ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA

Abstract. A grouped data model for Weibull distribution is considered. Under mild con-ditions, the maximum likelihood estimators(MLE) are shown to be identifiable, stronglyconsistent, asymptotically normal, and satisfy the law of iterated logarithm. Newton iter-ation algorithm is also considered, which converges to the unique solution of the likelihoodequation. Moreover, we extend these results to a random case.

STATISTICAL INFERENCE FOR A BIVARIATE EXPONENTIAL DISTRIBUTION BASED ON GROUPED DATA

Consider the bivariate exponential distribution due to Marshall and Olkin[2], whose survival function is F(x, g) = exp[-λ1x-λ2y-λ12 max(x, y)] (x 0,y 0)with unknown Parameters λ1 > 0, λ2 > 0 and λ12 0.Based on grouped data, a newestimator for λ1, λ2 and λ12 is derived and its asymptotic properties are discussed.Besides, some test procedures of equal marginals and independence are given. Asimulation result is given, too.

Modeling viscosity of methane,nitrogen,and hydrocarbon gas mixtures at ultra-high pressures and temperatures using group method of data handling and gene expression programming techniques

Accurate gas viscosity determination is an important issue in the oil and gas industries.Experimental approaches for gas viscosity measurement are timeconsuming,expensive and hardly possible at high pressures and high temperatures(HPHT).In this study,a number of correlations were developed to estimate gas viscosity by the use of group method of data handling(GMDH)type neural network and gene expression programming(GEP)techniques using a large data set containing more than 3000 experimental data points for methane,nitrogen,and hydrocarbon gas mixtures.It is worth mentioning that unlike many of viscosity correlations,the proposed ones in this study could compute gas viscosity at pressures ranging between 34 and 172 MPa and temperatures between 310 and 1300 K.Also,a comparison was performed between the results of these established models and the results of ten wellknown models reported in the literature.Average absolute relative errors of GMDH models were obtained 4.23%,0.64%,and 0.61%for hydrocarbon gas mixtures,methane,and nitrogen,respectively.In addition,graphical analyses indicate that the GMDH can predict gas viscosity with higher accuracy than GEP at HPHT conditions.Also,using leverage technique,valid,suspected and outlier data points were determined.Finally,trends of gas viscosity models at different conditions were evaluated.

Hourly traffic flow forecasting using a new hybrid modelling method

Short-term traffic flow forecasting is a significant part of intelligent transportation system.In some traffic control scenarios,obtaining future traffic flow in advance is conducive to highway management department to have sufficient time to formulate corresponding traffic flow control measures.In hence,it is meaningful to establish an accurate short-term traffic flow method and provide reference for peak traffic flow warning.This paper proposed a new hybrid model for traffic flow forecasting,which is composed of the variational mode decomposition(VMD)method,the group method of data handling(GMDH)neural network,bi-directional long and short term memory(BILSTM)network and ELMAN network,and is optimized by the imperialist competitive algorithm(ICA)method.To illustrate the performance of the proposed model,there are several comparative experiments between the proposed model and other models.The experiment results show that 1)BILSTM network,GMDH network and ELMAN network have better predictive performance than other single models;2)VMD can significantly improve the predictive performance of the ICA-GMDH-BILSTM-ELMAN model.The effect of VMD method is better than that of EEMD method and FEEMD method.To conclude,the proposed model which is made up of the VMD method,the ICA method,the BILSTM network,the GMDH network and the ELMAN network has excellent predictive ability for traffic flow series.

Real-Time and Intelligent Flood Forecasting Using UAV-Assisted Wireless Sensor Network

The Wireless Sensor Network(WSN)is a promising technology that could be used to monitor rivers’water levels for early warning flood detection in the 5G context.However,during a flood,sensor nodes may be washed up or become faulty,which seriously affects network connectivity.To address this issue,Unmanned Aerial Vehicles(UAVs)could be integrated with WSN as routers or data mules to provide reliable data collection and flood prediction.In light of this,we propose a fault-tolerant multi-level framework comprised of a WSN and a UAV to monitor river levels.The framework is capable to provide seamless data collection by handling the disconnections caused by the failed nodes during a flood.Besides,an algorithm hybridized with Group Method Data Handling(GMDH)and Particle Swarm Optimization(PSO)is proposed to predict forthcoming floods in an intelligent collaborative environment.The proposed water-level prediction model is trained based on the real dataset obtained fromthe Selangor River inMalaysia.The performance of the work in comparison with other models has been also evaluated and numerical results based on different metrics such as coefficient of determination(R2),correlation coefficient(R),RootMean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),and BIAS are provided.

