ARX Model Research Articles

Reduced model of MIMO systems using Meixner-like functions

This article investigates the use of orthogonal basis functions, particularly Meixner-like functions, to streamline and optimize the parameter complexity in multi-input multi-output (MIMO) system modeling. We introduce a new optimal model for MIMO systems, developed by decomposing the auto-regressive MIMO model with external inputs (ARX) using orthonormal Meixner-like bases. This model, referred to as the MIMO ARX Meixner-like model, enables filtering of the system’s inputs and outputs with Meixner-like functions. Parameter reduction is achieved through the optimization of Meixner-like poles using an iterative technique based on the Newton-Raphson method. The proposed model’s efficacy is demonstrated through simulations on two experimental systems: a two-degrees-of-freedom (DOF) helicopter and a two-tank process. Results reveal that the model effectively reduces approximation errors with fewer parameters. Comparative analysis with the traditional MIMO ARX model confirms the superior performance of the MIMO ARX Meixner-like model.

Research on an adaptive prediction method for restaurant air quality based on occupancy detection

This study evaluates the impact of personnel on air quality in air-conditioned restaurant environments during winter, summer, and transitional seasons, characterized by the peculiarities of personnel movement, high concentration of personnel in a short period of time, poor ventilation and high personnel density, leading to the accumulation of pollutants that can severely damage personnel health. This study examines carbon dioxide (CO2) and particulate matter (PM) concentrations and proposes an online adaptive model for their prediction.Environmental influence factors are analyzed through correlations of measured data, and appropriate input parameters (time-lagged cumulative number of people) are selected. The Auto-Regressive with Exogenous Inputs (ARX) model is used to predict the change of air quality with the movement and number of people, compared with classical models (LR, DT, SVM, ENS, GPR, NN, VARX). Results show that the ARX model performs excellently in predicting restaurant environments; the effect of different environmental factors on the predictive effectiveness of the model was also explored. When combined with real-time sensor data and AIC-based adaptive optimization, the prediction accuracy is further improved by more than 25 %. The R2 of the ARX model is 0.9549, the MAE is 0.8352 μg/m3 and the MAPE is 3.17 %. The adaptively optimized model can be adapted to different environments, overcoming the problem of poor adaptability of such models. Our results enable effective environmental control strategies in public spaces, contributing to Sustainable Development Goal (SDG) 3: Good Health and Well-being by reducing health risks associated with indoor air pollution.

Modeling engagement with a digital behavior change intervention (HeartSteps II): An exploratory system identification approach

ObjectiveDigital behavior change interventions (DBCIs) are feasibly effective tools for addressing physical activity. However, in-depth understanding of participants’ long-term engagement with DBCIs remains sparse. Since the effectiveness of DBCIs to impact behavior change depends, in part, upon participant engagement, there is a need to better understand engagement as a dynamic process in response to an individual’s ever-changing biological, psychological, social, and environmental context. MethodsThe year-long micro-randomized trial (MRT) HeartSteps II provides an unprecedented opportunity to investigate DBCI engagement among ethnically diverse participants. We combined data streams from wearable sensors (Fitbit Versa, i.e., walking behavior), the HeartSteps II app (i.e. page views), and ecological momentary assessments (EMAs, i.e. perceived intrinsic and extrinsic motivation) to build the idiographic models. A system identification approach and a fluid analogy model were used to conduct autoregressive with exogenous input (ARX) analyses that tested hypothesized relationships between these variables inspired by Self-Determination Theory (SDT) with DBCI engagement through time. ResultsData from 11 HeartSteps II participants was used to test aspects of the hypothesized SDT dynamic model. The average age was 46.33 (SD=7.4) years, and the average steps per day at baseline was 5,507 steps (SD=6,239). The hypothesized 5-input SDT-inspired ARX model for app engagement resulted in a 31.75 % weighted RMSEA (31.50 % on validation and 31.91 % on estimation), indicating that the model predicted app page views almost 32 % better relative to the mean of the data. Among Hispanic/Latino participants, the average overall model fit across inventories of the SDT fluid analogy was 34.22 % (SD=10.53) compared to 22.39 % (SD=6.36) among non-Hispanic/Latino Whites, a difference of 11.83 %. Across individuals, the number of daily notification prompts received by the participant was positively associated with increased app page views. The weekend/weekday indicator and perceived daily busyness were also found to be key predictors of the number of daily application page views. ConclusionsThis novel approach has significant implications for both personalized and adaptive DBCIs by identifying factors that foster or undermine engagement in an individual’s respective context. Once identified, these factors can be tailored to promote engagement and support sustained behavior change over time.

