ARMAX Model Research Articles

Physics-informed linear regression is competitive with two Machine Learning methods in residential building MPC

Because physics-based building models are difficult to obtain as each building is individual, there is an increasing interest in generating models suitable for building MPC directly from measurement data. Machine learning methods have been widely applied to this problem and validated mostly in simulation; there are, however, few studies on a direct comparison of different models or validation in real buildings to be found in the literature. Methods that are indeed validated in application often lead to computationally complex non-convex optimization problems. Here we compare physics-informed Autoregressive–Moving-Average with Exogenous Inputs (ARMAX) models to Machine Learning models based on Random Forests and Input Convex Neural Networks and the resulting convex MPC schemes in experiments on a practical building application with the goal of minimizing energy consumption while maintaining occupant comfort, and in a numerical case study. The building has a water-based emission system and is located in temperate climate. We demonstrate that Predictive Control leads to savings between 26% and 49% of heating and cooling energy, compared to the building’s baseline hysteresis controller. Moreover, we show that all model types lead to satisfactory control performance in terms of constraint satisfaction and energy reduction. However, we also see that the physics-informed ARMAX models have a lower computational burden, and a superior sample efficiency compared to the Machine Learning based models. Moreover, even if abundant training data is available, the ARMAX models have a significantly lower prediction error than the Machine Learning models, which indicates that the encoded physics-based prior of the former cannot independently be found by the latter.

Impact of Sustainable Development and Environmental Protection on the Volume of Domestic Hard Coal Sales in Poland

The paper presents the results of an analysis of the impact of activities related to the implementation of Poland’s climate policy on the level of demand for hard coal. The authors used sets of indicators built by Eurostat during the analysis. The analysis was based on a set of indicators that had not previously been used for this purpose. The applied ARAMAX model made it possible to study the impact of the presented indicators on the volume of demand for hard coal in Poland. They were introduced to the ARMAX model as explanatory variables. The demand for hard coal in Poland was the dependent variable. The set of indicators was verified, and finally only statistically significant factors were used to build the model. The forecast of the demand for hard coal was made until 2022. It showed that the volume of coal sales would systematically fall as long as factors affecting demand remain constant. However, an additional factor was taken into account in the analysis, namely the increase in demand and prices for hard coal on world markets. The ARIMA model was used to forecast price levels for the next 12 months. The forecast indicates that the time series of prices should maintain an upward trend within the examined time period. Building an accurate and reliable forecast is the basis for effective planning of coal production and is adjusted to the demand for this fuel.

Integrating seasonal forecasts into real-time drought management: Júcar River Basin case study

In future years, and due to climate change, the frequency and intensity of extreme droughts will increase in some areas of the planet with water scarcity problems, affecting the reliability and vulnerability of water resource systems (WRS). Therefore, several approaches for real-time drought management were proposed in this study to improve the predictive capacity of currently used methodologies.This study was conducted in the Júcar River Basin, a highly regulated Mediterranean WRS whose experience in drought management is currently based on the combination of a stochastic model for future inflow series generation (using previous historical inflows) and a risk assessment model. Here, the possibility of improving and updating this approach was analysed by proposing three different models that integrate seasonal meteorological forecasts into the series generation process: i) an auto-regressive moving-average model with exogenous variables (ARMAX); ii) a hydrological model (HBV); and iii) an Artificial Neural Network (ANN) model. These models were also combined (individually) with a risk assessment model to assist in the decision-making process through a very intuitive drought risk indicator for several months in advance.The main results confirmed the potential for improving the predictive capacity of the current method using seasonal forecasts, especially with the ARMAX and ANN models under drought scenarios. Their results were more robust, with lower variabilities and uncertainty even after seven months, which represents a good opportunity to improve the decision-making process of this basin in a changing near future.

