ARMAX Model Research Articles

Control of a Thermal Airflow Process - Part I: System Identification

This article was motivated from a practical work on modeling and control of a time-delayed thermal airflow process using adaptive techniques. The work was divided into two parts: (I) the modeling of the process using system identification methods, with main concerns to the numerical robustness of the identification, and (II) the digital control of the process using adaptive self-tuning control, with main concerns to the adaptation of the controller to changes in the process dynamics. This article presents the first part of the work. The thermal airflow system was represented by an ARMAX model, whose parameters were identified using the Recursive Least Squares method, based on two approaches: the Matrix Inversion Lemma, and the Bierman’s UD Factorization. The results obtained show that the last approach has greater numerical robustness and is more suitable for applications of adaptive control – the second part of the work, described in a separate article.

Integrating data from randomized controlled trials and observational studies to predict the response to pregabalin in patients with painful diabetic peripheral neuropathy

BackgroundMore patient-specific medical care is expected as more is learned about variations in patient responses to medical treatments. Analytical tools enable insights by linking treatment responses from different types of studies, such as randomized controlled trials (RCTs) and observational studies. Given the importance of evidence from both types of studies, our goal was to integrate these types of data into a single predictive platform to help predict response to pregabalin in individual patients with painful diabetic peripheral neuropathy (pDPN).MethodsWe utilized three pivotal RCTs of pregabalin (398 North American patients) and the largest observational study of pregabalin (3159 German patients). We implemented a hierarchical cluster analysis to identify patient clusters in the Observational Study to which RCT patients could be matched using the coarsened exact matching (CEM) technique, thereby creating a matched dataset. We then developed autoregressive moving average models (ARMAXs) to estimate weekly pain scores for pregabalin-treated patients in each cluster in the matched dataset using the maximum likelihood method. Finally, we validated ARMAX models using Observational Study patients who had not matched with RCT patients, using t tests between observed and predicted pain scores.ResultsCluster analysis yielded six clusters (287–777 patients each) with the following clustering variables: gender, age, pDPN duration, body mass index, depression history, pregabalin monotherapy, prior gabapentin use, baseline pain score, and baseline sleep interference. CEM yielded 1528 unique patients in the matched dataset. The reduction in global imbalance scores for the clusters after adding the RCT patients (ranging from 6 to 63% depending on the cluster) demonstrated that the process reduced the bias of covariates in five of the six clusters. ARMAX models of pain score performed well (R2: 0.85–0.91; root mean square errors: 0.53–0.57). t tests did not show differences between observed and predicted pain scores in the 1955 patients who had not matched with RCT patients.ConclusionThe combination of cluster analyses, CEM, and ARMAX modeling enabled strong predictive capabilities with respect to pain scores. Integrating RCT and Observational Study data using CEM enabled effective use of Observational Study data to predict patient responses.

Black-box identification of a pilot-scale dryer model: A Support Vector Regression and an Imperialist Competitive Algorithm approach

This report describes system identification by means of the hybrid black-box method. The identification was carried out on the regulation object (a dryer model) representing the pilot-scale processes occurring during air conditioning and drying. The new approach proposed in the paper is the use of the imperialist competitive algorithm (ICA) as a tool for selecting the best parameters for support vector regression (SVR) and for selecting an optimal set of regressors. The advantage of this method is that the selection of an optimal set of regressors and the optimal parameters of SVR for this set is performed automatically, which reduces the time needed for identification. The results of the SVR with the ARX, ARMAX, OE, Box-Jenkins (BJ) and low-order transfer function (Tf) models were compared. The research was conducted for two fan speeds, equal to 40% and 60%. The Fit and MSE indicators for the SVR achieved a higher value with respect to those of the ARX, ARMAX, OE, BJ and Tf models. This method is sufficiently universal and can be applied to any plant as an efficient alternative method. This report is supported by National Science Centre grant UMO-2015/17/B/NZ7/02937

Linear Dynamic Network Reconstruction from Heterogeneous Datasets

This paper addresses reconstruction of linear dynamic networks from heterogeneous datasets. Those datasets consist of measurements from linear dynamical systems in multiple experiments subjected to different experimental conditions, e.g., changes/perturbations in parameters, disturbance or noise. A main assumption is that the Boolean structures of the underlying networks are the same in all experiments. The ARMAX model is adopted to parameterize the general linear dynamic network representation “Dynamical Structure Function” (DSF), which provides the Granger Causality graph as a special case. The network identification is performed by integrating all available datasets and promote group sparsity to assure both network sparsity and the consistency of Boolean structures over datasets. In terms of solving the problem, a treatment by the iterative reweighted l1 method is used, together with its implementations via proximal methods and ADMM for large-dimensional networks.

