Parameter Estimation Approach Research Articles

Online Estimation of Three-Phase Induction Motor Parameters Using an Extended Kalman Filter for Energy Saving

In this paper, the online estimation of three-phase induction motor parameters using an extended Kalman filter for energy saving is proposed. The optimal value of the stator current on the d-axis is calculated to obtain the minimum power loss. Accurate motor parameters are required to calculate the optimal stator current value for energy saving. Hence, to estimate motor parameters in real time, an online estimator known as the extended Kalman filter is applied. The energy consumption results for the motor using the proposed approach (estimated parameters with extended Kalman filter) are compared with those obtained using the conventional approach and energy saving (fixed parameters without parameter estimation) approach. As revealed by the comparison results from implementation in a laboratory, the proposed approach can provide minimum power losses for the three-phase induction motor drive, and the maximum energy-saving percentage is 60.18% compared with using the conventional drive approach.

A stochastic framework for rainfall intensity–timescale–return period relationships. Part I: Theory and estimation strategies

This work presents a stochastic framework for the construction of rainfall intensity–timescale–return period relationships, which was applied in the recent regionalization of design rainfall curves over the Greek territory, described in a companion paper. The methodology outlined herein builds upon the Koutsoyiannis’ et al. 1998 framework, which has been recently revisited and upgraded, and incorporates two different versions: (a) a theoretically consistent stochastic model applicable for rainfall intensity over any scale of interest and (b) a simplified version valid over small scales, which makes parameter estimation easier. Special focus is given to the presentation of the simplified version, which suffices for most engineering tasks. Parameter estimation approaches are presented in detail including the K-moments framework that allows for reliable high-order moment estimation and handling of bias due to spatiotemporal dependence.

Evaluating the lifetime distribution parameters and reliability of products using successive approximation method

AbstractThe Weibull distribution is an extensively used statistical model for analyzing the reliability of mechanical and electrical components. Due to the complexity of the nonlinear equations and the scarcity of failure data, the common method may not provide satisfactory results of the reliability. In this case, a new approach for Weibull parameter estimation and reliability analysis, based on successive approximation schemes, is presented. The shape and scale parameters are estimated by maximizing the likelihood functions, and the location parameter is obtained by constructing an approximate correction model between it and the failure data. In order to show the performance of the proposed method, an extensive Monte‐Carlo simulation study is conducted. Simulation results show that the proposed method provides better estimates and efficient confidence intervals for Weibull parameters. In addition, the proposed method works well in presence of small sample sizes. Finally, two real examples are analyzed to illustrate the application of the proposed method.

Comparison of Traditional and Sequential Approaches for Estimation of Kinetic Parameters of Heavy Oil Upgrading

Comparison of Traditional and Sequential Approaches for Estimation of Kinetic Parameters of Heavy Oil Upgrading

Efficient parameter extraction of photovoltaic models with a novel enhanced prairie dog optimization algorithm

The growing demand for solar energy conversion underscores the need for precise parameter extraction methods in photovoltaic (PV) plants. This study focuses on enhancing accuracy in PV system parameter extraction, essential for optimizing PV models under diverse environmental conditions. Utilizing primary PV models (single diode, double diode, and three diode) and PV module models, the research emphasizes the importance of accurate parameter identification. In response to the limitations of existing metaheuristic algorithms, the study introduces the enhanced prairie dog optimizer (En-PDO). This novel algorithm integrates the strengths of the prairie dog optimizer (PDO) with random learning and logarithmic spiral search mechanisms. Evaluation against the PDO, and a comprehensive comparison with eighteen recent algorithms, spanning diverse optimization techniques, highlight En-PDO’s exceptional performance across different solar cell models and CEC2020 functions. Application of En-PDO to single diode, double diode, three diode, and PV module models, using experimental datasets (R.T.C. France silicon and Photowatt-PWP201 solar cells) and CEC2020 test functions, demonstrates its consistent superiority. En-PDO achieves competitive or superior root mean square error values, showcasing its efficacy in accurately modeling the behavior of diverse solar cells and performing optimally on CEC2020 test functions. These findings position En-PDO as a robust and reliable approach for precise parameter estimation in solar cell models, emphasizing its potential and advancements compared to existing algorithms.

