A Comparative Study of Empirical Mode Decomposition-Based Filtering for Impact Signal

A Novel Noise Reduction Method of UAV Magnetic Survey Data Based on CEEMDAN, Permutation Entropy, Correlation Coefficient and Wavelet Threshold Denoising

Despite the increased attention that has been given to the unmanned aerial vehicle (UAV)-based magnetic survey systems in the past decade, the processing of UAV magnetic data is still a tough task. In this paper, we propose a novel noise reduction method of UAV magnetic data based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), permutation entropy (PE), correlation coefficient and wavelet threshold denoising. The original signal is first decomposed into several intrinsic mode functions (IMFs) by CEEMDAN, and the PE of each IMF is calculated. Second, IMFs are divided into four categories according to the quartiles of PE, namely, noise IMFs, noise-dominant IMFs, signal-dominant IMFs, and signal IMFs. Then the noise IMFs are removed, and correlation coefficients are used to identify the real signal-dominant IMFs. Finally, the wavelet threshold denoising is applied to the real signal-dominant IMFs, the denoised signal can be obtained by combining the signal IMFs and the denoised IMFs. Both synthetic and field experiments are conducted to verify the effectiveness of the proposed method. The results show that the proposed method can eliminate the interference to a great extent, which lays a foundation for the further interpretation of UAV magnetic data.

Signal extraction using complementary ensemble empirical mode in pipeline magnetic flux leakage nondestructive evaluation

The magnetic flux leakage (MFL) evaluation is often used for the overhauling of oil extracting operation in the oil field to realize the real-time damage assessment of the pipeline. Since the MFL signal is affected by various noise sources in the field, this paper introduces the complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN). On the basis of this, a particle swarm optimization wavelet threshold (PSO-WT) method is proposed, and the signal reconstruction option is improved to extract the leakage magnetic flux signal of tubing defects. First, CEEMDAN is used to add pairs of positive and negative white noise to the MFL signal, and then the signal is decomposed into several intrinsic mode functions (IMFs). Second, the correlation coefficient selection limit is defined. Taking into account the characteristics of the decomposed signal, the useless IMFs and useful IMFs are selected from the IMF components, where some of the useful IMF components contain less noise. Third, the PSO-WT algorithm is combined to further filter the noisy and useful IMF components. Finally, the filtered IMF components and the pure useful IMF components are selected to reconstruct the signal. In the experiment, the ensemble empirical mode decomposition (EEMD) method and CEEMDAN are used to decompose the noisy MFL signals ensemble in the field. The MFL signal is reconstructed under the correlation coefficient selection. It can be seen from the comparison of EEMD that the MFL signal is reconstructed under the same conditions after CEEMDAN decomposition, and its signal-to-noise ratio is increased by 8%. At the same time, after CEEMDAN decomposition, the selected noisy useful IMFs are further filtered by the wavelet threshold (WT) method and the PSO-WT method. Also, it indicates that the reconstructed signal processed by PSO-WT is 17% higher than the reconstructed signal after WT processing.

Non-Contact Geomagnetic Detection Using Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Teager Energy Operator

During the non-contact geomagnetic detection of pipeline defects, measured signals generally contain noise, which reduces detection efficiency. Complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) has recently emerged as a signal filtering method, but its filtering performance is influenced by two parameters: the amplitude of added noise and the number of ensemble trials. To solve this issue and improve detection accuracy and distinguishability, a detection method based on improved CEEMDAN (ICEEDMAN) and the Teager energy operator (TEO) is proposed. The magnetic detection signal was first decomposed into a series of intrinsic mode functions (IMFs) by CEEMDAN with initial parameters. Signal IMFs were then distinguished using the Hurst exponent to reconstruct the preliminary filtered signal, and its maximum value (except the zero point) of the normalized autocorrelation function was defined as salp swarm algorithm (SSA) fitness. The optimal parameters that maximize fitness were found by SSA iterations, and their corresponding filtered signal was obtained. Finally, the gradient calculation and TEO were carried out to complete non-contact geomagnetic detection. The results of the simulated signal based on magnetic dipole under a noisy environment and field testing prove that ICEEMDAN denoising has better filtering performance than conventional CEEMDAN denoising methods, and ICEEMDAN-TEO has obvious advantages compared to other detection methods in the aspects of location error, peak side-lobe ratio, and integrated side-lobe ratio.

A Hybrid Energy Feature Extraction Approach for Ship-Radiated Noise Based on CEEMDAN Combined with Energy Difference and Energy Entropy

Influenced by the complexity of ocean environmental noise and the time-varying of underwater acoustic channels, feature extraction of underwater acoustic signals has always been a difficult challenge. To solve this dilemma, this paper introduces a hybrid energy feature extraction approach for ship-radiated noise (S-RN) based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) combined with energy difference (ED) and energy entropy (EE). This approach, named CEEMDAN-ED-EE, has two main advantages: (i) compared with empirical mode decomposition (EMD) and ensemble EMD (EEMD), CEEMDAN has better decomposition performance by overcoming mode mixing, and the intrinsic mode function (IMF) obtained by CEEMDAN is beneficial to feature extraction; (ii) the classification performance of the single energy feature has some limitations, nevertheless, the proposed hybrid energy feature extraction approach has a better classification performance. In this paper, we first decompose three types of S-RN into sub-signals, named intrinsic mode functions (IMFs). Then, we obtain the features of energy difference and energy entropy based on IMFs, named CEEMDAN-ED and CEEMDAN-EE, respectively. Finally, we compare the recognition rate for three sorts of S-RN by using the following three energy feature extraction approaches, which are CEEMDAN-ED, CEEMDAN-EE and CEEMDAN-ED-EE. The experimental results prove the effectivity and the high recognition rate of the proposed approach.

