Exogenous Input Model Research Articles

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.

Localizing structural damage based on auto-regressive with exogenous input model parameters and residuals using a support vector machine based learning approach

Machine learning algorithms operating in an unsupervised fashion has emerged as promising tools for detecting structural damage in an automated fashion. Its essence relies on selecting appropriate features to train the model using the reference data set collected from the healthy structure and employing the trained model to identify outlier conditions representing the damaged state. In this paper, the coefficients and the residuals of the autoregressive model with exogenous input created using only the measured output signals are extracted as damage features. These features obtained at the baseline state for each sensor cluster are then utilized to train the one class support vector machine, an unsupervised classifier generating a decision function using only patterns belonging to this baseline state. Structural damage, once detected by the trained machine, a damage index based on comparison of the residuals between the trained class and the outlier state is implemented for localizing damage. The two-step damage assessment framework is first implemented on an eight degree-of-freedom numerical model with the effects of measurement noise integrated. Subsequently, vibration data collected from a one-story one-bay reinforced concrete frame inflicted with progressive levels of damage have been utilized to verify the accuracy and robustness of the proposed methodology.

Key SDG7 Factors Shaping the Future of Clean Coal Technologies: Analysis of Trends and Prospects in Poland

This article presents the results of an analysis aimed at verifying the relationship between the implementation of SDG Goal 7 and the use of clean coal technologies in Poland. Clean coal technologies in the United Nations plans will constitute a crucial element of the strategy for sustainable development in the energy context. They are intended to be one of the tools for building an energy system based on renewable energy sources, constituting a bridge that enables the transition of Poland’s energy system from coal to renewable energy sources. To identify whether this relationship exists, the Autoregressive Moving Average with Exogenous Input (ARMAX) model was used. The structure of the model, its correctness, and its accuracy were confirmed using information criteria; statistical tests such as Dickey-Fuller, Doornik-Hansen, Durbin-Watson, and Breusch-Pagan; and measures of prediction accuracy such as MAPE, MAE, and RMSE. The explanatory variables were the Objective 7 indicators adopted by Eurostat. Before being introduced to the ARMAX model, they were standardized using the Compound Annual Growth Rate (CAGR) indicator. The analysis made it possible to indicate which of the explanatory variables has the greatest impact on the development of clean coal technologies in Poland, to determine a synthetic CAGR measure for all the explanatory variables, and to compare the results obtained with the indicator determined by the United Nations.

Forecasting ground-level ozone and fine particulate matter concentrations at Craiova city using a meta-hybrid deep learning model

Air quality forecasting is vital for managing and mitigating the adverse effects of air pollution on human health, crops, and the environment. This study aims to forecast daily time series of ozone and fine particulate matter (PM) concentrations using a meta-hybrid deep NARMAX (Nonlinear Auto-Regressive Moving Average with eXogenous inputs) model. Two datasets were utilised: (a) data on meteorological parameters (temperature, air pressure, relative humidity) and air pollutant concentrations (particulate matter, ozone, dioxide of carbon, volatile organic compounds, formaldehyde) provided by a sensor model A3 situated in the centre of Craiova city, and (b) data on wind direction, wind speed, and sunshine duration provided by the National Meteorological Administration. The data sets covered a time interval from December 10, 2020, to January 05, 2024. Initially, a statistical analysis was conducted to assess the correlation between variables. Results revealed that ozone concentration is primarily influenced by meteorological variables such as temperature (r = 0.79), sunshine duration (r = 0.55), and relative humidity (r = −0.48), and secondarily by air pollution indicators including VOC (r = −0.34), PM concentrations (r = −0.34), and CO2 (r = −0.3). In the subsequent stage, thirteen Machine Learning (ML) models were employed in conjunction with an integral feature selection (IFS) method to identify the best combinations of predictor variables for predicting ozone and PMs. Finally, a deep NARMAX model was developed to forecast the next periods of ozone and PMs based on the optimal combinations identified earlier. Results indicated the selection of sixty best models for ozone forecasting and four best models for PMs. The R2 values surpassed 0.97 for ozone and exceeded 0.8 for PMs, demonstrating the efficacy of the forecasting approach.

