Adaptive quasi-Monte Carlo method for uncertainty evaluation in centroid measurement of planetary rovers

2020 ◽  
pp. 014233122095003
Author(s):  
Qiang Na ◽  
Shurong Hu ◽  
Jianguo Tao ◽  
Yang Luo
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Nonlinear Models ◽  
Evaluation Process ◽  
Standard Uncertainty ◽  
Integrated System ◽  
Uncertainty Evaluation ◽  
Quasi Monte Carlo ◽  
The Monte Carlo Method ◽  
Adaptive Monte Carlo Method

The measurement of the centroid is of great significance to improve the control performance and reduce the energy consumption of the planetary rover (PR). The uncertainty is an essential indicator of the reliability of centroid measurement results. The purpose of the current study is to evaluate the uncertainty of centroid measurement in the multi-configuration rover. For the measurement of the centroid, the model with 37 parameters of two measurements as the input and the centroid coordinates as the output is derived. Further, the mechanical and electrical integrated system is developed, which can measure the centroid of PRs in different configurations and sizes. Moreover, to overcome the shortcomings of the Monte Carlo method (MCM) in uncertainty evaluation, an adaptive algorithm that automatically determines the number of input sequences is proposed. On this basis, an adaptive quasi-Monte Carlo method (AQMCM) is presented in order to accelerate the uncertainty evaluation, which is characterized by the randomized Sobol sequence. Besides, experiments are performed to compare the uncertainty evaluation process and results of the AQMCM and the adaptive Monte Carlo method (AMCM) in multiple configurations. The result shows that the standard uncertainty of the AQMCM is almost the same as that of the AMCM, but the sequence size of AQMCM is evidently smaller than that of AMCM. Taken together, we identify that the AQMCM evaluates the uncertainty of CM for the multi-configuration rover in an efficient and fast way. Furthermore, the AQMCM provides a new method for uncertainty evaluation, particularly for nonlinear models in different states.

A Simplified Software for Uncertainty Estimation Using Monte Carlo Method

2020 ◽  
Vol 12 (8) ◽  
pp. 1050-1053
Author(s):  
Jasveer Singh ◽  
L. A. Kumaraswamidhas ◽  
Neha Bura ◽  
Kapil Kaushik ◽  
Nita Dilawar Sharma
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Monte Carlo Method ◽  
Measurement Uncertainty ◽  
Standard Uncertainty ◽  
Uncertainty Estimation ◽  
End Points ◽  
The Monte Carlo Method ◽  
Adaptive Trials ◽  
Coverage Interval

The current paper discusses about the application of Monte Carlo method for the evaluation of measurement uncertainty using in-house developed program on C++ platform. The Monte Carlo method can be carried out by fixed trials as well as adaptive trials using this program. The program provides the four parameters viz. estimate of measurand, standard uncertainty in the form of standard deviation and end points of coverage interval as an output.

Uncertainty Evaluation in Distance Measurement by CMM Based on Monte Carlo Method

2013 ◽  
Vol 684 ◽  
pp. 429-433 ◽  
Author(s):  
Hong Li Li ◽  
Xiao Huai Chen ◽  
Hong Tao Wang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Evaluation Process ◽  
Mathematic Model ◽  
Distance Measurement ◽  
Uncertainty Evaluation ◽  
Measured Quantity ◽  
Complete Uncertainty ◽  
End Distance ◽  
Influence Measurement

There is presented a complete uncertainty evaluation process of end distance measurement by CMM. To begin with, the major sources of uncertainty, which would influence measurement result, are found out after analyzing, then, the general mathematic model of end distance measurement is established. Furthermore, Monte Carlo method (MCM) is used, and the uncertainty of the measured quantity is obtained. The complete results are given out, so the value of CMM is enhanced. Moreover, seen from the evaluation example, the results of uncertainty evaluation obtained from MCM method and from GUM method are compared, the comparison result indicates that the mathematic model is feasible, and using MCM method to evaluate uncertainty is easy and efficient, having practical value.

scholarly journals Uncertainty Analysis of a Test Bed for Calibrating Voltage Transformers vs. Temperature

Sensors ◽  
2019 ◽  
Vol 19 (20) ◽  
pp. 4472 ◽  
Author(s):  
Mingotti ◽  
Peretto ◽  
Tinarelli ◽  
Ghaderi
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Uncertainty Analysis ◽  
Random Effects ◽  
Evaluation Method ◽  
Uncertainty Evaluation ◽  
Test Bed ◽  
Uncertainty Sources ◽  
The Monte Carlo Method

