Rapid Parameter-Optimizing Strategy for Plug-and-Play Devices in DC Distribution Systems under the Background of Digital Transformation

By integrating advanced digital technologies such as cloud computing and the Internet of Things in sensor measurement,information communication,and other fields,the digital DC distribution network can efficiently and reliably access DistributedGenerator(DG)and Energy Storage Systems(ESS),exhibiting significant advantages in terms of controllability and meeting requirements of Plug-and-Play(PnP)operations.However,during device plug-in and-out processes,improper systemparametersmay lead to small-signal stability issues.Therefore,before executing PnP operations,conducting stability analysis and adjusting parameters swiftly is crucial.This study introduces a four-stage strategy for parameter optimization to enhance systemstability efficiently.In the first stage,state-of-the-art technologies in measurement and communication are utilized to correct model parameters.Then,a novel indicator is adopted to identify the key parameters that influence stability in the second stage.Moreover,in the third stage,a local-parameter-tuning strategy,which leverages rapid parameter boundary calculations as a more efficient alternative to plotting root loci,is used to tune the selected parameters.Considering that the local-parameter-tuning strategy may fail due to some operating parameters being limited in adjustment,a multiparameter-tuning strategy based on the particle swarm optimization(PSO)is proposed to comprehensively adjust the dominant parameters to improve the stability margin of the system.Lastly,system stability is reassessed in the fourth stage.The proposed parameter-optimization strategy’s effectiveness has been validated through eigenvalue analysis and nonlinear time-domain simulations.

A New Three-Parameter Inverse Weibull Distribution with Medical and Engineering Applications

The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.

Reliability-based Robust Optimization Design of Automobile Components with Non-normal Distribution Parameters

In the reliability designing procedure of the vehicle components, when the distribution styles of the random variables are unknown or non-normal distribution, the result evaluated contains great error or even is wrong if the reliability value R is larger than 1 by using the existent method, in which case the formula is necessary to be revised. This is obviously inconvenient for programming. Combining reliability-based optimization theory, robust designing method and reliability based sensitivity analysis, a new method for reliability robust designing is proposed. Therefore the influence level of the designing parameters’ changing to the reliability of vehicle components can be obtained. The reliability sensitivity with respect to design parameters is viewed as a sub-objective function in the multi-objective optimization problem satisfying reliability constraints. Given the first four moments of basic random variables, a fourth-moment technique and the proposed optimization procedure can obtain reliability-based robust design of automobile components with non-normal distribution parameters accurately and quickly. By using the proposed method, the distribution style of the random parameters is relaxed. Therefore it is much closer to the actual reliability problems. The numerical examples indicate the following: (1) The reliability value obtained by the robust method proposed increases (】0.04%) comparing to the value obtained by the ordinary optimization algorithm; (2) The absolute value of reliability-based sensitivity decreases (】0.01%), and the robustness of the products’ quality is improved accordingly. Utilizing the reliability-based optimization and robust design method in the reliability designing procedure reduces the manufacture cost and provides the theoretical basis for the reliability and robust design of the vehicle components.

A Novel Modified Alpha Power Transformed Weibull Distribution and Its Engineering Applications

This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha power transformed Weibull distribution.The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions,which are quite familiar in environmental investigations.Its hazard rate function can be decreasing,increasing,bathtub and upside-down then bathtub shaped.Diverse structural properties of the proposed model are acquired including quantile function,moments,entropies,order statistics,residual life and reversed failure rate function.The parameters of the distribution were estimated using the maximum likelihood function.The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed.Via a simulation study,the performance of the point and interval estimates are compared using different criteria.Employing real lifetime data sets,we verify that the offered model furnishes a better fit than some other lifetime models including Weibull,gamma and alpha powerWeibull models.

On Relations for Moments of Generalized Order Statistics for Lindley–Weibull Distribution

Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.

Statistical Inference of Truncated Weibull-Rayleigh Distribution: Its Properties and Applications

In this paper, we derived a new distribution named as truncated Weibull Rayleigh (TW-R) distribution. Its characterization and statistical properties are obtained, such as reliability function, hazard function, reversed hazard rate function, cumulative hazard rate function, quantile function, rth moment, incomplete moments, Rényi and q entropies and order statistic. Parameter estimation is implemented using method of maximum-likelihood estimation and Fisher information matrix is derived. Finally, application of the presented new distribution to a real data representing the failure times of 63 airbcraft Windshield is given and its goodness-of-fit is demonstrated. In addition to, comparisons to other models are implemented to show the flexibility of the presented model.

