Material Data Identification in an Induction Hardening Test Rig with Physics-Informed Neural Networks.

Physics-Informed neural networks (PINNs) have demonstrated remarkable performance in solving partial differential equations (PDEs) by incorporating the governing PDEs into the network's loss function during optimization. PINNs have been successfully applied to diverse inverse and forward problems. This study investigates the feasibility of using PINNs for material data identification in an induction hardening test rig. By utilizing temperature sensor data and imposing the heat equation with initial and boundary conditions, thermo-physical material properties, such as specific heat, thermal conductivity, and the heat convection coefficient, were estimated. To validate the effectiveness of the PINNs in material data estimation, benchmark data generated by a finite element model (FEM) of an air-cooled cylindrical sample were used. The accurate identification of the material data using only a limited number of virtual temperature sensor data points was demonstrated. The influence of the sensor positions and measurement noise on the uncertainty of the estimated parameters was examined. The study confirms the robustness and accuracy of this approach in the presence of measurement noise, albeit with lower efficiency, thereby requiring more time to converge. Lastly, the applicability of the presented approach to real measurement data obtained from an air-cooled cylindrical sample heated in an induction heating test rig was discussed. This research contributes to the accurate offline estimation of material data and has implications for optimizing induction heat treatments.

Error detection and filtering of incompressible flow simulations for aeroacoustic predictions of human voice.

The presented filtering technique is proposed to detect errors and correct outliers inside the acoustic sources, respectively, the first time derivative of the incompressible pressure obtained from large eddy simulations with prescribed vocal fold motion using overlay mesh methods. Regarding the perturbed convective wave equation, the time derivative of the incompressible pressure is the primary sound source in the human phonation process. However, the incompressible pressure can be erroneous and have outliers when fulfilling the divergence-free constraint of the velocity field. This error is primarily occurring for non-conserving prescribed vocal fold motions. Therefore, the method based on a continuous stationary random process was designed to detect rare events in the time derivative of the pressure. The detected events are then localized and treated by a defined window function to increase their probability. As a consequence, the data quality of the non-linearly filtered data is enhanced significantly. Furthermore, the proposed method can also be used to assess convergence of the aeroacoustic source terms, and detect regions and time intervals, which show a non-converging behavior by an impulse-like structure.

Helmholtz's decomposition for compressible flows and its application to computational aeroacoustics.

The Helmholtz decomposition, a fundamental theorem in vector analysis, separates a given vector field into an irrotational (longitudinal, compressible) and a solenoidal (transverse, vortical) part. The main challenge of this decomposition is the restricted and finite flow domain without vanishing flow velocity at the boundaries. To achieve a unique and L 2 -orthogonal decomposition, we enforce the correct boundary conditions and provide its physical interpretation. Based on this formulation for bounded domains, the flow velocity is decomposed. Combining the results with Goldstein's aeroacoustic theory, we model the non-radiating base flow by the transverse part. Thereby, this approach allows a precise physical definition of the acoustic source terms for computational aeroacoustics via the non-radiating base flow. In a final simulation example, Helmholtz's decomposition of compressible flow data using the finite element method is applied to an overflowed rectangular cavity at Mach 0.8. The results show a reasonable agreement with the source data and illustrate the distinct parts of the Helmholtz decomposition.

Aeroacoustic source term computation based on radial basis functions.

In low Mach number aeroacoustics, the known disparity of length scales makes it possible to apply well-suited simulation models using different meshes for flow and acoustics. The workflow of these hybrid methodologies include performing an unsteady flow simulation, computing the acoustic sources, and simulating the acoustic field. Therefore, hybrid methods seek for robust and flexible procedures, providing a conservative mesh to mesh interpolation of the sources while ensuring high computational efficiency. We propose a highly specialized radial basis function interpolation for the challenges during hybrid simulations. First, the computationally efficient local radial basis function interpolation in conjunction with a connectivity-based neighbor search technique is presented. Second, we discuss the computation of spatial derivatives based on radial basis functions. These derivatives are computed in a local-global approach, using a Gaussian kernel on local point stencils. Third, radial basis function interpolation and derivatives are used to compute complex aeroacoustic source terms. These ingredients are necessary to provide flexible source term calculations that robustly connect flow and acoustics. Finally, the capabilities of the presented approach are shown in a numerical experiment with a co-rotating vortex pair.