Unknown Parameters Research Articles

Development of a new exponential generalized family of distribution with its properties and application

In the field of reliability analysis, the selection of an appropriate lifespan model is critical. With a multitude of lifetime distributions accessible, the hunt for a more suited distribution remains essential. In this paper, we offer a unique class of distributions derived from the notion of exponential generalization, improved with changes to boost flexibility. Our suggested distribution incorporates multiple hazard rate profiles, giving enhanced flexibility. Analytical characteristics including the rth moment, moment generating function, quantile function, distribution of order statistics, and Rényi entropy are obtained. Employing maximum likelihood estimation, we estimate the unknown parameters. Through simulation tests and analysis of real-world datasets, we exhibit the model's usefulness compared to five existing lifespan distributions, emphasising the better performance of the GAYUF distribution. This research underlines the GAYUF distribution as a better model in the field of lifespan analysis

Dynamic properties, probability density, and estimation of an SIRIS epidemic model with an Ornstein-Uhlenbeck process★ ★This research is supported by the Research Innovation Program for Postgraduates of Xinjiang Uygur Autonomous Region under Grant (No. XJ2023G017), the National Natural Science Foundation of China (No. 12061070) and the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China (No. 2021D01E13).

Considering the relapse and temporary immunity of some diseases, a stochastic SIRIS epidemic model with saturation incidence is developed in this paper, in which the Ornstein-Uhlenbeck process is introduced to describe the randomness of the model. The existence and uniqueness of the global solution are first proved to investigate the dynamic properties of the SIRIS model. By constructing a series of Lyapunov functions, the thresholds R0E and R0S are further derived to determine the extinction and persistence of the disease. Subsequently, we prove that the solution of the model admits a stationary distribution. The probability density function is obtained by the algebraic method. In addition, the unknown parameters of the density function are estimated by using the maximum likelihood estimation. Finally, numerical simulations verify the results of the above properties.

Correcting an Off-Nadir to a Nadir Land Surface Temperature Using a Multitemporal Thermal Infrared Kernel-Driven Model during Daytime

Land surface temperature (LST) is a fundamental parameter in global climate, environmental, and geophysical studies. Remote sensing is an essential approach for obtaining large-scale and frequently updated LST data. However, due to the wide field of view of remote sensing sensors, the observed LST with diverse view geometries suffers from inconsistency caused by the thermal radiation directionality (TRD) effect, which results in LST products being incomparable, especially during daytime. To address this issue and correct current off-nadir LSTs to nadir LSTs, a semi-physical time-evolved kernel-driven model (TEKDM) is proposed, which depicts multitemporal TRD patterns during the daytime. In addition, we employ a Bayesian optimization method to calibrate seven unknown parameters in the TEKDM. Validation results using the U.S. Climate Reference Network (USCRN) sites show that the RMSE (MBE) for GOES-16 and MODIS off-nadir LST products is reduced from 3.29 K (−2.0 K) to 2.34 K (−0.02 K), with an RMSE reduction of 0.95 K (29%) and a significant reduction in systematic bias. Moreover, the proposed method successfully eliminates the angular and temporal dependence of the LST difference between the satellite off-nadir LST and in situ nadir LST. In summary, this study presents a feasible approach for estimating the high-accuracy nadir LST, which can enhance the applicability of LST products in various domains.

Semiparametric estimation of average treatment effects in observational studies

AbstractWe propose a semiparametric method to estimate average treatment effects in observational studies based on the assumption of unconfoundedness. Assume that the propensity score model and outcome model are a general single index model, which are estimated by the kernel method and the unknown index parameter is estimated via linearized maximum rank correlation method. The proposed estimator is computationally tractable, allows for large dimension covariates and not involves the approximation of link functions. We showed that the proposed estimator is consistent and asymptotically normally distributed. In general, the proposed estimator is superior to existing methods when the model is incorrectly specified. We also provide an empirical analysis on the average treatment effect and average treatment effect on the treated of 401(k) eligibility on net financial assets.

