Autoregressive With Exogenous Research Articles

Online neuro-fuzzy model learning of dynamic systems with measurement noise

Model identification of nonlinear time varying dynamic systems is challenging because the system behaviours may vary significantly in different operational conditions. If the changes are insufficiently captured by training data, the trained model is unable to capture the system response well when the operational condition changes. The model performance may also be deteriorated in real-time implementation due to the noise in sensors or the environment. This paper presents a self-adaptive Neuro-Fuzzy (NF) modelling framework to address these challenges. The NF model, trained offline based on experimental data, combines the Auto-Regressive with eXogenous (ARX) models and Gaussian activation functions to capture the nonlinear system behaviours. During online implementation, the ARX model parameters are updated using new data through a recursive generalised least squares method, which embeds a noise model to eliminate effects of the noise. The online updating algorithm has a provable convergence guarantee and enables the proposed NF model to adapt to changes in system behaviours automatically. Efficacy of the algorithm is verified through two numerical examples and an experiment on a commercial automotive engine.

Implementation of Evolutionary Algorithms to Parametric Identification of Gradient Flexible Plate Structure

This paper focused on modelling of a gradient flexible plate system utilizing an evolutionary algorithm, namely particle swarm optimization (PSO) and cuckoo search (CS) algorithm. A square aluminium plate experimental rig with a gradient of 30° and all edges clamped were designed and fabricated to acquire input-output vibration data experimentally. This input-output data was then applied in a system identification method, which used an evolutionary algorithm with a linear autoregressive with exogenous (ARX) model structure to generate a dynamic model of the system. The obtained results were then compared with the conventional method that is recursive least square (RLS). The developed models were evaluated based on the lowest mean square error (MSE), within the 95% confidence level of both auto and cross-correlation tests as well as high stability in the pole-zero diagram. Investigation of results indicates that both evolutionary algorithms provide lower MSE than RLS. It is demonstrated that intelligence algorithms, PSO and CS outperformed the conventional algorithm by 85% and 89%, respectively. However, in terms of the overall assessment, model order 4 by the CS algorithm was selected to be the ideal model in representing the dynamic modelling of the system since it had the lowest MSE value, which fell inside the 95% confidence threshold, indicating unbiasedness and stability.

Dynamic controlled pattern extraction and pattern-based model predictive control

Many latent variable modeling methods have been developed to extract the running pattern of industrial process, but the dynamic causality between control inputs and pattern is unmodeled or implicit, and thus the direct pattern control is impracticable. To overcome this limitation, the dynamic controlled pattern extraction and pattern-based model predictive control (MPC) are investigated in this paper. Firstly, a novel dynamic controlled principal component analysis (DCPCA) is proposed to extract the pattern of the industrial process from measured variables. Specially, the autoregressive with exogenous (ARX) model is introduced to characterize the dynamic relationships of the process. By maximizing the covariance of the ARX prediction and the spatial projection, the process running information can be captured by the pattern maximally with the minimum dimensions, and also benefiting from this way, both the free motions and the dynamic causality between the control inputs and pattern is established explicitly. Then, a well-designed robust tube-based MPC is implemented for optimal pattern tracking. Finally, case studies illustrate the effectiveness and advantages of the proposed DCPCA algorithm and pattern-based MPC strategy.

Modelling of Flexible Manipulator System via Ant Colony Optimization for Endpoint Acceleration

The application of flexible manipulators has increased in recent years especially in the fourth industrial revolution. It plays a significant role in a diverse range of fields, such as construction automation, environmental applications, space engineering and many more. Due to the lightweight, lower inertia and high flexibility of flexible manipulators, undesired vibration may occur and affect the precision of operation. Therefore, development of an accurate model of the flexible manipulator was presented prior to establishing active vibration control to suppress the vibration and increase efficiency of the system. In this study, flexible manipulator system was modelled using the input and output experimental data of the endpoint acceleration. The model was developed by utilizing intelligence algorithm via ant colony optimization (ACO), commonly known as a population-based trail-following behaviour of real ants based on autoregressive with exogenous (ARX) model structure. The performance of the algorithm was validated based on three robustness methods known as lowest mean square error (MSE), correlation test within 95% confidence level and pole zero stability. The simulation results indicated that ACO accomplished superior performance by achieving lowest MSE of 2.5171×10−7 for endpoint acceleration. In addition, ACO portrayed correlation tests within 95% confidence level and great pole-zero stability.

