An improved low-frequency noise reduction method in shock wave pressure measurement based on mode classification and recursion extraction.

The ill-posed problem of shock wave pressure (SWP) measurement comes from the influence of low-frequency noise components to measured responses and leads to an inaccurate result. To address this problem, an improved method, referred to as recursive empirical mode decomposition (REMD), is proposed for filtering low-frequency noises from the SWP measurement signals. By means of empirical mode decomposition (EMD), the measurement signal is adaptively decomposed into several intrinsic mode functions (IMFs) without any prior information. A mode classification scheme is firstly developed to select two mode indexes for separating the useful, mixed and noisy IMFs based on energy gradient and ringing amplitude ratio. Then, an adaptive diminishing white noise-assisted technology is presented to iteratively extract the remaining useful components from the mixed IMFs based on the damping ratio of SWP measurement signal. The final denoised result is achieved by a partial reconstruction with the useful IMFs and the useful components obtained from each extraction process. The effectiveness of the proposed method is verified through a series of simulated and real SWP measurement signals. Simulated results show that the REMD method always produces the largest SNR and the smallest RMSE and PRD in both single and mixed noise situations. Furthermore, the denoised results from real SWP measurement experiments with PR and PE sensors under different pressure conditions also demonstrate the superiority of the proposed method over the existing approaches in both denoising ability and signal integrity.