Monopoly pricing with unknown demand

AbstractThe optimal pricing of goods, especially when they are new and the innovating firm is a monopolist, must proceed without precise knowledge of the demand curve. This paper provides a pricing method with a relative robustness guarantee by maximizing a performance index which amounts to a worst‐case ratio of the obtained payoff to the best possible payoff. Assuming monotonicity and complementarity of demand in price and the unknown demand parameter, the performance index is fully determined by its behavior at the boundary of the parameter space. This allows for an efficient computation of an optimal robust price. In the linear case, which can also be used for nonlinear demand with bounded slope, the method provides a simple closed‐form solution. A comparison with the standard worst‐case payoff criterion reveals substantial improvements in both absolute and relative performance, at only a small cost relative to the maximized expected profit.

Untangling the stranglehold through mathematical modelling of Streptococcus equi subspecies equi transmission

Strangles, a disease caused by infection with Streptococccus equi subspecies equi (S. equi), is endemic worldwide and one of the most frequently diagnosed infectious diseases of horses. Recent work has improved our knowledge of key parameters of transmission dynamics, but important knowledge gaps remain. Our aim was to apply mathematical modelling of S. equi transmission dynamics to prioritise future research areas, and add precision to estimates of transmission parameters thereby improving understanding of S. equi epidemiology and quantifying the control effort required. A compartmental deterministic model was constructed. Parameter values were estimated from current literature wherever possible. We assessed the sensitivity of estimates for the basic reproduction number on the population scale to varying assumptions for the unknown or uncertain parameters of: (mean) duration of carriership (1∕γC), relative infectiousness of carriers (f), proportion of infections that result in carriership (p), and (mean) duration of immunity after natural infection (1∕γR). Available incidence and (sero-)prevalence data were compared to model outputs to improve point estimates and ranges for these currently unknown or uncertain transmission-related parameters. The required vaccination coverage of an ideal vaccine to prevent major outbreaks under a range of control scenarios was estimated, and compared available data on existing vaccines. The relative infectiousness of carriers (as compared to acutely ill horses) and the duration of carriership were identified as key knowledge gaps. Deterministic compartmental simulations, combined with seroprevalence data, suggest that 0.05<fˆ<0.5 and that the duration of protective immunity after infection is likely 4–6 years. The presence of carriers alone may suffice to keep S. equi endemic in a population, implying that carriers cannot be ignored in control efforts. Weekly screening of herds for signs of strangles could be sufficient to ensure R < 1, provided all horses are screened for carriership post-infection. In some of worst-case scenarios, vaccination alone would not suffice to prevent major outbreaks from occurring. A stochastic agent-based model was also constructed and validated, and used to simulate a remount depot, to evaluate whether historical incidence data of recurrence of strangles within individuals could be explained without the assumption that one in four horses fail to mount a lasting immune response. These simulations demonstrated that the observed data could have occurred without that assumption.

Parametric Optimization of Proton Exchange Membrane Fuel Cell Using Chaotic Swarm Intelligence Technique

AbstractThe proton exchange membrane fuel cell (PEMFC) converts chemical energy into electricity without pollution or noise. PEMFC has a stable electrolyte, reliable, fast start‐up, and lightweight portability. Optimal PEMFC parameter prediction is difficult. Due to inaccurate estimation, many meta‐heuristic models are inaccurate. Particle swarm, Ant colony, and grey wolf algorithms are tested for fuel cell parameter estimation. These traditional algorithms benefit from chaotic maps for exploitation and exploration. Analyzing V–I and P–I polarization curves, hybrid approaches estimate unknown parameters. Results are compared with others to support the identifying strategy. This project examined SR‐12 and NedSstack PS‐6 PEMFC stacks. The objective function was shown by the sum of square errors between the experiments, and once an appropriate map is identified, the single chaotic map inclusion method can perform better than the multiple chaotic map scheme, and the “Iterative” approach in chaotic swarm is the most promising for multidimensional challenges.