Development of Block Oriented Recursive and Constrained Parameter Estimation Schemes for ARMAX Models

In the process industry, black box linear perturbation models are often used for the development of model predictive controllers. Maintaining a high-quality model so as to achieve good control performance in the face of changing operating conditions is a difcult task. In adaptive control schemes, the model parameters are updated online using recursive least square schemes. These recursive schemes typically update the model parameters at every sampling instant. Since in many chemical/biological processes, the model parameters change at a relatively slow rate compared to state variables, it is beneficial to update the model parameters using blocks of data points instead of updating at each sampling instant. In this work, a constrained update scheme based on blocks of data is proposed for updating ARMAX model parameters online. The inclusion of constraints ensures that the noise model is stable and inversely stable. The constrained formulation is further simplifed to arrive at two unconstrained recursive parameter update schemes. The efficacy of the proposed schemes is demonstrated using a simulation study on an artificial system and experimental data obtained from a temperature control system and benchmark quadruple tank system.

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

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

MIMO auto-regressive modeling-based generalized predictive control for grid-connected hybrid systems

In this paper, we propose an energy management model for grid-connected hybrid systems. This model is based on the coupling of a multiple input multiple output (MIMO) AutoRegressive Moving Average with eXogenous inputs (ARMAX) model with generalized predictive control (GPC). The ARMAX model performs input–output mapping of the electrical system data in terms of energy costs and power values. The GPC system receives the input–output mapping provided by the ARMAX model and performs energy management by minimizing the consumed energy cost in the load. Cost minimization is accomplished by optimizing the use of renewable energy sources, thus consuming less energy from the grid. The effectiveness of the proposed model is verified, comparing its computational and experimental results to those of a conventional control model and a model predictive control approach presented in the literature.

Parametric identification of ARMAX models with unknown forming filters

Abstract In this paper, we present the parameter estimation algorithm for the class of an extended ARMAX model containing a ‘coloured’ noise sequence, formed by an unknown finite-dimensional linear filter. This algorithm represents the extended versions of residual whitening method and least squares method, working in parallel, to identify the extended parameters obtained after the suggested linear model transformation. The strong consistency of the suggested method (convergence with probability one of the obtained extended parameters to their exact values) is proven. A good performance of the proposed method is illustrated by a numerical example with all polynomials containing unknown parameters.

Compensation of Data Loss Using ARMAX Model in State Estimation for Control and Communication Systems Applications

Compensation of data loss in the state estimation plays an indispensable role in efficient and stable control and communication systems. However, accurate compensation of data loss in the state estimation is extremely challenging issue. To cater this challenging issue, two techniques such as the open-loop Kalman filter and the compensating closed-loop Kalman filter have emerged. The closed-loop technique compensates for the missing data using the autoregressive model. However, the autoregressive model used only past measurements for data loss compensation. Considering only one parameter, i.e., the past measurements, is insufficient and leads to inaccurate state estimation. Thus, in this work, autoregressive moving average with exogenous inputs model considers three parameters, i.e., the past measurements, the input signal, and the sensor noise, simultaneously to compensate data loss in state estimation. To endorse the effectiveness and applicability of the proposed model, a standard mass-spring-damper is employed in the case study. Simulation results show that the proposed model outperforms the existing autoregressive models in terms of performance parameters.

Parameter estimation of MIMO two-dimensional ARMAX model based on IGLS method

Abstract This paper presents an iterative method for the unbiased identification of linear Multiple-Input Multiple-Output (MIMO) discrete two-dimensional (2D) systems. The system discussed here has Auto-Regressive Moving-Average model with exogenous inputs (ARMAX model). The proposed algorithm functions on the basis of the traditional Iterative Generalized Least Squares (IGLS) method. In summary, this paper proposes a two-dimensional Multiple-Input Multiple-Output Iterative Generalized Least Squares (2DMIGLS) algorithm to estimate the unknown parameters of the ARMAX model. Finally, simulation results show the efficiency and accuracy of the presented algorithm in estimating the unknown parameters of the model in the presence of colored noise.