Noise Reduction Method of Underwater Acoustic Signals Based on Uniform Phase Empirical Mode Decomposition, Amplitude-Aware Permutation Entropy, and Pearson Correlation Coefficient

Noise reduction of underwater acoustic signals is of great significance in the fields of military and ocean exploration. Based on the adaptive decomposition characteristic of uniform phase empirical mode decomposition (UPEMD), a noise reduction method for underwater acoustic signals is proposed, which combines amplitude-aware permutation entropy (AAPE) and Pearson correlation coefficient (PCC). UPEMD is a recently proposed improved empirical mode decomposition (EMD) algorithm that alleviates the mode splitting and residual noise effects of EMD. AAPE is a tool to quantify the information content of nonlinear time series. Unlike permutation entropy (PE), AAPE can reflect the amplitude information on time series. Firstly, the original signal is decomposed into a series of intrinsic mode functions (IMFs) by UPEMD. The AAPE of each IMF is calculated. The modes are separated into high-frequency IMFs and low-frequency IMFs, and all low-frequency IMFs are determined as useful IMFs (UIMFs). Then, the PCC between the high-frequency IMF with the smallest AAPE and the original signal is calculated. If PCC is greater than the threshold, the IMF is also determined as a UIMF. Finally, all UIMFs are reconstructed and the denoised signal is obtained. Chaotic signals with different signal-to-noise ratios (SNRs) are used for denoising experiments. Compared with EMD and extreme-point symmetric mode decomposition (ESMD), the proposed method has higher SNR and smaller root mean square error (RMSE). The proposed method is applied to noise reduction of real underwater acoustic signals. The results show that the method can further eliminate noise and the chaotic attractors are smoother and clearer.

A New Underwater Acoustic Signal Denoising Technique Based on CEEMDAN, Mutual Information, Permutation Entropy, and Wavelet Threshold Denoising

Owing to the complexity of the ocean background noise, underwater acoustic signal denoising is one of the hotspot problems in the field of underwater acoustic signal processing. In this paper, we propose a new technique for underwater acoustic signal denoising based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), mutual information (MI), permutation entropy (PE), and wavelet threshold denoising. CEEMDAN is an improved algorithm of empirical mode decomposition (EMD) and ensemble EMD (EEMD). First, CEEMDAN is employed to decompose noisy signals into many intrinsic mode functions (IMFs). IMFs can be divided into three parts: noise IMFs, noise-dominant IMFs, and real IMFs. Then, the noise IMFs can be identified on the basis of MIs of adjacent IMFs; the other two parts of IMFs can be distinguished based on the values of PE. Finally, noise IMFs were removed, and wavelet threshold denoising is applied to noise-dominant IMFs; we can obtain the final denoised signal by combining real IMFs and denoised noise-dominant IMFs. Simulation experiments were conducted by using simulated data, chaotic signals, and real underwater acoustic signals; the proposed denoising technique performs better than other existing denoising techniques, which is beneficial to the feature extraction of underwater acoustic signal.

Trivariate Empirical Mode Decomposition via Convex Optimization for Rolling Bearing Condition Identification

As a multichannel signal processing method based on data-driven, multivariate empirical mode decomposition (MEMD) has attracted much attention due to its potential ability in self-adaption and multi-scale decomposition for multivariate data. Commonly, the uniform projection scheme on a hypersphere is used to estimate the local mean. However, the unbalanced data distribution in high-dimensional space often conflicts with the uniform samples and its performance is sensitive to the noise components. Considering the common fact that the vibration signal is generated by three sensors located in different measuring positions in the domain of the structural health monitoring for the key equipment, thus a novel trivariate empirical mode decomposition via convex optimization was proposed for rolling bearing condition identification in this paper. For the trivariate data matrix, the low-rank matrix approximation via convex optimization was firstly conducted to achieve the denoising. It is worthy to note that the non-convex penalty function as a regularization term is introduced to enhance the performance. Moreover, the non-uniform sample scheme was determined by applying singular value decomposition (SVD) to the obtained low-rank trivariate data and then the approach used in conventional MEMD algorithm was employed to estimate the local mean. Numerical examples of synthetic defined by the fault model and real data generated by the fault rolling bearing on the experimental bench are provided to demonstrate the fruitful applications of the proposed method.

A Hybrid De-Noising Algorithm for the Gear Transmission System Based on CEEMDAN-PE-TFPF

In order to remove noise and preserve the important features of a signal, a hybrid de-noising algorithm based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Permutation Entropy (PE), and Time-Frequency Peak Filtering (TFPF) is proposed. In view of the limitations of the conventional TFPF method regarding the fixed window length problem, CEEMDAN and PE are applied to compensate for this, so that the signal is balanced with respect to both noise suppression and signal fidelity. First, the Intrinsic Mode Functions (IMFs) of the original spectra are obtained using the CEEMDAN algorithm, and the PE value of each IMF is calculated to classify whether the IMF requires filtering, then, for different IMFs, we select different window lengths to filter them using TFPF; finally, the signal is reconstructed as the sum of the filtered and residual IMFs. The filtering results of a simulated and an actual gearbox vibration signal verify that the de-noising results of CEEMDAN-PE-TFPF outperforms other signal de-noising methods, and the proposed method can reveal fault characteristic information effectively.