Understanding the real-time characterization of impact events in mechanical systems is important for health monitoring and reliability analysis [

1,

2]. The instrumented falling weight impact (IFWI) technique really started to develop with the progress of electronic boards able to record short time events [

3,

4]. At present, experimental research for impact tests mainly focuses on the vertical falling weight impact [

5,

6]. However, there are few studies on the oblique impact test. To simulate these events and estimate the real-time characterization of impact events, an experimental rig was designed to measure the real-time signal under different pendulum angle conditions during the impact test.

However, the measured signal often contains noise when the experiment is conducted. The noise behaves as unwanted frequencies and amplitude oscillations. These oscillations corrupt the signal information. Thus, it is very much necessary to develop a method to extract signal information from the noisy signal. At present, there are many filtering methods that fall mainly into two classes: one is a linear filter and the other a non-linear filter. Linear filters such as an average filter [

7] and a Winer filter [

8] are suitable to filter signal from a stationary system. However, when the signal comes from a non-linear and non-stationary system, a non-linear filter works best for filtering out noise—the wavelet filter is widely used [

9]. The signal is split into low and high frequency coefficients in the wavelet filter. The filtered signal can be obtained by soft or hard threshold mechanisms [

10]. However, the wavelet basis function has to be pre-defined, and this method is not adaptive in essence.

Empirical Mode Decomposition (EMD) was introduced by Huang [

11]. This algorithm is an alternative method for analyzing data from non-stationary and non-linear systems, and behaves as the filter bank [

12]. The signal can be adaptively decomposed into a set of Intrinsic Mode Functions (IMFs) by EMD. The IMFs carry the detailed information of the signal. For noisy signals, the EMD can decompose the noisy signal into noisy signal modes and useful signal (noise-less) modes. The main task based on EMD filtering is to identify the two class modes (noisy and useful signal modes). Recently, Albert et al. [

13] and Peng [

14] used a correlation-based threshold to identify the relevant modes (noisy signal modes and useful signal modes). However, the strong correlation between the noisy signal and the first mode make it difficult to identify the relevant mode. Boudraa [

15] proposed the consecutive mean squared error (CMSE) to find the relevant modes by setting an appropriate threshold method, but the method can be trapped in a local minima in some situations. To void the case, Boudraa [

16] introduced a new method to select the relevant mode by the striking similarity between the probability density function (pdf) of the input signal and each IMF. However, this method performs poorly for the filtering signals containing fractional Gaussian noise when the Hurst parameter is close to unity [

17]. There are also some filtering algorithms based on EMD [

18,

19,

20]. However, mode mixing—in which oscillations of different amplitudes are found in a mode, or similar oscillations are encountered in different modes—often occurs in EMD decomposition. This phenomenon prevents the complete extraction of the signal information. To overcome this disadvantage, Wu and Huang [

21] introduced the Ensemble Empirical Mode Decomposition (EEMD), which is a method based on the EMD algorithm. The method follows a study of the statistical characteristic of white noise, and adds white noise of a uniform frequency distribution into EMD to avoid mode mixing. However, if the mean square error (MSE) of the added white noise is large, this will lead to a decrease in the signal-to-noise ratio (SNR) and influence the accuracy of the decomposed result. Even if the ensemble size is increased, the decomposed effect cannot improve dramatically, and the computation time is also increased. If the MSE of the added white noise is small, it will decrease the accuracy of the decomposed result, and it is inevitable to bring mode mixing in the low frequency part of IMF obtained by EEMD decomposition. So, EEMD does not completely solve the mode mixing problem. At present, some EEMD-based filtering methods are developed [

22,

23]. However, the EEMD algorithm introduces new problems. The added white noise is not eliminated fully, and the additional modes may have been produced because of the interaction between original signal and white noise. To resolve these problems, the complete EEMD with adaptive noise (CEEMDAN) was introduced [

24]. This method can overcome additional modes, and eliminates the added white noise. At present, the CEEMDAN has been applied in the analysis of laser speckle [

25] and short-term wind speed forecasting [

26]. However, its use in signal filtering can be found in a few references [

27,

28].

In this paper, a new filtering method is proposed. First, the original signal is decomposed by CEEMDAN to obtain IMFs. The axial symmetry waveform (new waveform) can be obtained by sorting IMFs and subsequent calculation of the energy of sorted IMFs. Through calculation the fuzzy entropy of the new waveform, the relevant modes (noisy modes and useful signal modes) can be identified. The criterion of the selected mode is the maximum of the difference between adjacent fuzzy entropies. The simulated signal and measured impact signal are used to filter by the proposed filtering method. For simulated signals with different noise levels, filtering with CEEMDAN and sample entropy, EEMD and fuzzy entropy, and EEMD and sample entropy are compared to evaluate the signal filtering performance. For the measured signal, CEEMDAN and fuzzy entropy, wavelet filter, moving averaging filter, and median filter are used to filter, respectively. The filter performance can be evaluated by de-trended fluctuation analysis (DFA) algorithm, revised mean squared error (RMSE), and revised signal-to-noise ratio (RSNR). The filtering result of simulated and measured signals show that the filtering method based on CEEMDAN and fuzzy entropy outperforms the other filtering methods.