Parameter Estimation Problem Research Articles

Precision parameter estimation in Proton Exchange Membrane Fuel Cells using depth information enhanced Differential Evolution

Proton Exchange Membrane Fuel Cell (PEMFC) models require parameter tuning for their design and performance improvement. In this study, Depth Information-Based Differential Evolution (Di-DE) algorithm, a novel and efficient metaheuristic approach, is applied to the complex, nonlinear optimization problem of PEMFC parameter estimation. The Di-DE algorithm was tested on twelve PEMFCs (BCS 500 W PEMFC, Nedstack 600 W PS6 PEMFC, SR-12 500 W PEMFC, H-12 PEMFC, STD 250 W PEMFC, HORIZON 500 W PEMFC and four 250W PEMFC and two H-12 12W PEMFC) and showed excellent accuracy. The Di-DE algorithm is was compared with other advanced evolutionary algorithms like iwPSO, CLPSO, DNLPSO, SLPSO, SaDE, SHADE, JADE, QUATRE, LSA, QUATRE-EMS and C-QUATRE, which obtained a minimum objective function value of 0.0255 and an average runtime improvement of 98.8%. The optimized parameters of the proposed method yielded the Sum of Squared Errors (SSE) as low as 0.00002 in some cases, which indicates better precision and stability. Moreover, the voltage–current (V–I) and power–voltage (P–V) characteristics predicted by Di-DE were within 1% error relative to the experimental data for all tested PEMFCs. The results of this work highlight the potential of the Di-DE algorithm to enable more sophisticated modelling and optimization of PEMFCs, which in turn will help to broaden the use of PEMFCs in clean energy applications.

Global quantum thermometry based on the optimal biased bound

Thermometry is a fundamental parameter estimation problem that is crucial for the advancement of natural sciences. One widely adopted approach to address this issue is the local thermometry theory, which employs classical and quantum Cramér-Rao bounds as benchmarks for thermometric precision. However, this theory is constrained to decrease temperature fluctuations around a known temperature value, hardly tackling the precision thermometry problem over a wide temperature range. To overcome this limitation, we derive two basic bounds on thermometry precision within a global framework, i.e., classical and quantum optimal biased bounds. By implementing energy measurements on a thermal equilibrium system, the quantum optimal biased bound can be saturated. Furthermore, we demonstrate their thermometry performance through two specific applications: a noninteracting spin-1/2 gas and a thermalized quantum harmonic oscillator. Our results indicate that, compared to local thermometry, global thermometry provides superior temperature estimation performance. Notably, global error bound approaches its local approximation under asymptotic cases. Published by the American Physical Society 2024

Method of moments estimation for the superposition of square-root diffusions

Abstract We consider the problem of parameter estimation for the superposition of square-root diffusions. We first derive the explicit formulas for the moments and auto-covariances based on which we develop our moment estimators. We then establish a central limit theorem for the estimators with the explicit formulas for the asymptotic covariance matrix. Finally, we conduct numerical experiments to validate our method.

Large-Scale Parameter Estimation for Crystal Structure Prediction. Part 1: Dataset, Methodology, and Implementation.

Crystal structure prediction (CSP) seeks to identify all thermodynamically accessible solid forms of a given compound and, crucially, to establish the relative thermodynamic stability between different polymorphs. The conventional hierarchical CSP workflow suggests that no single energy model can fulfill the needs of all stages in the workflow, and energy models across a spectrum of fidelities and computational costs are required. Hybrid ab initio/empirical force-field (HAIEFF) models have demonstrated a good balance of these two factors, but the force-field component presents a major bottleneck for model accuracy. Existing parameter estimation tools for fitting this empirical component are inefficient and have severe limitations on the manageable problem size. This, combined with a lack of reliable reference data for parameter fitting, has resulted in development in the force-field component of HAIEFF models having mostly stagnated. In this work, we address these barriers to progress. First, we introduce a curated database of 755 organic crystal structures, obtained using high quality, solid-state DFT-D calculations, which provide a complete set of geometry and energy data. Comparisons to various theoretical and experimental data sources indicate that this database provides suitable diversity for parameter fitting. In tandem, we also put forward a new parameter estimation algorithm implemented as the CrystalEstimator program. Our tests demonstrate that CrystalEstimator is capable of efficiently handling large-scale parameter estimation problems, simultaneously fitting as many as 62 model parameters based on data from 445 structures. This problem size far exceeds any previously reported works related to CSP force-field parametrization. These developments form a strong foundation for all future work involving parameter estimation of transferable or tailor-made force-fields for HAIEFF models. This ultimately opens the way for significant improvements in the accuracy achieved by the HAIEFF models.

