Synthetic Data Generation for Thermocouples. An Original Approach to Simulation Modelling of a Measurement Function

Thermocouples account for more than 60% of all temperature sensors in commercial applications. At the same time, operation of thermocouples under the influence of harsh environments results in thermoelectric properties shift of thermocouple wire and growth a thermocouple error. Error detection and compensation are key issues for metrological self-check methods based on tracking drift of a measurement function. Development and tuning of these methods require large datasets with corrupted measurements during operation thermocouple. However, limitations of industrial datasets cause poor sensitivity to error and bounded scalability of current self-check methods. This paper outlines an original approach to development, tuning and validation of a simulation model for deteriorated thermocouples. The model generates synthetic data for thermocouple with drift of the measurement function independent of operation conditions. The model relies on distortion of the low-order coefficients from a nominal measurement function. The coefficient distortion method implements a uniform random distribution for each coefficient with an overall limit for the maximum thermocouple error. A validation scheme consists of three steps: forming an experimental dataset with the established maximum error, estimating model possibility to represent the experimental dataset, evaluating homogeneity of the coefficients for the simulated and experimental datasets via a statistical criterion. The proposed approach was tested for the K-type thermocouple with a maximum error of up to 3 above compared to the standard allowed error for temperature range of 100…800°C. The simulation model represents the experimental dataset with an error less than 0.25 of the standard error allowed for more than 95% of experimental points. Statistical evaluation of coefficients samples confirms H0-hypothesis about the identity of the general sample for each low-order coefficient with significance level $a=0.01$ and above.