Data driven latent variable adaptive control for nonlinear multivariable processes

This article aims at a new partial least squares (PLS) control design and analysis in a data-driven framework for nonlinear multivariable processes whose mechanistic models are completely unknown. First, a general nonlinear autoregressive moving average with the exogenous input (NARMAX) model is used as the dynamic nonlinear PLS model. Then, by introducing a dynamic linearisation approach in each latent variable (LV) space, the unknown NARMAX-based PLS model is transformed to a linear dynamic PLS data model (dPLSDM), which can be improved in real time by estimating its unknown parameter using the latent input and output (I/O) data. Next, a data-driven latent variable adaptive control (DDLVAC) is proposed in each LV loop. By virtue of the dPLSDM, the multivariable nonlinear process is decoupled into multiple single-loop systems and the high dimensions of the process data are reduced such that the corresponding DDLVAC is simplified. Further, the DDLVAC only depends on the I/O data without requiring any model information of the original process. Theoretical analysis confirms the validity of the DDLVAC. The simulation study demonstrates the advantages of the DDLVAC such as less storage space, smaller computation burden, less control cost, as well as more robustness against uncertainties.

Adaptive model predictive control scheme for partially internal thermally coupled air separation column

Partially Internal Thermally Coupled Air Separation Column (P-ITCASC) is a highly energy-efficient and cost-effective technology. However, its complex dynamics resulting from thermal coupling pose a challenge to the operating stability of this technology. This article, therefore, proposes an adaptive model predictive control (AMPC) scheme for the P-ITCASC process. The controller incorporates an auto-regressive and exogenous inputs (ARX) model, a linear time-varying Kalman filter, and a recursive polynomial model estimator (RPME) algorithm. Within RPME, ARX polynomial models are identified and utilized to estimate the time-varying parameters and update the prediction model of the process. The process states are observed through the Kalman filter, and the constrained receding horizon optimization problem is solved using quadratic programming. This control scheme ensures the closed-loop system's feasibility and stability in the presence of output/input constraints. An adaptive generic model control, model predictive control, and adaptive internal model control schemes were also designed for benchmarking study. Numerical simulations show that AMPC is more efficient in handling nonlinear dynamics and maintaining product concentration to desired set points compared to other control schemes.

An Advanced Nonlinear Framework for Early Detection and Prognosis of Fatigue Cracks in Plate-Like Structures

Plate-like structures are prone to the initiation of fatigue cracks during operation, primarily due to the harmonic loading imposed by the external environment. These micro-cracks possess the potential to progress into more severe forms, compromising structural integrity and, in extreme cases, leading to catastrophic accidents. The primary focus of this research is to introduce an online nonlinear framework for the early diagnosis and prognosis of fatigue cracks. This framework aims to detect nascent fatigue cracks in plate-like structures, facilitating proactive measures to prevent structural failure and preserve the overall integrity. The initial phase of this study involves capturing Lamb waves generated by subjecting the inspected plate-like structures to an excitation signal. The excitation signal, along with the S0 mode Lamb wave, is employed to identify a Nonlinear Autoregressive with Exogenous inputs (NARX) model, serving as a representation of the underlying nonlinear dynamic mapping intrinsic to the inspected specimen. Subsequently, the Nonlinear Output Frequency Response Functions (NOFRFs) are identified based on the established NARX model. An early fatigue crack damage index, denoted as optimal NOFRFs weighted contribution rate based on the KL divergence (KLRm), is extracted from the NOFRFs and employed for estimating crack lengths. Additionally, the Particle Filter (PF) is utilized for predicting the Remain Useful Life (RUL). To validate the effectiveness of the proposed framework, fatigue experiments are conducted on aluminum lug joint specimens. The experimental results demonstrate the effectiveness and precision of the framework in estimating crack lengths and predicting RUL for nonlinear early fatigue cracks.

