scholarly journals The measurements results adjustment by the Least Square Method

2021 ◽  
Vol 1 ◽  
pp. 1-8
Author(s):  
Oleksandr Samoilenko ◽  
Yurii Kuzmenko
Keyword(s):  
Reference Value ◽  
Least Square Method ◽  
Systematic Errors ◽  
Least Square ◽  
Key Comparisons ◽  
System Of Equations ◽  
The Third ◽  
Measurement Results ◽  
Free Case ◽  
Degrees Of Equivalence

The method for processing of the measurement results obtained from Comite International des Poids et Measures (CIPM) Key, Regional Metrology Organizations (RMO) or supplementary comparisons, from the proficiency testing by interlaboratory comparisons and the calibrations is proposed. It is named by authors as adjustment by least square method (LSM). Additive and multiplicative parameters for each measuring standard of every particular laboratory will be the results of this adjustment. As well as the parameters for each artifact. The parameters of the measurements standards are their additive and multiplicative degrees of equivalence from the comparison and the estimations of the systematic errors (biases) from calibrations. The parameters of the artifacts are the key comparisons reference value from the comparison and the assigned quantity values from the calibrations. The adjustment is considered as a way to solving a problem of processing the great amount of homogeneous measurements with many measuring standards at a different comparison levels (CIPM, RMO or supplementary), including connected problems. Four different cases of the adjustments are considered. The first one is a free case of adjustment. It was named so because of the fact that none of participants has any advantage except their uncertainties of measurements. The second one is a fixed case of adjustment. Measuring results of RMO and supplementary comparisons are rigidly linked to additive and multiplicative parameters of measuring standards of particular laboratories participated in CIPM key comparisons. The third one is a case of adjustment with dependent equations. This one is not so rigidly linked of the new comparisons results to previous or to some other comparisons as for fixed case. It means that the new results of comparisons are influenced by the known additive and multiplicative parameters and vice versa. The fourth one is a free case of adjustment with additional summary equations. In that case certain checking equations are added to the system of equations. So, the sum of parameters multiplied by their weights of all measurement standards for particular laboratories participated in comparisons should be equal to zero.

scholarly journals Alternative approach to international comparisons

2021 ◽  
Vol 2 ◽  
Author(s):  
Oleksandr Samoilenko
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Length Measurement ◽  
Measurement Unit ◽  
Mathematical Apparatus ◽  
Measurement Standards ◽  
Degree Of Equivalence ◽  
Measurement Results ◽  
Degrees Of Equivalence ◽  
Network Software

According to the authors point of view, absence of the accepted by metrological society software based on simple and understandable and at the same time flexible and multipurpose mathematical apparatus is one of the restrictions on the way to arrangement of international comprehensive comparisons with expanded group of participants (hereinafter — comprehensive comparisons). General methodology of measurements adjustment by the least square method (LSM) may be used for this mathematical apparatus. Software named «Metrology Network» is defined. It was used for repeated processing of measurement results during the key comparisons of EURAMET.L-K1.2011 «Measurement of gage blocks by interferometer». «Metrology Network» software allowed to estimate simply and quickly systematic measurement error components of the gage blocks length measurement by each laboratory. They are called multiplicative and additive measurement standards degrees of equivalence. «Metrology Network» allowed to estimate strictly by LSM the uncertainties of length measurement. Additive degrees of equivalence are considered substantial and constant characteristics of the measurement standards for many laboratories. Thus, they coincide for steel and ceramic gage blocks. These additive degrees of equivalence may be used as corrections in the process of calibration or as the reference values for further comparisons. The simulation of measurement results for international comprehensive comparisons with complicated structure was provided. For 120 laboratories divided into 12 groups, totally 2442 length measurements of the steel or ceramic gage blocks were provided. They form together 24 sets of 8 gage blocks and provide 24 loops of comparisons. Necessity to provide the adjustment by the least square method is caused by the fact that two subgroups from each group of three laboratories took part in two different related loops of comparison. As a conclusion, «Metrology Network» software easily managed this complicated task of adjustment.  It allowed us to calculate each of 120 measurement standards additive degree of equivalence relative to the averaged zero for all measurement standards and multiplicative degree of equivalence relative to the averaged measurement unit.

scholarly journals Node Localization of Wireless Sensor Networks Based on Hybrid Bat-Quasi-Newton Algorithm

2015 ◽  
Vol 11 (6) ◽  
pp. 38 ◽  
Author(s):  
Shunyuan Sun ◽  
Baoguo Xu
Keyword(s):  
Least Square Method ◽  
Bat Algorithm ◽  
Least Square ◽  
Localization Algorithm ◽  
Positioning Precision ◽  
Newton Algorithm ◽  
The Third ◽  
Third Stage ◽  
Node Location ◽  
Quasi Newton

