Application of Monte Carlo Method for Evaluation of Uncertainties of ITS-90 by Standard Platinum Resistance Thermometer

Abstract

Evaluation of uncertainties of the temperature measurement by standard platinum resistance thermometer calibrated at the defining fixed points according to ITS-90 is a problem that can be solved in different ways. The paper presents a procedure based on the propagation of distributions using the Monte Carlo method. The procedure employs generation of pseudo-random numbers for the input variables of resistances at the defining fixed points, supposing the multivariate Gaussian distribution for input quantities. This allows taking into account the correlations among resistances at the defining fixed points. Assumption of Gaussian probability density function is acceptable, with respect to the several sources of uncertainties of resistances. In the case of uncorrelated resistances at the defining fixed points, the method is applicable to any probability density function. Validation of the law of propagation of uncertainty using the Monte Carlo method is presented on the example of specific data for 25 Ω standard platinum resistance thermometer in the temperature range from 0 to 660 °C. Using this example, we demonstrate suitability of the method by validation of its results.

A Fast-Multi-Channel Sub-Millikelvin Precision Resistance Thermometer Readout Based on the Round-Robin Structure

“…The results are shown in Table 2 The results show that the equivalent uncertainty (K = 2, at 1 Hz) of the multi-channel readout is better than 2.1 mK. Compared with some well-known primary resistance bridges, the measurement uncertainty of the multi-channel readout keeps a certain distance [18], [19]. The reason is that the temperature of the reference resistor has not been controlled and the nonlinear of the ADCs in the designed multi-channel readout has not been well calibrated yet.…”

Modelling of Conveyor Belt Passage by Driving Drum Using Finite Element Methods

“…For the metal parts, i.e. rollers and drum, the selected material was steel with a density of 7.85E -009 , Young modulus of elasticity 204000 MPa and Poisson`s number 0.25 [19] [20] (Figure 4). For the nonmetallic parts of the conveyor belt, a material with density 1,099E…”

Monte Carlo-Based Procedure for Determining the Maximum Energy at the Output of Accelerometers

“…In this way (e.g., by using the weighted least squares procedure (WLSP)), the accelerometer parameters and associated uncertainties can be obtained [3,13,14]. Additionally, when we want to determine the associated uncertainties, it is necessary to use the Monte Carlo procedure (MCP) [15][16][17][18], whose number of trials can be assumed in advance according to the guidelines included in the JCGM (Joint Committee for Guides in Metrology)-supplement 1 [13]. The model of the filter is expected to meet the so-called non-distortion transformation [19], according to which the amplitude-frequency and phase-frequency responses are flat and linear, respectively, within the frequency bandwidth of interest [20].…”

“…The maximum value of the reference energy can be determined by using the fixed-point algorithm (FPA) [5,[21][22][23] with its extension by the MCP [13,18]. The MCP can be implemented based on the same assumptions as in the case of the procedure intended for determining the uncertainties associated with the parameters of the accelerometer model by using the WLSP.…”