Assessment of temperature distributions based on the Adaptive Cross Approximation

During the production process of rolled steel plates quality control plays an important role. The temperature distribution in the plate, which is determined with a temperature measuring device, has to be assessed on homogeneity. The temperature data is stored in a rectangular array. A real-time assessment is required. A new method, the Adaptive Cross Approximation (ACA) for the temperature assessment is proposed. The ACA-method is applied to a two-dimensional rectangular temperature array. The temperature array as a result of measurements contains a stochastic measuring tolerance. Nevertheless, the temperature field, which is usually a full matrix, can be approximated by a series of low rank matrices according to the ACA-method. The number of iteration steps is used as the criterion on homogeneity. Numerical examples, based on real industrial data, illustrate the efficiency of the ACA-method. In most cases, the subjective human evaluation of temperature fields matches with the assessment made by the ACA-method. Furthermore, the ACA-method leads to a significant compression of the temperature arrays and can be also used for archiving of the measured data almost without loss of information.