MATLAB Algorithms for Multifractal Spectrum and Box-Counting Dimension Calculation

Through MATLAB software, we can develop and enhance algorithms for calculating multifractal spectrum and box-counting dimension. These algorithms have wide-ranging applications, particularly in mechanical equipment fault diagnosis and feature extraction. By implementing fundamental fractal theory for fault diagnosis, we obtain highly valuable reference information through computational methods that involve partitioning data into grid boxes of varying sizes and analyzing scaling behaviors. The research and optimization of these algorithms are significant for improving mechanical equipment reliability and performance. The MATLAB implementation typically includes functions for box-counting dimension calculation using logarithmic regression of box counts versus scale, and multifractal spectrum computation through moment analysis of probability measures across different scales. These algorithms can be further researched and refined to meet requirements across various domains and applications, with potential enhancements including parallel processing for large datasets and adaptive partitioning strategies. By deepening our study of fractal theory and methodologies, we can continuously expand research in fault diagnosis领域 and provide engineers and researchers with more advanced computational tools. The code structure often incorporates visualization functions for spectrum plotting and dimension validation, making the results accessible for practical applications. In summary, MATLAB-based algorithms for multifractal spectrum and box-counting dimension calculation demonstrate substantial application prospects and research value, with robust implementations featuring error handling and parameter optimization capabilities.