Calibration of European option pricing model in uncertain environment: Valuation of uncertainty implied volatility

Uncertain differential equations have been widely used in modeling financial markets, and option pricing formulae have been obtained by employing these equations. However, according to the existing literature, the parameter estimation of the option pricing model driven by the uncertain differential equation has not been evaluated so far, and the parameters have been assumed to be arbitrary numbers for such problems. Based on the mentioned gap, this study presents an approach for parameter estimation of European option pricing model in the uncertain environment for the first time. For this purpose, some of the most common uncertain models are considered, and the corresponding empirical examples are presented. Since implied volatility as an instrument provides traders a range of prices that securities change among them, this study evaluates the implied volatility of the European option under the geometric Liu process for the first time. Empirical comparison for both in sample and out of sample dataset based on the uncertainty framework and Black–Scholes model demonstrates that the uncertain models are more accurate for evaluating the European option prices and the implied volatilities.

Prestack sparse envelope seismic inversion method adopting the L0−L2-norm regularization

The high drilling costs limit the possibility of obtaining reliable low-frequency constrained models in marine environments or areas with sparse well-log data, making it difficult to constrain lateral continuity and deep data. To enhance stability and accuracy in prestack seismic inversion in these areas, an elastic parameter estimation approach using sparse envelope inversion with [Formula: see text]-norm regularization is proposed. The method combines signal sparse representation and modulation theories to derive a new formula for sparse envelope extraction at lower frequencies. By applying [Formula: see text]-norm regularization to the sparse envelope, we obtain parameter inversion results with smoothed trends, augmenting low-wavenumber information for improved model constraints. In addition, taking the envelope inversion results obtained by the [Formula: see text] norm as the model constraint, the sparsest inversion results with obvious block-like characteristics are obtained by regularizing the inversion equation with the [Formula: see text] norm. Notably, the new method effectively suppresses wavelet side lobes, resulting in stable and accurate inversions without the need for initial low-frequency models. A synthetic example is used to illustrate the feasibility and stability of proposed approach and further demonstrate its practicality in reservoir parameter estimation through a field case study of gas exploration.

Likelihood-based generalization of Markov parameter estimation and multiple shooting objectives in system identification

This paper considers system identification (ID) of linear and nonlinear non-autonomous systems from noisy and sparse data. We analyze an optimization objective derived from Bayesian inference for the dynamics of hidden Markov models. We then relate this objective to that used in several state-of-the-art approaches for both linear and nonlinear system ID. In the former, we analyze least squares approaches for Markov parameter estimation, and in the latter, we analyze the multiple shooting approach. We demonstrate the limitations of the optimization problems posed by these existing methods by showing that they can be seen as special cases of the proposed optimization objective under certain simplifying assumptions: conditional independence of data and zero model error. Furthermore, we observe that the proposed approach has improved smoothness and inherent regularization that make it well-suited for system ID and provide mathematical explanations for these characteristics’ origins. Finally, numerical simulations demonstrate a mean squared error over 8.7 times lower compared to multiple shooting when data are noisy and/or sparse. Moreover, the proposed approach identifies accurate and generalizable models even when there are more parameters than data or when the system exhibits chaotic behavior.

Model-based impending lithium battery terminal voltage collapse detection via data-driven and machine learning approaches

Lithium battery is an important power source of an electrical vehicle (EV). Practically, when a battery is about to fail, it needs to be removed from the load because keeping it connected can lead to permanent damage. Hence, it is important to detect battery failure to sustain the lifespan of the battery and avoid safety issues which will contribute to the sustainability of the EV. However, determining the effective disconnecting or discharging moment of the battery remains a challenging issue in EV applications. In order to solve the abovementioned problem, a control framework and maximum likelihood estimation are proposed to estimate the parameters of a battery model. In addition, both the sparse representation and dynamic mode decomposition (DMD) approaches are applied to protect the physical battery unit from a failure scenario. For comparison purposes, the proposed framework is compared to a Lyapunov-based detection approach along with neural network (NN) and linear discriminant analysis (LDA). Moreover, several state estimation algorithms are applied to estimate battery state of charge (SOC) at each time step: extended Kalman filter, extended Kalman smooth variable structure filter, and cubature Kalman filter. Finally, the experimental results showed that the proposed DMD approach outperforms the sparse representation, NN, LDA, and Lyapunov-based approaches in terms of detection accuracy. Moreover, the proposed DMD strategy is more robust towards the inaccuracy of the estimated SOC. Besides that, the proposed battery model parameter estimation approach exhibited fast processing time; therefore, it is a reliable choice for recomputing the model parameters from time to time to compensate aging effect. An autonomous unmanned aerial vehicle (UAV) was simulated as a proof-of-concept in a MATLAB environment to verify the detection performance of the proposed methods. Both actual and UAV results showed that the DMD demonstrated more robust detection performance than other methods in terms of processing time and detection accuracy.