A transfer sparse identification method for ARX model

AbstractThe aim of this paper is to improve the parameter estimation accuracy of the system to be identified by using measurements from a known system. By introducing the transfer gain matrix and setting the effective identification criterion, a novel transfer sparse identification method is raised, which deals with the sparse issues more precise. Besides, the unbiased form is given in the parameter analysis and the recursion form can prevent the dimension catastrophe related problems. Moreover, in order to test the effects of the transfer and avoid bad performance, a negative transfer analysis condition is carried out. Finally, the simulation verifies the enhancements and benefits of the proposed transfer sparse identification method, confirming that the transfer performance outperforms better than that of no transfer, especially on the zero parameters identification.

Piezoelectric-based smart structures for aero-engine blade: Piezoelectric layout optimization and vibration suppression tests

To promote the use of piezoelectric smart structures in aero-engine blades, this paper introduces a novel method for optimizing the layout of piezoelectric elements on the blade's surface and an active vibration control method, along with vibration suppression tests. A preprocessing method is introduced for the point cloud data of in-service blades to reconstruct the blade surface. An improved parameter-adaptive differential evolution algorithm is proposed to optimize the layout of piezoelectric actuators and sensors and accurately identify the hysteresis nonlinear model of piezoelectric elements. A Hammerstein model is constructed by cascading an asymmetric Bouc-Wen model with an ARX model to describe the rate-dependent hysteresis nonlinear characteristics of piezoelectric elements. An improved variable step-size FxLMS algorithm is proposed to balance the relationship between convergence speed and steady-state error in the control algorithm. The proposed layout optimization and vibration control algorithm are validated experimentally on an experimental platform under various disturbances, with results showing improved performance of the proposed VSS-FxLMS algorithm in terms of convergence and efficiency.

A Comparative Analysis of ARX and ANFIS Models for Tumor Growth Prediction Under Single and Multi-agent Chemotherapy.

Despite the advances in oncology and cancer treatment over the past decades, cancer remains one of the deadliest diseases. This study focuses on further understanding the complex nature of cancer by using mathematical tumor modeling to understand, capture as best as possible, and describe its complex dynamics under chemotherapy treatment. Focusing on autoregressive with exogenous inputs, i.e., ARX, and adaptive neuro-fuzzy inference system, i.e., ANFIS, models, this work investigates tumor growth dynamics under both single and combination anticancer agent chemotherapy treatments using chemotherapy treatment data on xenografted mice. Four ARX and ANFIS models for tumor growth inhibition were developed, estimated, and evaluated, demonstrating a strong correlation with tumor weight data, with ANFIS models showing superior performance in handling the multi-agent tumor growth complexities. These findings suggest potential clinical applications of the ANFIS models through further testing. Both types of models were also tested for their prediction capabilities across different chemotherapy schedules, with accurate forecasting of tumor growth up to five days in advance. The use of adaptive prediction and sliding (moving) data window techniques allowed for continuous model updating, ensuring more robust predictive capabilities. However, long-term forecasting remains a challenge, with accuracy declining over longer prediction horizons. While ANFIS models showed greater reliability in predictions, the simplicity and rapid deployment of ARX models offer advantages in situations requiring immediate approximations. Future research with larger, more diverse datasets and by exploring varying model complexities is recommended to improve the models' reliability and applicability in clinical decision-making, thereby aiding the development of personalized chemotherapy regimens.

ARX-Naïve Bayes based structural damage identification

ABSTRACT The nature of damage identification is close to a pattern recognition process that classifies different damage patterns. The naïve Bayes classifier (NBC) can effectively handle multiple-classification problems by choosing patterns with high probabilities. Therefore, by absorbing the autoregressive model with exogenous inputs (the ARX model), an ARX-Naïve Bayes damage identification strategy has been proposed in which the autoregressive coefficients of the ARX model are taken as the sensitive damage feature. The classification training and test sample datasets are then built on these coefficients corresponding to various damage scenarios. The model order of an AR model is first determined for the subsequent order selection of the ARX model, whose autoregressive coefficients are further used to construct the NBC. This procedure can enhance the pattern recognition robustness to uncertainties such as measurement noises. Different damage patterns are determined by calculating the sum of logarithmic likelihoods of testing samples. The effectiveness of the proposed method has been verified against a bridge benchmark model having different damage scenarios under the noise pollution. In addition, an experimental five-story shear frame structure was adopted for validation, showing that compared with the SVM algorithm suitable for handling binary classification problems, the proposed method excels in multi-classification of damage patterns.

