Values Of Unknown Parameters Research Articles

A modified uncertain maximum likelihood estimation with applications in uncertain statistics

In uncertain statistics, the uncertain maximum likelihood estimation is a method of estimating the values of unknown parameters of an uncertain statistical model that make the observed data most likely. However, the observed data obtained in practice usually contain outliers. In order to eliminate the influence of outliers when estimating unknown parameters, this article modifies the uncertain maximum likelihood estimation. Following that, the modified uncertain maximum likelihood estimation is applied to uncertain regression analysis, uncertain time series analysis, and uncertain differential equation. Finally, some real-world examples are provided to illustrate the modified uncertain maximum likelihood estimation.

Infrared spectroscopy and chemometric modelling of organic carbon measured by Rock-Eval pyrolysis of UK shale rock

Abstract Shale rock core from the Bowland Shale Formation, UK, was analysed in the laboratory using Rock-Eval pyrolysis and Fourier transform infrared spectroscopy (FTIR). These methods are used to characterize the organic constituents of soil and rock. This research is a proof-of-concept study to investigate whether regression models developed using FTIR and Rock-Eval data for the same length of core can be used to estimate selected Rock-Eval parameters. The accuracy of the regression models was assessed using statistical methods, the results of which were used to choose preferred models for each Rock-Eval parameter. The models produced were shown to have an acceptable level of uncertainty for total organic carbon and S1, S2 and S3 outputs, which led us to conclude that these are potentially suitable for estimating unknown down-core Rock-Eval parameter values. Conversely, the model for the temperature of the maximum rate of hydrocarbon generation ( T max ) had higher variability in the cross-validation data above the acceptable level of uncertainty, which could lead to erroneous estimates. Down-core interpolations of selected Rock-Eval parameters could be practically achieved by modelling FTIR data by maintaining standard sample frequencies for Rock-Eval while supplementing with higher frequencies for FTIR and chemometric analysis.

On the limit distribution of the power function induced by a design prior

The hybrid frequentist-Bayesian approach to sample size determination is based on the expectation of the power function of a test with respect to a design prior for the unknown parameter value. In clinical trials this quantity is often called probability of success (PoS). Determination of the limiting value of PoS as the number of observations tends to infinity, that is crucial for well defined sample size criteria, has been considered in previous articles. Here, we focus on the asymptotic behavior of the whole distribution of the power function induced by the design prior. Under mild conditions, we provide asymptotic results for the three most common classes of hypotheses on a scalar parameter. The impact of the design parameters choice on the distribution of the power function and on its limit is discussed.

Modelling optimal control of air pollution to reduce respiratory diseases

Respiratory diseases caused by inhalation of air pollutants are affected by seasonal changes and mitigated by air pollution control, resulting in complex dynamics. In order to investigate the effects of various factors such as random noise and air pollution control on respiratory diseases, we developed deterministic and stochastic two-dimensional coupled SIS models with multiple control measures. The proposed models and parameter estimation methods, including determinations of unknown parameter values, were used to fit the Air Quality Index (AQI) data for Xi’an city in recent 10 years. The existence of the optimal solutions for the deterministic and stochastic models were analyzed theoretically and provided to compare the parameter fitting solutions with the optimal solutions, and give theoretical support for seeking a more reasonable air pollution optimization prevention and control scheme. To show this, we conducted numerical simulations of the optimal control solution and state evolution trajectories under different weight coefficient ratios and control objectives. The results show that the stochastic optimal control problem is more consistent with the practical scenario. We also formulate the optimal control problem assuming that the control variable depends on the concentration of air pollutants. The optimal control solution reflected the periodic variation of the air pollution control strategy well. A comparison of cost values for different combinations of the three control measures illustrated that air pollution reduction is the most effective control measure.