On a New Version of Weibull Model:Statistical Properties,Parameter Estimation and Applications

In this paper,we introduce a new four-parameter version of the traditional Weibull distribution.It is able to provide seven shapes of hazard rate,including constant,decreasing,increasing,unimodal,bathtub,unimodal then bathtub,and bathtub then unimodal shapes.Some basic characteristics of the proposedmodel are studied,including moments,entropies,mean deviations and order statistics,and its parameters are estimated using the maximum likelihood approach.Based on the asymptotic properties of the estimators,the approximate confidence intervals are also taken into consideration in addition to the point estimators.We examine the effectiveness of the maximum likelihood estimators of the model’s parameters through simulation research.Based on the simulation findings,it can be concluded that the provided estimators are consistent and that asymptotic normality is a good method to get the interval estimates.Three actual data sets for COVID-19,engineering and blood cancer are used to empirically demonstrate the new distribution’s usefulness inmodeling real-world data.The analysis demonstrates the proposed distribution’s ability in modeling many forms of data as opposed to some of its well-known sub-models,such as alpha powerWeibull distribution.

The Distribution Population-based Genetic Algorithm for Parameter Optimization PID Controller

Enlightened by distribution of creatures in natural ecology environment, the distributionpopulation-based genetic algorithm (DPGA) is presented in this paper. The searching capability ofthe algorithm is improved by competition between distribution populations to reduce the search zone.This method is applied to design of optimal parameters of PID controllers with examples, and thesimulation results show that satisfactory performances are obtained.

Interval Estimation in a Two Parameter Weibull Distribution Based on Type-2 Censored Data

In this paper, we consider the construction of the approximate profile- likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.

Evaluation of the location parameter in Weibull distribution of CTOD testing results of high strength steel weldments

In this paper, the location parameter δ_(a) in Weibull distribution i.e. the lower limiting CTOD toughness of high strength steel weldments is evaluated from Gleeble simulated coarse grained specimens. The Charpy-V transition temperature obtained from these specimens is transformed to a fracture toughness K_(IC) value at a given temperature using Sanz' relation. Then, the location parameter a is δ_(a) evaluated. The predicted location parameter arrives at agreement with the lowest CTOD value as obtained from thick multilayer weldments. The improvement of the fracture toughness of multilayer weldments needs the increase of the lowering limiting CTOD.toughness i.e. the toughness of the coarse grained zone.

Parameter Estimation of Mixed Weibull Distributions Using Cuckoo Search

The lifetime data of products with multiple failure modes which are collected from life testing are often fitted by the mixed Weibull distributions. Since the mixed Weibull distributions contain no less than five parameters,the parameter estimation is difficult and inaccurate. In order to enhance the accuracy,a new method of parameter estimation based on Cuckoo search( CS) is proposed. An optimization model for the mixed Weibull distribution is formulated by minimizing the residual sum of squares. The optimal parameters are searched via CS algorithm. In the case study,the lifetime data come from the life testing of diesel injectors and are fitted by the twocomponent Weibull mixture. Regarding the maximum absolute error and the accumulative absolute error between estimated and observed values as the accuracy index of parameter estimation,the results of four parameter estimation methods that the graphic estimation method,the nonlinear least square method,the optimization method based on particle swarm optimization( PSO) and the proposed method are compared. The result shows that the proposed method is more efficient and more accurate than the other three methods.

Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana

Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.

Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana

Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.

Multi-Model Based PSO Method for Burden Distribution Matrix Optimization With Expected Burden Distribution Output Behaviors

Burden distribution is one of the most important operations, and also an important upper regulation in blast furnace(BF) iron-making process. Burden distribution output behaviors(BDOB) at the throat of BF is a 3-dimensional spatial distribution produced by burden distribution matrix(BDM),including burden surface output shape(BSOS) and material layer initial thickness distribution(MLITD). Due to the lack of effective model to describe the complex input-output relations,BDM optimization and adjustment is carried out by experienced foremen. Focusing on this practical challenge, this work studies complex burden distribution input-output relations, and gives a description of expected MLITD under specific integral constraint on the basis of engineering practice. Furthermore, according to the decision variables in different number fields, this work studies optimization of BDM with expected MLITD, and proposes a multi-mode based particle swarm optimization(PSO) procedure for optimization of decision variables. Finally, experiments using industrial data show that the proposed model is effective, and optimized BDM calculated by this multi-model based PSO method can be used for expected distribution tracking.