Model-Free Predictive Current Controller for Voltage Source Inverters Using ARX Model and Recursive Least Squares

Model-Free Predictive Current Controller for Voltage Source Inverters Using ARX Model and Recursive Least Squares

Wave excitation force prediction for arrays of wave energy converters in directional waves

The implementation of advanced control strategies is an effective means of maximizing the energy production of wave energy converters (WECs), and most of them require future wave excitation forces to determine the optimal control sequence. The WECs deployed in arrays can enable a significant reduction in the cost of wave energy and improve prediction performance by incorporating excitation forces from the array. In this paper, a critical comparison of the excitation prediction methods, including the time series, machine learning, and neural network, for a two-body heaving point absorber WEC is presented. Considering the symmetry of the WEC and arrays, the directional spectrum is utilized to determine the reference measurement of wave excitation. The prediction methods are applied to isolated WEC and different array layouts. Moreover, additional sensitivity analyses are performed to evaluate the performance. The results show that the autoregressive with extra input (ARX) model has the best performance in short-term wave excitation force prediction. In most cases, the ARX model is weakly influenced by the sampling period and can adapt well to changes in the directional distribution and sea states of irregular waves, and the ARX model requires the least amount of computational time in the simulations.

Data-Driven Identification of Crane Dynamics Using Regularized Genetic Programming

The meaningful problem of improving crane safety, reliability, and efficiency is extensively studied in the literature and targeted via various model-based control approaches. In recent years, crane data-driven modeling has attracted much attention compared to physics-based models, particularly due to its potential in real-time crane control applications, specifically in model predictive control. This paper proposes grammar-guided genetic programming with sparse regression (G3P-SR) to identify the nonlinear dynamics of an underactuated crane system. G3P-SR uses grammars to bias the search space and produces a fixed number of candidate model terms, while a local search method based on an l0-regularized regression results in a sparse solution, thereby also reducing model complexity as well as reducing the probability of overfitting. Identification is performed on experimental data obtained from a laboratory-scale overhead crane. The proposed method is compared with multi-gene genetic programming (MGGP), NARX neural network, and Takagi-Sugeno fuzzy (TSF) ARX models in terms of model complexity, prediction accuracy, and sensitivity. The G3P-SR algorithm evolved a model with a maximum mean square error (MSE) of crane velocity and sway prediction of 1.1860 × 10−4 and 4.8531 × 10−4, respectively, in simulations for different testing data sets, showing better accuracy than the TSF ARX and MGGP models. Only the NARX neural network model with velocity and sway maximum MSEs of 1.4595 × 10−4 and 4.8571 × 10−4 achieves a similar accuracy or an even better one in some testing scenarios, but at the cost of increasing the total number of parameters to be estimated by over 300% and the number of output lags compared to the G3P-SR model. Moreover, the G3P-SR model is proven to be notably less sensitive, exhibiting the least deviation from the nominal trajectory for deviations in the payload mass by approximately a factor of 10.

Retraction Note: ARX and ARMAX modelling of SBCNC-60 machine for surface roughness and MRR with optimization of system response using PSO

Retraction Note: ARX and ARMAX modelling of SBCNC-60 machine for surface roughness and MRR with optimization of system response using PSO

Augmented support vector regression with an autoregressive process via an iterative procedure

The Support Vector Regression (SVR) technique can approximate intricate systems by addressing learning and estimation challenges within a reproducing kernel Hilbert space, devoid of reliance on specific parameter assumptions. However, when dealing with correlated data like time series, the SVR method often falls short in accounting for underlying temporal structures, leading to limited enhancements in prediction efficiency. We introduce an enhanced SVR method that considers temporal correlations (TemporalSVR) to overcome this constraint. Our proposed method extends kernel functions to include additional linear kernels, facilitating learning temporal patterns. Additionally, we develope an iterative training procedure for the augmented regression model. During model training, we estimate the hyper-parameter in the corresponding loss function using a ‘working’ likelihood approach, enhancing the generalization capabilities of the proposed regression. To demonstrate superior forecasting performance, we conduct extensive numerical simulations on both linear and nonlinear systems and the TemporalSVR achieves improvements ranging from 8% to 114% based on the RMSE ratio from the AR-X model. Furthermore, we investigate the forecasting performance of three basic models (NARX-NN, Statistical SVR, and SVR-ARIMA) and four deep learning (DL) techniques (Transformer, Informer, Reformer, Autormer, and Autoformer) by using a WTI forecasting study. Our proposed TemporalSVR achieves the smallest RMSE at 2.22 and attains the highest success ratio of stock direction prediction at 71.30%. All these numerical results highlight the effectiveness and advantages of our TemporalSVR in handling temporal data and making accurate predictions.