Design of Model Predictive Controller for Pasteurization Process

This research paper is about developing a better type of controller, known as MPC (Model Predictive Control) for pasteurization process plant. MPC is an advanced control strategy that uses the internal dynamic model of the process and a history of past control moves and a combination of many different technologies to predict the future plant output.. The dynamics of the pasteurization process was estimated by using system identification from the experimental data. The quality of model structures like ARX, ARMAX, BJ and CT model structures was checked based on best fit with validation data, residual analysis and stability analysis. Auto-regressive with exogenous input (ARX322) model was chosen as a model structure of the pasteurization process dynamics and fits about 79.75% with validation data. Finally MPC control strategies were designed using ARX322 model structure.

Design of Model Predictive Controller for Pasteurization Process

This research paper is about developing a better type of controller, known as MPC (Model Predictive Control) for pasteurization process plant. MPC is an advanced control strategy that uses the internal dynamic model of the process and a history of past control moves and a combination of many different technologies to predict the future plant output.. The dynamics of the pasteurization process was estimated by using system identification from the experimental data. The quality of model structures like ARX, ARMAX, BJ and CT model structures was checked based on best fit with validation data, residual analysis and stability analysis. Auto-regressive with exogenous input (ARX322) model was chosen as a model structure of the pasteurization process dynamics and fits about 79.75% with validation data. Finally MPC control strategies were designed using ARX322 model structure.

Economic Implications of Ageing Lithuanian Population

Increased life expectancy combined with declining birth rates and massive emigration flows have caused many to worry about the various impacts of an ageing population in Lithuania. This suggests a very big increase in the dependency ratio and is consequently a cause for concern about a future slowing of economic growth. However, there is little research carried out regarding economic or financial effects of this phenomenon in the country. The aim of this paper is to evaluate the impact of Lithuanian ageing population on economic variables. A new research design is implemented by using VAR and ARMAX models to compare two different approaches, treating ageing as an endogenous and exogenous variable. The authors find that old age dependency ratio has no statistically significant impact on Lithuania’s GDP growth, employment rate, final household consumption and gross national savings in the short run. The results achieved can be explained by incomplete and only short run data available for Lithuania. Also, joining the EU and other favorable economic conditions might have boosted Lithuania’s economic performance over the whole research period and significantly reduced the negative effects of ageing population. However, the impact of shifts in the structure of population age might soon come into effect, as Lithuania‘s society is gathering the pace of ageing, which is also seen in other emerging markets that are progressing toward becoming advanced.

Pricing the ECB's forward guidance with the EONIA swap curve

On July 4, 2013, following several other major central banks, the European Central Bank (ECB) gave for the first time forward guidance on interest rates, which affected market participants' expectations of future interest rates in the context of a Zero Lower Bound. Using an ARMAX(1,1) model in which the effect of the communication of negative macroeconomic news was disentangled from the commitment positive shock, the impact of the forward guidance on money market interest rates is estimated through the Euro Overnight Index Average swap, also called overnight index swap, at maturities between 2 months and 10 years using abnormal returns from an event study. The results and robustness checks suggest that the ECB's guidance lowered overnight index swap rates for maturities within 10 months to 3 years. These results imply the existence of a commitment effect from the ECB's communication. In the context of decreasing market liquidity because of the 3-year long-term refinancing operation repayment, market participants priced the low period of interest rates until mid-2016.

