Refine
Document Type
- Article (1)
- Conference Proceeding (1)
Institute
Keywords
- Angewandte Informatik (1)
- Angewandte Mathematik (1)
- Building Information Modeling (1)
- Computerunterstütztes Verfahren (1)
- Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications (1)
- Elektrostatische Welle (1)
- Empire XPU 8.01 (1)
- MATLAB (1)
- Matlab (1)
- OA-Publikationsfonds2022 (1)
- Rotorblatt (1)
- Windkraftwerk (1)
- crack detection (1)
- electromagnetic waves (1)
- wind turbine rotor blades (1)
One of the most important renewable energy technologies used nowadays are wind power turbines. In this paper, we are interested in identifying the operating status of wind turbines, especially rotor blades, by means of multiphysical models. It is a state-of-the-art technology to test mechanical structures with ultrasonic-based methods. However, due to the density and the required high resolution, the testing is performed with high-frequency waves, which cannot penetrate the structure in depth. Therefore, there is a need to adopt techniques in the fields of multiphysical model-based inversion schemes or data-driven structural health monitoring. Before investing effort in the development of such approaches, further insights and approaches are necessary to make the techniques applicable to structures such as wind power plants (blades). Among the expected developments, further accelerations of the so-called “forward codes” for a more efficient implementation of the wave equation could be envisaged. Here, we employ electromagnetic waves for the early detection of cracks. Because in many practical situations, it is not possible to apply techniques from tomography (characterized by multiple sources and sensor pairs), we focus here on the question of whether the existence of cracks can be determined by using only one source for the sent waves.
The p-Laplace equation is a nonlinear generalization of the Laplace equation. This generalization is often used as a model problem for special types of nonlinearities. The p-Laplace equation can be seen as a bridge between very general nonlinear equations and the linear Laplace equation. The aim of this paper is to solve the p-Laplace equation for 2 < p < 3 and to find strong solutions. The idea is to apply a hypercomplex integral operator and spatial function theoretic methods to transform the p-Laplace equation into the p-Dirac equation. This equation will be solved iteratively by using a fixed point theorem.