Concerning the problem that the least square method in the third stage of DV-Hop algorithm has low positioning accuracy, a localization algorithm was proposed which is the fusion of hybrid bat-quasi-Newton algorithm and DV-Hop algorithm. First of all, the Bat Algorithm ( BA) was improved from two aspects: firstly, the random vector β was adjusted adaptively according to bats fitness so that the pulse frequency had the adaptive ability. Secondly, bats were guided to move by the average position of all the best individuals before the current iteration so that the speed had variable performance; Then in the third stage of DV-Hop algorithm the improved bat algorithm was used to estimate node location and then quasi-Newton algorithm was used to continue searching for the node location from the estimated location as the initial searching point. The simulation results show that, compared with the traditional DV-Hop algorithm and the improved algorithm of DV-Hop based on bat algorithm( BADV-Hop) , positioning precision of the proposed algorithm increases about 16. 5% and 5. 18%, and the algorithm has better stability, it is suitable for high positioning precision and stability situation.

Construction of a Relational Leadership Model Based on a Two-Stage Least Square Method and an Investigation on the Interaction Among the Factors in the Model

2018 ◽  
Vol 11 (1) ◽  
pp. 14-30 ◽  
Author(s):  
Shubing Guo ◽  
Xueli Zhan ◽  
Junhai Ma
Keyword(s):  
Reference Value ◽  
Least Square Method ◽  
Least Square ◽  
Leader Member Exchange ◽  
Relational Leadership ◽  
Two Stage ◽  
Leadership Model ◽  
Member Exchange ◽  
Five Elements ◽  
Positive Correlations

This article conducts a theoretical analysis and empirical study on the complex relations among five elements (leadership, followership, leader-member exchange, leadership situation, and leadership performance) based on a two-stage least square method (TSLS). Results show that in China leadership and followership are positively correlated with performance; LMX (Leader–Member eXchange) is negatively correlated with performance; LMX show significant positive correlations with leadership and followership; circle and face are positive correlated with leadership and followership, but favor is negatively correlated with leadership, followership, and LMX. Moreover, a SLRFP (Situation, Leadership, Relationship, Followership, Performance) five-force relational leadership model was constructed, revealing the core contents of relational leadership. These elements mainly include relational structure, dynamics and process, and provide a theoretical framework for establishing a unified theory of leadership based on the integration of traditional theories. The present study has high academic and favorable reference value.

The Calculation of Earth Capacitance Based on Least Square Method

2012 ◽  
Vol 433-440 ◽  
pp. 6028-6032
Author(s):  
Heng Xu Ha ◽  
Xiao Liu ◽  
Xi Tong Hu
Keyword(s):  
Power System ◽  
Single Phase ◽  
Least Square Method ◽  
Least Square ◽  
Neutral System ◽  
Negative Effects ◽  
Capacitive Current ◽  
Measurement Results ◽  
Simulation Results ◽  
Capacitance Current

The grounding capacitive current is one of the most important parameters of ungrounded neutral system. Usually this parameter is obtained with the method of additional capacitor or metal grounding. However, the former is complicated and the additional capacitor has negative effects on measurement results, and the later is dangerous when used in testing. In view of that, the paper proposes a new method to calculate grounding capacitance current based on the data of single-phase-grounding faults in power system with indirectly earthed neutral. This method reduces the error by using the least-square method .The ATP simulation results show that this method is accurate basically.

Optimal Weighted Least Square Data Fusion Method for Redundant IMU Based on Calculation of Measurement Error

2012 ◽  
Vol 241-244 ◽  
pp. 149-155
Author(s):  
Chuan Xing ◽  
Hai Zhang
Keyword(s):  
Measurement Error ◽  
Data Fusion ◽  
Measurement Errors ◽  
Least Square Method ◽  
Least Square ◽  
Weighted Least Square ◽  
Weighted Matrix ◽  
Measurement Results ◽  
The Difference ◽  
Projection Error

A dodecahedron non-orthogonal redundant IMU configuration was selected as model. To improve fusion accuracy, we proposed an effective calculation method for measurement errors based on the correlation between measurement errors and fusion errors. The method considered the difference between traditional data fusion vector’s projection and measurement results, and then made a conversion from projection error to measurement error. Combined with optimal weighted least square method, measurement error was used to generate an optimal weighted matrix, and this made data fusion errors minimum. Simulations also proved that the fusion result of this method is more accurate than the result of traditional method.

scholarly journals A Method of Containment Leakage Rate Estimation Based on Convolution Neural Network

2021 ◽  
Vol 9 ◽  
Author(s):  
Hao Wang ◽  
Jingquan Liu ◽  
Guangyao Xie ◽  
Xianping Zhong ◽  
Xiangqi Fan
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Nuclear Power ◽  
Power Plants ◽  
Least Square Method ◽  
Leakage Rate ◽  
Least Square ◽  
Nonlinear Fitting ◽  
The Third ◽  
Start Up