Multivariate Hydrological Modeling Based on Long Short-Term Memory Networks for Water Level Forecasting

In the Department of Chocó, flooding poses a recurrent and significant challenge due to heavy rainfall and the dense network of rivers characterizing the region. However, the lack of adequate infrastructure to prevent and predict floods exacerbates this situation. The absence of early warning systems, the scarcity of meteorological and hydrological monitoring stations, and deficiencies in urban planning contribute to the vulnerability of communities to these phenomena. It is imperative to invest in flood prediction and prevention infrastructure, including advanced monitoring systems, the development of hydrological prediction models, and the construction of hydraulic infrastructure, to reduce risk and protect vulnerable communities in Chocó. Additionally, raising public awareness of the associated risks and encouraging the adoption of mitigation and preparedness measures throughout the population are essential. This study introduces a novel approach for the multivariate prediction of hydrological variables, specifically focusing on water level forecasts for two hydrological stations along the Atrato River in Colombia. The model, utilizing a specialized type of recurrent neural network (RNN) called the long short-term memory (LSTM) network, integrates data from hydrological variables, such as the flow, precipitation, and level. With a model architecture featuring four inputs and two outputs, where flow and precipitation serve as inputs and the level serves as the output for each station, the LSTM model is adept at capturing the complex dynamics and cross-correlations among these variables. Validation involves comparing the LSTM model’s performance with linear and nonlinear Autoregressive with Exogenous Input (NARX) models, considering factors such as the estimation error and computational time. Furthermore, this study explores different scenarios for water level prediction, aiming to utilize the proposed approach as an effective flood early warning system.

Identification of heat exchanger process through Hammerstein and polynomial models

Process industries extensively use heat exchangers in their operations, playing a crucial role in various sectors by facilitating efficient heat transfer, conserving energy, and reducing operational costs. This paper focuses on identifying and validating the system model, with the primary task of designing the controller involving the determination of the mathematical representation of the system. The First Order Plus Dead Time (FODT) model, derived from basic principles, is used to represent the system. To analyze the system’s behavior and construct a suitable controller, model development is essential, achieved by constructing principles models using energy balance equations to identify the heat exchanger process. Data collected from the model are utilized in the identification process, with the temperature at the outlet of the hot air blower being the controlled variable in this investigation. The research aims to determine the mathematical model based on time versus temperature data acquired from the Heat Exchanger. Various system identification methods, such as Hammerstein Wiener (HW), Auto Regressive with Exogenous Input (ARX), Box-Jenkins (BJ), Output-Error (OE), and Auto Regressive Moving Average with Exogenous Input (ARMAX) models, are implemented for the heat exchanger. The models obtained undergo validation, and the best-fit model closest to the physical system is considered for controller design. After conducting the analysis, it was found that the Output-Error (OE) model outperforms other models in terms of achieving the best fit.

A dynamic hybrid model for efficient tuberculosis incidence rate prediction

ABSTRACT Tuberculosis remains a global health challenge, predicting its incidences is crucial for effective planning and intervention strategies. This study combines AutoRegressive Integrated Moving Average (ARIMA) and Nonlinear AutoRegressive with exogenous input (NARX) models as an innovative approach for TB incidence rate prediction. The performance of the proposed model (ARIMA-NARX) was evaluated using standard metrics (MSE, RMSE, MAE, and MAPE), and it was refined to achieve the best average predictive accuracies with an MSE: 0.0622, RMSE: 0.0851, MAE: 0.07520, and MAPE: 0.05535 followed by NARX 0.1597, 0.3189, 0.2724, and 0.3366, and ARIMA (2,0,0) 0.7781, 0.5959, 0.6524, and 0.6080 Models. These findings are expected to shed light on the TB incidence rate, providing valuable information to policymakers such as the World Health Organization (WHO) and health professionals. The developed model can potentially serve as a predictive tool for proactive TB control and intervention strategies in the region and the world at large.

