Zygmunt L. Warsza

Application of Double Current Bridge-Circuit for Simultaneous Measurements of Strain and Temperature

A four-terminal (4T) bridge-circuit unconventionally supplied by current sources connected in parallel to opposite arms, named double current bridge (2J) is presented. It has two different outputs from both diagonals. Their output voltages as the functions of arm resistance increments in absolute and in relative units are given. Example of its application is proposed. Signals conditioning formulas of the two-parameter (2D) measurement - of strain and temperature are discussed in details. Some results of experimentally design instrumentation of this bridge-circuit are shortly presented.

Semi-parametric Estimation of the Change-Point of Parameters of Non-gaussian Sequences by Polynomial Maximization Method

This paper deals with application of the maximization method in the synthesis of polynomial adaptive algorithms for a posteriori estimation of the change-point of the mean value or variance of random non-Gaussian sequences. Statistical simulation shows a significant increase in the accuracy of polynomial estimates, which is achieved by taking into account the non-Gaussian character of statistical data.

A Polynomial Estimation of Measurand Parameters for Samples of Non-Gaussian Symmetrically Distributed Data

The non-standard method for evaluating of the average and standard deviation of the symmetrically non-Gaussian-distributed data of sample with a priori partial description (unknown PDF) is proposed. This method of statistical estimation is based on the apparatus of stochastic polynomials and uses the higher-order statistics (moment & cumulant description) of random variables. The analytical expressions for finding estimates for the degree of the polynomial s = 3 and their accuracy analyzes are given. It is shown that the uncertainty estimates received for polynomial are generally less than the uncertainty estimates obtained based on the mean (arithmetic average). Reduction factor, which depends on the MSE values of higher order cumulant coefficients, characterizes the degree of the sampling distribution differences from the Gaussian model. The results of statistical modeling, based on the Monte Carlo method, confirmed the effectiveness of the proposed approach are presented.

Simple Methods to Measure the Additive Error and Integral Nonlinearity of Precision Thermometric Bridges

Determination of the accuracy of AC bridges with the high precision adjustable transformer voltage dividers based on the strongly magnetic coupling coils is referred in this paper. Metrological model of the temperature measurements by resistive sensors connected to these bridges is presented. The additive, multiplicative and linearity components of error in temperature measurement are considered. Method for determining the zero of the bridge error is developed. It is based on the non standard connection mode of the equipotential pairs of current and voltage terminals of standard resistance to the bridge. It is estimated that up to 1 MΩ of this resistance, the effective resistance obtained on the bridge input is less than 10− 10 Ω. Four-terminal standard resistors of 0.1 Ω up to 1 MΩ are used in experiments to find bridge zero readings. Results indicate that the additive error of the tested precision bridge is about 0.5 LSB and is independent from the nominal standard resistance value. The conditions under which in temperature measurements remains only the linearity bridge error are formulated. Proposed is the unconventional method of measure and estimating the bridge nonlinearity named as dichotomy method. It applies algorithm based on the division of the measurement range and then obtained subsequent intervals always in half. Graphical interpretation and the analytical expression for the nonlinearity error are given. Sets of paired four terminal reference standard resistors are proposed for use in control. The resistance of each of them separately and of the given serial physical connection of them both has to be measured by tested bridge. The reasons affecting the accuracy of the physical realization of resistance summation is discussed. By calculations and experimental verification is find that in measurements by dichotomy method the bridge linearity error of 0.1 ppm or less can be discovered. Conclusions and final remarks are included. Both methods are simply and can be easily implemented in any metrology lab and be used also in automatic calibrators.

Improving of the Type A Uncertainty Evaluation by Refining the Measurement Data from a Priori Unknown Systematic Influences

A new approach to improving the type A uncertainty evaluation by cleaning of the collected data from unwanted influences which appears as non- periodical and periodical systematic components identified in the data is presented in the paper. The approach refers to regularly in time sampled data. The cleaning process comply with the main stream of ISO GUM recommendation and can be recognized as good practice in the proper estimation of the type A uncertainty. The proposed approach is discussed in the paper and the numerical example is presented as well.