Instrument variable method based on nonlinear transformed instruments for Hammerstein system identification

An extended instrumental variable (EIV) method is considered for the stochastic Hammerstein system (ARMAX and general model structure). The EIV method provides consistent parameter estimates by eliminating noise-induced bias in the least square (LS) method. To estimate the parameters, the Hammerstein model is formulated using the bilinear parameterization. The bilinear model is identified by introducing the nonlinear instrumental variables obtained from transformed delayed outputs using nonlinear mapping and polynomial basis of delayed inputs. These instruments are analyzed in full generality by computing the bounds on expected relationship between instruments and noise for the general noise disturbance structure. Then, a specific case with hyperbolic tangent (tanh) transformation is considered. Comparative performance analysis of the proposed IV method with the existing IV method, the data filtering-based LS methods, and the extended LS method shows improvement in the statistical properties of parameters estimates.

Price modelling in the Canadian fish supply chain with forecasts and simulations of the producer price of fish

ABSTRACTThis research article reports the results of two time-series models defined on the producer price of fish in Canada. An ARMAX model is specified to provide a parsimonious characterization of producer prices and used to simulate price effects from exchange rate shocks. Results show the importance of exogenous shocks, outside the control of fisheries management on welfare/income of Canadian fishermen. An error-correction model is specified to link the price in the first-hand market to the price in the processing market. This model measures both the short- and long-run parameters in defining price, provides estimates on the length of time to regain the equilibrium from price shocks and to forecast producer price response. Interestingly, results show that process price can be considered weakly exogenous with respect to both the short and long run and is the price leader in determining producer price.

An Innovative Substructure Damage Identification Approach for Shear Structures Based on ARMAX Models

Shear structures are used to model tall buildings which play important roles in supporting people's living and working in large cities. These buildings will be gradually deteriorated with the material aging and environmental corrosions. In this paper, an innovative substructure approach is proposed to locate and quantify damages in any storeys of a shear structure with only using three accelerometers. A multiple partition technology is used to extract physical parameters such as stiffness and damping of single inter-storey connection from an independent substructure only containing one storey cut out from the whole structure. By doing this multiple division, damages happened in multi storeys can be identified separately which is a big progress compared to previous researches that mainly consider one damaged storey in whole structure. As in the previous researches, an autoregressive-moving average with exogenous inputs (ARMAX) model is introduced to extract the modal information of each lower substructure and to encapsulate the complex input information on the boundaries of substructure, which can effectively reduce the number of sensors and the calculation process. A damage indicator combining both the information of ARMAX model parameters and model residuals is utilized to enhance the damage identification robustness, where the Kolmogorov-Smirnov (K-S) statistic test is used to evaluate the difference between ARMAX model residuals of tested substructure and of referenced substructure. Simulation of a 10-storey shear structure and an experiment of a 5-storey shear structure have been conducted to verify the effectiveness of the proposed approach, which demonstrate that the innovative approach can accurately identify the structural damages in multi storeys even with large environmental noise disturbance.

Regularized estimation of Hammerstein systems using a decomposition-based iterative instrumental variable method

This paper presents a two-step instrumental variable (IV) method to obtain the regularized and consistent parameter estimates of the Hammerstein ARMAX model based on the bilinear parameterized form. The two-step identification method consists of estimating the bilinear parameters in the first step, followed by parameter reduction in the second step. An iterative identification method is proposed, based on the idea of separating the bilinear form in the two separable forms with partial parameters and solving the decomposed model forms iteratively. The IV-based estimation is integrated into the formulated decomposed structure by introducing the instruments constructed from the estimated auxiliary model outputs. It is shown that in a stochastic environment the proposed IV method produces consistent estimates in the presence of correlated noise disturbances. The validity of the proposed algorithm is verified with the help of extensive simulations using a Monte Carlo study.

