Search Results (38)

The theoretical modeling of a dynamic system will have derivatives of the response (y) with respect to time (t). Two common physical attributes (i.e., parameters) of dynamic systems are dead-time (θ) and lag (τ). Theoretical dynamic modeling will contain physically interpretable parameters such as τ and θ with physical constraints. In addition, the number of unknown model-based parameters can be considerably smaller than empirically based (i.e., lagged-based) approaches. This work proposes a Theoretically based Dynamic Regression (TDR) modeling approach that overcomes critical lagged-based modeling limitations as demonstrated in three large, multiple input, highly dynamic, real data sets. Dynamic Regression (DR) is a lagged-based, empirical dynamic modeling approach that appears in the statistics literature. However, like all empirical approaches, the model structures do not contain first-principle interpretable parameters. Additionally, several time lags are typically needed for the output, y, and input, x, to capture significant dynamic behavior. TDR uses a simplistic theoretically based dynamic modeling approach to transform x_t into its dynamic counterpart, v_t, and then applies the methods and tools of static regression to v_t. TDR is demonstrated on the following three modeling problems of freely existing (i.e., not experimentally designed) real data sets: 1. the weight variation in a person (y) with four measured nutrient inputs (x_i); 2. the variation in the tray temperature (y) of a distillation column with nine inputs and eight test data sets over a three year period; and 3. eleven extremely large, highly dynamic, subject-specific models of sensor glucose (y) with 12 inputs (x_i). Full article

This research provides valuable insights into the application of mathematical modeling to real-world scenarios, as exemplified by the COVID-19 pandemic. After data collection, the preparation stage included exploratory analysis, standardization and normalization, computation, and validation. A mathematical model initially developed for COVID-19 dynamics in Romania was subsequently applied to data from Italy and Switzerland during the same time interval. The model is structured as a multiple-input single-output (MISO) system, where the inputs underwent a neural network-based training stage to address inconsistencies in the acquired data. In parallel, an ARMAX model was employed to capture the stochastic nature of the epidemic process. Results demonstrate that the Romanian-based model generalized effectively across the three countries, achieving a strong predictive accuracy (forecast accuracy > 98.59%). Importantly, the model maintained robust performance despite significant cross-country differences in testing strategies, policy measures, timing of initial cases, and imported infections. This work contributes a novel perspective by showing that a unified data-driven modeling framework can be transferable across heterogeneous contexts. More broadly, it underscores the potential of integrating mathematical modeling with predictive analytics to support evidence-based decision-making and strengthen preparedness for future global health crises. Full article

Through system identification for robust control methods and utilizing real-time experimental field data, a comprehensive mathematical model is derived that represents the dynamic performance of a single electrode positioning system (EPS) in an industrial electric arc melting furnace (EAF). This EPS is characterized by large, time-varying dynamic parameters, which fluctuate based on operating conditions, specifically as the electrode weight changes within its operational range. The system identification methodology for robust control is developed in four main steps, progressing from experimental design to model validation. This approach yields a nominal model of the actual system and provides a trustworthy estimate of the region of uncertainty of the model, bounded by models of the real system under maximum and minimum electrode weight conditions (limit operating models). The methodology generates three fourth-order time-delay models using an ARMAX structure. The results are promising, as system identification for robust control enables the derivation of mathematical models specifically tailored for designing robust controllers. These controllers significantly enhance the EPS control system’s performance and substantially reduce energy consumption and environmental emissions. Full article

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. Full article

The identification (and control) of nonlinear systems is one of the most important and actual research directions. Moreover, many systems are multivariable. Different from linear system identification (where only a few classes of models are available), in the case of nonlinear systems, the class set of models is quite diverse. One of the most appealing nonlinear models belongs to the nonlinear ARMAX (NARMAX) class. This article focusses on the identification of such a model, which can be compared with other models (such as nonlinear ARX (NARX) and linear ARMAX) in an application based on the didactical installation ASTANK2. The mathematical foundation of NARMAX models and their identification method are described at length within this article. One of the most interesting parts is concerned with the identification of optimal models not only in terms of numerical parameters but also as structure. A metaheuristic (namely, the Cuckoo Search Algorithm) is employed with the aim of finding the optimal structural indices based on a special cost function, referred to as fitness. In the end, the performances of all three models (NARMAX, NARX, and ARMAX) are compared after the identification of the ASTANK2 installation. Full article

