ARMAX Model Research Articles

Artic Determination of Dynamic Characteristics the Structure with ARX and ARMAX Estimation Methods

In this study, the dynamic behavior of a single-span four-storey steel model structure is tried to determine by using 2 different methods. Connections between beams and columns are produced as rigid and the structure is connected to the shake table by a fixed support. In order to measure the forced vibration values applied to the model structure with the help of the shaking table, the smartphone was placed on the shaking table base and the top of the steel model structure and acceleration records were taken. After the records have been processed, structural algorithm is created using MATLAB autoregressive ARX and autoregressive moving average ARMAX models. Smartphone records from the shake table are defined as inputs and smartphone from the top of the structure are defined as outputs in MATLAB autoregressive ARX and autoregressive moving average ARMAX models. By doing this, structure’s dynamic behavior is to be obtained by MATLAB autoregressive ARX and autoregressive moving average ARMAX models when only vibrating table acceleration record is inputted. Dynamic characteristics obtained by ARX and ARMAX were tried to be confirmed by finite element method using Sap2000 software. In order to determine the dynamic characteristics of the building, the earthquake records of Kobe, Sakarya, Loma-Priate and El-Centro were used as forced vibration. At the end of the study, dynamic properties obtained by numeric models (ARX and ARMAX) using input acceleration record are compared to the dynamic properties obtained by Sap2000 analysis. By doing this it was determined whether dynamic properties can be reliably obtained using autoregressive ARX and autoregressive moving average ARMAX models. Advantages and disadvantages of using this method to define structural behavior are discussed.

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).

Proyecciones de tablas generacionales dinámicas de mortalidad y riesgo de longevidad en países en vías de desarrollo: El caso chileno

El riesgo de longevidad es un factor determinante a evaluar en las reformas de pensiones públicas de reparto y en el cálculo de rentas vitalicias en las pensiones privadas. Uno de los elementos principales para mitigar dicho riesgo es el de disponer de tablas de mortalidad generacionales de la máxima calidad. Generalmente los países desarrollados disponen de información demográfica suficiente para poder confeccionarlas con garantías. Sin embargo, muchos países en vías de desarrollo no disponen de dicha información y toman las tablas de otro país como propias con algunos ajustes. En este trabajo se propone la utilización de unos test de igualdad de muestras a partir de contrastes no paramétricos para establecer qué país con tablas de mortalidad largas es estadísticamente el más comparable con la tabla de mortalidad del país sin información. Proyectando a largo plazo la tabla del país desarrollado seleccionado con un modelo ARMAX, obtendríamos la proyección del país en vías de desarrollo. Así mismo evaluamos algunas consecuencias de no utilizar y no proyectar tablas de mortalidad en el caso de Chile.

OUTLIER ROBUST IDENTIFICATION OF THE THERMAL POWER PLANT: COMBUSTION CONTROL AND VIBRATORY TRANSPORT

The goal of this paper is to contribute to environmental improvement. This goal has been achieved by the development of an algorithm that allows the optimization of fuel consumption and transport of combustion products. The paper considers the outlier robust recursive algorithm. This algorithm is used for identification of multivariable ARMAX (Autoregressive Moving Average with Exogenous Variables) models. In this paper, we introduce pseudo-Huber loss function which is a continuous nonlinear approximation of Huber loss function and which has derivatives of all degrees. The structure of the recursive algorithm is: the relation for parameter estimation is based on Huber function and the relation for matrix gain is based on pseudo-Huber function. The novelty of this work is a new robust algorithm for recursive identification of MIMO ARMAX models. The main contributions of the paper are: (i) the new form of the extended least squares algorithm based on mixed Huber and pseudo-Huber functions; (ii) approximation of the second derivative of pseudo-Huber loss function and exact determination of matrix gain of the algorithm using the Laplace function. A special case of the algorithm, in this paper, is standard linear extended least squares algorithm. The results can be extended to an area of adaptive control, prediction, and filtering. They are suitable for practical processes such as thermal processes, vibration transport of bulk materials and other processes with multiple input variables. Practical behaviour of robust recursive procedure is illustrated by simulations.

Predictability of Vibration Loads From Experimental Data by Means of Reduced Vehicle Models and Machine Learning

Nowadays electric cars are in the spotlight of automotive research. In this context we consider data based approaches as tools to improve and facilitate the car design process. Hereby, we address the challenge of vibration load prediction for electric cars using neural network based machine learning (ML), a data-based frequency response function approach, and a hybrid combined model. We extensively study the challenging case of vibration load prediction of car components, such as the traction battery of an electric car. We show using experimental data from Fiat 500e and VWeGolf cars that the proposed ML approach is able to outperform the classical model estimation by means of ARX and ARMAX models. Moreover, we evaluate the performance of a hybrid-ML concept for combination of ML and ARMAX. Our promising results motivate further research in the field of vibration load prediction using machine learning based approaches in order to facilitate design processes.

