scholarly journals AN ALGORITHM OF TREATMENT OF THE RESULTS OF MULTIPLE MEASUREMENTS OF COMPOSITION AND PROPERTIES OF PETROLEUM PRODUCTS

2021 ◽  
pp. 56-61
Author(s):  
К.В. Шаталов
Keyword(s):  
Empirical Distribution ◽  
Weighted Average ◽  
Petroleum Products ◽  
Robust Estimators ◽  
Robust Algorithms ◽  
Scale Parameters ◽  
Initial Values ◽  
Multiple Observations ◽  
M Estimator ◽  
Multiple Measurements

Разработаны новые робастные алгоритмы обработки результатов многократных измерений состава и свойств нефтепродуктов, учитывающие тот факт, что эмпирическая функция распределения результатов измерений состава и свойств нефтепродуктов представляет собой смесь двух нормальных распределений с разными значениями параметров положения и масштаба. В случае измерений состава и свойств нефтепродуктов в качестве робастных оценок параметра положения и параметра масштаба выборки предложено использовать М-оценки с предварительным масштабированием на основе модифицированной функции Хампеля. Для нахождения М-оценки предложены два итеративных способа вычисления на основе средневзвешенного метода наименьших квадратов, отличающиеся процедурами расчета начальных оценок параметров положения и масштаба выборки. При числе результатов в выборке более двадцати в качестве начальных значений параметров положения и масштаба целесообразно использовать α‑урезанное среднее и α‑урезанное стандартное отклонение с долей усечения 0,05. При числе результатов в выборке менее двадцати в качестве начальных значений параметра положения и параметра масштаба обоснованно использование робастных оценок, не требующих удаления части данных. В качестве начальной оценки параметра положения предложено использовать оценку Ходжеса – Лемана; в качестве параметра масштаба – медианы абсолютных разностей. Предложенные робастные алгоритмы могут быть использованы при обработке результатов эксперимента по определению показателей прецизионности, правильности и точности методик измерений состава и свойств нефтепродуктов, итогов межлабораторных сравнительных испытаний нефтепродуктов, расчете аттестованного значения стандартных образцов состава и свойств нефтепродуктов, а также в других случаях многократных наблюдений. New robust algorithms of treatment of the results of multiple measurements of composition and properties of petroleum products were developed in respect that empirical distribution function of the results of measurements of composition and properties of petroleum products are the mixture of two normal distributions with different values of position and scale parameters. In case of measurements of composition and properties of petroleum products it has been proposed to use M-estimator with pre-scaling based on modified Hampel function as robust estimators of position and scale parameters. To calculation M-estimator two iterative methods based on weighted average method of least squares were suggested which differs by procedures of initial estimators of position and scale parameters of sample. In case of more than twenty results in sample, it is expedient to apply α-truncated mean and α-truncated standard deviation with 0,05 truncation share as initial values of position and scale parameters. In case of less than twenty results in sample, it is reasonable to apply robust estimators as initial values of position and scale parameters, which don’t require removal of some part of the data. It was proposed to use Hodges-Lehmann estimator as an initial value of position parameter and median of absolute differences as a scale parameter. The proposed robust algorithms can be used in treatment of experiment results on determination of indexes of precision, trueness and accuracy of the methods of measurement of composition and properties of petroleum products; results of interlaboratory comparison tests of petroleum products; calculation of certified value of standard samples of composition and properties of petroleum products and in other cases of multiple observations.

scholarly journals COMPARING THE PREDICTIVE PERFORMANCE OF OLS AND 7 ROBUST LINEAR REGRESSION ESTIMATORS ON A REAL AND SIMULATED DATASETS

2021 ◽  
Vol 5 (11) ◽  
Author(s):  
Sacha Varin
Keyword(s):  
Linear Regression ◽  
High Efficiency ◽  
Robust Regression ◽  
Mean Squared Error ◽  
Predictive Performance ◽  
Ordinary Least Squares ◽  
Small Samples ◽  
Robust Estimators ◽  
Absolute Deviation ◽  
M Estimator

Robust regression techniques are relevant tools for investigating data contaminated with influential observations. The article briefly reviews and describes 7 robust estimators for linear regression, including popular ones (Huber M, Tukey’s bisquare M, least absolute deviation also called L1 or median regression), some that combine high breakdown and high efficiency [fast MM (Modified M-estimator), fast ?-estimator and HBR (High breakdown rank-based)], and one to handle small samples (Distance-constrained maximum likelihood (DCML)). We include the fast MM and fast ?-estimators because we use the fast-robust bootstrap (FRB) for MM and ?-estimators. Our objective is to compare the predictive performance on a real data application using OLS (Ordinary least squares) and to propose alternatives by using 7 different robust estimations. We also run simulations under various combinations of 4 factors: sample sizes, percentage of outliers, percentage of leverage and number of covariates. The predictive performance is evaluated by crossvalidation and minimizing the mean squared error (MSE). We use the R language for data analysis. In the real dataset OLS provides the best prediction. DCML and popular robust estimators give good predictive results as well, especially the Huber M-estimator. In simulations involving 3 predictors and n=50, the results clearly favor fast MM, fast ?-estimator and HBR whatever the proportion of outliers. DCML and Tukey M are also good estimators when n=50, especially when the percentage of outliers is small (5% and 10%%). With 10 predictors, however, HBR, fast MM, fast ? and especially DCML give better results for n=50. HBR, fast MM and DCML provide better results for n=500. For n=5000 all the robust estimators give the same results independently of the percentage of outliers. If we vary the percentages of outliers and leverage points simultaneously, DCML, fast MM and HBR are good estimators for n=50 and p=3. For n=500, fast MM, fast ? and HBR provi

