Improving Hilbert-Huang transform(HHT) method

Aim. The HHT method has great advantages in processing non-linear and non-steady-state signals. But, when the signals are complex, there are, in our opinion, some disadvantages pointed out in the introduction of the full paper. Section 1, 2, 3 explain our improvements in the following three aspects: end effect problem, overshoot problem, sifting stop criteria and filtering of false low-frequency components. Section 1 improves the HHT method by defining two extreme value points, connecting adjacent maximum extreme value point and minimum extreme value point, and by fitting the envelope line of the complex signal to be decomposed. Section 2 first finds the overshoot points, which have the maximum difference between the original signal and the envelope signal, and then takes these overshoot points as maximum values to carry out the cubic spline refitting of the envelope line thrice. Section 3 gives eqs.(2) and (3) to obtain the time for stopping the signal decomposition when the correlation coefficient of a certain order IMF signal becomes obviously small, as shown in Table 1. To verify the effectiveness of our improvements, section 4 gives a numerical example for analyzing the response of a composite shell and detecting its small damage. The numerical results, gives in Table 2, 3 and 4, and their analysis show preliminarily that our improved HHT method can effectively decompose IMF signals and detect small structural damage.