태양광 및 풍력 확률모형을 이용한 2030 재생에너지 순수요 불확실성 추정 연구

Under mounting pressure to reduce carbon emission and fine dust, South Korea set a challenging 2030 target for renewable generation. However, the rapid deployment of variable renewable generation undermines the reliability of the power system and causes problems for stable electricity supply. In this study, we analyzed uncertainty and variability of a net load in 2030, which is a key factor for a system operator to run a power system reliably. Two methodologies are applied to estimate the net load: the 2-stage ARMAX model and Monte Carlo simulation. The analysis showed that while spring and fall seasons have a serious duck curve problem that significantly affects the base load, the duck curve problem was not significant in summer or winter due to high peak demand. The duck curve problem, which is mainly caused by the variability of solar PV generation, creates a distinct problem by generating a net load plunge of approximately 44% compared to the peak of net load. The uncertainty of renewable generation was a relatively minor problem by having approximately 5% level of forecasting error compared to peak demand. In conclusion, policy implications for the duck curve problem in 2030 are proposed.

On partial-sum processes of ARMAX residuals

We establish general and versatile results regarding the limit behavior of the partial-sum process of ARMAX residuals. Illustrations include ARMA with seasonal dummies, misspecified ARMAX models with autocorrelated errors, nonlinear ARMAX models, ARMA with a structural break, a wide range of ARMAX models with infinite-variance errors, weak GARCH models and the consistency of kernel estimation of the density of ARMAX errors. Our results identify the limit distributions, and provide a general algorithm to obtain pivot statistics for CUSUM tests.

A time series based damage detection method for obtaining separate mass and stiffness damage features of shear-type structures

One of the main challenges in damage detection of in-service civil structures is the effect of operational and environmental changes. This paper presents a novel output-only vibration based method for detection of stiffness and mass changes in shear-type structures using a proposed time series analysis along with sensor clustering technique. AutoRegressive Moving Average models with eXogenous inputs (ARMAX) are incorporated with the equations of motion written for different sensor clusters. Together with two assumptions, changes in the ARMAX model coefficients are employed to build Stiffness Damage Features (SDF) and Mass Damage Features (MDF). Using SDFs and MDFs, existence, location, severity of changes, i.e., stiffness reduction due to damage, and changes in mass due to operational conditions, can be identified separately and accurately. To demonstrate the effectiveness of the proposed method in its current form, first, the shear-type IASC-ASCE numerical benchmark problem is employed. Subsequently, a laboratory-scale four-storey steel structure is developed and tested to study the proposed approach with experimental data. The results show that the approach can successfully identify the location and severity of damage and mass changes separately and very accurately using output-only vibration data.

ARMAX-based method for inertial constant estimation of generation units using synchrophasors

With the increase of wind and solar power plants connected to the grid, frequency stability has become a concern for transmission system operators. The large penetration of these sources reduces the inertia of the system, which naturally reacts to active power perturbations. In this scenario, a method capable of estimating the inertia constant, as perceived by a particular bus, is of practical importance. This paper presents a novel methodology to automatically assess the power system inertial constant using an autoregressive moving average exogenous input (ARMAX) model and demonstrate it using power system disturbance responses measured by a Wide-Area Measurement System (WAMS). The proposed approach can be divided into three parts: (i) Time window selection, which includes the identification of the start of the disturbance as well as the inertial response; (ii) A low-order ARMAX model method to estimate the constant of inertia as perceived by a particular bus; (iii) Accuracy evaluation. The proposed method is evaluated considering simulated signals corrupted with noise and outliers as well as real measurements from the New York transmission system.

A causal investigation on the determinants of CO2 in China

ABSTRACTThis article examines the causal relationship among carbon dioxide emissions, energy consumption, per capita economic growth, and international trade using temporal econometric models with serial data for the period 1980–2017 in China. In the Armax model all regressors are significant in having influenced the dependent CO2 variable. Subsequently, unidirectional causalities are identified from energy consumption and from commercial opening to carbon dioxide emissions, from commercial opening to energy consumption, from carbon dioxide emissions to per capita economic growth and from economic growth to commercial opening. These results show that, over time, more energy consumption in China results in more carbon dioxide emissions so there will be more environment pollution.