Nonlinear extensions of new causality

New causality (NC) is a relatively recent method for inferring causal relationships between time-series data. Similar to other popular causal inference methods, like Granger causality (GC), NC can be evaluated in time or frequency domain. NC derives its value by partitioning a predictive model, grouping them by different inputs, and finding a normalized ratio of the power of all contributions. In its seminal form, NC is defined atop a linear ARMAX models. If the contribution between two time-series cannot be accurately expressed with a linear model, the seminal form of NC cannot accurately measure the causal relationship. In the frequency domain, linear models also prevent cross-frequency contributions from being measured. This work introduces an extension to NC to NARMAX models. This extension reduces to the seminal form when applied to linear models and can be also evaluated in the frequency domain. The nonlinear extension is applied to a range of synthetic models and real EEG data with promising results. A discussion on modeling and its effect on linear and nonlinear NC estimates is provided.

Identification of CO$$_{\mathrm{2}}$$ and O$$_{\mathrm{2}}$$ emissions dynamics in a natural gas furnace through flame images, ARMAX models, and Kalman filtering

Identification of CO$$_{\mathrm{2}}$$ and O$$_{\mathrm{2}}$$ emissions dynamics in a natural gas furnace through flame images, ARMAX models, and Kalman filtering

Bitcoin Returns and the Frequency of Daily Abnormal Returns

This paper investigates the relationship between Bitcoin returns and the frequency of daily abnormal returns over the period from June 2013 to February 2020 using a number of regression techniques and model specifications including standard OLS, weighted least squares (WLS), ARMA and ARMAX models, quantile regressions, Logit and Probit regressions, piecewise linear regressions, and non-linear regressions. Both the in sample and out-of-sample performance of the various models are compared by means of appropriate selection criteria and statistical tests. These suggest that, on the whole, the piecewise linear models are the best, but in terms of forecasting accuracy they are outperformed by a model that combines the top five to produce “consensus” forecasts. The finding that there exist price patterns that can be exploited to predict future price movements and design profitable trading strategies is of interest both to academics (since it represents evidence against the EMH) and to practitioners (who can use this information for their investment decisions).

Inspecting debt servicing mechanism in Nigeria using ARMAX model of the Koyck-kind

The burden of external debt affects the wellbeing of an economy (or a country) by making the economy vulnerable to external shocks and crowding out investment. When dealing with debt management in indebted poor countries like Nigeria, the rational approach is to allocate a portion of export earnings for debt service payments. Along this line, there is a need to identify the link between debt servicing and export earnings. Hence, the current and long-run effects of export earnings on debt service payments is modelled as a single-input-single-output discrete-time dynamical system within the framework of Autoregressive Moving Average Explanatory Input model of the Koyck-kind (KARMAX). The KARMAX model is identified for Nigeria, using data from the World Bank database from 1970 to 2018 based on the maximum likelihood (ML) method, and the obtained results are compared to the prediction error and the instrumental variable methods. From a theoretical perspective, the KARMAX specification identified by the ML method is more ideal and inspiring. By doing so, this article contributes to the literature on the econometrics of public debt management.

Forecasting Copper Electrorefining Cathode Rejection by Means of Recurrent Neural Networks With Attention Mechanism

Electrolytic refining is the last step of pyrometallurgical copper production. Here, smelted copper is converted into high-quality cathodes through electrolysis. Cathodes that do not meet the physical quality standards are rejected and further reprocessed or sold at a minimum profit. Prediction of cathodic rejection is therefore of utmost importance to accurately forecast the electrorefining cycle economic production. Several attempts have been made to estimate this process outcomes, mostly based on physical models of the underlying electrochemical reactions. However, they do not stand the complexity of real operations. Data-driven methods, such as deep learning, allow modeling complex non-linear processes by learning representations directly from the data. We study the use of several recurrent neural network models to estimate the cathodic rejection of a cathodic cycle, using a series of operational measurements throughout the process. We provide an ARMAX model as a benchmark. Basic recurrent neural network models are analyzed first: a vanilla RNN and an LSTM model provide an initial approach. These are further composed into an Encoder-Decoder model, that uses an attention mechanism to selectively weight the input steps that provide most information upon inference. This model obtains 5.45% relative error, improving by 81.4% the proposed benchmark. Finally, we study the attention mechanism’s output to distinguish the most relevant electrorefining process steps. We identify the initial state as critical in predicting cathodic rejection. This information can be used as an input for decision support systems or control strategies to reduce cathodic rejection and improve electrolytic refining’s profitability.