Time history response prediction of stochastic SDOF structures through Kriging-NARX modeling and adaptive real-time hybrid simulation

Emulating time history response is a critical benchmark for evaluating the seismic resilience of structures and assessing their reliability in the face of uncertainties. Traditional computational simulations, while commonly favored, often fall short in accurately describing the behavior of intricate structural components. Real-time hybrid simulation (RTHS) offers an effective and efficient experimental technique for replicating the responses of deterministic systems in a cyber-physical manner but encounters challenges when dealing with stochastic systems. This study proposes an innovative application of RTHS for time history response prediction of nonlinear stochastic structures. A cross-validation (CV)-Voronoi sampling strategy is applied to sequentially select uncertain parameter samples for RTHS. Nonlinear autoregressive with exogenous input (NARX) model is identified and updated from RTHS results in a sequential manner. Coefficients of final NARX model are surrogated using the Kriging meta-models to account for given uncertainties. Laboratory tests on single-degree-of-freedom (SDOF) structures with self-centering viscous dampers (SC-VD) were conducted to demonstrate the effectiveness of the proposed approach. Predicted time history responses from the final Kriging-NARX model are further compared and validated. It is demonstrated that the proposed approach provides an effective and efficient method for time history response prediction of stochastic systems especially when accurate numerical models are not available.

Enhancing battery system identification: nonlinear autoregressive modeling for Li-ion batteries

Precisely characterizing Li-ion batteries is essential for optimizing their performance, enhancing safety, and prolonging their lifespan across various applications, such as electric vehicles and renewable energy systems. This article introduces an innovative nonlinear methodology for system identification of a Li-ion battery, employing a nonlinear autoregressive with exogenous inputs (NARX) model. The proposed approach integrates the benefits of nonlinear modeling with the adaptability of the NARX structure, facilitating a more comprehensive representation of the intricate electrochemical processes within the battery. Experimental data collected from a Li-ion battery operating under diverse scenarios are employed to validate the effectiveness of the proposed methodology. The identified NARX model exhibits superior accuracy in predicting the battery's behavior compared to traditional linear models. This study underscores the importance of accounting for nonlinearities in battery modeling, providing insights into the intricate relationships between state-of-charge, voltage, and current under dynamic conditions.

Rainfall-Runoff Modeling Using Artificial Neural Network for Batu Pahat River Basin

This research delves into the effectiveness of Artificial Neural Networks with Multilayer Perceptron (ANN-MLP) and Nonlinear AutoRegressive with eXogenous inputs (NARX) models in predicting short-term rainfall-runoff patterns in the Batu Pahat River Basin. This study aims to predict river water levels using historical rainfall and river level data for future intervals of 1, 3, and 6 hours. Data preprocessing techniques, including the management of missing values, identification of outliers, and reduction of noise, were applied to enhance the accuracy and dependability of the models. This study assessed the performance of the models for ANN-MLP and NARX by comparing their effectiveness across various forecast timeframes and evaluating their performance in different scenarios. The findings of the study revealed that the ANN-MLP model showed robust performance in short-term prediction. On the contrary, the NARX model exhibited higher accuracy, particularly in capturing intricate temporal relationships and external impacts on river behavior. The ANN-MLP produces 99% accuracy for 1-hour prediction, and NARX yields 98% accuracy with 0.3245 Root Mean Squared Error and 0.1967 Mean Absolute Error. This study makes a valuable contribution to hydrological forecasting by presenting a rigorous and precise modeling methodology.

Analysis and forecasting of syphilis trends in mainland China based on hybrid time series models.

Syphilis remains a serious public health problem in mainland China that requires attention, modelling to describe and predict its prevalence patterns can help the government to develop more scientific interventions. The seasonal autoregressive integrated moving average (SARIMA) model, long short-term memory network (LSTM) model, hybrid SARIMA-LSTM model, and hybrid SARIMA-nonlinear auto-regressive models with exogenous inputs (SARIMA-NARX) model were used to simulate the time series data of the syphilis incidence from January 2004 to November 2023 respectively. Compared to the SARIMA, LSTM, and SARIMA-LSTM models, the median absolute deviation (MAD) value of the SARIMA-NARX model decreases by 352.69%, 4.98%, and 3.73%, respectively. The mean absolute percentage error (MAPE) value decreases by 73.7%, 23.46%, and 13.06%, respectively. The root mean square error (RMSE) value decreases by 68.02%, 26.68%, and 23.78%, respectively. The mean absolute error (MAE) value decreases by 70.90%, 23.00%, and 21.80%, respectively. The hybrid SARIMA-NARX and SARIMA-LSTM methods predict syphilis cases more accurately than the basic SARIMA and LSTM methods, so that can be used for governments to develop long-term syphilis prevention and control programs. In addition, the predicted cases still maintain a fairly high level of incidence, so there is an urgent need to develop more comprehensive prevention strategies.