As the nuclear power plant containment is the third barrier to nuclear safety, real-time monitoring of containment leakage rate is very important in addition to the overall leakage test before an operation. At present, most of the containment leakage rate monitoring systems calculate the standard volume of moist air in the containment through monitoring parameters and calculate the daily leakage rate by the least square method. This method requires several days of data accumulation to accurately calculate. In this article, a new leakage rate modeling technique is proposed using a convolutional neural network based on data of the monitoring system. Use the daily monitoring parameters of nuclear power plants to construct inputs of the model and train the convolutional neural network with daily leakage rates as labels. This model makes use of the powerful nonlinear fitting ability of the convolutional neural network. It can use 1-day data to accurately calculate the containment leakage rate during the reactor start-up phase and can timely determine whether the containment leak has occurred during the start-up phase and deal with it in time, to ensure the integrity of the third barrier.

Profile Voltage on One Phase Cable Channel at Every Distance 17 Meters in All 102 Meter That was 1000 Watt with Least Square Method

2019 ◽  
Vol 16 (12) ◽  
pp. 5175-5179
Author(s):  
Sofiah ◽  
Abdul Majid ◽  
Cekmas Cekdin
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Least Square Method ◽  
Equation Model ◽  
Least Square ◽  
Cable Channel ◽  
Percentage Difference ◽  
Measurement Results ◽  
The Mathematical Model

In this paper, it is discussed to determine a voltage modeling on a 102 meter one-phase cable channel which is loaded with a 1000 Watt lamp with the least square method. To obtain this method is by measuring the voltage at the points specified in the cable. After the measurement data is obtained then it is calculated to determine the mathematical model with the least square method. The least square method is a method for predicting a certain price. This method is also called the smallest quadratic method with the equation V = a + bX. With V is the measurement voltage (Volt) at distance X from the source, X distance from the source (meter), n ila a and b are calculated based on the measurement data. After the equation model is obtained, then we compare it with the measurement results. This comparison is useful to know what percentage difference between the results of the measurement and calculation.

The Speeds and Accelerations of the Galaxies Movements According to Redshift Measurements

2017 ◽  
Author(s):  
Jonas Skeivalas ◽  
Eimuntas Parseliunas
Keyword(s):  
Doppler Effect ◽  
Least Square Method ◽  
Systematic Errors ◽  
Least Square ◽  
Signal Frequency ◽  
Time Interval ◽  
The Galaxy ◽  
Speed Change ◽  
The Doppler Effect ◽  
The Universe

The theoretical presumptions and some experimental calculations to analyse the speeds of the galaxies movements according to redshift measurements applying the Doppler effect are presented. The speed of the galaxy movement is treated as multidimensional continuous value, when values of the speed vector are calculated according to measurements of the redshift parameter z at corresponding moments of the universe lookback time. The most reliable values of the galaxy speeds vector are calculated applying the least square method to the vector of z measurements and including the additional parameters to eliminate the possible systematic errors. The acceleration of the galaxy movement is calculated as a speed fluxion according to period of the adopted redshift signal frequency and as a speed change during the lookback time interval. The expressions of functions of the galaxies speeds and accelerations are received by the polynomial approximation, when values of the polynomial parameters are calculated by the least square method.

scholarly journals The Method and the Results of the Direct Comparison of the Laser Interferometers Renishaw Xl-80

2018 ◽  
pp. 15-21
Author(s):  
O. Samoylenko ◽  
O. Adamenko ◽  
V. Kalynichenko
Keyword(s):  
Measurement Error ◽  
Least Square Method ◽  
Least Square ◽  
Additive Part ◽  
Measurement Results ◽  
Laser Interferometers

The method of the direct comparison of the laser interferometers and method processing of the interferometry measurement results by the least square method (LSM) is present. The additive part of the measurement error for each pair of the interferometers is evaluated and the multiplicative part of the measurement error for each interferometer is evaluated too by LSM. Uncertainty by A tape by LSM is evaluated for all parameters. Results of the comparison of the three interferometers are presented.

scholarly journals Processing by Least Square Method of the Measurements Results for Key, Regional and Supplementary Comparison of the Measurement Standards

2018 ◽  
pp. 3-13 ◽  
Author(s):  
Yu. Kuzmenko ◽  
O. Samoylenko
Keyword(s):  
Data Processing ◽  
Least Squares ◽  
Least Square Method ◽  
Least Square ◽  
Mathematical Apparatus ◽  
Method Of Least Squares ◽  
Unknown Parameters ◽  
Measurement Standards ◽  
Measurement Results

The methods of processing the measurement results of several homogeneous transfer standards existing in the form of single-valued or multi-valued measures/sensors or devices performed at many points on several stationary standards, which participate in key, regional or additional comparisons, are proposed in the article. The number of measurements far exceeds the number of unknown parameters of the standards, which are determined by the results of comparisons, that’s why the method of least squares was chosen as the mathematical apparatus for data processing.

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