Cross-sectional layout optimization framework of an umbilical with fillers based on image processing method

Umbilicals are the critical component to connect the offshore renewable energy system (e.g., floating wind turbines, wave energy converters) and floating platform. Their cross-sectional layout plays a crucial role in ensuring mechanical performance, energy transmission reliability, and structural integrity. Traditional layout optimizations mainly focus on functional components (e.g., steel tubes, electrical and optical cables), often leaving substantial internal gaps. These gaps reduce compactness and radial stiffness of cross-section, and thereby potentially compromise the system reliability and safety. Additionally, direct steel tube contact increases failure risks caused by inner wear. Integrating fillers into the optimization process is crucial, but the coupling between filler and functional component layouts, along with irregular gaps, makes determining optimal filler parameters (e.g., number, position, radius) highly challenging. So, a cross-sectional filling method based on morphological image processing is proposed to automatically determine filler parameters. In this method, grayscale and binarization operations identify the filling domain, while morphological dilation and erosion remove minor regions. The flood-fill algorithm is then performed to segment the domain, and detect subdomain boundaries. Finally, the filler radii are determined through Euclidean distances between pixels. To reduce manufacturing costs, three schemes, i.e., maximum, minimum, and average radius filling schemes are applied to uniform the filler radii. Based on this, a cross-sectional layout optimization model is formulated to maximize compactness while ensuring the performances of inner wear, and heat dissipation. To efficiently solve this optimization problem, a two-stage approach based on Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP) is proposed. In comprehensive solving stage, GA and SQP are combined to ensure a global searching capability while enhancing the local searching efficiency. In the fine-tuning stage, only SQP is used for a rapid cross-sectional layout adjustment. Finally, we validate the effectiveness and applicability of our method through numerical examples. The proposed framework is helpful to improve layout efficiency, ensure the reliability of umbilical systems, and enhance the safety and performance of offshore renewable energy infrastructure.