Akademik Veri Yönetim Sistemi
Engineering Research Express, cilt.7, sa.1, ss.1-18, 2025 (ESCI, Scopus)
Accurate reconstruction of blade vibrations is essential in the safe and efficient operation of turbomachinery. Blade Tip Timing (BTT) is a non-contact technique that enables vibration monitoring without requiring physical sensors on blades. However, since each sensor provides only one data point per rotation, BTT is highly under-sampled. This makes sensor placement a critical factor in ensuring accurate signal reconstruction. Previous methods, especially those based on Particle Swarm Optimization (PSO), have attempted to address this challenge. While PSO can explore large solution spaces, it also has several shortcomings: it is computationally expensive, sensitive to parameter settings, and non-deterministic producing different results on each run. These factors limit its usability in real-time and safety-critical applications. In this study, we propose a novel graph-theoretic approach for optimal sensor placement in BTT systems. Candidate sensor angles are modeled as nodes in a weighted graph, and their pairwise compatibility is measured using the condition number of the sensing matrix, which reflects numerical stability. To find the best sensor configuration, a brute-force maximum clique search is applied, ensuring that all possible combinations are evaluated and the most stable set is selected. This method offers several contributions: it is fully deterministic, requires no parameter tuning, and gives the same result every time. It is significantly faster than PSO and easier to interpret, making it suitable for practical use. Results show that it achieves similar or better reconstruction accuracy compared to PSO, especially when the number of sensors is small. Unlike previous black-box optimization methods, our approach offers clear insight into why specific sensor angles are chosen. However, the brute-force nature of the algorithm can become computationally expensive when the number of candidate angles or sensors is large. Future work may focus on improving scalability, adapting the method to real-time applications, and testing it with experimental data from real blades. Overall, this work presents a reliable, interpretable, and efficient alternative to existing sensor placement techniques for BTT, addressing key limitations of earlier methods and laying the foundation for further development in the field.