Abstract: A hearth erosion monitoring model for blast furnace was proposed based on the temperature data from the embedded thermocouples in the blast furnace hearth， and combining the numerical heat transfer calculation and gradient descent method of optimization theory to find the optimum boundary moving step length factor. The unknown-boundary inverse heat-transfer problem can be effectively solved with the model. Using the monitoring temperature data from thermocouples as input， the hearth inner lining erosion profile and residual thickness were computationally obtained by the proposed model through solving the unknown-boundary heat-transfer problem. Taking the collected known hearth erosion profiles and the corresponding temperature data from thermocouples as check samples， the comparison shows that the average relative error of the model prediction is about 3.6%， and the reliability of the model is thus confirmed.

Key words: boundary movement method, gradient descent method, hearth erosion;monitoring model, blast furnace