Research on Ship-Radiated Noise Denoising Using Secondary Variational Mode Decomposition and Correlation Coefficient

A new hybrid prediction model of COVID-19 daily new case data

With the emergence of new mutant corona virus disease 2019 (COVID-19) strains such as Delta and Omicron, the number of infected people in various countries has reached a new high. Accurate prediction of the number of infected people is of far-reaching sig Nificance to epidemiological prevention in all countries of the world. In order to improve the prediction accuracy of COVID-19 daily new case data, a new hybrid prediction model of COVID-19 is proposed, which consists of four modules: decomposition, complexity judgment, prediction and error correction. Firstly, singular spectrum decomposition is used to decompose the COVID-19 data into singular spectrum components (SSC). Secondly, the complexity judgment is innovatively divided into high-complexity SSC and low-complexity SSC by neural network estimation time entropy. Thirdly, an improved LSSVM by GODLIKE optimization algorithm, named GLSSVM, is proposed to improve its prediction accuracy. Then, each low-complexity SSC is predicted by ARIMA, and each high-complexity SSC is predicted by GLSSVM, and the prediction error of each high-complexity SSC is predicted by GLSSVM. Finally, the predicted results are combined and reconstructed. Simulation experiments in Japan, Germany and Russia show that the proposed model has the highest prediction accuracy and the lowest prediction error. Diebold Mariano (DM) test is introduced to evaluate the model comprehensively. Taking Japan as an example, compared with ARIMA prediction model, the RMSE, average error and MAPE of the proposed model are reduced by 93.17%, 91.42% and 81.20% respectively.

A novel prediction model based on decomposition-integration and error correction for COVID-19 daily confirmed and death cases

Coronavirus disease (COVID-19) has infected billion people around the world and affected the economy, but most countries are considering reopening, so the COVID-19 daily confirmed and death cases have increased greatly. It is very necessary to predict the COVID-19 daily confirmed and death cases in order to help every country formulate prevention policies. To enhance the prediction performance, this paper proposes a prediction model based on improved variational mode decomposition by sparrow search algorithm (SVMD), improved kernel extreme learning machine by Aquila optimizer algorithm (AO-KELM) and error correction idea, named SVMD-AO-KELM-error for short-term prediction of COVID-19 cases. Firstly, to solve mode number and penalty factor selection of variational mode decomposition (VMD), an improved VMD based on sparrow search algorithm (SSA), named SVMD, is proposed. SVMD decomposes the COVID-19 case data into some intrinsic mode function (IMF) components and residual is considered. Secondly, to properly selected regularization coefficients and kernel parameters of kernel extreme learning machine (KELM) and improve the prediction performance of KELM, an improved KELM by Aquila optimizer (AO) algorithm, named AO-KELM, is proposed. Each component is predicted by AO-KELM. Then, the prediction error of IMF and residual are predicted by AO-KELM to correct prediction results, which is error correction idea. Finally, prediction results of each component and error prediction results are reconstructed to get final prediction results. Through the simulation experiment of the COVID-19 daily confirmed and death cases in Brazil, Mexico, and Russia and comparison with twelve comparative models, simulation experiment gives that SVMD-AO-KELM-error has best prediction accuracy. It also proves that the proposed model can be used to predict the pandemic COVID-19 cases and offers a novel approach for COVID-19 cases prediction.

Denoising method of machine tool vibration signal based on variational mode decomposition and Whale-Tabu optimization algorithm

The noise from other sources is inevitably mixed in the vibration information of CNC machine tools obtained using the sensors. In this work, a de-noising method based on joint analysis is proposed. The variational mode decomposition (VMD), correlation analysis (CA), and wavelet threshold (WT) denoising are used to denoise the original signal. First, VMD decomposes noisy signals into multiple intrinsic mode functions (IMFs). The penalty factor and decomposition level of VMD parameters are selected by the optimization algorithm by combining the whale optimization algorithm (WOA) and tabu search (TS). The minimum permutation entropy of IMF is used as the fitness function of the proposed fusion algorithm. Then, the IMF is divided into three categories by using the cross-correlation number. They include the pure components, signals containing noise, and complete noise components. Then, the WT method is used to further denoise the signals, and signal reconstruction is performed with the pure component to obtain the denoised signal. This joint analysis denoising method is named TS-WOA-VMD-CA-WT. The simulation results show that the fusion optimization algorithm proposed in this work has better performance as compared to the single optimization algorithm. It performs effectively when applied to the actual machine tool vibration signal denoising. Therefore, the proposed TS-WOA-VMD-CA-WT method is superior to other existing denoising techniques and has good generality, which is expected to be popularized and applied more widely.