Krori–Barua Bardeen compact stars in [formula omitted] gravity

The current study emphasizes the impact of electric charge for static spherically symmetric stellar structures using isotropic distribution in f(R,T) theory of gravity. For this purpose, we assume the Krori–Barua metric potential, ν(r)=Br2+C and λ(r)=Ar2, where A,B and C are the unknowns constants. The simplified phenomenological MIT bag equation of state, p=13(ρ−4Bg), and a precise form of electrical charge distribution q(r)=Q(rR)3=χr3 to be evaluated for the solution of Einstein–Maxwell field equations. To get the value of unknown parameters of the compact structures, we compare the Krori–Barua spacetime to external Bardeen geometry. Moreover, we examine the physical attributes of compact objects by presuming three viable f(R,T) models. We analyze the graphical behavior of density and pressure, the Tolman–Oppenheimer–Volkov equation, energy conditions, mass function, surface redshift, and adiabatic index. It is recognized that all the obtained results deliver emphatic evidence for the stability of our considered realistic stars.

L-SHADE with parameter decomposition for photovoltaic modules parameter identification under different temperature and irradiance

The performance of photovoltaic (PV) system relies on the accurate determination of unknown parameters in PV models, such as photo-generated current, diode current, and resistance. These unknown parameters may vary with different temperature and irradiance conditions, which greatly increases the difficulty of identifying these unknown parameters. Although some parameter identification methods have been proposed to solve such a problem, the accuracy and reliability of solutions obtained by these methods suffers from great challenges when temperature and irradiance are changing. In this paper, a simple and effective approach called success-history adaptation differential evolution with linear population size reduction (L-SHADE) and decomposition referred as (L-SHADED), is presented to accurately and reliably identify the unknown parameters of PV models under different temperature and irradiance. In L-SHADED, firstly, an unknown parameters decomposition technique is used to reduce the complexity of the problem. Then an advanced evolutionary algorithm L-SHADE is employed to identify the optimal unknown parameter values. The performance of proposed L-SHADED has been investigated by testing two single-diode-based PV modules (multi-crystalline KC200GT and mono-crystalline SM55) under different temperature and irradiance. The experimental comparison results demonstrate that proposed L-SHADED is almost 10 times smaller in RMSE than other methods. Furthermore, the coefficient of determination of L-SHADED reaches 1.0 in almost all conditions, which indicates that the parameters identified by L-SHADED are quite accurate.

An accurate method for parameter estimation of proton exchange membrane fuel cell using Dandelion optimizer

Abstract The Proton Exchange Membrane Fuel Cell (PEMFC) has found widespread use for regulated output voltage applications because of its quick response time and mobility. A different form of hydrogen is employed in fuel cell-based electric vehicles for smart transportation for the reduction of global warming and the development of smart cities. To properly manage the operation of Fuel Cells (FCs), there is a need for accurate modeling. One of the most common challenges is finding the exact values of unknown parameters in the PEMFC. In the current study, a new method called Dandelion Optimizer (DO) is used for parameter identification. DO is used to estimate the parameters of the PEMFC based on Current-Voltage (I-V) characteristics. The Ballard Mark V and BCS 500-W PEMFC stacks use the DO method to identify unknown parameters. The performance of the DO algorithm is compared to that of other optimization techniques and the Sum of Squared Errors (SSE) is used to represent the objective function of the current optimization problem. In contrast to traditional and other efficient techniques, the simulation results proposed by the DO algorithm have excellent accuracy in extracting the PEMFC optimal parameters.

Development of technology for standardization of parameters of winter route registration of game animals

The need to develop a new technology for planning survey routes is caused not only by the difficulty of implementing the recommendations of the current methodology for winter route accounting (ZMU) for the “equidistant placement” of survey routes with “observance of a proportional survey of land categories forest, field, swamp”, but also by the inability of the method of grouping the sample into categories of land to reduce the heterogeneity of the examined material. To standardize the placement of accounting routes, the technology of stratification of the territory is put, in which the virtual boundaries of the stratum serve to determine the extrapolation area and the location of the survey route. For the total area of the hunting farm, a tabular, or calculated (for farms with a different area), value of the route length standard, km/thousand ha, is established. The free navigation program SAS Planet determines the length and width of the territory within the boundaries of the hunting area and the principle layout of the registration routes in the strata. According to the algorithms, the following parameters are calculated: the total length of the routes, the average values of the length and width of the territory, the number of strata, the distance between the registration routes, the length of the route in the stratum, the area of the strata, which are necessary for designing the stratification of the territory. On the example of a specific farm with unknown values of parameters, except for the area of the territory, the suitability of algorithms for calculating parameters is shown; a map of the boundaries of the strata and the location of the accounting traces was created; the area of the strata and the design length of the registration route in each stratum were determined; digitized files of traces necessary for work on their reference to the terrain have been created; the technology of binding is given. The results of the study confirmed the manufacturability and simplicity of the method for localizing routes and extrapolation sites, as well as the compatibility of their ordered placement in compliance with a standardized sample size for territories with any area and boundary configuration.