Modeling PVA degradation in a continuous photochemical reactor using experimental step testing and process identification

In advanced oxidation processes (AOPs) operating in continuous mode, the flow rate and the concentration of oxidants such as H2O2 at the mixing point of the influent must be controlled so that the oxidant residuals in the effluent are minimized while the organic degradation is maximized. Designing a controller to regulate the oxidant flow rate and therefore, its concentration at the mixing point of the photoreactor influent, needs the determination of a reliable process dynamic model. In this study, a step testing technique is employed to construct a dynamic model for the degradation of polyvinyl alcohol (PVA) in a UV/H2O2 continuous annular photoreactor. The experimental design consists of preparing three initial PVA concentrations of 60, 280, and 500 mg PVA/L and conducting eight experimental tests for different inlet mass flow rates of H2O2 ranging from 0.336 to 125 mg H2O2/min. The process responses of pH solution and total organic carbon (TOC) are measured versus time for different step changes of H2O2 inlet flow rates. Process dynamic models represented by transfer functions of the continuous UV/H2O2 photoreactor are determined from the collected input-output data using graphical method, identification algorithm, and ARX (AutoRegressive with eXogenous) in Matlab environment. The dynamic models predict the data trend quite well. Variations of the steady state gain demonstrate that the PVA degradation in UV/H2O2 continuous photoreactor is a nonlinear process. Besides, the ARX algorithm generates reliable dynamic discrete models that could be used to develop digital controllers for computer control of the UV/H2O2 photochemical reactor.

Using Autoregressive with Exogenous Input Models to Study Pulsatile Flows

The content of this paper shows the first outcomes of a supplementary method to simulate the behavior of a simple design formed by two rectangular leaflets under a pulsatile flow condition. These problems are commonly handled by using Fluid-Structure Interaction (FSI) simulations; however, one of its main limitations are the high computational cost required to conduct short time simulations and the vast number of parameter adjustments to simulate different scenarios. In order to overcome these disadvantages, we propose a system identification method with hereditary computation—AutoRegressive with eXogenous (ARX) input method—to train a model with FSI simulation outcomes and then use this model to simulate the outputs that are commonly measured from this kind of simulation, such as the pressure difference and the opening area of the leaflets. Numerical results of the presented methodology show that our model is able to follow the trend with significant agreement with the FSI results, with an average correlation coefficient R of Rtr=90.14% and Rtr=92.27% in training; whereas for validation, the average R is Rval=93.31% and Rval=83.08% for opening area and pressure difference, respectively. The system identification model is efficiently capable of estimating the outputs of the FSI approach; however, it is not intended to substitute FSI simulations, but to complement them when the requirement is to conduct many repetitions of the phenomena with similar conditions.

Simulation and modeling of two-level DC/DC boost converter using ARX, ARMAX, and OE model structures

<span>This paper presents simulation and modeling of two-level DC/DC boost converter using system identification technique. The main objective is to identify the unknown mathematical model from designated converter that has 2 modes of operation. Signals from the converter were processed based on the impulse response from input and output voltages, which were in time domain data. Auto Regressive with eXogenous (ARX), Auto Regressive Moving Average with eXogenous (ARMAX), and Output-Error (OE) model structure techniques had been employed to generate a model from the converter, whose validation was based on coefficient of determination (R<sup>2</sup>) or best fits criterion. The result shows that the ARX model structure produced the best model with 94.03%, compared to ARMAX and OE with 93.70% and 92.25% respectively. In terms of stability for open-loop analysis, the ARX model structure gave the most stable system.</span>

Quantitative Diagnosis Method of Gearbox Under Varying Conditions Based on ARX Model and Generalized Canonical Correlation Analysis

Fault diagnosis of gearboxes under the condition of varying speed and varying load is a hotspot and difficulty in the research of gearboxes. The response signals of gearbox under varying conditions exhibit non-linear and non-stationary characteristics, which increase the complexity of quantitative diagnosis of gearbox faults. A quantitative diagnosis method of gearbox faults based on the improved autoregressive with exogenous (ARX) model and generalized canonical correlation analysis (GCCA) is proposed in this paper. The ARX model is improved based on incremental recursive identification of Kalman filter to build system transfer characteristic models using the excitation and response signals of gearboxes. ARX models of gearboxes are nonlinear and the GCCA is proposed to build the quantitatively relationship between models with faulty status and healthy status. Simulation and experiment results indicate that the proposed method can effectively identify the severity of the gearbox failures under varying conditions and provides a promising method for the quantitative diagnosis of rotating machinery.