Considering a class of complex nonlinear systems whose dynamics are mostly governed by statistical regulations, the pattern-moving theory was developed to characterise such systems and successfully estimate the outputs or states. However, since the pattern class variable is not computable directly, this study establishes a clustered generalized cell mapping (C-GCM) to reveal system characteristics. C-GCM is a two-stage approach consisting of a pattern-moving-based description and analysis method. First, a density algorithm, named density-based spatial clustering of applications with noise (DBSCAN), is designed to obtain cell space $\Omega$ and the corresponding classification guidelines; this algorithm is initiated after the initial pre-image cells, and the total number of entity cells amounts to $N_s$. Then, the GCM provides several image cells based on a cell mapping function that refers to the multivariate ARMAX model. The global dynamic analysis employing both searching and storing algorithms depend on the attractor, domain of attraction, and periodic cell groups. At last, simulation results of two examples emphasise the practicality as well as efficacy of the technique suggested. The chief aim of this study was to offer a new perspective for a class of complex systems that could inspire research into nonmechanistic principles modelling and application to nonlinear systems. Full article

This paper investigates the problem of real-time parameter identification for ship maneuvering parameters and wave peak frequency in an ocean environment. Based on the idea of Euler discretion, a combined model of ship maneuvering and wave peak frequency (ship–wave) is made a discretion, and a discrete-time auto-regressive moving-average model with exogenous input (ARMAX) is derived for parameter identification. Based on the ideas of stochastic gradient identification and multi-innovation theory, a multi-innovation stochastic gradient (MI-SG) algorithm is derived for parameter identification of the ship–wave discretion model. Maximum likelihood theory is introduced to propose a maximum likelihood-based multi-innovation stochastic gradient (ML-MI-SG) algorithm. Compared to the MI-SG algorithm, the ML-MI-SG algorithm shows improvements in both parameter identification accuracy and identification convergence speed. Simulation results verify the effectiveness of the proposed algorithm. Full article

This paper presents the results of research on the development of photovoltaic systems in Poland. The authors’ goal was to identify factors that can potentially shape the dynamics of solar energy development in Poland and that will affect the implementation of the PEP2040 goals. The authors also wanted to find a forecasting method that would enable the introduction of many explanatory variables—a set of identified factors—into the model. After an initial review of the literature, the ARMAX and MLR models were considered. Finally, taking into account MAPE errors, multiple regression was used for the analysis, the error of which was 0.87% (minimum 3% for the ARMAX model). The model was verified based on Doornik–Hansen, Breusch–Pagan, Dickey–Fuller tests, information criteria, and ex post errors. The model indicated that LCOE, CO₂ emissions, Cu consumption, primary energy consumption, patents, GDP, and installed capacity should be considered statistically significant. The model also allowed us to determine the nature of the variables. Additionally, the authors wrote the WEKR 2.0 program, which allowed to determine the necessary amount of critical raw materials needed to build the planned PV energy generating capacity. Solar energy in Poland currently covers about 5% of the country’s electricity demand. The pace of development of photovoltaic installations has exceeded current expectations and forecasts included in the Polish Energy Policy until 2040 (PEP2040). The built model showed that if the explanatory variables introduced into the model continue to be subject to the same trends shaping them, a dynamic increase in photovoltaic energy production should be expected by 2025. The model indicates that the PEP2040 goal of increasing the installed capacity to 16 GW by 2040 can be achieved already in 2025, where the PV production volume could reach 8921 GWh. Models were also made taking into account individual critical raw materials such as Cu, Si, Ge, and Ga. Each of them showed statistical significance, which means that access to critical raw materials in the future will have a significant impact on the further development of photovoltaic installations. Full article