Constrained generalised minimum variance controller design using projection‐based recurrent neural network

In this study, a generalised minimum variance control (GMVC) method using the projection-based recurrent neural network (PRNN) is proposed to minimise the error variance in the output of the non-linear plant. One the main drawbacks of the conventional GMVC approaches is the lack of a systematic procedure to deal with the input constraints. In this study, the PRNN is employed for incorporating the input constraints to the minimum variance index. This network is based on the optimality conditions of a constrained problem and is designed using projection theorem. To formulate the proposed approach, by considering an ARMAX model of the system and converting the cost function to a quadratic programming problem, the dynamics and output equations of the PRNN is obtained. The stability and global convergence of the PRNN is analytically shown. Moreover, suitable conditions for the weighting matrices of the cost function are determined to ensure the closed-loop stability. The proposed control method is applied to the non-linear quadruple tank and a comparative analysis between MVC, GMVC and the proposed approach is performed.

Singular spectrum analysis combined with ARMAX model for structural damage detection

Time series analysis is being used popularly in structural health monitoring mainly because of its output-only and non-modal approach. Generally, the damage features are extracted either from the coefficients or the prediction errors of the time series models. However, when the incipient damage is small like minor cracks, the damage features of popularly used time series models, constructed using only the coefficients/prediction errors, are not sensitive. Therefore, identifying the presence or exact spatial damage location becomes difficult. In view of this, in this paper, we present an approach to enhance the sensitivity of the damage features by augmenting Singular Spectrum Analysis (SSA) to ARMAX model, enabling it to locate the smaller damage like cracks. The damage index is obtained from the Cepstral distance between any two ARMAX models. Numerical simulation studies have been carried out by considering an example of a simply supported beam girder with single and multiple cracks. Experimental studies on a simply supported RCC beam is conducted to demonstrate the effectiveness of the proposed algorithm. A benchmark problem associated with the bookshelf frame structure, proposed by Engineering Institute –Los Alamos National Laboratory, is used as another example for experimental verification of the proposed technique. SSA is found to improve the sensitivity of the damage features devised from the ARMAX models for detection of minor damage and damage localization on the structures.

Modeling the dynamic behavior of turbine runner blades during transients using indirect measurements

Turbine start-up transients are induced by the wicket gates opening sequence and generate high amplitude stress cycles. These stress cycles have a detrimental effect leading to faster crack growth in the runner blades. Using a series of direct measurements taken on a prototype runner in order to find the optimal start-up parameters exposes both the runner and the instrumentation to a series of successive damaging transient events during the optimization process. To solve this, finding sensors strongly correlated to strain gauges and whose signals can be easily obtained to identify a model to predict the strain, instead of directly measuring it, would reduce the risk, cost and downtime associated with a measurement campaign. This paper shows that turbine shaft torsion measurements is highly correlated to the strain at a runner blade hotspot, and we demonstrate that the ARMAX model can be used to represent the dynamic system in order to minimize the strain on blades.

Glycemia Prediction Accuracy of Simple Linear Models with Online Parameter Identification

This paper deals with the glycemia prediction accuracy comparison of 7 simple linear model structures, with prediction based on Continuous Glucose Monitoring (CGM) data. Different model structures presented are ARX, ARMAX and Box Jenkins models and their single and multiple input variations, which can represent known or not known meal intake. For each model structure the recursive parameter identification algorithm is presented. All prediction model structures are tested on 7 selected CGM datasets of several type 1 diabetes subjects, acquired in DiaDAQ project. Prediction performance is evaluated using a model fit metrics and an error grid analysis. The results show good prediction performance with low variability among different model structures, despite the simplicity of the prediction algorithm.

Process Identification with Autoregressive Linear Regression Method using Experimental Data: Review

Objective: To obtain mathematical model and parameters of poorly understood and imprecisely known plant/process. Methods: One solution to this problem is to obtain these using identification techniques. Process identification is a technique where a mathematical model of the process under study is build from process input-output data. Several autoregressive models are used to estimate the present value of the model using its past values of the process. Initially, the data set is generated for the given system and the auto regressive model is fitted to it, for the estimation of the model parameters. Residual error for a system is calculated using auto regression model parameters. Findings: A mathematical model for plant under study can be formulated with different system identification using Linear Regression methods like Auto Regressive eXogenous variable (ARX), Auto Regressive Moving Average with an eXogenous variable (ARMAX), Output Error (OE) and Box-Jenkins (BJ). For high model order ARX model is preferred and takes low computations but only suitable for white noise. The ARMAX model considers disturbance affecting process and provides higher performance index i.e. fitness which reveals percentage variation in output estimated by respective model. The Output-Error (OE) model estimates process model but cannot model disturbance features. The residual analysis of Box- Jenkins model shows that the prediction error is not auto-correlated, correlated and is uncorrelated with the input applied to process, thus showing Box- Jenkins model ability to capture noise dynamics of process. Applications/Improvements: The process model can be identified for the unknown, poorly known or partially known system and formulated model can be used in model Predictive controller design and Adaptive control techniques.