Mathematical Models of Wound Healing and Tissue Regeneration: Insights with Numerical Solution

Understanding and forecasting the dynamics of wound healing processes heavily relies on mathematical modeling. Researchers can understand the complicated connections between cells, tissues, and biochemical components involved in wound healing by using mathematical equations and computational simulations. One such mathematical model that has seeks the interest of researchers in exploring wound healing phenomenon is Fisher’s equation. In the present work, the equation is solved using differential quadrature method with trigonometric tension B-spline (TTBs) basis function. The obtained results are compared with the results obtained from earlier studies and the results are presented in form of tables and figures. The implementation of the particle swarm optimization algorithm has removes the dilemma of unknown parameter involvement in the TTBs and hence resulted in a novel technique to find the numerical results.

Improved linear/nonlinear active disturbance rejection switching control for bearingless induction motor

ABSTRACT To achieve high-performance operation control for bearingless induction motor (BIM) systems, an improved linear/nonlinear active disturbance rejection switching control strategy is proposed (SADRC). The key innovation lies in the automatic switching between linear and nonlinear control modes based on system stability and disturbance magnitude. First of all, based on the principle of air-gap magnetic field directional control of the BIM, the first-order and second-order ADRC are designed for the rotating and suspending parts of the BIM, respectively. In addition, the nonlinear active disturbance rejection control (NLADRC) has the shortcoming of tracking performance degradation when the disturbance amplitude is large. Then, an active disturbance rejection controller that can automatically switch between linear and nonlinear based on the stability of the system and the magnitude of the disturbance is designed with the introduction of linear active disturbance rejection control (LADRC). The trigonometric function is introduced to improve the fal function to optimise the abrupt change at the linear interval and the high-frequency chattering phenomenon at the origin. The unknown parameters are rectified using the bandwidth method and the particle swarm algorithm, respectively, to ensure the robustness and adaptiveness of the control strategy. Finally, both simulation and experimental results show that the proposed SADRC strategy not only combines the advantages of linear and nonlinear self-anti-disturbance control but also improves the BIM rotor suspension performance and anti-disturbance capability.

Multiparameter critical quantum metrology with impurity probes

Quantum systems can be used as probes in the context of metrology for enhanced parameter estimation. In particular, the delicacy of critical systems to perturbations can make them ideal sensors. Arguably the simplest realistic probe system is a spin- 12 impurity, which can be manipulated and measured in-situ when embedded in a fermionic environment. Although entanglement between a single impurity probe and its environment produces nontrivial many-body effects, criticality cannot be leveraged for sensing. Here we introduce instead the two-impurity Kondo model as a novel paradigm for critical quantum metrology, and examine the multiparameter estimation scenario at finite temperature. We explore the full metrological phase diagram numerically and obtain exact analytic results near criticality. Enhanced sensitivity to the inter-impurity coupling driving a second-order phase transition is evidenced by diverging quantum Fisher information (QFI) and quantum signal-to-noise ratio (QSNR). However, with uncertainty in both coupling strength and temperature, the multiparameter QFI matrix becomes singular—even though the parameters to be estimated are independent—resulting in vanishing QSNRs. We demonstrate that by applying a known control field, the singularity can be removed and measurement sensitivity restored. For general systems, we show that the degradation in the QSNR due to uncertainties in another parameter is controlled by the degree of correlation between the unknown parameters.

Evaluation of a Simplified Modeling Approach for SEE Cross-Section Prediction: A Case Study of SEU on 6T SRAM Cells

Electrical models play a crucial role in assessing the radiation sensitivity of devices. However, since they are usually not provided for end users, it is essential to have alternative modeling approaches to optimize circuit design before irradiation tests, and to support the understanding of post-irradiation data. This work proposes a novel simplified methodology to evaluate the single-event effects (SEEs) cross-section. To validate the proposed approach, we consider the 6T SRAM cell a case study in four technological nodes. The modeling considers layout features and the doping profile, presenting ways to estimate unknown parameters. The accuracy and limitations are determined by comparing our simulations with actual experimental data. The results demonstrated a strong correlation with irradiation data, without requiring any fitting of the simulation results or access to process design kit (PDK) data. This proves that our approach is a reliable method for calculating the single-event upset (SEU) cross-section for heavy-ion irradiation.