Building energy model calibration using a surrogate neural network

Energy studies of buildings are becoming more widespread as stakeholders strive to improve energy efficiency and reduce carbon emissions. As a result, there is an increased need for novel numerical techniques to automatically calibrate building energy models (BEMs) for these energy studies. In this paper, a new automated building calibration methodology was developed, which uses a surrogate (i.e., meta) multilayer perceptron artificial neural network (ANN) to infer unknown building parameters. Typically, in the field of BEM calibration, surrogate models are used as a time-saving technique. Instead of running the building simulation software during each iteration of an optimization search, a surrogate model can approximate the output of the BEM very quickly, leading to much faster optimization of the unknown building parameters. However, we show that, once trained, the surrogate model itself can be used to find the unknown building parameters. Since the surrogate model is differentiable, gradient descent can be used to find the building parameters that minimize the error between true and predicted metered energy consumption. Previous surrogate modeling approaches for calibrating BEMs map only the unknown building parameters to the BEM’s output. As a result, they are blind to the effects of other crucial variables like weather and the building’s schedules. On the other hand, our surrogate ANN model accounts for these other predictors of energy consumption. With this advantage, our method was able to outperform a powerful black box optimizer when finding 14 unknown building parameter values in a controlled case study with hourly energy data. In a real metered data case study, our ANN method and the black box optimizer performed similarly on average, but our method had less variance in performance across trials.

Shortest Confidence Intervals for Weibull Modulus for Small Samples in Materials Reliability Analysis

The Weibull distribution has been widely used to model strength properties of brittle materials. Estimation of confidence intervals for Weibull shape parameter has been an important concern, since small sample sizes in materials science experiments bring about large intervals. Many methods have been proposed in the literature for constructing shorter intervals; the methods of maximum likelihood, least square, and Menon are among the most extensively studied methods. However, they all use an equal-tails approach. The pivotal quantities used for constructing confidence intervals have right-skewed and unimodal distributions, thus, they clearly do not produce the shortest intervals for a given confidence level in equal tail form. This study constructs the shortest confidence intervals for the three aforementioned methods and compares their performances by their equal-tails counterparts. To this end, a comprehensive simulation study has been conducted for the shape parameter values between 1 to 80 and the sample sizes between 3 to 20. The comparison criterion is chosen as the expected interval length. The results show that the shortest confidence intervals in each of three methods have yielded considerably narrower intervals. Further, the unknown parameter values are more centered in these intervals.

Role of theory on charged compact stars

The main purpose of this paper is to examine the viable attributes of charged compact stellar objects with anisotropic matter configuration in the framework of theory. For this purpose, we use Tolman V solution and consider a specific functional form of this modified theory to examine the geometry of compact stars. The values of unknown parameters are found by the smooth matching of interior (static spherical metric) and exterior (modified Reissner-Nordstrom metric) spacetimes. We investigate the behavior of effective matter variables, anisotropy, equation of state parameters and energy bounds in the interior of the charged stellar objects. The stability of the compact stars is examined by speed of sound and adiabatic index. We find that the considered stars are viable as well as stable with all the required conditions in this modified theory of gravity.

Study of Charged Anisotropic Karmarkar Stars in f(R,T2)$f(\mathcal {R},\mathbb {T}^{2})$ Theory

AbstractThis paper examines the viable attributes of charged compact stars with anisotropic matter configuration in theory. For this purpose, we use the embedding class‐1 technique and consider a specific functional form of this modified theory, i.e, to examine the geometry of compact objects. The values of unknown parameters are found by the smooth matching of interior (static spherical metric) and exterior (Reissner‐Nordstrom metric of energy‐momentum squared gravity) spacetimes. We investigate the impact of effective fluid parameters anisotropy, equation of state parameters and energy bounds in the inner region of the charged stellar objects. The stability of the stellar models in the presence of charge is examined by speed of sound and adiabatic index. We find that embedding class‐1 solution is physically viable and stable for charged anisotropic stellar objects in this modified theory.