A hybrid predictive sequencing control for multi-chiller plant with considerations of indoor environment control, energy conservation and economical operation cost

Reliable automatic control of heating, ventilating and air-conditioning (HVAC) systems is essential to address buildings energy efficiency and response to the worldwide challenges of human health, energy conversation and carbon emissions. Among the various controls of HVAC systems, chiller sequencing control is of great importance for multi-chiller plant to keep cooling reliability, system stability and energy efficiency. However, conventional chiller sequencing control usually lacks consideration of system stability and the accessional cost caused by the sequencing actions. Especially, those short-time or unnecessary sequencing actions become the main reason for operators to shut down automatic control. To enhance the reliability of chiller sequencing control, a hybrid predictive control is developed. This control is developed based on a typical sequencing control strategy and use an autoregressive with exogenous (ARX) prediction model to double check the necessity of sequencing commands so as to reduce the unexpected sequencing actions. Case studies were carried out on a secondary school in subtropical city. Results showed that the switch number and economical operation cost can be reduced more than 20% and 6.72%, respectively. Additionally, energy consumption was also reduced while keeping acceptable indoor environment, which is of great importance for carbon emissions’ reduction and sustainable city development.

Development of a cooling load prediction model for air-conditioning system control of office buildings

Building cooling load prediction is of critical importance for achieving energy saving of air-conditioning system in office buildings. It not only benefits the energy-efficiency of the air-conditioning system, but is also important for the system stability. Many techniques have been developed for building cooling load prediction. These methods are normally arranged into three categories: regression analysis, energy simulation and artificial intelligence. Among them, the regression analysis methods are simple in mechanism and much practical for real application. However, traditional regression models are not sufficient to manage multi-parameter dynamic changes, and the outliers in prediction has not been well considered, making the accuracy of cooling load prediction not satisfactory. To promote the feasibility of regression methods for cooling load prediction of office buildings, an efficient regression model based on sensitivity analysis and the traditional autoregressive with exogenous (ARX) model (named as improved ARX model) is proposed in this paper. The improved ARX model keeps the constitution of ARX model, but uses specified variables that selected by sensitivity analysis. The quadratic terms of vital variables are included to reduce the impact of system non-linearity. A least square method is used to get the weight coefficient matrix for model training. Comparison studies are used to evaluate the prediction accuracy of the improved ARX model. The proposed model will largely improve prediction accuracy and more adaptive for real applications in the perspective of optimal control for HVAC systems.

A transmittance-based methodology for damage detection under uncertainty: An application to a set of composite beams with manufacturing variability subject to impact damage and varying operating conditions

Oftentimes, the complexity in manufacturing composite materials leads to corresponding structures which although they may have the same design specifications they are not identical. Thus, composite parts manufactured in the same production line present differences in their dynamics which combined with additional uncertainties due to different operating conditions may lead to the complete concealment of effects caused by small, incipient, damages making their detection highly challenging. This damage detection problem in nominally identical composite structures is pursued in this study through a novel data-based response-only methodology that is founded on the autoregressive with exogenous (ARX) excitation parametric representation of the transmittance function between vibration measurements at two different locations on the structure. This is a statistical time series methodology within which two schemes are formulated. In the first, a single-reference transmittance model representing the healthy structure is employed, while multiple transmittance models from a sample of available healthy structures are used in the second. The model residual signal constitutes for both schemes the damage detection characteristic quantity that is used in appropriate hypothesis testing procedures with the likelihood ratio test. The methodology is experimentally assessed via damage detection for a population of composite beams which are manufactured in the same production line representing the half of the tail of a twin-boom unmanned aerial vehicle. The damage detection results demonstrate the superiority of the multiple transmittance models based scheme that may effectively detect damages under significant manufacturing variability and varying boundary conditions.