Estimation of Measurand Parameters for Data from Asymmetric Distributions by Polynomial Maximization Method

In this paper the non-conventional method for evaluating the standard uncertainty of the estimator of measurand value obtained from the non-Gaussian asymmetrically distributed sampled data with a priori partial description (known only few initial moments, unknown PDF distribution of population) is proposed. This method of statistical estimation is based on the apparatus of maximization the stochastic polynomials (PMM method proposed by Kunchenko [11]) and uses the higher-order statistics (moment or cumulant description) of random variables. The analytical expressions for finding estimates and analyzing their accuracy to the degree of the polynomial s = 2 is given. It is shown that for the asymmetric PDF-s the uncertainty estimates for received polynomial are generally smaller than the uncertainty estimates obtained based on the mean (arithmetic average). Reducing the uncertainty of measurement depends on the skewness and kurtosis. On the basis of the Monte Carlo method statistical modelling is carried out, the results confirm the effectiveness of the proposed approach.

Errors and uncertainties of imbalanced bridge-circuits as primary converters for RTD sensors

The original way of evaluating accuracy of the resistance-to-voltage converter (imbalanced bridge-circuit) is presented. It is important because this converter is used as the input stage of industrial and laboratory temperature measurement systems. From circuit theory point of view it is the two-port circuit of type X with four variable resistances and it is supplied by a current (or voltage) source. Formulas of transfer coefficients are presented in general forms and in relative units. Moreover, two particular cases of this converter used in temperature measurements, i.e. with one or two RTD elements, are considered in detail. Error propagation functions are determined in two-component form, i.e. separately for both initial value and relative increment of a transfer coefficient (dependent on temperature). Values of limited errors and expanded uncertainties are calculated for a few variants of this converter with the Class A and B industrial Pt100 sensors. Formulas and example results allow to determine accuracy measures for the selected configuration of bridge-circuit and to compare with other configurations. Null adjustment, inside and outside the bridge, is also considered.

Method of upgrading the reliability of measurement inspection

Applying an auxiliary quantity, homogeneous with the measured one, is proposed in the quality control of an object made with the use of measuring channel and decision-making module. The result of processing this quantity in the measurement channel is applied for the additive and multiplicative correction of decision limits. This allows to reduce the impact of imperfect processing characteristics of measuring channel. The significant effectiveness of such correction, at different ratio of the components of processing error, is presented. The influence of errors of forming auxiliary quantity is also estimated.

Electromagnetic Protection in High Precision Tri-axial Thermometric AC Bridge

The effective protection against electromagnetic influences in the measuring circuit of thermometric AC bridges is discussed. The equivalent AC circuit of the SPRT sensor when connected to the bridge is discussed. The capacitance C of the connection cable and output capacitance of the bridge inductive divider can change impedance of this circuit from the serial RL to parallel RC one. The tangent of the impedance phase angle as a criterion of the type of equivalent circuit is proposed. The precision AC thermometric bridge with the double shielding technique is designed. Bifilar connections by two-axial concentric cables with two shields and equipotential protection is used. Circuit is automatically balanced and has advantages of the coaxial bridges and the equipotential protection. The term tri-axial bridge is proposed for it. The detail analysis of this automatically balanced circuit resulted on its high immunity to interferences and over 100 times smaller impact of the capacitive leakage. The efficiency of solution is verified experimentally in a few high accuracy (10− 7‒10− 8) AC bridges.

The influence of the characteristics of the measuring instrument on the reliability of decision making in the assessment of conformity

Shown necessity accounting function conversion of measuring instrument when assessing the reliability decision making on the conformity of the object to the requirements on the basis of the results of measurements of its parameters. Considered is the influence of the parameters of the measuring instrument conversion function on the character of decisions and its probability. It is shown that the actual shift characteristic and its sensitivity is within these limits may have different values, which may lead not only to change the probability (uncertainty) of the received solutions, but also to change its character. Applying an auxiliary quantity, homogeneous with the measured one, is proposed in the quality control of an object made with the use of measuring channel and decision-making module. The result of processing this quantity is applied for the additive and multiplicative correction of decision limits. This allows to reducing the impact of imperfect processing characteristics of measuring instrument on the decision making on the conformity of the object (shown on the numerical example).