Number Of Intrinsic Mode Functions Research Articles

Residual Life Prediction of Rolling Bearings Based on a CEEMDAN Algorithm Fused with CNN–Attention-Based Bidirectional LSTM Modeling

This paper presents a methodology for predicting the remaining usability of rolling bearings. The method combines a fully adaptive ensemble empirical modal decomposition of noise (CEEMDAN), convolutional neural network (CNN), and attention bidirectional long short-term memory network (ABiLSTM). Firstly, a finite number of intrinsic mode functions (IMFs) are obtained from breaking down the initial vibration signals using CEEMDAN. The IMFs are further screened by combining the correlation criterion and the craggy criterion. Then, time-frequency domain features, which are extracted from the screened IMFs, are reconstructed into a feature set. The SPT is recognized through some features, like the root mean square (RMS), variance, and kurtosis. Secondly, the deterioration character of rolling bearings was extracted using CNN and used to train the ABiLSTM network. Based on the output of the ABiLSTM network, it forecasts how long rolling bearings will last during use. Finally, the XJTU-SY rolling bearing dataset validated the validity of the suggested rolling bearing remaining life prediction method. We compare our algorithm with other algorithms, such as GRU, LSTM, and CNN–BiLSTM, in which the accuracy of MAE, MSE, RMSE, MAPE, and R2_score is significantly improved. Thus, the results of the validation experiments demonstrate that our proposed algorithm has excellent prediction accuracy.

Forecasting of the true satellite carbon monoxide data with ensemble empirical mode decomposition, singular value decomposition and moving average

The forecasting of carbon monoxide in the atmosphere is essential as it causes the pollution of the atmosphere and hence severe health problems for humans. This study proposes a time-series prognosis EEMD-SVD-MA technique which incorporates Ensemble Empirical Mode Decomposition, Singular Value Decomposition and Moving Average, to predict the prospects of carbon monoxide data taken from the Indian region. The collected data are non-linear. The technique can be applied for non-stationary and non-linear data. In this approach, there are three levels: EEMD level, SVD level and MA level. The first level deploys EEMD to fragment data series into a limited number of Intrinsic Mode Function (IMF) components along with a residue. To denoise each IMF component, SVD is deployed in the second level. In the third level, each denoised IMF component is predicted by MA. The future values of the original data are obtained by adding all the predicted series of the components. In this study, we proposed two variants of the model: EEMD-SVD-MA(3) and EEMD-SVD-MA(4) and compared the results with other forecasting techniques, namely LSTM (Long Short Term Memory network), EMD-LSTM, EMD-MA, EEMD-MA and CEEMDAN-MA. The results show that the proposed EEMD-SVD-MA model is more efficient than other models.

Research on fault diagnosis of rolling bearing based on multi-sensor bi-layer information fusion under small samples.

To address the challenge of low fault diagnosis accuracy due to insufficient bearing fault data collected by single-sensor, a rolling bearing fault diagnosis method based on multi-sensor bi-layer information fusion under small samples is proposed. In the first-layer feature fusion, first, aiming at the problem that the number of intrinsic mode functions (IMFs) and the penalty factor in the variational mode decomposition (VMD) is challenging to determine, the Aquila optimizer algorithm is introduced to search for the optimal solution independently. Decomposition of bearing vibration signals acquired by multiple sensors using a parameter optimized the VMD method to obtain IMFs. The 12 time-domain features are then extracted for each IMF, and the maximum information coefficient (MIC) between each IMF time-domain feature and raw signal time-domain features is calculated. Finally, the feature fusion composition ratio is calculated according to the MIC mean of each. In the second layer of data fusion, the fusion composition ratio calculated in the first layer is used as a weight-to-weight and reconstructs the signals of each sensor to constitute a fused signal. Then, the fused signals are input into the fault diagnostic model, and fault pattern recognition and fault severity recognition are performed at the same time. The results show that the accuracy of the method proposed in this paper is higher than that of the comparison method on both the public dataset and the self-built experimental bench dataset, and it is an accurate, stable, and efficient fault diagnosis method.