A new hybrid prediction model of cumulative COVID-19 confirmed data

Establishing an accurate and efficient prediction model is of great significance for governments and other social organizations to formulate prevention and control policies and curb the explosive spread of the pandemic. To improve prediction accuracy of cumulative COVID-19 confirmed data, a new hybrid prediction model based on gradient-based optimizer variational mode decomposition (GVMD), extreme learning machine (ELM), and autoregressive integrated moving average (ARIMA), named GVMD-ELM-ARIMA, is proposed. To solve the problem of selecting the k value and the penalty factor α in variational mode decomposition (VMD), this paper proposes gradient-based optimizer variational mode decomposition (GVMD), which realizes the self-adaptive determination of k value and α value. Firstly, GVMD decomposes the cumulative COVID-19 confirmed data into some intrinsic mode functions (IMFs) and a residual component (IMFr). Secondly, IMFs are predicted by ELM. Then, IMFr is predicted by ARIMA. Finally, the final prediction results are obtained by reconstructing the prediction result of IMFs and IMFr. The cumulative COVID-19 confirmed data of the United States, India and Russia is used to verify its effectiveness. Taking the United States as an example, compared with the average MAPE, RMSE and MAE of the single model, the average MAPE of the hybrid model is reduced by 47.27%, the average RMSE is reduced by 44.50%, and the average MAE is reduced by 55.34%. Compared with GVMD-ELM-ELM, GVMD-ELM-ARIMA proposed in this paper reduces the MAPE by 60%, the RMSE by 56.85%, and the MAE by 61.61%. The experimental results show that GVMD-ELM-ARIMA has best prediction accuracy, and it provides a new method for predicting the cumulative COVID-19 confirmed data.

MEMS Hydrophone Signal Denoising and Baseline Drift Removal Algorithm Based on Parameter-Optimized Variational Mode Decomposition and Correlation Coefficient

Underwater acoustic technology is an important means of detecting the ocean. Due to the complex influence of the marine environment, there is a lot of noise and baseline drift in the signals collected by hydrophones. In order to solve this problem, this paper proposes a denoising and baseline drift removal algorithm for MEMS vector hydrophone based on whale-optimized variational mode decomposition (VMD) and correlation coefficient (CC). Firstly, the power spectrum entropy (PSE), which reflects the variation characteristics of the signal frequency is selected as the fitness function of the whale-optimization algorithm to find the parameters (K,α) of the VMD. It is easier to find the global optimal solution of the parameters by combining the whale-optimization algorithm. Then, using the VMD algorithm after obtaining the parameters, the original signal is decomposed to obtain the intrinsic mode functions (IMFs), and calculating the correlation coefficients (CCs) between the IMFs and the original signal. Finally, the CC threshold is used to remove the noise IMFs, and the rest of the useful IMFs are reconstructed to complete the denoising and baseline drift removal process of the original signals. In the simulation experiments, the algorithm proposed in this paper shows better performance by comparing conventional digital signal-processing methods and the related algorithms proposed recently. Applied in the experiments of a MEMS hydrophone, the effectiveness of the proposed algorithm is also verified. This algorithm can provide new ideas for signal denoising and baseline drift removal.

A Novel Linear Spectrum Frequency Feature Extraction Technique for Warship Radio Noise Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, Duffing Chaotic Oscillator, and Weighted-Permutation Entropy

Warships play an important role in the modern sea battlefield. Research on the line spectrum features of warship radio noise signals is helpful to realize the classification and recognition of different types of warships, and provides critical information for sea battlefield. In this paper, we proposed a novel linear spectrum frequency feature extraction technique for warship radio noise based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), duffing chaotic oscillator (DCO), and weighted-permutation entropy (W-PE). The proposed linear spectrum frequency feature extraction technique, named CEEMDAN-DCO-W-PE has the following advantages in comparison with other linear spectrum frequency feature extraction techniques; (i) as an adaptive data-driven algorithm, CEEMDAN has more accurate and more reliable decomposition performance than empirical mode decomposition (EMD) and ensemble EMD (EEMD), and there is no need for presetting parameters, such as decomposition level and basis function; (ii) DCO can detect the linear spectrum of narrow band periodical warship signals by way of utilizing its properties of sensitivity for weak periodical signals and the immunity for noise; and (iii) W-PE is used in underwater acoustic signal feature extraction for the first time, and compared with traditional permutation entropy (PE), W-PE increases amplitude information to some extent. Firstly, warship radio noise signals are decomposed into some intrinsic mode functions (IMFs) from high frequency to low frequency by CEEMDAN. Then, DCO is used to detect linear spectrum of low-frequency IMFs. Finally, we can determine the linear spectrum frequency of low-frequency IMFs using W-PE. The experimental results show that the proposed technique can accurately extract the line spectrum frequency of the simulation signals, and has a higher classification and recognition rate than the traditional techniques for real warship radio noise signals.

