The fractal energy measurement and the singularity energy spectrum analysis

► We propose the fractal energy measurement (FEM) and the singularity energy spectrum (SES). ► We study the Hausdorff measure and local direction angle of the fractal energy element. ► The compatibility between the FEM and the traditional energy is proved. ► The approximation algorithm of SES is deduced. ► Simulation shows SES represents the energy distribution in singularity domain.