Optimizing one-axis twists for variational Bayesian quantum metrology

Quantum metrology and sensing seek advantages in estimating an unknown parameter of some quantum state or channel, using entanglement such as spin squeezing produced by one-axis twists or other quantum resources. In particular, qubit phase estimation, or rotation sensing, appears as a ubiquitous problem with applications to electric field sensing, magnetometry, atomic clocks, and gyroscopes. By adopting the Bayesian formalism to the phase estimation problem to account for limited initial knowledge about the value of the phase, we formulate variational metrology and treat the state preparation (or encoding) and measurement (or decoding) procedures as parameterized quantum circuits. It is important to understand how effective various parametrized protocols are as well as how robust they are to the effects of complex noise such as spatially correlated noise. First, we propose a family of parametrized encoding and decoding protocols called arbitrary-axis twist ansatzes, and show that it can lead to a substantial reduction in the number of one-axis twists needed to achieve a target estimation error. Furthermore, we demonstrate that the estimation error associated with these strategies decreases with system size in a faster manner than classical (or no-twist) protocols, even in the less-explored regimes where the prior information is limited. Last, using a polynomial-sized tensor network algorithm, we numerically analyze practical variational metrology beyond the symmetric subspace of a collective spin and find that quantum advantage persists for the arbitrary-axis twist ansatzes with a few one-axis twists and smaller total twisting angles for practically relevant noise levels. Published by the American Physical Society 2024

Optimal estimation of pure states with displaced-null measurements

Abstract We revisit the problem of estimating an unknown parameter of a pure quantum state, and investigate ‘null-measurement’ strategies in which the experimenter aims to measure in a basis that contains a vector close to the true system state. Such strategies are known to approach the quantum Fisher information for models where the quantum Cramér-Rao bound is achievable but a detailed adaptive strategy for achieving the bound in the multi-copy setting has been lacking. We first show that the following naive null-measurement implementation fails to attain even the standard estimation scaling: estimate the parameter on a small sub-sample, and apply the null-measurement corresponding to the estimated value on the rest of the systems. This is due to non-identifiability issues specific to null-measurements, which arise when the true and reference parameters are close to each other. To avoid this, we propose the alternative displaced-null measurement strategy in which the reference parameter is altered by a small amount which is sufficient to ensure parameter identifiability. We use this strategy to devise asymptotically optimal measurements for models where the quantum Cramér-Rao bound is achievable. More generally, we extend the method to arbitrary multi-parameter models and prove the asymptotic achievability of the the Holevo bound. An important tool in our analysis is the theory of quantum local asymptotic normality which provides a clear intuition about the design of the proposed estimators, and shows that they have asymptotically normal distributions.

New sexually transmitted HIV infections from 2016 to 2050 in Guangdong Province, China: a study based on a dynamic compartmental model

BackgroundIn Guangdong Province, China, there is lack of information on the HIV epidemic among high-risk groups and the general population, particularly in relation to sexual transmission, which is a predominant route. The new HIV infections each year is also uncertain owing to HIV transmission from men who have sex with men (MSM) to women, as a substantial proportion of MSM also have female sexual partnerships to comply with social demands in China.MethodsA deterministic compartmental model was developed to predict new HIV infections in four risk groups, including heterosexual men and women and low- and high-risk MSM, in Guangdong Province from 2016 to 2050, considering HIV transmission from MSM to women. The new HIV infections and its 95% credible interval (CrI) were predicted. An adaptive sequential Monte Carlo method for approximate Bayesian computation (ABC-SMC) was used to estimate the unknown parameter, a mixing index. We calibrated our results based on new HIV diagnoses and proportions of late diagnoses. The Morris and Sobol methods were applied in the sensitivity analysis.ResultsNew HIV infections increased during and 2 years after the COVID-19 pandemic, then declined until 2050. New infections rose from 8,828 [95% credible interval (CrI): 6,435–10,451] in 2016 to 9,652 (95% CrI: 7,027–11,434) in 2019, peaking at 11,152 (95% CrI: 8,337–13,062) in 2024 before declining to 7,084 (95% CrI: 5,165–8,385) in 2035 and 4,849 (95% CrI: 3,524–5,747) in 2050. Women accounted for approximately 25.0% of new HIV infections, MSM accounted for 40.0% (approximately 55.0% of men), and high-risk MSM accounted for approximately 25.0% of the total. The ABC-SMC mixing index was 0.504 (95% CrI: 0.239–0.894).ConclusionsGiven that new HIV infections and the proportion of women were relatively high in our calibrated model, to some extent, the HIV epidemic in Guangdong Province remains serious, and services for HIV prevention and control are urgently needed to return to the levels before the COVID-19 epidemic, especially in promoting condom-based safe sex and increasing awareness of HIV prevention to general population.