The paper addresses the evaluation of the uncertainty sources of a test bed system for calibrating voltage transformers vs. temperature. In particular, the Monte Carlo method has been applied in order to evaluate the effects of the uncertainty sources in two different conditions: by using the nominal accuracy specifications of the elements which compose the setup, or by exploiting the results of their metrological characterization. In addition, the influence of random effects on the system accuracy has been quantified and evaluated. From the results, it emerges that the choice of the uncertainty evaluation method affects the overall study. As a matter of fact, the use of a metrological characterization or of accuracy specifications provided by the manufacturers provides respectively an accuracy of 0.1 and 0.5 for the overall measurement setup.

scholarly journals MEASUREMENT UNCERTAINTY EVALUATION OF BRINELL HARDNESS TEST: GUM AND MONTE CARLO METHOD

2018 ◽  
Vol 15 (30) ◽  
pp. 252-258
Author(s):  
L. TREVISAN ◽  
D. A. K. FABRICIO
Keyword(s):  
Mathematical Method ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Measurement Uncertainty ◽  
Brinell Hardness ◽  
Hardness Test ◽  
Mechanical Tests ◽  
Uncertainty Evaluation ◽  
The Monte Carlo Method ◽  
Measurement Uncertainty Evaluation

The Brinell hardness test is one of the most used mechanical tests in the industry to assure the quality of metallurgical processes. Based on the measured values, it is necessary to describe the measurement uncertainty values associated with the mathematical method used. Thus, measurement uncertainty values describe the reliability of the experimental results. The calculation of measurement uncertainty can be performed in several ways, and the method described by ISO/GUM is the most used by ISO/IEC 17025 accredited laboratories. The main objective of this work is to compare measurement uncertainty values based on different sources of uncertainty used in the measurement uncertainty evaluation for two Brazilian laboratories accredited by Cgcre/INMETRO. In addition, uncertainty values obtained by the GUM method and by the Monte Carlo method were compared. The results show that there is no great variation in the measurement uncertainty values as a function of the mathematical method used.

A second-order discretization for degenerate systems of stochastic differential equations

2020 ◽  
Author(s):  
Yuga Iguchi ◽  
Toshihiro Yamada
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Second Order ◽  
Weak Approximation ◽  
Hörmander Condition ◽  
Quasi Monte Carlo ◽  
Control Variate ◽  
The Monte Carlo Method

Abstract The paper proposes a new second-order weak approximation scheme for hypoelliptic diffusions or degenerate systems of stochastic differential equations satisfying a certain Hörmander condition. The scheme is constructed by a Gaussian process and a stochastic polynomial weight through a technique based on Malliavin calculus, and is implemented by a Monte Carlo method and a quasi-Monte Carlo method. A variance analysis for the Monte Carlo method is discussed, and further control variate methods are introduced to reduce the variance. The effectiveness of the proposed scheme is illustrated through numerical experiments for some hypoelliptic diffusions.

scholarly journals Modelling and numerical assessment of a maintenance strategy with stock through piecewise deterministic Markov processes and quasi Monte Carlo methods

2017 ◽  
Vol 231 (4) ◽  
pp. 429-445
Author(s):  
Jeanne Demgne ◽  
Sophie Mercier ◽  
William Lair ◽  
Jérôme Lonchampt
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Markov Processes ◽  
Net Present Value ◽  
Spare Parts ◽  
Present Value ◽  
Quasi Monte Carlo ◽  
The Monte Carlo Method ◽  
Piecewise Deterministic Markov Processes ◽  
The Right

To ensure a power generation level, the French national electricity supply (EDF) has to manage its producing assets by putting in place adapted preventive maintenance strategies. In this article, a fleet of identical components is considered, which are spread out all around France (one per power plant site). The components are assumed to have stochastically independent lifetimes, but they are made functionally dependent through the sharing of a common stock of spare parts. When available, these spare parts are used for both corrective and preventive replacements, with priority to corrective replacements. When the stock is empty, replacements are delayed until the arrival of new spare parts. These spare parts are expensive, and their manufacturing time is long, which makes it necessary to rigorously define their ordering process. The point of the article is to provide the decision maker with the tools to take the right decision (make or not the overhaul). To do that, two indicators are proposed, which are based on an economic variable called the net present value. The net present value stands for the difference between the cumulated discounted cash-flows of the purely corrective policy and the preventive one which including the overhaul. Piecewise deterministic Markov processes are first considered for the joint modelling of the stochastic evolution of the components, stock and ordering process with and without overhaul. The indicators are next expressed with respect to these piecewise deterministic Markov processes, which have to be numerically assessed. Instead of using the most classical Monte Carlo simulations, we here suggest alternate methods based on quasi Monte Carlo simulations, which replace the random uniform numbers of the Monte Carlo method by deterministic sequences called low-discrepancy sequences. The obtained results show a real gain of the quasi Monte Carlo methods in comparison with the Monte Carlo method. The developed tools can hence help the decision maker to take the right decision.

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