Estimation of heat flux by using reduced model and the adjoint method. Application to a brake disc rotating

In this study, an approach for inverse problem is proposed to estimate a time dependent heat flux on a braking system. This approach combines modal reduction and conjugate gradient method with adjoint method. A brake disc with variable velocity and thermal solicitations is treated. In a first step, Branch Eigenmodes Reduction Method is used to build a reduced model which allows reduction of computing time while conserving a satisfying precision on temperature field. In a second step, an inverse algorithm based on adjoint method is applied to recover time dependent heat flux from temperature calculation. Compared to Beck method, adjoint method gives accurate results without any regularization. The proposed approach enables to perform a quasi on-line estimation.