A new fatigue damage prediction model applicable to multi-slope S-N curves

The S-N curve methodology, deeply rooted in fatigue data derived from testing specimens, continues to be a prevalently utilized and foundational approach for fatigue evaluation within engineering disciplines. Nonetheless, the occurrence of fatigue limits frequently induces multi-segment patterns within S-N curves, thereby instigating discrepancies in both the slope and intercept values. This study introduces a fatigue damage prediction model tailored for multi-slope S-N curves. It employs a novel rainflow stress range distribution function, integrating two Rayleigh distributions to improve the accuracy of stress distribution moments while minimizing unknown parameters. Initially, the research delineates four bimodal power spectral density configurations and formulates a parameter search strategy for the identification of standard spectra that correspond with a wide array of bandwidth parameters. Subsequent to the parameter filtration process, a selection of 2241 standard spectra, encompassing a diverse range of bandwidth parameters, is made. Through the application of these meticulously selected standard spectra, a series of comparative analyses are executed amongst the predictive outcomes derived from the DK, ZB, JB, MN, ZL models, and the newly proposed model, across varied multi-slope S-N curves and differential fatigue limits. The insights gleaned from the relative error assessments underscore the commendable predictive precision of the novel model across multiple bandwidth processes. Notably, the model exhibits significant enhancements in predictive performance for processes delineated by a normalized spectral width parameter below 0.8.

Optimal parameters identification for PEMFC using autonomous groups particle swarm optimization algorithm

The precise model for Polymer Electrolyte Membrane Fuel Cells (PEMFCs) is vital for simulation, control, and performance analysis of PEMFCs. It is crucial to accurately estimate the model parameters. Over the past decade, the extraction of unknown parameters of PEMFCs model is formulated as optimization problem and several meta-heuristic techniques have emerged to solve this problem. Despite the development of these techniques to tackle the problem, the slow convergence rate and susceptibility to being trapped in local minima are regarded as weaknesses of these methods. Additionally, because the PEMFC model is a nonlinear and complex model, not all optimization algorithms are suitable for solving it. This article introduces a novel approach that utilizes the Autonomous Groups Particle Swarm Optimization (AGPSO) algorithm for extracting precise values for uncertain parameters inherent in PEMFC model of 250Wstack and BCS-500W stack utilized significantly in the literature. The optimization problem's fitness function is formulated as the total squared errors (TSEs) between the voltage datasets measured and estimated. Three different versions of AGPSO algorithm are presented. Statistical analysis is performed on these three versions to assess their robustness, and the most robust version is identified. Furthermore, the performance of the most robust version is extensively tested and analyzed through a complete comparison with recent optimization algorithms findings from the updated state-of-the-art literature such as BO, QOBO, TGA, HHO and ASO. Further, a statistical analysis was carried out that ensured the reliability and robustness of the introduced AGPSO. The results highlight the efficacy and feasibility of AGPSO-based approach across all compared algorithms, demonstrating an enhancement in the accuracy of the PEMFC model. A two-phase sensitivity analysis, conducted through Monte Carlo Simulation (MCS), was employed to assess how variations in optimized parameters affect the objective function (TSEs). Furthermore, the uncertainty in the maximum power reference current is identified.

