Improved ensemble local mean decomposition based on cubic trigonometric cardinal spline interpolation and its application for rotating machinery fault diagnosis

Ensemble local mean decomposition has been gradually introduced into mechanical vibration signal processing due to its excellent performance in electroencephalogram signal analysis. However, an unsatisfactory problem is that ensemble local mean decomposition cannot effectively process vibration signals of complex mechanical system due to the constraints of moving average. The process of moving average is time-consuming and inaccurate in complex signal analysis. Therefore, an improved ensemble local mean decomposition method called C-ELMD with modified envelope algorithm based on cubic trigonometric cardinal spline interpolation is proposed in this article. First, the shortcomings in sifting process of ensemble local mean decomposition is discussed and, furthermore, advantages and disadvantages of the common interpolation methods adopted to improve ensemble local mean decomposition are compared. Then, cubic trigonometric cardinal spline interpolation is employed to construct the local mean and envelope curves in a more precise way. In addition, the influence of shape-controlling parameter on envelope estimation accuracy in cubic trigonometric cardinal spline interpolation is also discussed in detail to select an optimal shape-controlling parameter. The effectiveness of cubic trigonometric cardinal spline interpolation for improving the accuracy of ensemble local mean decomposition is demonstrated using a synthetic signal. Finally, the proposed cubic trigonometric cardinal spline interpolation is tested to be effective in gear and bearing fault detection and diagnosis.

On Cardinal Spline Interpolation

In the present paper it is shown that the interpolation problem for multiple knot cardinal splines subject to general interpolation conditions has a unique solution with polynomial growth if the data grow correspondingly provided a certain determinantal condition is satisfied. An application to Hs error estimates for the interpolation with periodic multiple knot splines is given.