Stability analysis on the effects of heart rate variability and premature activation of atrial ECG dynamics using ARMAX model.

The cellular action potential of cardiac muscles generates Electrocardiogram (ECG) signals. Disturbances in cardiac cells are determined by analyzing the stability of ECG intervals. The PTa Interval (PTaI) of ECG represents the atrial Action Potential Duration (APD) and the evaluation of the causes of PTaI instability can predict the onset of arrhythmia. This study developed an Autoregressive Moving Average with Exogenous Input (ARMAX) model to explore the roles of Heart Rate Variability (HRV) and Premature Activation (PA) in PTaI dynamics using PTaI and PP Interval (PPI) as exogenous inputs. Minute ECG signals were collected from twenty Normal Sinus Rhythm (NSR) and ten Atrial Tachycardia (AT) volunteers. The EDAN PC ECG system was used in the Modified Limb Lead (MLL)configuration to evaluate instability. The instabilities of PTaI were found at the minimum model orders (Amin) of 10 and 11, in the NSR and AT groups, respectively. In the NSR group, the predominant reason for PTaI instability was HRV, whereas among AT patients, it was largely due to PA that preceded the onset of AT. The proposed model showed better prediction of PTaI with minimum Mean Square Error(MSE) between the measured and predicted PTa Intervals (PTaIs). The factor that led to PTaI instability in AT patients was found to be different from that of the NSR group. The frequency of PA (fPA) was found to contribute more in the AT than the NSR group. The developed ARMAX model was better in predicting instability of atrial ECG dynamics in both groups than other autoregressive models currently in use.

Microcontroller Based Data Acquisition and System Identification of a DC Servo Motor Using ARX, ARMAX, OE, and BJ Models

Microcontroller Based Data Acquisition and System Identification of a DC Servo Motor Using ARX, ARMAX, OE, and BJ Models

Análise em séries temporais da radiação solar na Cidade do Recife/PE

Objetivo: analisar e descrever o melhor ajuste para série temporal de radiação solar na cidade do Recife/PE, aplicando os modelos ARMA e ARMAX, além de prever os níveis de radiação para os próximos seis anos. Método: utilizaram-se dados de séries climáticas do Instituto Nacional de Meteorologia (INMET), disponibilizados no período de janeiro de 2009 a dezembro de 2018. A comparação dos modelos foi realizada pelos critérios de informação de Akaike. Resultados: a série de radiação solar apresenta uma alta variabilidade das médias mensais, indicando a presença de sazonalidade e uma forte assimetria negativa. Os resultados da estatística de erros mostram a acurácia do modelo ARMAX(2,1), com erro percentual próximo de 18,68%, comparando-se a série observada e ajustadas, além disso, foi possível identificar que a previsão consegue captar a existência de sazonalidade. Conclusão: o modelo ARMAX foi adequado para descrever a radiação solar incluindo variáveis exógenas, apresentando melhor previsão com boa acurácia, sendo uma ferramenta capaz de auxiliar em políticas de saúde pública no combate ao câncer de pele e intervenções.

Forecasting seasonal influenza-like illness in South Korea after 2 and 30 weeks using Google Trends and influenza data from Argentina.

