A spectral stochastic approach to the inverse heat conduction problem

A spectral stochastic approach to the inverse heat conduction problem (IHCP) is presented. In IHCP, one computes an unknown boundary heat flux from given temperature history data at a sensor location. In the stochastic inverse heat conduction problem (SIHCP), the full statistics of the boundary heat flux are computed given the stochastic nature of the temperature sensor data and in general accounting for uncertainty in the material data and process conditions. The governing continuum equations are solved using the spectral stochastic finite element method (SSFEM). The stochasticity of inputs is represented spectrally by employing orthogonal polynomials as the trial basis in the random space. Solution to the ill-posed SIHCP is then sought in an optimization sense in a function space that includes the random space. The gradient of the objective function is computed in a continuum sense using an adjoint framework. Finally, an example is presented in the solution of a one-dimensional stochastic inverse heat conduction problem in order to highlight the methodology and potential applications of the proposed techniques.