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.

Since COVID-19 pneumonia broke out, the Chinese government has taken a series of measures to control the spread of the epidemic, which has made the air quality of Taiyuan in February 2020 significantly better than during the same period in previous years. In this paper, the Gray Relational Analysis (GRA) method was first applied to evaluate and analyze the influence of six major pollutants on air quality. Then, the improved seagull optimization algorithm (ISOA) was proposed and combined with Support Vector Regression (SVR) to establish a hybrid predicted model ISOA-SVR. Finally, the proposed ISOA-SVR was utilized to predict air quality index (AQI). The experimental results on two kinds of different data showed that the proposed ISOA-SVR had the better generalization ability and robustness compared with other predicted models. Further, the proposed ISOA-SVR is suitable for the prediction of AQI.

Direction of arrival (DOA) estimation has always been a hot topic for researchers. The complex and changeable environment makes it very challenging to estimate the DOA in a small snapshot and strong noise environment. The direction-of-arrival estimation method based on compressed sensing (CS) is a new method proposed in recent years. It has received widespread attention because it can realize the direction-of-arrival estimation under small snapshots. However, this method will cause serious distortion in a strong noise environment. To solve this problem, this paper proposes a DOA estimation algorithm based on the principle of CS and density-based spatial clustering (DBSCAN). First of all, in order to make the estimation accuracy higher, this paper selects a signal reconstruction strategy based on the basis pursuit de-noising (BPDN). In response to the challenge of the selection of regularization parameters in this strategy, the power spectrum entropy is proposed to characterize the noise intensity of the signal, so as to provide reasonable suggestions for the selection of regularization parameters; Then, this paper finds out that the DOA estimation based on the principle of CS will get a denser estimation near the real angle under the condition of small snapshots through analysis, so it is proposed to use a DBSCAN method to process the above data to obtain the final DOA estimate; Finally, calculate the cluster center value of each cluster, the number of clusters is the number of signal sources, and the cluster center value is the final DOA estimate. The proposed method is applied to the simulation experiment and the micro electro mechanical system (MEMS) vector hydrophone lake test experiment, and they are proved that the proposed method can obtain good results of DOA estimation under the conditions of small snapshots and low signal-to-noise ratio (SNR).

Underwater acoustic technology is a major method in current ocean research and exploration, which support the detection of seabed environment and marine life. However, the detection accuracy is directly affected by the quality of underwater acoustic signals collected by hydrophones. Hydrophones are efficient and important tools for collecting underwater acoustic signals. The collected signals of hydrophone often contain lots kinds of noise as the work environment is unknown and complex. Traditional signal denoising methods, such as wavelet analysis and empirical mode decomposition, product unsatisfied results of denoising. In this paper, a denoising method combining wavelet threshold processing and empirical mode decomposition is proposed, and correlation analysis is added in the signal reconstruction process. Finally, the experiment proves that the proposed denoising method has a better denoising performance. With the employment of the proposed method, the underwater acoustic signals turn smoothly and the signal drift of the collected hydroacoustic signal is improved. Comparing the signal spectrums of other methods, the spectral energy of the proposed denoising method is more concentrated, and almost no energy attenuation occurred.

We investigate $L_2$-approximation problems in the worst case setting in the weighted Hilbert spaces $H\left(K_{R_{d,\mathit{\alpha },\mathit{\gamma }}}\right)$ with weights $R_{d,\mathit{\alpha },\mathit{\gamma }}$ under parameters $1\ge {\gamma }_1\ge {\gamma }_2\ge \cdots \ge 0$ and $1<{\alpha }_1\le {\alpha }_2\le \cdots$. Several interesting weighted Hilbert spaces $H\left(K_{R_{d,\mathit{\alpha },\mathit{\gamma }}}\right)$ appear in this paper. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. We discuss tractability of $L_2$-approximation problems for the involved Hilbert spaces, which describes how the information complexity depends on d and ${\epsilon }^{-1}$. As a consequence we study the strongly polynomial tractability (SPT), polynomial tractability (PT), weak tractability (WT), and $(t_1,t_2)$-weak tractability ($(t_1,t_2)$-WT) for all $t_1>1$ and $t_2>0$ in terms of the introduced weights under the absolute error criterion or the normalized error criterion.

We investigate \texorpdfstring{$L_2$}{}-approximation problems in the worst case setting in the weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} with weights \texorpdfstring{$R_{d,\a,{\bm \ga}}$}{} under parameters \texorpdfstring{$1\ge \ga_1\ge \ga_2\ge \cdots\ge 0$ and $1<\az_1\le \az_2\le \cdots$}{}. Several interesting weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} appear in this paper. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. Multivariate approximation; information complexity; tractability; weighted Hilbert spacesWe discuss tractability of \texorpdfstring{$L_2$}{}-approximation problems for the involved Hilbert spaces, which describes how the information complexity depends on \texorpdfstring{$d$}{} and \texorpdfstring{$\va^{-1}$}{}. As a consequence we study the strongly polynomial tractability (SPT), polynomial tractability (PT), weak tractability (WT), and \texorpdfstring{$(t_1,t_2)$}{}-weak tractability (\texorpdfstring{$(t_1,t_2)$}{}-WT) for all \texorpdfstring{$t_1>1$}{} and \texorpdfstring{$t_2>0$}{} in terms of the introduced weights under the absolute error criterion or the normalized error criterion.