We aimed to identify variables for forecasting seasonal and short-term targets for influenza-like illness (ILI) in South Korea, and other input variables through weekly time-series of the variables. We also aimed to suggest prediction models for ILI activity using a seasonal autoregressive integrated moving average, including exogenous variables (SARIMAX) models. We collected ILI, FluNet surveillance data, Google Trends (GT), weather, and air-pollution data from 2010 to 2019, applying cross-correlation analysis to identify the time lag between the two respective time-series. The relationship between ILI in South Korea and the input variables were evaluated with Linear regression models. To validate selected input variables, the autoregressive moving average, including exogenous variables (ARMAX) models were used to forecast seasonal ILI after 2 and 30 weeks with a three-year window for the training set used in the fixed rolling window analysis. Moreover, a final SARIMAX model was constructed. Influenza A virus activity peaks in South Korea were roughly divided between the 51st and the 7th week, while those of influenza B were divided between the 3rd and 14th week. GT showed the highest correlation coefficient with forecasts from a week ahead, and seasonal influenza outbreak patterns in Argentina showed a high correlation with those 30 weeks ahead in South Korea. The prediction models after 2 and 30 weeks using ARMAX models had R2 values of 0.789 and 0.621, respectively, indicating that reference models using only the previous seasonal ILI could be improved. The currently eligible input variables selected by the cross-correlation analysis helped propose short-term and long-term predictions for ILI in Korea. Our findings indicate that influenza surveillance in Argentina can help predict seasonal ILI patterns after 30 weeks in South Korea, and these can help the Korea Centers for Disease Control and Prevention determine vaccine strategies for the next ILI season.

Machine Learning in Internet Search Query Selection for Tourism Forecasting

Prior studies have shown that Internet search query data have great potential to improve tourism forecasting. As such, selecting the most relevant information from large amounts of search query data is crucial to enhancing forecasting accuracy and reducing overfitting; however, such feature selection methods have not been considered in the tourism forecasting literature. This study employs four machine learning–based feature selection methods to extract useful search query data and construct relevant econometric models. We examined the proposed methods based on monthly forecasting of tourist arrivals in Beijing, China, along with weekly forecasting of hotel occupancy in the city of Charleston, South Carolina, USA. Our findings indicate that the forecasting model with the selected search keywords outperformed the benchmark ARMAX model without feature selection in forecasting tourism demand and hotel occupancy. Therefore, machine learning methods can identify the most useful search query data to significantly improve forecasting accuracy in tourism and hospitality.

Sensör ve Akıllı Telefon Kayıtları Yardımı ile Yapının Dinamik Karakteristiklerin Belirlenmesi

Çalışma kapsamında, sarsma tablasındaki çelik model yapıya yerleştirilen sensör ve akıllı telefondan elde edilen titreşim değerleri ile MATLAB matematiksel tahmin modeli kullanılarak oluşturulan titreşim değerleri arasındaki uyum oranları karşılaştırılmıştır. Deneysel çalışmada kullanılan çelik model yapı; tek açıklıklı, dört katlı çelik malzemesinden üretilmiştir. Çelik model yapıda bulunan kolon-kiriş bağlantıları rijit, model binanın dört tarafında bulunan temel bağlantıları sarsma tablasına ankastre olacak şekilde montelenmiştir. Deneysel çalışmadan elde edilen titreşim değerleri, sarsma tablasının tabanına ve çelik model yapının tepe noktasına yerleştirilen sensör ve akıllı telefondan elde edilmiştir. Sarsma tablası El-Centro, Loma-Prieta, Kobe ve Sakarya depremlerinin titreşim değerleriyle zorlanmış ve oluşan zorlanmanın yapıda meydana getirdiği titreşimler sensör ve akıllı telefon yardımıyla kaydedilmiştir. Sarsma tablasının tabanında bulunan sensör ve akıllı telefon titreşim değerleri girdi, çelik model yapının tepe noktasında bulunan sensör ve akıllı telefonlar titreşim değerleri sisteme çıktı olarak tanımlanmıştır. Çalışmaların sonucunda deneysel olarak elde edilen girdi-çıktı verileri arasındaki uyumluluk oranları, Matlab programındaki otoregresif ARX ve otoregresif hareketli ortalamalar ARMAX modelinde bulunan tahmin-öngörü ile üretilen girdi-çıktı arasındaki uyumluluk oranları karşılaştırılmıştır.