Predicting Lower Band Chorus With Autoregressive‐Moving Average Transfer Function (ARMAX) Models

AbstractWe model lower band chorus observations from the DEMETER satellite using daily and hourly autoregressive‐moving average transfer function (ARMAX) equations. ARMAX models can account for serial autocorrelation between observations that are measured close together in time and can be used to predict a response variable based on its past behavior without the need for recent data. Unstable distributions of radiation belt source electrons (tens of keV) and the substorm activity (SMEd from the SuperMAG array) that is thought to inject these electrons were both statistically significant explanatory variables in a daily ARMAX model describing chorus. Predictions from this model correlated well with observations in a hold‐out test data set (validation correlation of 0.675). Source electron flux was most influential when observations came from the same day or the day before the chorus measurement, with effects decaying rapidly over time. Substorms were more influential when they occurred on previous days, presumably due to their injecting source electrons from the plasma sheet. A daily ARMAX model with interplanetary magnetic field (IMF)|B|, IMF Bz, and solar wind pressure as inputs instead of those given above was somewhat less predictive of chorus (r=0.611). An hourly ARMAX model with only solar wind and IMF inputs was even less successful, with a validation correlation of 0.502.

An efficient dark fermentative hydrogen production by GMV control of pH

This study proposes that the on-line pH control via a model-based adaptive controller markedly improves the dark fermentative hydrogen production. According to the dynamic behavior of the dark fermentation process, pH, which rapidly declines with the beginning of the biogas production, should be precisely controlled around its optimal value in a narrow range. The success of on-line pH control was guaranteed by performing the preliminary simulation studies by experimental data obtained from dynamic analysis to determine ARMAX model order with Recursive Least Squares parameter estimation method and then to control the pH with Generalized Minimum Variance (GMV) controller. On-line control of pH at the optimal value of 6.0 during the 25 h dark fermentation process resulted in 5.4 times higher biogas production, 6.2 times higher biogas production potential, nearly doubled the duration of fermentation, and 18.4% biogas production rate increment in comparison with the uncontrolled pH case.

ARMAX Modeling and Impedance Analysis of Voltammetric E-Tongue for Evaluation of Infused Tea

This paper presents a modeling technique to analyze the performance of the electrodes of a custom made voltammetric e-tongue. In this methodology, autoregressive moving average models are estimated for five working electrodes of the e-tongue made of different noble metals in classifying three different classes of infused tea. The experimental input-output responses of the electrodes are used for modeling. The model transfer functions are fitted to an equivalent circuit from which the circuit impedances and electrical parameters are derived. We propose that there is a transition frequency at which values of the electrical parameters shift from positive to negative. The performance of the electrodes is analyzed in terms of data consistency, stability, and formation of negative parameters. Therefore, the proposed modeling technique can be used for selecting the electrodes and the operating frequency to improve the performance of the e-tongue.

Bitcoin fluctuations and the frequency of price overreactions

This paper investigates the role of the frequency of price overreactions in the cryptocurrency market in the case of BitCoin over the period 2013–2018. Specifically, it uses a static approach to detect overreactions and then carries out hypothesis testing by means of a variety of statistical methods (both parametric and non-parametric) including ADF tests, Granger causality tests, correlation analysis, regression analysis with dummy variables, ARIMA and ARMAX models, neural net models, and VAR models. Specifically, the hypotheses tested are whether or not the frequency of overreactions (i) is informative about Bitcoin price movements (H1) and (ii) exhibits no seasonality (H2). On the whole, the results suggest that it can provide useful information to predict price dynamics in the cryptocurrency market and for designing trading strategies (H1 cannot be rejected), whilst there is no evidence of seasonality (H2 cannot be rejected).

Forecasting monthly farm tractor demand for India using MSARIMA and ARMAX models

Because of long product development cycles, effective production planning of automobiles requires accurate demand forecasting in order to effectively managing resources and maximizing revenue. Errors in demand forecasts have often led to enormous costs and loss of revenue due to suboptimal utilization of resources. Since early 2000 India has been the largest manufacturer and consumer of farm tractors in the world. This paper develops multiplicative seasonal autoregressive integrated moving average (MSARIMA) and autoregressive moving average model with exogenous variable (ARMAX) to forecast monthly demand for farm tractor. The result indicates that ARMAX with real agriculture credit has found to be outperformed MSARIMA model in forecasting demand of farm tractors in the horizon of six months. The accurate monthly forecasting of farm tractor would help the manufacturers for better raw material, inventory and supply chain management. Keywords

Impact of solar activity on precipitation in the United States

In this paper we analyze the relationship between the sunspot numbers and the average monthly precipitation measured at meteorological stations in the US. The results indicate that there is a significant correlation between the solar activity and the monthly average precipitation data for selected months and time delays. In order to confirm the relationship, for the precipitation data we check the forecasting abilities of a popular time series model with and without additional information on the sun activity. Namely, first we fit the autoregressive moving average (ARMA) time series model to the US precipitation data and calculate one-step ahead forecasts. Next, we repeat the same steps with the ARMA model with exogenous input (ARMAX) which is the sunspot number data. We show that the forecast errors are essentially lower for the ARMAX model for months and time delays found in the correlation analysis.