Parameter estimation for Gipps’ car following model in a Bayesian framework

Car following model is an important part in traffic modelling and has attracted a lot of attentions in the literature. As the proposed car following models become more complex with more components, reliably estimating their parameters becomes crucial to enhance model predictive performance. While most studies adopt an optimisation-based approach for parameters estimation, we present a statistically rigorous method that quantifies uncertainty of the estimates. We present a Bayesian approach to estimate parameters using the popular Gipps’ car following model as demonstration, which allows proper uncertainty quantification and propagation. Since the parameters of the car following model enter the statistical model through the solution of a delay-differential equation, the posterior is analytically intractable so we implemented an adaptive Markov Chain Monte Carlo algorithm to sample from it. Our results show that predictive uncertainty using a point estimator versus a full Bayesian approach are similar with sufficient data. In the absence of adequate data, the former can make over-confident predictions while such uncertainty is more appropriately incorporated in a Bayesian framework. Furthermore, we found that the congested flow parameters in the Gipps’ car following model are strongly correlated in the posterior, which not only causes issues for sampling efficiency but more so suggests the potential ineffectiveness of a point estimator in an optimisation-based approach. Lastly, an application of the Bayesian approach to a car following episode in the NGISM dataset is presented.

Collaborative Parameter Estimation of Multiple Unmanned Surface Vessels: A Robust Distributed Estimator-Based Approach

In this paper, the collaborative parameter estimation of multiple unmanned surface vessels (USVs) with model structure uncertainties is studied. The considered parameter estimation problem is first converted into a distributed state and parameter joint estimation problem. Then, the robust distributed estimator is constructed to handle the inevitable model structure uncertainties, and the upper bounds of prediction and estimation error covariance matrices are derived respectively. Additionally, the upper bound of the estimation error covariance matrix is minimized by designing appropriate estimator gains. Finally, the advantages of the proposed distributed parameter estimation approach from the perspectives of information interaction and consideration of model structure uncertainties are verified via simulations and practical experiments.

Optimizing photovoltaic models: A leader artificial ecosystem approach for accurate parameter estimation of dynamic and static three diode systems

AbstractThe utilization of accurate models is crucial in the various stages of development for photovoltaic (PV) systems. Modelling these systems effectively allows developers to assess new modifications prior to the manufacturing phase, resulting in cost and time savings. This research paper presents a viable approach to accurately estimate both static and dynamic PV models. The proposed estimation method relies on a novel and enhanced optimization algorithm called leader artificial ecosystem‐based optimization (LAEO), which improves upon the original artificial ecosystem‐based optimization (AEO). The proposed LAEO algorithm integrates the adaptive probability (AP) and leader‐based mutation‐selection strategies to enhance the search capability, improve the balance between exploration and exploitation, and overcome local optima. To evaluate the effectiveness of LAEO, it was tested on 23 different benchmark functions. Additionally, LAEO was applied to estimate the parameters of static three‐diode PV models, as well as integral‐order and fractional‐order dynamic models. This paper showcases practical implementations of photovoltaic (PV) parameter estimation in various scenarios, including the static three‐diode model, dynamic integral order model (IOM), and fractional order model (FOM). The results were assessed from various angles to examine the precision, performance, and stability of the LAEO algorithm.

Simultaneous estimation of a model-derived input function for quantifying cerebral glucose metabolism with [18F]FDG PET