Parameter Estimation Analysis in a Model of Honey Production

Honeybee losses are an extensive global problem. In this study, a new compartment model of honeybee population that mainly concerns honey production is developed. The model describes the interaction of the food stock with the brood (immature bees), adult bees and produced honey. In the present paper, the issue of an adequate model recovery is addressed and the parameter identification inverse problem is solved. An adjoint equation procedure to obtain the unknown parameter values by minimizing the functional error during a period of time is proposed. Numerical simulations with realistic data are discussed.

Optimal Parameter Estimation of Solar Photovoltaics Through Nature Inspired Metaheuristic and Hybrid Approaches

Estimation of solar photovoltaic (PV) equivalent model parameters through the manufacturer's datasheet or experimental performance current voltage (I-V) characteristics is an apprehension among researchers. In this paper, two approaches are instigated and compared i.e. metaheuristic pheromone value black widow optimisation (pv-BWO) and hybrid sailfish optimisation (h-SFO) for the estimation of a single-diode model (SDM) and double-diode model (DDM) parameters for the accurate solar PV modelling. Four distinct case studies that incorporate four different PV modules i.e. RTC France, PWP 201, SHARP ND-R250A5, and EIL 75W PV are investigated, where the validation of the proposed methods is carried out through the experimental performance characteristics of solar PV under test i.e. the I-V and power-voltage (P-V) performance characteristics. Moreover, the performance is evaluated on various error functions, and experimental I-V and P-V characteristics, where the results are also compared with the various techniques of parameter estimation in the literature. It is important to underline that the closeness of the objective function to zero exhibits the congruence of estimated parameters with the exact parameters, where the exact parameter value is not accessible. Therefore, the preciseness rests on the experimental data only, where any significant reduction in OF i.e. RMSE considered as an improvement towards the exactness of real unknown parameter values. The pv-BWO exhibits an average of 69.89% of lower error results when compared with few existing methods, whereas h-SFO recorded a higher RMSE of about 93% when compared with the pv-BWO which suggests the suitability of pv-BWO over h-SFO and few existing methods.

Soliton solutions of the (2+1)-dimensional Kadomtsev–Petviashvili equation via two different integration schemes

In this research paper, we take into account the ([Formula: see text])-dimensional Kadomtsev–Petviashvili equation which is important in the soliton theory of nonlinear physics. To get the desired soliton solutions, the modified F-expansion method using the Riccati equation which has many solution functions, as well as the modified generalized Kudryashov’s method, had been effectively implemented. One of the reasons for the preference of the methods is that the proposed methods have been widely used before and they have not been applied to this problem. First, the wave transform is applied to the considered nonlinear partial differential equation (NLPDE), the nonlinear ordinary differential equation (NODE) form and the balancing constant are determined. The next step is to use the auxiliary equation depending on the proposed method to find the solution of the NODE form and to obtain the linear algebraic equation system. The solution of this system gives different solution sets for unknown parameter values. Then, soliton solution functions are constructed by using the suitable solution sets. After testing and confirming that the obtained solution functions satisfy the main equation, the three- and two-dimensional illustrations are depicted.

Проблема оценки точности параметров цунамиактивности

The subject of the article is the theoretical development of the probabilistic model for a Poisson-type tsunami sequence that is consistent with data on the manifestations of historical events, in order to obtain estimates of the accuracy of the tsunami activity parameters. An example of a tsunami recurrence function, which is the most important quantitative characteristic of tsunami activity for the Port of Malokurilskoye, one of the places in the South Kuril Islands region with the most reliable tsunami height dataset, was created on the basis of a theoretical essay. An explanation for the weak statistical stability of all large values of the tsunami heights, especially for the largest one in the series of observations, was given based on the probability density functions of the ranked tsunami heights. In particular, it means, for example, that the maximum tsunami height recorded at a certain location during a 30-year observation period should be correlated with a wide range of possible recurrence periods of about 10 to 100 years. Synthetic catalogs of the tsunami heights, built for the Port of Malokurilskoye, showed that the tsunami height datasets with a duration of at least 250 or 500 years without gaps are needed to obtain the tsunami activity parameters with an acceptable accuracy of 10 or 5 %. The most important results are the analytical equations for the variances of estimates of the tsunami activity parameters, which characterize the accuracy of these estimates, depending on a priori unknown values of the tsunami activity parameters and the amount of data used.