Servo turntable adaptive step size momentum projection identification algorithm based on ARX model

In this paper, two improved projection algorithms are proposed for a servo turntable system based on the autoregressive exogenous (ARX) model. The improvement pertains to the complexity, convergence speed and estimation accuracy of the algorithm. First, the ARX model structure to be identified is obtained from the open-loop velocity model of the servo turntable. To solve the problems of imprecise step size calculation and slow convergence, the adaptive step size momentum projection (AMP) algorithm is proposed, in which segmented adaptive step sizes are adopted and momentum factors are introduced. On this basis, the latest estimation-based hierarchical adaptive step size momentum projection (LE-AMP) algorithm, which has faster convergence, is proposed as a combination of the hierarchical strategy and the latest estimation approach. Second, the complexity and convergence performance of the proposed algorithms are compared and analyzed. Finally, the effectiveness of the algorithms is verified using two examples. Theoretical analysis and simulation experiments show that the AMP algorithm has excellent parameter estimation accuracy, and its convergence speed is further improved through the addition of the momentum factor and the latest estimation, and these improved strategies do not cause any significant increase in complexity.

Parameter Optimization of Steam Generator Water Level Control System Based on Piecewise ARX Modeling

Parameter Optimization of Steam Generator Water Level Control System Based on Piecewise ARX Modeling

Data-Driven Models to Forecast the Impact of Temperature Anomalies on Rice Production in Southeast Asia

Models are a core element in performing local estimation of the climate change input. In this work, a novel approach to perform a fast downscaling of global temperature anomalies on a regional level is presented. The approach is based on a set of data-driven models linking global temperature anomalies and regional and global emissions to regional temperature anomalies. In particular, due to the limited number of available data, a linear autoregressive structure with exogenous input (ARX) has been considered. To demonstrate their relevance to the existing literature and context, the proposed ARX models have been employed to evaluate the impact of temperature anomalies on rice production in a socially, economically, and climatologically fragile area like Southeast Asia. The results show a significant impact on this region, with estimations strongly in accordance with information presented in the literature from different sources and scientific fields. The work represents a first step towards the development of a fast, data-driven, holistic approach to the climate change impact evaluation problem. The proposed ARX data-driven models reveal a novel and feasible way to downscale global temperature anomalies to regional levels, showing their importance in comprehending global temperature anomalies, emissions, and regional climatic conditions.

The Nesterov accelerated gradient algorithm for Auto-Regressive Exogenous models with random lost measurements: Interpolation method and auxiliary model method

For ARX models with random lost measurements, this article proposes an interpolation and auxiliary model based Nesterov accelerated gradient algorithm. This algorithm utilizes the interpolation and auxiliary model methods to fill in lost measurements. The parameters are estimated with better accuracy based on the interpolated input and predicted output data. Two simulation examples are presented to verify the effective of the proposed algorithm.

Comparative Analysis of Nonlinear Methods for Multivariable Water Level Prediction: The Case Study of the Atrato River