Substructural damage detection in shear structures via ARMAX model and optimal subpattern assignment distance

A novel substructural damage detection approach based on auto-regressive moving average with exogenous inputs (ARMAX) model and optimal subpattern assignment (OSPA) distance is proposed to locate and quantify the damages. Firstly, the shear structure is divided into independent substructures so that damage identification can be performed on each substructure modeling with multi-input multi-output (MIMO) model, which is promising for practical application and distributed structural health monitoring. Compared with the auto-regressive (AR) model, the ARMAX model structure involves not only the outputs but also the inputs and the disturbance dynamics, which help to improve the performance of modeling every substructure and gain the flexibility to handle the disturbance caused by environmental noises even the structural responses contain strong correlations under different excitations. The features of a linear dynamic system can be represented by its poles estimated from ARMAX model, transforming the damage detection into multi-target tracking of system poles. The OSPA distance is used as an innovative damage indicator of a function of the ARMAX model poles in this study, and is calculated by Hungarian algorithm. Experimental verifications were conducted to prove satisfactory damage detection. The application on nonlinear damage identification in a complex three-dimensional reinforced concrete structure shows the great potential of the proposed pole-based OSPA distance in multi-sensor information fusion of structural responses from different directions.

Estimating the Cost of Solar Generation Uncertainty and the Impact of Collocated Energy Storage: The Case of Korea

As a major option for reducing greenhouse gas emission and sustainable development, renewable generation is rapidly expanding in the power sector. However, the variability and uncertainty of renewable generation undermine the reliability of the power system, requiring additional reserve capacities. This study estimates the costs induced by additional reserve capacities to reduce the uncertainty of solar generation in the Korean power system and analyzes the effectiveness of the Energy Storage System (ESS) in reducing these costs, using the stochastic form of multi-period security-constraint optimal power flow. To determine the input of stochastic solar generation, an ARMAX model and Monte Carlo method are applied for representative solar farms. The results indicate solar power generation by 2029 would increase the required reserve by 56.2% over the current level but coupling a 10 GWh of lithium-ion ESS would reduce it by 61.1% compared to increased reserve level for 2029. The operating cost reduction (benefit) by ESS would be 80.8% higher in 2029 compared to the current level and cover 89.9% of its installation cost. The benefit of ESS will be improved when (1) offer prices of reserves correctly reflect the true opportunity cost of providing reserve services and (2) more variable renewable energies are deployed.

System Identification of Wood Drying Process Based on ARMAX Model

This article presents system identification of wood drying process based on ARMAX model. Temperature and equivalent moisture content are considered as inputs, and moisture content of the wood sample during drying is taken as output of the system. The comparative study of RLS and FF-RLS to identify the system parameters is presented. Simulation results are presented to val-idate the efficacy of the ARMAX model for wood drying process.

Detection of Subtle Damage in Structures through Smart Signal Reconstruction

The primary function of structural health monitoring (SHM) is the process of extracting the damage features from the measured raw data, recorded using sensors on the structure of interest. The efficiency of SHM techniques lies in their capability to detect early damage, which alters the dynamic characteristics of only a few modal responses but in a feeble manner, in its incipient stage. Isolating these modal responses, hidden in the overall raw response, for damage diagnosis, is a real challenge to the SHM community. In order to handle this issue, an improved version of Empirical Mode Decomposition (EMD) is employed in this paper. EMD decomposes the measured response signals into mono-component signals, called intrinsic mode functions (IMFs). The mixed modes in EMD are handled using Intermittency criteria in the proposed EMD. Once the IMFs are extracted from the raw signal, the IMFs (signal components) which possess the valuable information of incipient damage called ‘critical IMFs’, are isolated. To determine the spatial location of damage, these critical IMFs are combined to reconstruct a new signal with enriched information on minor/incipient damage. ARMAX model is employed on the new signal with enriched damage information. A normalized distance measure of ARMAX models, in terms of subspace angles, is used as a damage indicator. The numerical and experimental investigations presented in this paper clearly reflect that the proposed output-only damage diagnostic technique using the smart reconstruction of the measured raw signal is capable of detecting the incipient subtle damages in the structures.