An improved ARX model for hourly cooling load prediction of office buildings in different climates

An attempt was made to develop an improved autoregressive with exogenous (ARX) model for office buildings cooling load prediction in five major climates of China. The cooling load prediction methods can be arranged into three categories: regression analysis, energy simulation, and artificial intelligence. Among them, the regression analysis methods using regression models are much simple and practical for real applications. However, traditional regression models are often helpless to manage multiparameter dynamic changes, making it not accurate as the other two categories. Many of the existing cooling load prediction studies use piecewise linearization to manage nonlinearity. To improve the prediction accuracy of regression analysis methods, higher order and interaction terms are included in improved ARX based on traditional ARX model. The improved ARX model consists of eight variables, with eleven coefficients accessed at a time. For applications and evaluations, an office building in major cities within each climatic zone was selected as a representation. These cities were Harbin, Beijing, Nanjing, Kunming and Guangzhou respectively. The coefficient of determination R2 is greater than 0.9 in five cities. The prediction results show that the improved ARX model can adapt to different climatic conditions, including those nonlinearity cases.

Prognostic Methods on Accelerator’s Anode Voltage Regulator

This study investigated an adaptive control, fault diagnostics and prognostics of the anode voltage regulator system at an ion implantation accelerator. The system was modeled as a 4th order AutoRegressive with eXogenous (ARX) model, controlled by a Fuzzy Logic Controller (FLC). This model was then used as a basis for constructing and updating a fault diagnosis module and a failure prognostics module. To maintain the system’s performance, the controller’s response was continuously re-adjusted through an optimization scheme. A Failure Mode and Effect Analysis (FMEA) was conducted resulting on five failure modes of the regulator system. Fault data were generated in MATLAB simulation to train a random forest fault classification engine. The optimal random forest classifier was 20 decision trees with a fault diagnostics accuracy of 98.06%. A Hidden Markov Model (HMM) was constructed as the system’s fault progression model based on the interaction between environmental conditions and controller actions. The particle filter and Bayesian inference methods were then employed to continuously update the HMM and predict the system’s Remaining Useful Lifetime (RUL). The proposed methodology was able to integrate an adaptive fuzzy logic control, prognosis and failure diagnosis altogether allowing a continual satisfactory performance of the voltage regulator system throughout its lifetime.

An ARX-based method for the vibration control of flexible beams manipulated by industrial robots

The vibration control problem of flexible objects manipulated by industrial robots under normal production conditions is investigated. This is an important problem as the quick and precise manipulation of such objects may reduce the production lead time and thus its cost. The problem is in the present study tackled for flexible beams via a novel method which overcomes various practical difficulties and can be easily applied in industrial environments with the least human intervention. The method is based on: (i) AutoRegressive with eXogenous (ARX) input stochastic modeling of the robot-beam system using exclusively experimental data, (ii) the design of an appropriate control system consisting of a typical feedforward PID-type controller and a feedback that enables the attenuation of the force at the robot's wrist and thus the suppression of the vibration at the beam's free-end and, (iii) a synthetic environment within which the performance of the control system may be tested under realistic operating conditions through simulation before its final implementation in the robot. The effectiveness of the method is experimentally assessed through the vibration control of a flexible metallic beam that is manipulated by an industrial robot for its insertion into a slot, testing additionally the control system's performance under various operating conditions for which it is not designed to deal with.

A simple approach for designing a PID controller for an experimental air blower system

This paper focuses on the identification and control of an air blower system PT-326. Modelling of the PT-326 system is required before designing the controller. Hence, it is estimated by using system identification toolbox available in MATLAB. The process of identification began with the collection of input and output data from an experiment. The collected data is used for model estimation based on the selection of auto-regressive with exogenous (ARX) model structure of the PT-326 system. Based on the input and output data of the system, best fit criterion and correlation analysis of the residual are analysed to determine the adequate parameters of ARX model representing the PT-326 system. To achieve a good performance for the air blower system, right selection of the PID controller parameters is essential. This paper also presents a simple approach for designing a PID controller using minimum square error tuning scheme and compares it with a conventional Ziegler-tuning method for the identified model via simulation and experiment. The results obtained from both tuning methods show that the outputs of the system with the PID controller in simulation and experiment are almost similar.