To address the contradiction between the convergence error and convergence rate in the LMS algorithm, this study proposes a variable-step-size adaptive filter algorithm with a momentum term based on the logistic function. First, the normalization LMS algorithm is obtained by seeking the extremum under the Lagrange function constraint. Second, to reduce the convergence error of the algorithm, the logistic model is used as a function model of step size variation with error, resulting in a variable-step normalization LMS algorithm. Our experimental results demonstrate that this algorithm achieves smaller convergence errors compared to those of the traditional LMS algorithm. Finally, to further improve the convergence rate of the algorithm, a momentum term is introduced into the weight coefficient update process of the LMS algorithm. This leads to the development of a variable-step adaptive filter algorithm with a momentum term based on the logistic function. The impact of different parameters on the algorithm performance is also investigated. In order to verify the rationality of the proposed algorithm, a dynamic system mathematical model was identified using the proposed algorithm. The results showed that the proposed algorithm had an identification accuracy of over 97% for the mathematical model parameters and a suppression of over 99% for noise. In order to verify the engineering application value of the proposed algorithm, real-time vibration data fitting experiments were conducted in the Aeroelasticity Laboratory of the China Aerodynamics Research and Development Center, and their results were compared with three algorithms: ARMAX, N4SID, and LMS. The results showed that the proposed algorithm had a higher fitting accuracy than the three others. Through simulations and experiments, it is demonstrated that this study has value both theoretically and in engineering applications, promoting engineering applications of adaptive filtering algorithms and providing strong support for the research of adaptive control. Full article

A compact, 3-degrees-of-freedom (DoF), low-cost, remotely operated unmanned underwater vehicle (UUV), or MicroROV, is custom-designed, developed, instrumented, and interfaced with a PC for real-time data acquisition and control. The nonlinear equations of motion (EoM) are developed for the under-actuated, open-frame, cross-coupled MicroROV utilizing the Newton-Euler approach. The cross-coupling between heave and yaw motion, an important dynamic of a class of compact ROVs that is barely reported, is investigated here. This work is thus motivated towards developing an understanding of the physics of the highly coupled compact ROV and towards developing model-based stabilizing controllers. The linearized EoM aids in developing high-fidelity experimental data-driven transfer function models. The coupled heave-yaw transfer function model is improved to an auto-regressive moving average with exogenous input (ARMAX) model structure. The acquired models facilitate the use of the multi-parameter root-locus (MPRL) technique to design baseline controllers for a cross-coupled multi-input, multi-output (MIMO) MicroROV. The controller gains are further optimized by employing an innovative Marine Predator Algorithm (MPA). The robustness of the designed controllers is gauged using gain and phase margins. In addition, the real-time controllers were deployed on an onboard embedded system utilizing Simulink′s automatic C++ code generation capabilities. Finally, pool tests of the MicroROV demonstrate the efficacy of the proposed control strategy. Full article

The COVID-19 infectious disease spread in the world represents, by far, one of the most significant moments in humankind’s recent history, affecting daily activities for a long period of time. The data available now allow important modelling developments for the simulation and prediction of the process of an infectious disease spread. The current work provides strong insight for estimation and prediction mathematical model development with emphasis on differentiation between three distinct methods, based on data gathering for Romanian territory. An essential aspect of the research is the quantification and filtering of the collected data. The current work identified five main categories considered as the model’s inputs: inside temperatures (°C), outside temperatures (°C), humidity (%), the number of tests and the quantified value of COVID-19 measures (%) and, as the model’s outputs: the number of new cases, the number of new deaths, the total number of cases or the total number of deaths. Three mathematical models were tested to find the optimal solution: transfer vector models using transfer functions as elements, autoregressive-exogenous (ARX) models, and autoregressive-moving-average (ARMAX) models. The optimal solution was selected by comparing the fit values obtained after the simulation of all proposed models. Moreover, the manuscript includes a study of the complexity of the proposed models. Based on the gathered information, the structure parameters of the proposed models are determined and the validity and the efficiency of the obtained models are proven through simulation. Full article