Parameters estimation for ornstein-uhlenbeck processes with time periodic modulated drift

Abstract This work mainly delves into the parameter estimation problem concerning Ornstein-Uhlenbeck processes with time-periodic modulated drift based on continuous observations. A least squares estimator is constructed by minimizing a contrast function. It is demonstrated that as the number of observed periods approaches infinity, the least squares estimator exhibits asymptotic unbiasedness, strong consistency, and asymptotic normality. The important technique in the asymptotic study relies on the central limit theorem for multiple Wiener integrals. Finally, numerical simulations of the least squares estimator are presented.

Enhancing 4‐D Landslide Monitoring and Block Interaction Analysis With a Novel Kalman‐Filter‐Based InSAR Approach

AbstractIn recent years, Synthetic Aperture Radar Interferometry (InSAR) has become widely utilized for slow‐moving landslide monitoring due to its high resolution, accuracy, and extensive coverage. By integrating data from various orbits/platforms and monitoring sources, one‐dimensional (1‐D) line‐of‐sight (LOS) InSAR measurements can be explored to infer three‐dimensional (3‐D) movements. However, inconsistencies in observation times among different orbits and monitoring sources pose challenges in accurately capturing dynamic 3‐D movements over time (referred to as 4‐D). In this study, we propose a novel method, termed KFI‐4D that incorporates spatiotemporal constraints into the traditional Kalman filter. This enhancement transforms the underdetermined problem of 4‐D movement acquisition into a dynamic parameter estimation problem, enabling precise monitoring of landslide movements. The KFI‐4D method was evaluated using both synthetic data sets and real data from the Hooskanaden landslide, demonstrating an improvement exceeding 50% in root mean square errors (RMSEs) compared to conventional methods. Additionally, the high‐resolution characteristics of InSAR‐derived 4‐D movements allow for the analysis of strain invariants, providing insights into block interactions and landslide dynamics. Our findings reveal that strain invariants effectively indicate the distribution and activity of landslide blocks and slip surfaces as well as their response to triggers. Notably, abnormal signals identified in strain invariants prior to the catastrophic event at Hooskanaden suggest potential for early warning of landslides. The future integration of data from advanced satellites, such as NISAR, ALOS4 PALSAR3, and Sentinel‐1C, is expected to further enhance the KFI‐4D method's capabilities, improving temporal resolution and early warning potential for landslide monitoring.

Mitigating the Impact of Lognormal Atmospheric Turbulence Channel Estimation on FSO Communication Systems Using Advanced Deep Learning Modules

ABSTRACTCurrently, researchers and commercial entities worldwide are highly interested in optical wireless communication links operating in terrestrial environments. These links offer the distinct advantage of enabling high‐speed data transmission while keeping operational and installation costs low, all without requiring licensing. Free‐space optical (FSO) communication has established itself as a reliable method for delivering ultra‐high data‐rate services. However, the presence of atmospheric turbulence‐induced fading poses a significant challenge for FSO communication systems, particularly when operating over channels affected by time‐varying turbulence. The effectiveness of FSO systems is greatly influenced by atmospheric conditions in a specific area because the laser beam propagates through the atmosphere. As a consequence, this can lead to a significant degradation such as high complexity, high estimation error, and high bit error rate (BER) in the performance of FSO systems. This paper presents a stacked dual attention LSTM network with layered neural Turing machine (SDALSTM‐LaNTM) for FSO channel estimation over lognormal turbulence‐induced fading channels. In this approach, the stacked structure ensures a robust feature extraction capacity of SDALSTM and enhances its ability to capture intricate relationships among multiple atmospheric variables. After employing the stacked LSTM networks, the extracted features are combined with the augmented features obtained through the dual attention (DAttn) mechanism by concatenation. Then the LaNTM architecture used external memory to solve the channel parameter estimation problem and update new set of hidden features for estimation task. The ability to access and update memory enables the model to capture long‐term dependencies and context, making it beneficial for channel prediction in FSO systems. Presently, we are in the process of verifying the channel estimation model using measured FSO channel data. Simulation results clearly demonstrate the outstanding estimation performance of the SDALSTM‐LaNTM model in FSO systems, specifically when dealing with lognormal turbulence‐induced fading channels. Moreover, we highlight the effectiveness of the SDALSTM‐LaNTM model by conducting a comprehensive comparison with existing models, considering factors such as average capacity performance, outage probability estimation, and BER.