Feature Extraction and Reconstruction by Using 2D-VMD Based on Carrier-Free UWB Radar Application in Human Motion Recognition

As the size of the radar hardware platform becomes smaller and smaller, the cost becomes lower and lower. The application of indoor radar-based human motion recognition has become a reality, which can be realized in a low-cost device with simple architecture. Compared with narrow-band radar (such as continuous wave radar, etc.), the human motion echo signal of the carrier-free ultra-wideband (UWB) radar contains more abundant characteristic information of human motion, which is helpful for identifying different types of human motion. In this paper, a novel feature extraction method by two-dimensional variational mode decomposition (2D-VMD) algorithm is proposed. And it is used for extracting the primary features of human motion. The 2D-VMD algorithm is an adaptive non-recursive multiscale decomposition method for nonlinear and nonstationary signals. Firstly, the original 2D radar echo signals are decomposed by the 2D-VMD algorithm to capture several 2D intrinsic mode function (BIMFs) which represent different groups of central frequency components of a certain type of human motion. Secondly, original echo signals are reconstructed according to the several BIMFs, which not only have a certain inhibitory effect on the clutter in the echo signal, but can also further demonstrate that the BIMFs obtained by the 2D-VMD algorithm can represent the original 2D echo signal well. Finally, based on the measured ten different types of UWB radar human motion 2D echo analysis signals, the characteristics of these different types of human motion are extracted and the original echo signal are reconstructed. Then, the three indicators of the PCC, UQI, and PSNR between the original echo signals and extraction/reconstruction 2D signals are analyzed, which illustrate the effectiveness of 2D-VMD algorithm to extract feature of human motion 2D echo signals of the carrier-free UWB radar. Experimental results show that BIMFs by 2D-VMD algorithm can well represent the echo signal characteristics of this type of human motion, which is a very effective tool for human motion radar echo signal feature extraction.

Feature Extraction of Ship-Radiated Noise Based on Regenerated Phase-Shifted Sinusoid-Assisted EMD, Mutual Information, and Differential Symbolic Entropy

To improve the recognition accuracy of ship-radiated noise, a feature extraction method based on regenerated phase-shifted sinusoid-assisted empirical mode decomposition (RPSEMD), mutual information (MI), and differential symbolic entropy (DSE) is proposed in this paper. RPSEMD is an improved empirical mode decomposition (EMD) that alleviates the mode mixing problem of EMD. DSE is a new tool to quantify the complexity of nonlinear time series. It not only has high computational efficiency, but also can measure the nonlinear complexity of short time series. Firstly, the ship-radiated noise is decomposed into a series of intrinsic mode functions (IMFs) by RPSEMD, and the DSE of each IMF is calculated. Then, the MI between each IMF and the original signal is calculated; the sum of MIs is taken as the denominator; and each normalized MI (norMI) is obtained. Finally, each norMI is used as the weight coefficient to weight the corresponding DSE, and the weighted DSE (WDSE) is obtained. The WDSEs are sent into the support vector machine (SVM) classifier to classify and recognize three types of ship-radiated noise. The experimental results demonstrate that the recognition rate of the proposed method reaches 98.3333%. Consequently, the proposed WDSE method can effectively achieve the classification of ships.

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.

The Data-Driven Optimization Method and Its Application in Feature Extraction of Ship-Radiated Noise with Sample Entropy

The data-driven method is an important tool in the field of underwater acoustic signal processing. In order to realize the feature extraction of ship-radiated noise (S-RN), we proposed a data-driven optimization method called improved variational mode decomposition (IVMD). IVMD, as an improved method of variational mode decomposition (VMD), solved the problem of choosing decomposition layers for VMD by using a frequency-aided method. Furthermore, a novel method of feature extraction for S-RN, which combines IVMD and sample entropy (SE), is put forward in this paper. In this study, four types of S-RN signals are decomposed into a group of intrinsic mode functions (IMFs) by IVMD. Then, SEs of all IMFs are calculated. SEs are different in the maximum energy IMFs (EIMFs), thus, SE of the EIMF is seen as a novel feature for S-RN. To verify the effectiveness of the proposed method, a comparison has been conducted by comparing features of center frequency and SE of the EIMF by IVMD, empirical mode decomposition (EMD) and ensemble EMD (EEMD). The analysis results show that the feature of S-RN can be obtain efficiently and accurately by using the proposed method.