Performance of Weibull function as a diameter distribution model for Pinus thunbergii stands in the eastern coast of South Korea

This study was carried out to determine the performance of percentile-based Weibull diameter distribution model for Pinus thunbergii stands thriving along the eastern coast of South Korea. The parameter recovery technique was used to estimate the three parameters of the Weibull model. The analysis demonstrated satisfactory results based on the following test statistics for the principal percentile models： fit index （FI） range from 0.501（minimum diameter） to 0.932 （50th diameter percentiles） and root mean square error （RMSE） range from 0.112 （quadratic mean diameter） to 3.572 （minimum diameter）. The developed model was further evaluated by determining the mean bias （E） in trees per ha （TPH） for each diameter class, and the results showed highest over-prediction in the 20 cm, and under-prediction in the x6 cm and 24 cm diameter classes. The goodness of fit tested by Kolmogorov- Smirnov （KS） test showed no significant differences （P〉0.05） between the observed and predicted diameter distributions for almost all plots. Using site index and aboveground biomass （AGB） models developed for P. thunbergii in South Korea, a model to predict the AGB per ha for each diameter class and subsequently the total AGB of the stand was created. An application guide was also created, which will serve as a decision-support tool for forest managers in quantifying the future total AGB in P. thunbergii stands located in the eastern coast of South Korea and, subsequently, the quantification of potential carbon stocks aside from being a vital input in designing efficient management and protection strategies for these stands.

The Marshall-Olkin Right Truncated Fréchet-Inverted Weibull Distribution: Its Properties and Applications

In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.

Estimation of Fading Statistics of Nakagami Channel with Weibull Distributed Tolerable Outage Time

Characterization of a mobile radio channel plays an important role in designing a reliable wireless communication system. Such channels are analyzed by two state model, namely satisfactory and outage state. This paper presents the analysis to estimate fading parameters of wireless channel with omission of certain outage durations which are considered as “Tolerance time”. Minimum outage duration which can be tolerated by a wireless fading channel to achieve desired packet error rate is defined as tolerance time. Normally a system with tolerable minimum outage time is analyzed based on Fade Duration Distribution (FDD) function over Rayleigh channel. In this paper Weibull function is used as FDD for varying tolerance time. The approach is simple and in general applicable from Rayleigh to Nakagami channels. The analysis is extended to study the effect of Tolerance time on channel fading statistics such as Average Fade Duration (AFD) and frequency of outage. Further the effects of various fade margin and Doppler spread on fading parameters are also investigated. The analysis can also be used in case of timeout expiration, connection resetting and congestion window control.

Gumbel-Exponentiated Weibull {Logistic} Lifetime Distribution and Its Applications

A new generalized exponentiated Weibull model called Gumbel-exponentiated Weibull {Logistic} distribution is introduced and studied. The new distribution extends the exponentiated Weibull distribution with additional parameters and bimodal densities. Some new and earlier distributions formed the sub-models of the proposed distribution. The mathematical properties of the new distribution including expressions for the hazard function, survival function, moments, order statistics, mean deviation and absolute mean deviation from the mean, and entropy were derived. Monte Carlo simulation study was carried out to assess the finite sample behavior of the parameter estimates by maximum likelihood estimation approach. The superiority of the new generalized exponentiated Weibull distribution over some competing distributions was proved empirically using the fitted results from three real life datasets.

One-sided empirical Bayes test for location parameter in Gamma distribution

In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.

Coverage-optimization based guidance of mobile agents for improved control of distributed parameter systems

The control problem of a class of parabolic distributed parameter systems (DPSs) is investigated by using mobile agents with capabilities of sensing and actuating. The guidance strategies of mobile agents based on coverage optimization methods are proposed to improve the control performance of the system and make the state norm of the system converge to zero faster. The coverage optimization problems are constructed based on the measurement of each agent. By solving the coverage optimization problems, the local optimal moving direction of each agent can be obtained. Then the gradient-based agent motion control laws are established. With the indicator function and the surface delta function, this method is generalized to n-dimensional space, and suitable for any sensing region with piecewise smooth boundaries. The stability and control performance of the system are analyzed. Numerical simulations show the effectiveness of the proposed methods.