Comparisons between numerical models and present day tokamak devices rely upon accurate diagnostic measurements of the key plasma parameters. In assessing the effect of energetic particle-driven instabilities upon their confinement, it is extremely important to measure the amplitude of internal modes. This is generally difficult to do accurately as it usually involves extrapolating field measurements at the edge to determine the mode amplitudes in the plasma core. In this work we demonstrate how it may be possible to calculate the absolute value of the amplitude of these modes from the measured spectrum of frequency sweeping that has been observed in the excitation of Toroidal Alfvén Eigenmodes (TAE). In particular, numerical simulations of the bump-on-tail kinetic instabilities near marginal instability have shown how a hole and clump spontaneously appear in the particle distribution function and how this process supports a set of long-lived Bernstein, Greene, Kruskal (BGK) nonlinear waves that shift up and down in frequency. A similar nonlinear kinetic process of hole-clump production also occurs for TAE modes driven unstable by the radial gradient of the fast ion pressure. This mechanism is a primary candidate to explain the fast frequency sweeping observed in several experiments. Figures 1 and 2 show two such experimental examples in the JET and MAST tokamaks respectively.