BackgroundQuantification of the cerebral metabolic rate of glucose (CMRGlu) by dynamic [18F]FDG PET requires invasive arterial sampling. Alternatives to using an arterial input function (AIF) include the simultaneous estimation (SIME) approach, which models the image-derived input function (IDIF) by a series of exponentials with coefficients obtained by fitting time activity curves (TACs) from multiple volumes-of-interest. A limitation of SIME is the assumption that the input function can be modelled accurately by a series of exponentials. Alternatively, we propose a SIME approach based on the two-tissue compartment model to extract a high signal-to-noise ratio (SNR) model-derived input function (MDIF) from the whole-brain TAC. The purpose of this study is to present the MDIF approach and its implementation in the analysis of animal and human data.MethodsSimulations were performed to assess the accuracy of the MDIF approach. Animal experiments were conducted to compare derived MDIFs to measured AIFs (n = 5). Using dynamic [18F]FDG PET data from neurologically healthy volunteers (n = 18), the MDIF method was compared to the original SIME-IDIF. Lastly, the feasibility of extracting parametric images was investigated by implementing a variational Bayesian parameter estimation approach.ResultsSimulations demonstrated that the MDIF can be accurately extracted from a whole-brain TAC. Good agreement between MDIFs and measured AIFs was found in the animal experiments. Similarly, the MDIF-to-IDIF area-under-the-curve ratio from the human data was 1.02 ± 0.08, resulting in good agreement in grey matter CMRGlu: 24.5 ± 3.6 and 23.9 ± 3.2 mL/100 g/min for MDIF and IDIF, respectively. The MDIF method proved superior in characterizing the first pass of [18F]FDG. Groupwise parametric images obtained with the MDIF showed the expected spatial patterns.ConclusionsA model-driven SIME method was proposed to derive high SNR input functions. Its potential was demonstrated by the good agreement between MDIFs and AIFs in animal experiments. In addition, CMRGlu estimates obtained in the human study agreed to literature values. The MDIF approach requires fewer fitting parameters than the original SIME method and has the advantage that it can model the shape of any input function. In turn, the high SNR of the MDIFs has the potential to facilitate the extraction of voxelwise parameters when combined with robust parameter estimation methods such as the variational Bayesian approach.

An IDE-based nonlinear grey Bernoulli model and applications to daily traffic flow pattern identification

The nonlinear grey Bernoulli model is a powerful tool for modelling and forecasting time series exhibiting a rough inverted U-shape behaviour. Traditionally, it is considered an indirect dynamical model, informed by empirical knowledge that the accumulation of the inverted U-shape series leads to a growth behaviour, which is subsequently characterized by the Bernoulli ordinary differential equation (ODE). However, its mechanism remains incomplete, particularly concerning the modelling paradigm and parameter estimation. To this end, we propose an equivalent and simplified variant in the form of an integro-differential equation (IDE), enabling direct modelling of the inverted U-shaped series and thereby enhancing the interpretability. By taking the IDE as a state equation in the state space framework, separable nonlinear least squares (SLS) and nonlinear least squares (NLS) are respectively formulated to simultaneously estimate structural parameters and the initial condition. Then, by combining the state equation (ODE/IDE) and parameter estimation approach (SLS/NLS), the generated ODE-based indirect paradigms are comprehensively compared with the IDE-based direct ones. Numerical simulations show that (i) IDE-based models outperform ODE-based ones and (ii) NLS outperforms SLS. Real-world applications indicate that the nonlinear grey Bernoulli model combining IDE and NLS can accurately discover the underlying dynamics of daily traffic flow, outperforming the competitive models.

A novel wall parameter estimation approach based on transmission line method from through-wall radar measurements

A novel technique for estimation of the wall’s relative permittivity, thickness and conductivity from signals measured from the through-wall radar is presented in this paper. The retrieval process is built around an electromagnetic circuit model that represents the wall structure as a transmission line segment. The propagation of the radar signal through the wall is equivalently described as a pair of voltage and current waves that propagate along the transmission line, using analogies between the electrical parameters of the transmission line segment and the constituent parameters of the materials of the wall structure. The synthetic time domain signal obtained analytically and the real through wall imaging time domain signal were correlated to estimate the wall parameters of the layers that comprise the wall structure. The effectiveness of the proposed estimation technique has been demonstrated through simulation and experimentation on two actual building walls. A comparison with conventional methods revealed consistent results between the estimated wall parameters using the proposed technique and those obtained through traditional approaches. These findings highlight the potential of the proposed method in enhancing the accuracy of real-time target localization and tracking in through-wall imaging applications.

Integrated Sensing and Communication with Massive MIMO: A Unified Tensor Approach for Channel and Target Parameter Estimation

Integrated Sensing and Communication with Massive MIMO: A Unified Tensor Approach for Channel and Target Parameter Estimation

МОДЕЛЬНЫЙ АНАЛИЗ ДЕМОГРАФИЧЕСКИХ ПРОЦЕССОВ В ПОПУЛЯЦИЯХ ПУШНЫХ ОХОТНИЧЬИХ ЖИВОТНЫХ (НА ПРИМЕРЕ ЕВРЕЙСКОЙ АВТОНОМНОЙ ОБЛАСТИ)