Best compromising crashworthiness design of automotive S-rail using TOPSIS and modified NSGAⅡ

In order to reduce both the weight of vehicles and the damage of occupants in a crash event simultaneously, it is necessary to perform a multi-objective optimal design of the automotive energy absorbing components. Modified non-dominated sorting genetic algorithm II(NSGA II) was used for multi-objective optimization of automotive S-rail considering absorbed energy(E), peak crushing force(Fmax) and mass of the structure(W) as three conflicting objective functions. In the multi-objective optimization problem(MOP), E and Fmax are defined by polynomial models extracted using the software GEvo M based on train and test data obtained from numerical simulation of quasi-static crushing of the S-rail using ABAQUS. Finally, the nearest to ideal point(NIP)method and technique for ordering preferences by similarity to ideal solution(TOPSIS) method are used to find the some trade-off optimum design points from all non-dominated optimum design points represented by the Pareto fronts. Results represent that the optimum design point obtained from TOPSIS method exhibits better trade-off in comparison with that of optimum design point obtained from NIP method.

Parameters estimation and application of generalized exponential distribution under grouped and right-censored data

Generalized exponential distribution is a class of important distribution in lifedata analysis,especially in some skewed lifedata.The Parameter estimation problem for generalized exponential distribution model with grouped and right-censored data is considered.The maximum likelihood estimators are obtained using the EM algorithm.Some simulations are carried out to illustrate that the proposed algorithm is effective for the model.Finally,a set of medicine data is analyzed by generalized exponential distribution.

Estimation of dynamic stress spectrum distribution in structural fatigue test

The determination of structural dynamic stress spectrum distribution is of great signifi- cance in the structural fatigue strength evaluation as well as reliability design. In previous empirical data processing methods, the data grouping and distribution fitting were excessively coarse and contained distinctive defects. This paper proposed an effective approach to statistically group actual measured dynamic stress data and validly extrapolate the combined distribution to fit the dynamic stress spectrum distribution. This approach has been verified its effectiveness through chi-square test, stress spectrum extrapolation and damage calculation in dynamic stress study.

Global Solar Radiation Maps of Saudi Arabia

This paper uses Abductive network to predict global solar radiation in any location in the Kingdom of Saudi Arabia （KSA） based on sunshine duration, month number, latitude, longitude, and altitude of the location. Results indicate good agreement between measured and predicted GSR values for each of the 35 locations with known GSR values. Finally, the data from all available stations are used to train an abductive network to estimate the GSR values anywhere in the Kingdom based on latitude and longitude. GSR values are estimated using the developed method at 25 additional locations throughout the kingdom and used with the measured data from the 35 available measurement stations to draw a comprehensive contour map of GSR values for KSA.

Predicting beach profile evolution with group method data handling-type neural networks on beaches with seawalls

A major goal of coastal engineering is to develop models for the reliable prediction of short-and longterm near shore evolution.The most successful coastal models are numerical models,which allow flexibility in the choice of initial and boundary conditions.In the present study,evolutionary algorithms(EAs)are employed for multi-objective Pareto optimum design of group method data handling(GMDH)-type neural networks that have been used for bed evolution modeling in the surf zone for reflective beaches,based on the irregular wave experiments performed at the Hydraulic Laboratory of Imperial College(London,UK).The input parameters used for such modeling are significant wave height,wave period,wave action duration,reflection coefficient,distance from shoreline and sand size.In this way,EAs with an encoding scheme are presented for evolutionary design of the generalized GMDH-type neural networks,in which the connectivity configurations in such networks are not limited to adjacent layers.Also,multi-objective EAs with a diversity preserving mechanism are used for Pareto optimization of such GMDH-type neural networks.The most important objectives of GMDH-type neural networks that are considered in this study are training error(TE),prediction error(PE),and number of neurons(N).Different pairs of these objective functions are selected for two-objective optimization processes.Therefore,optimal Pareto fronts of such models are obtained in each case,which exhibit the trade-offs between the corresponding pair of the objectives and,thus,provide different non-dominated optimal choices of GMDH-type neural network model for beach profile evolution.The results showed that the present model has been successfully used to optimally prediction of beach profile evolution on beaches with seawalls.