This paper presents an innovative multivariate forecasting application for hydrological variables, using an online model based on backpropagation (BP) neural networks. The effectiveness of this approach is verified by using the Nonlinear Autoregressive with Exogenous Inputs (NARX) and the linear Autoregressive with Exogenous Inputs (ARX) methods. The proposed methodology is implemented in two hydrological stations in the department of Chocó, Colombia, located along the Atrato River. The BP neural network structure is applied to establish correlations between water level, flow, and precipitation. This structure is designed to handle the dynamic complexity of the hydrological variables and their interconnections. In addition, a short‐term water level prediction is developed for incorporation into a flood early warning system. Validation of the approach is performed by comparing various estimation errors using regression metrics such as root mean square error (RMSE), relative mean square error (MSRE), mean absolute error (MAE), relative mean absolute error (MARE), and Nash–Sutcliffe efficiency coefficient (NSE). The computation time and the accuracy of the estimated weights versus real data are also considered. The results show that the proposed structure is the most suitable for accurately predicting water levels. It is shown that the backpropagation neural network structure of the proposed model is more effective for water level prediction. This is observed when evaluating the real data compared to the estimated data, obtaining values corresponding to the regression metrics. In particular, for output 2, the RMSE is 0.0742. Compared to the NARX model (RMSE of 0.0985) and the ARX model (RMSE of 0.1265), it is observed that the backpropagation neural network model improves the estimation by 32.6 over the NARX model and by 70.4% over the ARX model. As for the NSE coefficient for output 2 of the model, the backpropagation neural network is the closest to 1 compared to the other two models. For output 2, the backpropagation model obtains a value of 0.9966, the NARX model 0.9958, and the ARX model 0.9914. Another evaluation metric applied to this model is the Kling–Gupta efficiency coefficient (KGE), which is used to evaluate the performance of hydrological models. For the output of the two hydrological stations located in the Atrato River, we observed that for the backpropagation model a value of 0.9992 was obtained, for the NARX model a value of 0.9988 was obtained, and for the linear ARX model with nonlinear structure a value of 0.9984 was obtained. This indicates that the backpropagation neural network model provides a better estimate, as its value is closer to 1. Furthermore, the computational time executed in the algorithm of the three proposed nonlinear models is calculated, where the backpropagation obtains a calculated value of 350.9 microseconds, for the NARX model the computational time is 5908.7 microseconds and for the ARX nonlinear model, the computational time is 5172.6 microseconds. The model put forward demonstrates its effectiveness in accurately predicting water levels at two key hydrological stations along Colombia’s Atrato River. By incorporating intricate interactions among hydraulic structures and dynamic hydrological conditions, it enhances prediction accuracy. This not only aids in disaster risk management but also streamlines planning processes, particularly within flood early warning systems.

Temperature effect on the modal frequencies of a steel railway bridge

This paper presents the dynamic identification of the Ostiglia-Revere railway bridge, a steel truss girder bridge located in Northern Italy. The bridge is 6.6 m wide, about 940 m long and composed of 12 spans. The accelerations of a bridge span caused by both ambient excitation and train passages have been continuously measured from August to November. The monitoring system consists of 4 temperature sensors and 4 biaxial MEMS accelerometers, acquiring accelerations with a sampling frequency of 80 Hz. Modal properties are estimated adopting two different identification approaches, namely the Enhanced Frequency Domain Decomposition and the Stochastic Subspace Identification. Particular attention is paid to two crucial issues for vibration-based structural health monitoring: the recognition of the same structural mode from results identified during different time windows (i.e., mode clustering), and the temperature effect on estimated modal properties. As the latter is concerned, two regressive models, namely a linear regression model and an ARX model, are fitted to the frequency-temperature data, strongly reducing the eventuality of false vibration-based damage detections in the future.

A kernel-based PEM estimator for forward models

This paper addresses the problem of learning the impulse responses characterizing forward models by means of a regularized kernel-based Prediction Error Method (PEM). The common approach to accomplish that is to approximate the system with a high-order stable ARX model. However, such choice induces a certain undesired prior information in the system that we want to estimate. To overcome this issue, we propose a new kernel-based paradigm which is formulated directly in terms of the impulse responses of the forward model and leading to the identification of a high-order MAX model. The most challenging step is the estimation of the kernel hyperparameters optimizing the marginal likelihood. The latter, indeed, does not admit a closed form expression. We propose a method for evaluating the marginal likelihood which makes possible the hyperparameters estimation. Finally, some numerical results showing the effectiveness of the method are presented.

Построение и калибровка DSGE модели для российской экономики с использованием импульсных откликов векторной авторегрессии

The paper proposes a two‐sector macroeconomic model of the Russian economy based on the standard assumptions of New Keynesian DSGE models used to model household consumption, price and wage rigidities, and endogenous capital utilization. We consider two options for describing the investment process: the traditional approach with the investment adjustment costs and the approach using the investment accelerator model. The model parameters are calibrated based on minimizing the distance between the theoretical and “empirical” impulse response functions to the terms of trade shock derived from estimating simple ARX models with terms of trade as an exogenous variable. The constructed model quite accurately reproduces the influence of the terms of trade on the Russian economy for both investment modeling options. Based on the calibrated model, the authors examined the impact of a monetary policy shock on macroeconomic indicators and constructed a historical decomposition of the dynamics of macroeconomic indicators by an extended set of structural shocks to economic variables.