Among biological resources, hunting animals, including fur-bearing species, take a special place. The study of such populations dynamics is a crucial stage in fur harvesting planning and organizing. This work aims to describe and analyze by mathematical modeling methods the dynamics of fur-bearing animal populations inhabiting the Jewish Autonomous region. We consider the populations whose newborn individuals reach maturity by the next breeding season, for example, squirrel, white hare, Manchurian hare, raccoon dog, and weasel. The study is based on the discrete-time model of population dynamics with a simple stage structure. To take into account density-dependent regulation of population growth in the model, birth or survival rates of the immature class are represented by exponential functions of the total population size. To estimate the model parameters, we propose the use of data corresponding to the total population size. The obtained point estimates, based on this approach, are demonstrated to be within the range of biologically meaningful parameter values and exhibit the population dynamics similar to those observed in nature. Specifically, according to the model estimates, squirrel and hare populations are characterized by unstable dynamics with sharp annual fluctuations. In general, the proposed approach for parameter estimation allows for analyzing and modeling the age composition of the animal population, as well as determining demographic parameters that characterize the animal population dynamics based on the total population size data.

An integrated approach for parameter estimation of a propyl propionate synthesis model

This paper introduces an innovative approach to the ProPro synthesis process, aiming to improve the modeling and parameter estimation by integrating and optimizing existing methodologies. It combines well-established models available in the literature with a hybrid solution approach, emphasizing computational efficiency. Additionally, it assesses and enhance the modeling results by calculating confidence regions and uncertainties in both kinetic and thermodynamic modeling. To this end, a batch reactor with Amberlyst 46 catalyst is modeled. The parameter estimation approach combines Particles Swarm Optimization and Gradient Method to estimate both thermodynamic and kinetic parameters, sequentially and simultaneously. Confidence regions and uncertainties are determined for the sequential approach, guiding the search space for the simultaneous estimation. By utilizing PSO, the parameters are estimated, and their confidence regions are determined, providing a comprehensive understanding of their uncertainty. The uncertainty is propagated through the model predictions of the batch reactor, allowing for a comprehensive analysis of the system's behavior. The results demonstrate a good agreement between the model predictions and experimental data, with the expanded uncertainty adequately reflecting the statistical variability of the experimental observations. Furthermore, the heterogeneous Langmuir-Hinshelwood model yields improved representation of the experimental data in both transient and steady states compared to the pseudo-homogeneous model. The Root Mean Square Deviation (RMSD) for parameter estimation shows significant improvement compared to literature values. The simultaneous parameter estimation approach exhibits the best fit performance for the model predictions, confirming its effectiveness in accurately representing the system.

PEM fuel cells: Two novel approaches for mathematical modeling and parameter estimation

Proton Exchange Membrane Fuel Cells (PEMFCs) voltage-current characteristics are typically employed in PEMFC modeling and parameter estimation. The inverse current-voltage dependence is first reduced into one nonlinear equation in this study, examined, and then solved using two innovative iterative techniques. The proposed iterative processes’ accuracy has been examined in terms of the number of iterations necessary to reach a particular degree of accuracy.For both proposed iterative procedures, a high level of accuracy is achieved. Moreover, increasing the number of iterations increases the accuracy of calculations significantly. Second, a new hybrid variation of the Osprey optimization algorithm (OOA) and the Coati optimization algorithm (COA), two newly published optimization methods in the literature, is proposed for PEMFC parameter estimation. The sum of squares error (SSE) and root mean square error (RMSE) between measured and estimated PEMFC current are used as two objective functions. The comparisons indicate that the proposed algorithm outperforms the literature-known algorithms regarding convergence speed, accuracy, and statistical performance. The numerical findings from the parameter estimation testing for two different PEMFC cells validated the effectiveness of the proposed approaches for modeling and parameter estimation of the PEMFCs under investigation.

Implementation of Latent Gaussian Model in the Forecasting Process

This research aims to determine the implementation of the Latent Gaussian Model in the forecasting process. This research focuses on developing a forecasting model using the Multivariate Latent Gaussian Model (LGM) approach with shared components. which offers a more accurate representation without the assumption of stationarity and cointegration as it accommodates random components in the model. The forecasting results for the five KPPs are considered to have a very good level of accuracy with MAPE values < 10%. This shows that LGM can achieve reliable forecasting when applied to the real life problems. This condition supports forecasting and can be an effective and targeted benchmark. The Latent Gaussian Model using the Bayesian Approach in parameter estimation can be utilized in forecasting Personal Income Tax Article 25/29. This is supported by the highly accurate MAPE value of 0.01%. The implementation of the developed model is not limited to forecasting Personal Income Tax Article 25/29. but can also be used in various other fields. With its hierarchical structure. the Bayesian approach proves to be an effective method for addressing complex modeling challenges.