Identification of a Non‐Commensurate Fractional‐Order Nonlinear System Based on the Separation Scheme

ABSTRACTThis article is aimed to study the parameter estimation problems of a non‐commensurate fractional‐order system with saturation and dead‐zone nonlinearity. In order to reduce the structural complexity of the system, the model separation scheme is used to decompose the fractional‐order nonlinear system into two subsystems, one includes the parameters of the linear part and the other includes the parameters of the nonlinear part. Then, we derive an auxiliary model separable gradient‐based iterative algorithm with the help of the model separation scheme. In addition, to improve the utilization of the real time information, an auxiliary model separable multi‐innovation gradient‐based iterative algorithm is presented based on the sliding measurement window. Finally, the feasibility of the presented algorithms is validated by numerical simulations.

Deep optimal experimental design for parameter estimation problems

Abstract Optimal experimental design is a well studied field in applied science and engineering. Techniques for estimating such a design are commonly used within the framework of parameter estimation. Nonetheless, in recent years parameter estimation techniques are changing rapidly with the introduction of deep learning techniques to replace traditional estimation methods. This in turn requires the adaptation of optimal experimental design that is associated with these new techniques. In this paper we investigate a new experimental design methodology that uses deep learning. We show that the training of a network as a Likelihood Free Estimator can be used to significantly simplify the design process and circumvent the need for the computationally expensive bi-level optimization problem that is inherent in optimal experimental design for non-linear systems. Furthermore, deep design improves the quality of the recovery process for parameter estimation problems. As proof of concept we apply our methodology to two different systems of Ordinary Differential Equations.

Sensitivity fields and parameter estimation from dielectric objects

The quantitative phase image formation process is posed as a problem of parameter estimation from intensity measurements. This approach is inclusive of traditional pixel-oriented imaging, where the sought parameters are the pixel values. The resulting optimization process to find the parameters is then seen to depend on the sensitivity field: this is the gradient of the scattered field with respect to the parameters, and it turns out to obey a scattering relationship that is analogous to that of the original scattered field. Examples are given from several regimes of scattering strength.

James-Stein estimator improves accuracy and sample efficiency in human kinematic and metabolic data.

Human biomechanical data are often accompanied with measurement noise and behavioral variability. Errors due to such noise and variability are usually exaggerated by fewer trials or shorter trial durations, and could be reduced using more trials or longer trial durations. Speeding up such data collection by lowering number of trials or trial duration, while improving the accuracy of statistical estimates, would be of particular interest in wearable robotics applications and when the human population studied is vulnerable (e.g., the elderly). Here, we propose the use of the James-Stein estimator (JSE) to improve statistical estimates with a given amount of data, or reduce the amount of data needed for a given accuracy. The JSE is a shrinkage estimator that produces a uniform reduction in the summed squared errors when compared to the more familiar maximum likelihood estimator (MLE), simple averages, or other least squares regressions. When data from multiple human participants are available, an individual participant's JSE can improve upon MLE by incorporating information from all participants, improving overall estimation accuracy on average. Here, we apply the JSE to multiple time-series of kinematic and metabolic data from the following parameter estimation problems: foot placement control during level walking, energy expenditure during circle walking, and energy expenditure during resting. We show that the resulting estimates improve accuracy - that is, the James-Stein estimates have lower summed squared error from the 'true' value compared to more conventional estimates.

Parameter Estimation of Uncertain Differential Equations Driven by Threshold Ornstein–Uhlenbeck Process with Application to U.S. Treasury Rate Analysis

Uncertain differential equations, as an alternative to stochastic differential equations, have proved to be extremely powerful across various fields, especially in finance theory. The issue of parameter estimation for uncertain differential equations is the key step in mathematical modeling and simulation, which is very difficult, especially when the corresponding terms are driven by some complicated uncertain processes. In this paper, we propose the uncertainty counterpart of the threshold Ornstein–Uhlenbeck process in probability, named the uncertain threshold Ornstein–Uhlenbeck process, filling the gaps of the corresponding research in uncertainty theory. We then explore the parameter estimation problem under different scenarios, including cases where certain parameters are known in advance while others remain unknown. Numerical examples are provided to illustrate our method proposed. We also apply the method to study the term structure of the U.S. Treasury rates over a specific period, which can be modeled by the uncertain threshold Ornstein–Uhlenbeck process mentioned in this paper. The paper concludes with brief remarks and possible future directions.