In this article, we present a synthetic inertia (SI) algorithm that allows for the simulation of the inertia response of a traditional generator to an electrical power system. To obtain the algorithm, detailed dynamic calculations were performed using a large real-system dynamic model in Siemens PSS/E modeling packages (PSS/E). Output error (OE), autoregressive moving average model with exogenous inputs (ARMAX), and Box–Jenkins (BJ) models of parametric identification were used to obtain the SI algorithm. The dynamic calculation results such as active power output, frequency variation in the presence of the active power deficit, surplus, and short circuit in the power system were used to compare the algorithm accuracy with comparable generator results. For this purpose, the power system stabilizer (PSS) and the turbine governor were not evaluated to obtain the most accurate possible active power change due to the characteristics of the generator. The errors were evaluated by using the models to determine the error estimates for the correlation coefficient (R_yŷ), root mean square deviation (RMSE), and coefficient of determination (R²). Based on the obtained results, we established that the OE mathematical model should be used, as it is more efficient compared to the ARMAX and BJ models. Full article

Despite regional warming, fire activity is decreasing in the Mediterranean region, blurring the well-established relationship between climate and wildfires. Here, we analyzed this relationship by focusing on the fire severity component of the fire regime. We determined the temporal trends of several climate, fire activity, and fire severity variables and the relationship of the latter two to the first in West-Central Spain (30,000 km²) for a 33 year period (1985 to 2017). Annually, fire variables at summer season were number of fires, burned area, fire size and fire severity (calculated using the relativized burn ratio (RBR) from Landsat satellite images). Fire severity was estimated for the whole area and for each of the main land use/land cover (LULC) types. Finally, the climate variables were maximum temperature, precipitation, and water deficit for all seasons (winter, spring, summer, and fall). Trends in those variables were assessed using the Mann–Kendal test, and the relationship between climate and fire variables was ascertained using autoregressive moving average (ARMAX) models. Main results indicated that number of fires and burned areas decreased, whereas drought conditions increased. Wildfires tended to burn preferentially in treeless areas, with conifer forests burning less frequently, and shrublands burning more so. Median RBR increased, as well as low (P₅) and high (P₉₀) percentiles. The percentage of burned areas at low severity decreased. All LULC types tended to burn at higher fire severities over time. The decreasing fire activity, but with increasing fire severity, coincides with rising maximum temperatures and drought (lower precipitation and higher water deficit). The temporal dynamics of fire activity and severity were well explained and predicted by spring and summer climate variables. Thus, while fire activity decreased, fire severity increased, driven by a more severe climate that was consistent with regional warming. Full article

Estimating the impact of climate change risks on residential consumption is one of the important elements of climate risk management, but there is too little research on it. This paper investigates the impact of climate change risks on residential consumption and the heterogeneous effects of different climate risk types in China by an ARMAX model and examines the Granger causality between them. Empirical results based on monthly data from January 2016 to January 2019 suggest a significant positive effect of climate change risks on residential consumption, but with a three-month lag period. If the climate risk index increases by 1 unit, residential consumption will increase by 1.29% after three months. Additionally, the impact of climate change risks on residential consumption in China mainly comes from drought, waterlogging by rain, and high temperature, whereas the impact of typhoons and cryogenic freezing is not significant. Finally, we confirmed the existence of Granger-causality running from climate change risks to residential consumption. Our findings establish the linkage between climate change risks and residential consumption and have some practical implications for the government in tackling climate change risks. Full article

The vision-guided robot is intensively embedded in modern industry, but it is still a challenge to track moving objects in real time accurately. In this paper, a hybrid adaptive control scheme combined with an Extreme Learning Machine (ELM) and proportional–integral–derivative (PID) is proposed for dynamic visual tracking of the manipulator. The scheme extracts line features on the image plane based on a laser-camera system and determines an optimal control input to guide the robot, so that the image features are aligned with their desired positions. The observation and state–space equations are first determined by analyzing the motion features of the camera and the object. The system is then represented as an autoregressive moving average with extra input (ARMAX) and a valid estimation model. The adaptive predictor estimates online the relevant 3D parameters between the camera and the object, which are subsequently used to calculate the system sensitivity of the neural network. The ELM–PID controller is designed for adaptive adjustment of control parameters, and the scheme was validated on a physical robot platform. The experimental results showed that the proposed method’s vision-tracking control displayed superior performance to pure P and PID controllers. Full article