Addressing multi-step inverse heat transfer problems via reduced order models in a cooling process for polymer pipes with sparse measurements

In modern polymer pipe extrusion processes with connected post-processing steps, the intermediate cooling and conditioning process is essential for the resulting product quality. In such cases, computationally efficient models are required for real-time process control and optimization. Unfortunately, heat transfer coefficients are rarely known for actual production processes, leading to an inverse heat transfer problem. Existing methods mainly rely on computationally intensive numerical models or on data intensive neural networks. Both are not suitable, if only sparse measurements are available and a fast execution time is required. In contrast to that, we propose to use a proper orthogonal decomposition and project the governing heat equation onto extracted basis functions via the Galerkin method. This leads to an efficient and accurate reduced order model, which can be used for parameter identification and subsequent process control. Regarding the identification, we address the ill-posed problem with well-known relative constraints, l 2 regularization and decomposition of coefficients based on the Nusselt number. Simulation and experimental results show that the heat transfer coefficients are consistently identified and robust against initial parameter guesses despite sparse and noisy temperature measurements. Consequently, the proposed method can be efficiently applied in cooling and conditioning processes in polymer extrusion and related applications such as identifying the heat transfer coefficients and thermal resistance in pressurized surge lines of nuclear power plants and brick walls in melting furnaces respectively. • Reduced order model via Galerkin method and proper orthogonal decomposition. • Relative constraints and L 2 regularization to address the ill-posed problem. • Theory-based coefficient decomposition to reduce the number of unknowns. • Validation with an actual production process with multiple product dimensions. • Consistent identification of coefficients despite sparse and noisy measurements.