Field validation study of a time and temperature indexed autoregressive with exogenous (ARX) model for building thermal load prediction

Building load prediction algorithms are becoming an essential component of building energy technologies as intelligent building technologies are rapidly evolving and require accurate load predictions to make real-time operational decisions. This paper presents a field validation study of an autoregressive with exogenous (ARX) model, indexed with respect to time and temperature, and used for hourly building thermal load prediction with an aim for integration with real time predictive control strategies. Indexing of the ARX model implies that different sets of coefficients are used in the predictive equation depending on different time intervals and temperature ranges. Although many regressive prediction models have been proposed, no field validation has been reported in the literature, which is an essential step before implementation in actual practice. The validation study was carried out using field data from three buildings located in the main campus of Mississippi State University. The proposed model was able to predict hourly thermal load accurately and within the uncertainty bounds of the measured thermal load most of the time. Results also demonstrated that proper indexing of the model allowed it to capture different cooling and heating load profiles and abrupt changes in the load pattern.

Order reduction of MIMO ARX systems using Laguerre bases

In this article, we explore the use of the Laguerre functions for the estimation of multivariable autoregressive with exogenous (ARX) input model. Each polynomial function of the MIMO ARX model associated to the inputs and to the outputs is expanded on independent Laguerre orthonormal bases. The resulting model is entitled MIMO ARX-Laguerre model. The optimal approximation of which is ensured once the poles characterising each Laguerre orthonormal basis are set to their optimal values. In this paper, a minimal recursive representation realisations for MIMO discrete-time linear systems are derived using Laguerre functions. Further we propose, from input/output measurements, an iterative optimisation algorithm for the free parameters (Laguerre poles). Simulation results show the effectiveness of the proposed optimal modelling method.

A Comparative Study of Linear ARX and Nonlinear ANFIS Modeling of an Electro-Hydraulic Actuator System

The existence of a high degree of nonlinearity in Electro-Hydraulic Actuator (EHA) has imposed a challenge in development of a representable model for the system such as that significant control performance can be proposed. In this work, linear Autoregressive with Exogenous (ARX) model and nonlinear Adaptive Neuro-Fuzzy Inference System (ANFIS) model of an EHA system are obtained based on the mathematical model of the system. Linear ARX modeling technique has been widely applied on EHA system and satisfying result has been obtained. On the other hand, ANFIS modeling technique can model nonlinear system at high accuracy. Both models are validated offline using data set obtained and using different stimulus signals when doing online validation. Offline validation test shows that ANFIS model has 99.37% best fitting accuracy, which is more accurate than 93.75% in ARX model. ARX model fails in some online validation tests, while ANFIS model has been consistently accurate in all tests with RMSE lower than 0.25.

A Nonlinear Generalization of Spectral Granger Causality

Spectral measures of linear Granger causality have been widely applied to study the causal connectivity between time series data in neuroscience, biology, and economics. Traditional Granger causality measures are based on linear autoregressive with exogenous (ARX) inputs models of time series data, which cannot truly reveal nonlinear effects in the data especially in the frequency domain. In this study, it is shown that the classical Geweke's spectral causality measure can be explicitly linked with the output spectra of corresponding restricted and unrestricted time-domain models. The latter representation is then generalized to nonlinear bivariate signals and for the first time nonlinear causality analysis in the frequency domain. This is achieved by using the nonlinear ARX (NARX) modeling of signals, and decomposition of the recently defined output frequency response function which is related to the NARX model.

Intelligence Swarm Model Optimization of Flexible Plate Structure System

This paper presents the performance of modeling the flexible plate structure with free-free-clamped-clamped (FFCC) edges boundary condition using conventional Recursive Least Squares (RLS) and evolutionary algorithm of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The auto-regressive with exogenous (ARX) structure was used in this study to obtain the dynamic model of a flexible plate structure. Data acquisition and instrumentation system were designed and integrated with the experimental rig and several experimental procedures were conducted to acquire the input and output of the flexible plate. The input and output data collected from the experimental study were utilized to develop the model of the system. The 4000 data sets collected in the experiment were divided into two parts for training and testing. The first 3000 data sets were used to train the model developed while the last 1000 data sets were used to test the performance of thus developed model. All developed model using RLS, GA and PSO were validated using one step-ahead prediction (OSA), mean squared error (MSE) and correlation tests. Amongst all, it was found that PSO algorithm has performed better in term of lowest mean squared error achieved (0.00032719) as compared to conventional algorithm (RLS) and evolutionary algorithm (GA). However, by comparing in term of estimating the first mode of vibration which the dominant mode of structure, GA has performed better by presented the lowest percentage error (3.63 %). Besides that, it was found that, all estimated models using all methods proposed are comparable, acceptable and possible to be used as a platform of controller development and verification to suppress the vibration of the flexible plate structure.