Using nonlinear auto-regressive with exogenous input neural network (NNARX) in blood glucose prediction

BackgroundPredicting of future blood glucose (BG) concentration is important for diabetes control. Many automatic BG monitoring or controlling systems use BG predictors. The accuracy of the prediction for long prediction time is a major factor affecting the performance of the control system. The predicted BG can be used for glycemia management in the form of early hypoglycemic/hyperglycemic alarms or adjusting insulin injections. Recent developments in continuous glucose monitoring (CGM) devices open new opportunities for glycemia management of diabetic patients. Many of those systems need prediction for long prediction horizons to avoid going through hypo or hyperglycemia.MethodsIn this article a nonlinear autoregressive exogenous input neural network (NNARX) is proposed to predict the glucose concentration for longer prediction horizons (PHs) than that was obtained previously with an established recurrent neural network (RNN). The proposed NNARX is a modified version from our previously published RNN with different initialization and building technique but has the same architecture. The modification is based on starting with building nonlinear autoregressive exogenous input model using MATLAB and train it, then close the loop to get NNARX network.ResultsThe results of using the proposed NNARX indicate that the proposed NNARX is better in prediction and stability than unmodified RNN as PH becomes higher than 45 minutes.ConclusionsModification in RNN building extends the ability of the prediction till 100 minutes. It performs statistically significant improvements in the FIT and RMSE values for 100 minutes prediction. It also decreases root mean squared error (RMSE) for both 45 and 60 minutes of prediction.

Estimating the as-built thermal performance of dwellings using simulated on-board data: From ideal to limited monitoring

Advancement in non-intrusive monitoring of energy usage in households presents an ideal opportunity to get insight into the as-built performance of buildings and assess performance indicators such as the Heat Loss Coefficient (HLC) of the building fabric. The availability of in-use monitored data contributes to bridging the energy performance gap while avoiding costly and exhaustive dedicated measurement campaigns. Methodologies to assess the building performance by combining on-board monitoring and statistical data-driven models are widely accepted. However, their unsupervised and automated applicability on a large scale, with limited data and no insight into the building characteristics and occupants’ behaviour still needs to be investigated. Therefore, this work aims at assessing the reliability and performance of statistical black-box AutoRegressive with eXogenous input (ARX) models on artificial measurement campaigns starting from idealistic setups and progressing towards limited ones. In this investigation, the uncertainty in the estimate inherited from inputs, such as different heat sources or weather data, and their post-processing is combined with the uncertainty originating from different monitoring packages, which results in a thorough overview of the statistical modelling limitations. Results show that disaggregation of the final heating usage poses a major challenge. In cases where gross gas usage is measured, and the system efficiency and domestic hot water consumption are not taken into account, the HLC can deviate by 49% in low-performing houses and by 106% in well-performing houses. However, by applying data pre-processing methods the discrepancy can be lowered to 8% and 23% respectively, but with high uncertainty. On the other hand, the installation of an additional heat meter could yield deviations from the target of 26% for low-performing and 11% for well-performing dwellings without data manipulation, both with low uncertainties.

Analysis of China's carbon market price fluctuation and international carbon credit financing mechanism using random forest model.

This study aims to investigate the price changes in the carbon trading market and the development of international carbon credits in-depth. To achieve this goal, operational principles of the international carbon credit financing mechanism are considered, and time series models were employed to forecast carbon trading prices. Specifically, an ARIMA(1,1,1)-GARCH(1,1) model, which combines the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and Autoregressive Integrated Moving Average (ARIMA) models, is established. Additionally, a multivariate dynamic regression Autoregressive Integrated Moving Average with Exogenous Inputs (ARIMAX) model is utilized. In tandem with the modeling, a data index system is developed, encompassing various factors that influence carbon market trading prices. The random forest algorithm is then applied for feature selection, effectively identifying features with high scores and eliminating low-score features. The research findings reveal that the ARIMAX Least Absolute Shrinkage and Selection Operator (LASSO) model exhibits high forecasting accuracy for time series data. The model's Mean Squared Error, Root Mean Squared Error, and Mean Absolute Error are reported as 0.022, 0.1344, and 0.1543, respectively, approaching zero and surpassing other evaluation models in predictive accuracy. The goodness of fit for the national carbon market price forecasting model is calculated as 0.9567, indicating that the selected features strongly explain the trading prices of the carbon emission rights market. This study introduces innovation by conducting a comprehensive analysis of multi-dimensional data and leveraging the random forest model to explore non-linear relationships among data. This approach offers a novel solution for investigating the complex relationship between the carbon market and the carbon credit financing mechanism.