Analysis of Autoregressive Predictive Models and Artificial Neural Networks for Irradiance Estimation

Objectives: A model predictive controller was designed for a DC microgrid performed in Universidad Militar Nueva Granada at Cajica campus, which requires a 24-hours estimation of solar irradiance. Methods/Statistical Analysis: Autoregressive and neural networks based predictive models were designed and tested in order to be used, as well as an Artificial Neural Network (ANN) that was trained to be compared as an alternative solution to the problem. All models were coded and simulated on MATLAB and their performance were verified and mutually compared in order to define the best forecasting approach in the target allocation. Findings: The lack of seasons and the stochastically recorded irradiance time series, caused by sudden cloudy moments are the main characteristics of the local weather behavior. Therefore, a 5-years hourly meteorological database was used to estimate and train the ARMAX, NNF, NAR and NARX models, with the main feature of using six time and meteorological variables (air temperature, solar irradiance, atmospheric pressure, day, month and hour of measurements) to estimate a single output of hourly future irradiance. All of them were tested with statistical comparison functions such as square and absolute error criteria, Retrogression coefficient (R) and autocorrelation. Application/Improvements: The results let to define the most appropriate model to be used to generate the online data required for MPC designing to assure efficient operation of DC microgrids.

Forecasting Destination Weekly Hotel Occupancy with Big Data

Hospitality constituencies need accurate forecasting of future performance of hotels in specific destinations to benchmark their properties and better optimize operations. As competition increases, hotel managers have urgent need for accurate short-term forecasts. In this study, time-series models incorporating several tourism big data sources, including search engine queries, website traffic, and weekly weather information, are tested in order to construct an accurate forecasting model of weekly hotel occupancy for a destination. The results show the superiority of ARMAX models with both search engine queries and website traffic data in accurate forecasting. Also, the results suggest that weekly dummies are superior to Fourier terms in capturing the hotel seasonality. The limitations of the inclusion of multiple big data sources are noted since the reduction in forecasting error is minimal.

Estimation of rotor effective wind speeds using autoregressive models on Lidar data

Lidars have become increasingly useful for providing accurate wind speed measurements in front of the wind turbine. The wind field measured at distant meteorological masts changes its structure or was too distorted before it reaches the turbine. Thus, one cannot simply apply Taylor's frozen turbulence for representing this distant flow field at the rotor. Wind turbine controllers can optimize the energy output and reduce the loads significantly, if the wind speed estimates were known in advance with high accuracy and low uncertainty. The current method to derive wind speed estimations from aerodynamic torque, pitch angle and tip speed ratio after the wind field flows past the turbine and have their limitations, e.g. in predicting gusts. Therefore, an estimation model coupled with the measuring capability of nacelle based Lidars was necessary for detecting extreme events and for estimating accurate wind speeds at the rotor disc. Nacelle-mounted Lidars measure the oncoming wind field from utpo 400m(5D) in front of the turbine and appropriate models could be used for deriving the rotor effective wind speed from these measurements. This article proposes an auto-regressive model combined with a method to include the blockage factor in order to estimate the wind speeds accurately using Lidar measurements. An Armax model was used to determine the transfer function that models the physical evolution of wind towards the wind turbine, incorporating the effect of surface roughness, wind shear and wind variability at the site. The model could incorporate local as well as global effects and was able to predict the rotor effective wind speeds with adequate accuracy for wind turbine control actions. A high correlation of 0.86 was achieved as the Armax modelled signal was compared to a reference signal. The model could also be extended to estimate the damage potential during high wind speeds, gusts or abrupt change in wind directions, allowing the controller to act appropriately under extreme conditions.