A Fusion Frequency Feature Extraction Method for Underwater Acoustic Signal Based on Variational Mode Decomposition, Duffing Chaotic Oscillator and a Kind of Permutation Entropy

In order to effectively extract the frequency characteristics of an underwater acoustic signal under sensor measurement, a fusion frequency feature extraction method for an underwater acoustic signal is presented based on variational mode decomposition (VMD), duffing chaotic oscillator (DCO) and a kind of permutation entropy (PE). Firstly, VMD decomposes the complex multi-component underwater acoustic signal into a set of intrinsic mode functions (IMFs), so as to extract the estimated center frequency of each IMF. Secondly, the frequency of the line spectrum can be obtained by using DCO and a kind of PE (KPE). DCO is used to detect the actual frequency of the line spectrum for each IMF and KPE can determine the accurate frequency when the phase space track is in the great periodic state. Finally, the frequency characteristic parameters acted as the input of the support vector machine (SVM) to distinguish different types of underwater acoustic signals. By comparing with the other three traditional methods for simulation signal and different kinds of underwater acoustic signals, the results show that the proposed method can accurately extract the frequency characteristics and effectively realize the classification and recognition for the underwater acoustic signal.

Noise Reduction Method of Underwater Acoustic Signals Based on CEEMDAN, Effort-To-Compress Complexity, Refined Composite Multiscale Dispersion Entropy and Wavelet Threshold Denoising

Owing to the problems that imperfect decomposition process of empirical mode decomposition (EMD) denoising algorithm and poor self-adaptability, it will be extremely difficult to reduce the noise of signal. In this paper, a noise reduction method of underwater acoustic signal denoising based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), effort-to-compress complexity (ETC), refined composite multiscale dispersion entropy (RCMDE) and wavelet threshold denoising is proposed. Firstly, the original signal is decomposed into several IMFs by CEEMDAN and noise IMFs can be identified according to the ETC of IMFs. Then, calculating the RCMDE of remaining IMFs, these IMFs are divided into three kinds of IMFs by RCMDE, namely noise-dominant IMFs, real signal-dominant IMFs, real IMFs. Finally, noise IMFs are removed, wavelet soft threshold denoising is applied to noise-dominant IMFs and real signal-dominant IMFs. The denoised signal can be obtained by combining the real IMFs with the denoised IMFs after wavelet soft threshold denoising. Chaotic signals with different signal-to-noise ratio (SNR) are used for denoising experiments by comparing with EMD_MSE_WSTD and EEMD_DE_WSTD, it shows that the proposed algorithm has higher SNR and smaller root mean square error (RMSE). In order to further verify the effectiveness of the proposed method, which is applied to noise reduction of real underwater acoustic signals. The results show that the denoised underwater acoustic signals not only eliminate noise interference also restore the topological structure of the chaotic attractors more clearly, which lays a foundation for the further processing of underwater acoustic signals.

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.

Improved Morphological Filter Based on Variational Mode Decomposition for MEMS Gyroscope De-Noising

An adaptive multi-scale method based on the combination generalized morphological filter (CGMF) is presented for de-noising of the output signal from a MEMS gyroscope. A variational mode decomposition is employed to decompose the original signal into multi-scale modes. After choosing a length selection for the structure element (SE), the adaptive multi-scale CGMF method reduces the noise corresponding to the different modes, after which a reconstruction of the de-noised signal is obtained. From an analysis of the effect of de-noising, the main advantages of the present method are that it: (i) effectively overcomes deficiencies arising from data deviation compared with conventional morphological filters (MFs); (ii) effectively targets the different components of noise and provides efficacy in de-noising, not only primarily eliminating noise but also smoothing the waveform; and (iii) solves the problem of SE-length selection for a MF and produces feasible formulae of indicators such as the power spectral entropy and root mean square error for mode evaluations. Compared with the other current signal processing methods, the method proposed owns a simpler construction with a reasonable complexity, and it can offer better noise suppression effect. Experiments demonstrate the applicability and feasibility of the de-noising algorithm.