The author′s previous work proposed the curvature difference probability method of the waveform fractal dimension for a simply supported beam with pulse or step excitation. However, such excitation methods suffer from limitations in engineering. The main purpose of this paper is to study the method′s applicability to the structures excited by stochastic excitation at their bases. Firstly, the characteristic value of the acceleration signal is extracted based on the fractal dimension. Then, the curvature difference method is used to deal with these characteristic values. Finally, the statistic value from multiple identifications (i.e. damage probability) is determined as the index to identify and locate the damage. Based on the most basic system, i.e. the mass-spring-damper (MSD) system, many single and multiple damage cases of a 20 DOF MSD system with white noise excitation at the base are studied. Furthermore, a 6-story lumped-mass shear frame model is built in the laboratory, and experimental cases based on the shaking table are also implemented. Results show that the proposed technique can locate the damage very well with the stochastic excitation at the base of the structure, and has very strong robustness against the noise (it still works at a 15% noise level). Morever, the technique has low dependence on the accuracy of the structural finite element model. All of these lay a good foundation for its applications in engineering.