model-plant mismatch as it will give accurate location of mismatched submodel. In this work of model parameter mismatch detection in closed-loop system, a simplified method of partial correlation analysis is proposed. In this method, the identification step for input sensitivities relating setpoints and manipulated variables, Sru, is omitted due the ability of ARX model structure to capture the dynamic of the input-output data even though in the presence of unmeasured disturbance in closed-loop system. The ARX model structure is implemented in decorrelating the observed data from the correlated inputs. By using the ARX model, the mismatch is detected at the precise location compared to the detection using FIR decorrelation model.

Identification of model structure parameters via combination of AFMM and ARX from seismic response data

To identify the model structure parameters in shaking table tests from seismic response, especially from time-varying response records, this paper presents a new methodology by combining the online recursive Adaptive Forgetting through Multiple Models (AFMM) and offline Auto-Regression with eXogenous variables (ARX) model. First, the AFMM is employed to detect whether the response of model structure is time-invariant or time-varying when subjected to strong motions. Second, if the response is time-invariant, the modal parameters are identified from the entire response record, such as the acceleration time-history using the ARX model. If the response is time-varying, the acceleration record is divided into three segments according to the accurate time-varying points detected by AFMM, and parameters are identified by only using the tail segment data, which is time-invariant and suited for analysis by the ARX model. Finally, the changes in dynamic properties due to various strong motions are obtained using the presented methodology. The feasibility and advantages of the method are demonstrated by identifying the modal parameters of a 12-story reinforced concrete (RC) frame structure in a shaking table test.

Subspace identification with non-steady Kalman filter parameterization

Most existing subspace identification methods use steady-state Kalman filter (SKF) in parameterization, hence, infinite data horizons are implicitly assumed to allow the Kalman gain to reach steady state. However, using infinite horizons requires collecting infinite data which is unrealistic in practice. In this paper, a subspace framework with non-steady state Kalman filter (NKF) parameterization is established to provide exact parameterization for finite data horizon identification problems. Based on this we propose a novel subspace identification method with NKF parameterization which can handle closed-loop data and avoid assumption on infinite horizons. It is shown that with finite data, the proposed parameterization method provides more accurate and consistent solutions than existing SKF based methods. The paper also reveals why it is often beneficial in practice to estimate a bank of ARX models over a single ARX model.

Potential of evolving AR and ARX models in signal recovering

Linear dynamic models, due to their agile structure, are capable to follow and predict fast variations of real-world systems. On the other hand, recovering outcome signals of real-world systems is a straightforward approach to predict them. In this paper, potential of some dynamic linear models—including autoregressive (AR), autoregressive with exogenous inputs (ARX) models and their extended adaptive and evolving versions–are studied in signal recovering. At first, a common signal is represented as summation of some basic temporal functions named TMs (TMs); then, capabilities of the considered models are explained and compared in generating signals with different combinations of TMs. The given explanations and results are supported by theorems, Corollaries, illustrative examples and a real-world example of signal recovering. It is demonstrated that adaptive and particularly evolving AR and ARX models are more capable in signal recovering than regular AR and ARX models. Also, it is proved that if exogenous inputs as incoming signals of an ARX model were not available, under some constraints, there is an AR model which can produce the output of the ARX model. This result is extended for adaptive and evolving AR and ARX models, too.

Daily Load Forecasting Based on RBF-ARX Model

Short-term load forecasting plays a vital role for the power system’s safe operation and production arrangements. This paper regards electric load forecasting as a nonlinear time series prediction problem, and establishes the electric load autoregressive prediction model (ARX Model) based on historical load data, approaching ARX model parameters with RBF neural network, estimating model parameters with using a Structured Nonlinear Parameters Optimization Method (SNPOM), proposing cycle prediction method for short-term electric load forecasting. Experimental results show that the method has higher prediction accuracy for short-term electric load forecasting. Keywords: Short-term load forecasting; time series; RBF-ARX model; cycle forecasting; structured nonlinear parameter optimization method

Comparison between ARX and FIR Decorrelation Models in Detecting Model-plant Mismatch

Comparison between ARX and FIR Decorrelation Models in Detecting Model-plant Mismatch

ARX model based fault detection and diagnosis for chillers using support vector machines

Efficient and robust fault detection and diagnosis (FDD) can potentially play an important role in developing building management systems (BMS) for high performance buildings. Our research indicates that, in comparison to traditional model-based or data-driven methods, the combination of time series modeling and machine learning techniques produces higher accuracy and lower false alarm rates in FDD for chillers. In this paper, we study a hybrid method incorporating auto-regressive model with exogenous variables (ARX) and support vector machines (SVM). A high dimensional parameter space is constructed by the ARX model and SVM sub-divides the parameter space with hyper-planes, enabling fault classification. Experimental results demonstrate the superiority of our method over conventional approaches with higher prediction accuracy and lower false alarm rates.