Cubic spline estimation for non parametric uncertain differential equation

. In the history of researching to estimate the unknown parameters that were in the uncertain differential equation (UDE), the problem of parameter estimation with known functional forms is often studied. However, in practical situations, its functional form is often unknown. In order to deal with this problem, this article proposes the cubic spline method to approximate the autonomous UDE, and perform non parametric estimation on it. The cross validation is introduced to determine the number of term (J), which is in the approximate cubic spline. In addition, the uncertain hypothesis testing is given to verify the rationality of this method. Finally, some numerical examples are given. Then this method is applied to a case study of the Beijing Air Quality Index, and a comparative analysis is given to verify the practicability and superiority of the cubic spline method.

Adaptive Phase Estimation with Squeezed Vacuum Approaching the Quantum Limit

Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum-correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of [0,π/2). Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from [0,π), where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology.

A Novel Spotted Hyena Optimizer for the Estimation of Equivalent Circuit Model Parameters in Li-Ion Batteries

Li-ion batteries possess significant advantages like large energy density, fast recharge, and high reliability; hence, they are widely adopted in electric vehicles, portable electronics, and military and aerospace applications. Albeit having their merits, accurate battery modeling is subjected to problems like prior information on internal chemical reactions, complexity in problem formulation, a large number of unknown parameters, and the need for extensive experimentation. Hence, this article presents a reliable Spotted Hyena Optimizer (SHO) to determine the equivalent circuit parameters of lithium-ion (Li-ion) batteries. The methodology of the SHO is derived from the living and hunting tactics of spotted hyenas, and it is efficiently applied to solve the battery parameter estimation problem. Nine unknown battery model parameters of a Samsung INR 18650-25R are determined using this method. The model parameters estimated are endorsed for five different datasets with various discharge current values. Further, the effect of parameter range and its selection is also emphasized. Secondly, for validation, various performance metrics such as Integral Squared Error, mean best, mean worst, and Standard Deviation are evaluated to authenticate the superiority of the proposed parameter extraction. From the computed results, the SHO algorithm is able to explore the search area up to 89% in the case of larger search ranges. The chosen model and range of the SHO precisely predict the behavior of the proposed Li-ion battery, and the results are in accordance with the catalog data.

A novel hybrid genetic algorithm and Nelder-Mead approach and it’s application for parameter estimation

Background Traditional optimization methods often struggle to balance global exploration and local refinement, particularly in complex real-world problems. To address this challenge, we introduce a novel hybrid optimization strategy that integrates the Nelder-Mead (NM) technique and the Genetic Algorithm (GA), named the Genetic and Nelder-Mead Algorithm (GANMA). This hybrid approach aims to enhance performance across various benchmark functions and parameter estimation tasks. Methods GANMA combines the global search capabilities of GA with the local refinement strength of NM. It is first tested on 15 benchmark functions commonly used to evaluate optimization strategies. The effectiveness of GANMA is also demonstrated through its application to parameter estimation problems, showcasing its practical utility in real-world scenarios. Results GANMA outperforms traditional optimization methods in terms of robustness, convergence speed, and solution quality. The hybrid algorithm excels across different function landscapes, including those with high dimensionality and multimodality, which are often encountered in real-world optimization issues. Additionally, GANMA improves model accuracy and interpretability in parameter estimation tasks, enhancing both model fitting and prediction. Conclusions GANMA proves to be a flexible and powerful optimization method suitable for both benchmark optimization and real-world parameter estimation challenges. Its capability to efficiently explore parameter spaces and refine solutions makes it a promising tool for scientific, engineering, and economic applications. GANMA offers a valuable solution for improving model performance and effectively handling complex optimization problems.

