Modelling and Calculation of Micro-resistance Measurement

Mirco resistors are the core components of precision instruments, and the accuracy of tiny resistance values measurement largely determines the performance of precision instruments. However, the laboratory has found a bottleneck in measuring micro-resistance, so this paper combines mathematical models based on voltage measurement locations and current measurement locations to estimate tiny resistance values. This paper firstly uses least squares method to fit the experimental data globally once and globally twice, and greatly improves the ill-conditioned system of equations by means of the selection of independent variables for multivariate fitting. Moreover, in order to improve the accuracy and optimize the model, the idea of piecewise fitting is introduced to the model, and finally the model is found to be better under piecewise fitting. In addition, in order to meet the needs of actual industrial production, continuity constraints are added to the piecewise linear fitting (PLF) model in this paper. In order to improve the generalization ability of the model, some random perturbations are added to the data set in this paper and then fitted to observe the fitting error compared with the error before the random perturbations are added. The final empirical evidence indicates that the model finally derived in this paper estimates the resistance value of tiny resistors with high accuracy, high interpretability and easy operation, and has some practical engineering application production value.