Computer Simulation Methods of Redundant Measurements with the Nonlinear Transformation Function

The studies of possibilities of methods of redundant measurements have found the high efficiency of the presented methods for increasing the accuracy of measurements. It is proved that the equation of redundant measurements ensures the independence of the measurement result of the parameters of the transformation function and their deviations from the nominal values. The possibility of obtaining an equation of redundant measurements of the parameters of the transformation functionis also proved, which will enable the implementation of metrological self-control. Experimental studies have confirmed that the accuracy of measurement is increased by processing the results of intermediate measurements by the equation of redundant measurements. In the proposed equation, due to the subtraction operation, the additive component of the error is excluded, and the multiplicative component is excluded due to the division operation. This leads to the stability of the result of measurement by the redundant method to changes in the parameters of the transformation function. In particular, it is found that the change of the parameters of the transformation function by (1÷10) % does not affect the result of redundant measurements, that is, the relative error in the given operating range will be δ1=(0.04÷0.01) %. This allows us to assert that the mathematical model underlying the presented method is consistent with the results of computer simulation. The latter, in particular, relates to the comparative analysis of the methods of redundant and non-redundant measurements for the stability to changes in the parameters of the transformation function. It is shown that the methods of redundant measurements provide the automatic exclusion of the systematic error component due to the change in the parameters of the transformation function. This is ensured by eliminating the influence of the absolute values of the parameters of the nonlinear transformation function of the photodetector and their deviations from the nominal valueson the measurement result.There are grounds to argue about the promising development of methods of redundant measurements with various types of transformation functions of the sensor in accuracy improvement. This result is achieved by processing the results of intermediate measurements in accordance with the equation of redundant measurements. In addition, if necessary, the proposed methods allow the implementation of metrological self-contro