Narrow Results

In this paper, we deal with two different problems. First, we provide the convergence rates of multiresolution approximations, with respect to the supremum norm, for the class of elliptic splines defined in Ref. 10, and in particular for polyharmonic splines. Secondly, we consider the problem of recovering a function from a sample of noisy data. To this end, we define a linear and smooth estimator obtained from a multiresolution process based on polyharmonic splines. We discuss its asymptotic properties and we prove that it converges to the unknown function almost surely.

As for the problems of loud noise of the rotary machine’s vibration signal and incomplete denoising effects by the application of the traditional EEMD denoise method, a new denoise method that combined EEMD with the improved generalized morphological filter has been proposed. Using this method, the EEMD first disintegrates the vibration signal and obtains IMF components, and then denoises the obtained IMF components by the improved generalized morphological filter, and reconstructs IMF components after handling. Improved genetic algorithm is introduced into the generalized morphological filter, in order to establish a quick, accurate and flexible structural element selection mode. Through digital simulation experiment and compared with the traditional EEMD method, it is proved that this method has better denoising effect of the vibration signal and ensures the better signal integrity.