Efficient Processing of Skyline Group Queries over a Data Stream

In this paper, we study the skyline group problem over a data stream. An object can dominate another object if it is not worse than the other object on all attributes and is better than the other object on at least one attribute. If an object cannot be dominated by any other object, it is a skyline object. The skyline group problem involves finding k-item groups that cannot be dominated by any other k-item group. Existing algorithms designed to find skyline groups can only process static data. However, data changes as a stream with time in many applications,and algorithms should be designed to support skyline group queries on dynamic data. In this paper, we propose new algorithms to find skyline groups over a data stream. We use data structures, namely a hash table, dominance graph, and matrix, to store dominance information and update results incrementally. We conduct experiments on synthetic datasets to evaluate the performance of the proposed algorithms. The experimental results show that our algorithms can efficiently find skyline groups over a data stream.

White-box machine-learning models for accurate interfacial tension prediction in hydrogen-brine mixtures

The severity of climate change and global warming necessitates the need for a transition from traditional hydrocarbon-based energy sources to renewable energy sources.One intrinsic challenge with renewable energy sources is their intermittent nature,which can be addressed by transforming excess energy into hydrogen and storing it safely for future use.To securely store hydrogen underground,a comprehensive knowledge of the interactions between hydrogen and residing fluids is required.Interfacial tension is an important variable influenced by cushion gases such as CO_(2) and CH4.This research developed explicit correlations for approximating the interfacial tension of a hydrogen–brine mixture using two advanced machine-learning techniques:gene expression programming and the group method of data handling.The interfacial tension of a hydrogen–brine mixture was considered to be heavily influenced by temperature,pressure,water salinity,and the average critical temperature of the gas mixture.The results indicated a higher performance of the group method of data handling-based correlation,showing an average absolute relative error of 4.53%.Subsequently,Pearson,Spearman,and Kendall methods were used to assess the influence of individual input variables on the outputs of the correlations.Analysis showed that the temperature and the average critical temperature of the gas mixture had considerable inverse impacts on the estimated interfacial tension values.Finally,the reliability of the gathered databank and the scope of application for the proposed correlations were verified using the leverage approach by illustrating 97.6%of the gathered data within the valid range of the Williams plot.

PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION

Because of the importance of grouped data, many scholars have been devoted to the study of this kind of data. But, few documents have been concerned with the thresh-old parameter. In this paper, we assume that the threshold parameter is smaller than the first observing point. Then, on the basis of the two-parameter exponential distribution, the maximum likelihood estimations of both parameters are given, the sufficient and necessary conditions for their existence and uniqueness are argued, and the asymptotic properties of the estimations are also presented, according to which approximate confidence intervals of the parameters are derived. At the same time, the estimation of the parameters is generalized, and some methods are introduced to get explicit expressions of these generalized estimations. Also, a special case where the first failure time of the units is observed is considered.

Developing a robust correlation for prediction of sweet and sour gas hydrate formation temperature

There are numerous correlations and thermodynamic models for predicting the natural gas hydrate formation condition but still the lack of a simple and unifying general model that addresses a broad ranges of gas mixture.This study was aimed to develop a user-friendly universal correlation based on hybrid group method of data handling(GMDH)for prediction of hydrate formation temperature of a wide range of natural gas mixtures including sweet and sour gas.To establish the hybrid GMDH,the total experimental data of 343 were obtained from open articles.The selection of input variables was based on the hydrate structure formed by each gas species.The modeling resulted in a strong algorithm since the squared correlation coefficient(R2)and root mean square error(RMSE)were 0.9721 and 1.2152,respectively.In comparison to some conventional correlation,this model represented not only the outstanding statistical parameters but also its absolute superiority over others.In particular,the result was encouraging for sour gases concentrated at H2S to the extent that the model outstrips all available thermodynamic models and correlations.Leverage statistical approach was applied on datasets to the discovery of the defected and doubtful experimental data and suitability of the model.According to this algorithm,approximately all the data points were in the proper range of the model and the proposed hybrid GMDH model was statistically reliable.