Event‐triggered obstacle avoidance control for autonomous surface vehicles with actuator faults

AbstractThe article addresses the event‐triggered obstacle avoidance control problem for autonomous surface vehicles subject to actuator faults. In order to tackle the challenges presented by unknown actuator faults, internal model uncertainties, and external disturbances, we propose a fault‐tolerant control scheme that relies on an extended state observer to estimate the unknown parameters. In addition, considering the occurrence of actuator faults, a novel event‐triggered mechanism is developed to reduce wear of actuator and ensures the performance of system. On this basis, we employ backstepping technique and an improved artificial potential function methods to develop an event‐triggered obstacle avoidance control scheme with the capability of fault tolerance. This proposed control strategy ensures the uniform ultimate boundedness of tracking errors. In contrast to existing results, the presented control strategy simultaneously holds the performance of obstacle avoidance and fault tolerance and reduce the update frequency of actuators. The effectiveness of the provided control scheme has been confirmed through simulation.

Damping accumulative NDAGM(1,N, α) power model and its applications

PurposeIn this essay, a new NDAGM(1,N,α) power model is recommended to resolve the hassle of the distinction between old and new information, and the complicated nonlinear traits between sequences in real behavior systems.Design/methodology/approachFirstly, the correlation aspect sequence is screened via a grey integrated correlation degree, and the damped cumulative generating operator and power index are introduced to define the new model. Then the non-structural parameters are optimized through the genetic algorithm. Finally, the pattern is utilized for the prediction of China’s natural gas consumption, and in contrast with other models.FindingsBy altering the unknown parameters of the model, theoretical deduction has been carried out on the newly constructed model. It has been discovered that the new model can be interchanged with the traditional grey model, indicating that the model proposed in this article possesses strong compatibility. In the case study, the NDAGM(1,N,α) power model demonstrates superior integrated performance compared to the benchmark models, which indirectly reflects the model’s heightened sensitivity to disparities between new and old information, as well as its ability to handle complex linear issues.Practical implicationsThis paper provides a scientifically valid forecast model for predicting natural gas consumption. The forecast results can offer a theoretical foundation for the formulation of national strategies and related policies regarding natural gas import and export.Originality/valueThe primary contribution of this article is the proposition of a grey multivariate prediction model, which accommodates both new and historical information and is applicable to complex nonlinear scenarios. In addition, the predictive performance of the model has been enhanced by employing a genetic algorithm to search for the optimal power exponent.

Generalized data thinning using sufficient statistics

Our goal is to develop a general strategy to decompose a random variable X into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural exponential families, X can be thinned into independent random variables X ( 1 ) , … , X ( K ) , such that X = ∑ k = 1 K X ( k ) . These independent random variables can then be used for various model validation and inference tasks, including in contexts where traditional sample splitting fails. In this paper, we generalize their procedure by relaxing this summation requirement and simply asking that some known function of the independent random variables exactly reconstruct X. This generalization of the procedure serves two purposes. First, it greatly expands the families of distributions for which thinning can be performed. Second, it unifies sample splitting and data thinning, which on the surface seem to be very different, as applications of the same principle. This shared principle is sufficiency. We use this insight to perform generalized thinning operations for a diverse set of families.

Evaluating the quantum optimal biased bound in a unitary evolution process

Seeking the available precision limit of unknown parameters is a significant task in quantum parameter estimation. One often resorts to the widely utilized quantum Cramér–Rao bound (QCRB) based on unbiased estimators to finish this task. Nevertheless, most actual estimators are usually biased in the limited number of trials. For this reason, we introduce two effective error bounds for biased estimators based on a unitary evolution process in the framework of the quantum optimal biased bound. Furthermore, we show their estimation performance by two specific examples of the unitary evolution process, including the phase encoding and the SU(2) interferometer process. Our findings will provide an useful guidance for finding the precision limit of unknown parameters.