Application of nonlinear system identification and feature extraction in fault diagnosis of the cracked cantilever beam

The cantilever beam structure is extensively applied in civil, transportation, and mechanical fields. It is generally prone to structural damage like cracks arising from material defects, operation conditions, and environmental factors. Cracks in a cantilever beam generally induce nonlinear behavior, potentially compromising structural durability and even posing threats to production safety. The present study primarily focuses on online and quantitative fault diagnosis of cracks in the cantilever beam. A simulation model is established for the cantilever beam with varying cracks, where responses corresponding to excitation signals are collected. A Nonlinear Autoregressive with Exogenous inputs (NARX) model for the cantilever beam is identified, and Nonlinear Output Frequency Response Functions weighted contribution rate (WNOFRFs) are evaluated from the established NARX model. A WNOFRFs-associated index is extracted to quantify the severity of breathing cracks. Simulation results indicate that this approach can online diagnose and quantify the severity of crack faults to a certain extent. The applicability of this approach is further verified through experiments on a cracked cantilever beam.

On Gait Consistency Quantification Through ARX Residual Modeling and Kernel Two-Sample Testing.

The quantification of the way an individual walks is key to the understanding of diseases affecting the neuromuscular system. More specifically, to improve diagnostics and treatment plans, there is a continuous interest in quantifying gait consistency, allowing clinicians to distinguish natural variability of the gait patterns from disease progression or treatment effects. To this end, the current article presents a novel objective method for assessing the consistency of an individual's gait, consisting of two major components. Firstly, inertial sensor accelerometer data from both shanks and the lower back is used to fit an AutoRegressive with eXogenous input model. The model residuals are then used as a key feature for gait consistency monitoring. Secondly, the non-parametric maximum mean discrepancy hypothesis test is introduced to measure differences in the distributions of the residuals as a measure of gait consistency. As a paradigmatic case, gait consistency was evaluated both in a single walking test and between tests at different time points in healthy individuals and those affected by multiple sclerosis (MS). It was found that MS patients experienced difficulties maintaining a consistent gait, even when the retest was performed one-hour apart and all external factors were controlled. When the retest was performed one-week apart, both healthy and MS individuals displayed inconsistent gait patterns. Gait consistency has been successfully quantified for both healthy and MS individuals. This newly proposed approach revealed the detrimental effects of varying assessment conditions on gait pattern consistency, indicating potential masking effects at follow-up assessments.

Mechanism of single-mode panel flutter in low supersonic flow

Supersonic panel flutter can be of two possible types: single-mode flutter and coupled-mode flutter. Compared to coupled-mode flutter, the physical mechanism of single-mode flutter is less studied at present. In order to reveal the inducing mechanism of single-mode flutter, the present paper constructed a reduced-order fluid model by using the system identification and the Auto Regressive with eXogenous input (ARX) model. Coupling the reduced-order model (ROM) for unsteady aerodynamics in low supersonic flow with the structural equation, a highly efficient ROM-based aeroelastic model in state space is formulated, then the flutter boundaries are obtained and the stability of aeroelastic modes are investigated by the complex eigenvalue analysis. According to the physical meaning of relevant parameters in unsteady aerodynamic reduced order model ARX, it is found that the unsteady characteristic of the flow, specifically the history effects of the unsteady aerodynamic forces, plays a dominant role in causing the single-mode panel flutter at low supersonic speeds. It is also shown that the higher modes are indeed weakly unstable in the absence of any structural damping or a viscous boundary layer.