Fitness Dependent Optimizer Based Computational Technique for Solving Optimal Control Problems of Nonlinear Dynamical Systems

This paper presents a pragmatic approach established on the hybridization of nature-inspired optimization algorithms and Bernstein Polynomials (BPs), achieving the optimum numeric solution for Nonlinear Optimal Control Problems (NOCPs) of dynamical systems. The approximated solution for NOCPs is obtained by the linear combination of BPs with unknown parameters. The unknown parameters are evaluated by the conversion of NOCP to an error minimization problem and the formulation of an objective function. The Fitness Dependent Optimizer (FDO) and Genetic Algorithm (GA) are used to solve the objective function, and subsequently the optimal values of unknown parameters and the optimum solution of NOCP are attained. The efficacy of the proposed technique is assessed on three real-world NOCPs, including Van der Pol (VDP) oscillator problem, Chemical Reactor Problem (CRP), and Continuous Stirred-Tank Chemical Reactor Problem (CSTCRP). The final results and statistical outcomes suggest that the proposed technique generates a better solution and surpasses the recently represented methods in the literature, which eventually verifies the efficiency and credibility of the recommended approach.

Trajectory Tracking Control of a Mobile Robot with the ROS System

This article provides a simulation and laboratory study of a control system for a two-wheeled differential-drive mobile robot with ROS system. The authors propose an approach to designing a control system based on a parametric model of the robot’s dynamics. The values of unknown parameters of the dynamic model have been determined by means of a Levenberg-Marguardt identification method. By comparing the desired trajectories with those obtained from simulation and laboratory tests, and based on errors analysis, the correctness of the model parameter identification process and the control system operation was then determined.

Path Loss Modelling for High Speed Rail in 5G Communication System

A new path loss model for high-speed rail (HSR) in the 5G communication system is constructed in this paper. The model is identified to obtain an accurate mathematical representation of path loss multipath propagation in line of sight of HSR scenarios. The grey box modelling utilization of Generalized Reduced Gradient (GRG) and Genetic algorithm (GA) is applied to find the unknown parameters of the constructed path loss model since some uncertainties in obtaining the corresponded parameters are unavoidable to be collected in the field. Both algorithms achieve excellent results in finding the unknown parameter values with RMSE and MAPE evaluation which are converging finally to 2.779 and 1.701 %. The visualization of fitting plots is also presented, and GA provides a better-adjusted agreement with the measurement dataset of HSR. Accordingly, the constructed path loss model is successfully validated since it is capable of following

Non-parametric data-driven background modelling using conditional probabilities

Background modelling is one of the main challenges in particle physics data analysis. Commonly employed strategies include the use of simulated events of the background processes, and the fitting of parametric background models to the observed data. However, reliable simulations are not always available or may be extremely costly to produce. As a result, in many cases uncertainties associated with the accuracy or sample size of the simulation are the limiting factor in the analysis sensitivity. At the same time, parametric models are limited by the a priori unknown functional form and parameter values of the background distribution. These issues become ever more pressing when large datasets become available, as it is already the case at the CERN Large Hadron Collider, and when studying exclusive signatures involving hadronic backgrounds.A widely applicable approach for non-parametric data-driven background modelling is proposed, which addresses these issues for a broad class of searches and measurements. It relies on a relaxed version of the event selection to estimate conditional probability density functions and two different techniques are discussed for its realisation. The first relies on ancestral sampling and uses data from a relaxed event selection to estimate a graph of conditional probability density functions of the variables used in the analysis, while accounting for significant correlations. A background model is then generated from events drawn from this graph, on which the full event selection is applied. In the second, a novel generative adversarial network is trained to estimate the joint probability density function of the variables used in the analysis. The training is performed on a relaxed event selection, which excludes the signal region, and the network is conditioned on a blinding variable. Subsequently, the conditional probability density function is interpolated into the signal region to model the background. The application of each method on a benchmark analysis and on ensemble tests is presented in detail, and the performance is discussed.