Particle Filtering for Enhanced Parameter Estimation in Bilinear Systems Under Colored Noise

This paper addresses the challenging problem of parameter estimation in bilinear systems under colored noise. A novel approach, termed B-PF-RLS, is proposed, combining a particle filter (PF) with a recursive least squares (RLS) estimator. The B-PF-RLS algorithm tackles the complexities arising from system nonlinearities and colored noise by effectively estimating unknown system states using the particle filter, which are then integrated into the RLS parameter estimation process. Furthermore, the paper introduces an enhanced particle filter that eliminates the need for explicit knowledge of the measurement noise variance, enhancing the method's practicality for real-world applications. Numerical examples demonstrate the B-PF-RLS algorithm's superior performance in accurately estimating both system parameters and states, even under uncertain noise conditions. This work offers a robust and effective solution for system identification in various engineering applications involving bilinear models subject to complex noise environments.

An improved nutcracker optimization algorithm for discrete and continuous optimization problems: Design, comprehensive analysis, and engineering applications

This study is presented to examine the performance of a newly proposed metaheuristic algorithm within discrete and continuous search spaces. Therefore, the multithresholding image segmentation problem and parameter estimation problem of both the proton exchange membrane fuel cell (PEMFC) and photovoltaic (PV) models, which have different search spaces, are used to test and verify this algorithm. The traditional techniques could not find approximate solutions for those problems in a reasonable amount of time, so researchers have used metaheuristic algorithms to overcome those shortcomings. However, the majority of metaheuristic algorithms still suffer from slow convergence speed and stagnation into local minima problems, which makes them unsuitable for tackling these optimization problems. Therefore, this study proposes an improved nutcracker optimization algorithm (INOA) for better solving those problems in an acceptable amount of time. INOA is based on improving the performance of the standard algorithm using a newly proposed convergence improvement strategy that aims to improve the convergence speed and prevent stagnation in local minima. This algorithm is first applied to estimating the unknown parameters of the single-diode, double-diode, and triple-diode models for a PV module and a solar cell. Second, four PEMFC modules are used to further observe INOA's performance for the continuous optimization challenge. Finally, the performance of INOA is investigated for solving the multi-thresholding image segmentation problem to test its effectiveness in a discrete search space. Several test images with different threshold levels were used to validate its effectiveness, stability, and scalability. Comparison to several rival optimizers using various performance indicators, such as convergence curve, standard deviation, average fitness value, and Wilcoxon rank-sum test, demonstrates that INOA is an effective alternative for solving both discrete and continuous optimization problems. Quantitively, INOA could solve those problems better than the other rival optimizers, with improvement rates for final results ranging between 0.8355 % and 3.34 % for discrete problems and 4.97 % and 99.9 % for continuous problems.

Identification of fractional Hammerstein systems with the conformable fractional derivative

SummaryIn this article, we study parameter estimation problems for fractional commensurate Hammerstein systems utilizing the conformable fractional derivative. Two algorithms are investigated: first, the Poisson moment functions (PMF) method, aiming to transfer the fractional derivative of the measurement signal into PMF using the fractional Laplace transform and convolution; second, a proposed new instrumental variable algorithm, which is based on the conformable fractional derivative. Both algorithms have been analyzed and shown to be consistent. A comprehensive complexity analysis is provided for each algorithm. Furthermore, a kind of special time‐varying systems are discussed under the conformable fractional derivative. Finally, an example is given to illustrate the effectiveness of the proposed algorithms.

Parameter Estimation of Chikungunya in the Case of Incomplete Information about Its Model

This paper presents solutions to the problem of parameter estimation of mathematical model of Chikungunya with incomplete information about the model parameters. The process involves finding a set of unknown parameters from the given model such that the behavior of the predicted system reflects the original behavior (measurement) using the same scientific assumptions. To achieve this, we solve the differential equations which describe the relation between unknown functions and their derivatives using the fundamental theorem of ordinary differential equation (ODE) (i.e., the theorem of existence) to obtain solutions for the initial value problems. The solutions to the ODE give unknown parameters which functionally depend on the original unknown parameters. And these parameters have two constraints between them. We further find solutions to the constraints minimization problem to obtain estimations of a-parameters. But, the method of constraint minimization problem stipulates the ill-conditioned problem and makes it impossible to accurately identify a-parameters. It is necessary therefore to formulate the goal function using the Least squares method to determine the unknown parameters. This method works reliably well and converges at a large interval of initial guess values of parameters.