Automatic Measurement System for Vertical Tank Volume by Electro-Optical Distance-Ranging Method

2010 ◽  
Vol 26-28 ◽  
pp. 416-421
Author(s):  
Jin Tao Wang ◽  
Zi Yong Liu ◽  
Long Zhang ◽  
Li Gong Guo ◽  
Xue Song Bao ◽  
...  
Keyword(s):  
Measurement System ◽  
Weighted Average ◽  
Automatic Measurement ◽  
Petroleum Products ◽  
Laser Ranging ◽  
Absolute Value ◽  
Space Model ◽  
Weighted Average Method ◽  
Optical Distance ◽  
Automatic Measurement System

The precision measurement of vertical tank volume is one of key problems for the international trade of liquefied petroleum products. One measurement system based on Electro-Optical Distance-Ranging (EODR) principle was proposed. Laser ranging and optic-encoding methods were applied to determine the location of each point on the tank shell. Based on the coordinate computation, the space model of vertical tank was established. Regarded as cylinder, the volume of tank can be calculated by using fitted radius of each course. Weighted Average Method and Direct Iterative Method were used to carry out radius fitting. One comparison experiment was designed, in which one 1000m3 vertical tank was used as test object, and Strapping Method was regarded as reference according to OIML R71. The maximal radius errors of two methods were 2.05mm and 1.48mm, and the absolute value of mean radius errors were 0.97mm and 0.63mm, which verified the system discussed.

Improving Pulse Phase Estimation Accuracy with Sampling and Weighted Averaging

2019 ◽  
Vol 72 (04) ◽  
pp. 1007-1020
Author(s):  
Haoye Lin ◽  
Bo Xu
Keyword(s):  
Signal To Noise Ratio ◽  
Weighted Average ◽  
Correlation Method ◽  
Weighted Averaging ◽  
Estimation Accuracy ◽  
Phase Estimation ◽  
Pulse Phase ◽  
Improve Accuracy ◽  
Multiple Measurements ◽  
Novel Method

The accuracy in an X-ray pulsar-based navigation system depends mainly on the accuracy of the pulse phase estimation. In this paper, a novel method is proposed which combines an epoch folding process and a cross-correlation method with the idea of “averaging multiple measurements”. In this method, pulse phase is estimated multiple times on the sampled subsets of arriving photons' time tags, and a final estimation is obtained as the weighted average of these estimations. Two explanations as to how the proposed method can improve accuracy are provided: a Signal to Noise Ratio (SNR)-based explanation and an “error-difference trade-off” explanation. Numerical simulations show that the accuracy in pulse phase estimation can be improved with the proposed algorithm.

The Multilevel p2 Model

Methodology ◽  
2006 ◽  
Vol 2 (1) ◽  
pp. 42-47 ◽  
Author(s):  
Bonne J. H. Zijlstra ◽  
Marijtje A. J. van Duijn ◽  
Tom A. B. Snijders
Keyword(s):  
Social Network ◽  
Network Data ◽  
Mcmc Algorithm ◽  
Independent Observation ◽  
Single Observation ◽  
Multiple Networks ◽  
Social Network Data ◽  
Multiple Observations ◽  
Practical Support ◽  
The Social

The p 2 model is a random effects model with covariates for the analysis of binary directed social network data coming from a single observation of a social network. Here, a multilevel variant of the p 2 model is proposed for the case of multiple observations of social networks, for example, in a sample of schools. The multilevel p 2 model defines an identical p 2 model for each independent observation of the social network, where parameters are allowed to vary across the multiple networks. The multilevel p 2 model is estimated with a Bayesian Markov Chain Monte Carlo (MCMC) algorithm that was implemented in free software for the statistical analysis of complete social network data, called StOCNET. The new model is illustrated with a study on the received practical support by Dutch high school pupils of different ethnic backgrounds.

Equipment dentifying Vapor Leakages and Recovery of Petroleum Product Vapor When Stored

2020 ◽  
Vol 05 ◽  
pp. 60-64
Author(s):  
Y.N. Rybakov ◽  
◽  
V.E. Danilov ◽  
I.V. Danilov ◽  
◽  
...  
Keyword(s):  
Environmental Pollution ◽  
Environmental Protection ◽  
Petroleum Product ◽  
Petroleum Products ◽  
Oil Products ◽  
Carnot Cycle ◽  
Oil Supply ◽  
Gas Stations ◽  
Environmental Situation ◽  
Vapor Absorption

The problem of losses of oil products from leaks during their storage and transportation at oil supply facilities is considered. The influence of oil product leaks on the environmental situation around oil depots and gas stations is shown. A detailed overview of existing methods and tools for detecting leaks of petroleum products from storage facilities is presented. The evaluation of their effectiveness. Two methods for detecting oil leaks and devices based on them are proposed. The first device monitors the movement of liquid in the tank, the second-detects petroleum products in wastewater. The problem of recovery of petroleum vapors and environmental pollution from the release of vapors of light fractions into the atmosphere is also considered. An overview of existing methods and means of recovery of petroleum vapors is presented. Two methods and devices for capturing oil vapors and returning them to the reservoir are proposed, based on different principles: vapor absorption in the cooled oil product and vapor recovery on the principle of the Carnot cycle. It is shown that these devices can provide effective detection of oil leaks and recovery of their vapors, as well as improve the effectiveness of environmental protection at modern gas stations and tank farms.

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