Airborne Radio-Echo Sounding Data Denoising Using Particle Swarm Optimization and Multivariate Variational Mode Decomposition

Radio-echo sounding (RES) is widely used for polar ice sheet detection due to its wide coverage and high efficiency. The multivariate variational mode decomposition (MVMD) algorithm for the processing of RES data is an improvement to the variational mode decomposition (VMD) algorithm. It processes data encompassing multiple channels. Determining the most effective component combination of the penalty parameter (α) and the number of intrinsic mode functions (IMFs) (K) is fundamental and affects the decomposition results. α and K in traditional MVMD are provided by subjective experience. We integrated the particle swarm optimization (PSO) algorithm to iteratively optimize these parameters—specifically, α and K—with high precision. This was then combined with the four quantitative parameters: energy entropy, signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR), and root-mean-square error (RMSE). The RES signal decomposition results were judged, and the most effective component combination for noise suppression was selected. We processed the airborne RES data from the East Antarctic ice sheet using the combined PSO–MVMD method. The results confirmed the quality of the proposed method in attenuating the RES signal noise, enhancing the weak signal of the ice base, and improving the SNR. This combined PSO–MVMD method may help to enhance weak signals in deeper parts of ice sheets and may be an effective tool for RES data interpretation.

Application of the Empirical Mode Decomposition Method to Noise Reduction Using Seismic Event Data Recorded at Kirkuk Seismological Station.

This study aims to use the Empirical Mode Decomposition for reducing the noise of passive seismic signals recorded across seismic event recorded at Kirkuk station which is one of the Iraqi Meteorological Organization and Seismology data, where human activities in Iraq's populous cities significantly impact the seismic recordings at Iraqi Meteorological Organization and Seismology stations sites. In this paper, we present an algorithm based on the Empirical Mode Decomposition. It is a data driven method used as a propelling tool for analyzing and decomposing non-stationary and non-linear data without any previous assumptions. Empirical Mode Decomposition generates a finite and often small number of Intrinsic Mode Functions. The decomposition is based on the direct extraction of the energy related to various intrinsic time scales, an important parameter of the system. Empirical Mode Decomposition technique is applied to the available seismic records to reduce the noise level in the records, which helps in the interpretation of the records.

Learning classifiers in clustered data: BCI pattern recognition model for EEG-based human emotion recognition

Evidence suggests that human emotions can be detected using Electroencephalography (EEG) brain signals. Recorded EEG signals, due to their large size, may not initially perform well in classification. For this reason, various feature selection methods are used to improve the performance of classification. The nature of EEG signals is complex and unstable. This article uses the Empirical Mode Decomposition (EMD) method, which is one of the most successful methods in analyzing these signals in recent years. In the proposed model, first, the EEG signals are decomposed using EMD into the number of Intrinsic Mode Functions (IMF), and then, the statistical properties of the IMFs are extracted. To improve the performance of the proposed model, using the RBF kernel and Least Absolute Shrinkage and Selection Operator (LASSO) feature selection, an effective subset of the features that have changed the space is selected. The data are then clustered, and finally, each cluster is classified with a decision tree and random forest and KNN. The purpose of clustering is to increase the accuracy of the classification, which is achieved by focusing each cluster on a limited number of classes. This experiment was performed on the DEAP dataset. The results show that the proposed model with 99.17% accuracy could perform better than recent research such as deep learning and show good performance. In the latest years, with the development of the BCI system, the demand for recognizing emotions based on EEG has increased. We provide a method for classifying clustered data that is efficient for high accuracy.

A Hybrid Forecasting Model to Simulate the Runoff of the Upper Heihe River

River runoff simulation and prediction are important for controlling the water volume and ensuring the optimal allocation of water resources in river basins. However, the instability of medium- and long-term runoff series increases the difficulty of runoff forecasting work. In order to improve the prediction accuracy, this research establishes a hybrid deep learning model framework based on variational mode decomposition (VMD), the mutual information method (MI), and a long short-term memory network (LSTM), namely, VMD-LSTM. First, the original runoff data are decomposed into a number of intrinsic mode functions (IMFs) using VMD. Then, for each IMF, a long short-term memory (LSTM) network is applied to establish the prediction model, and the MI method is used to determine the data input lag time. Finally, the prediction results of each subsequence are reconstructed to obtain the final forecast result. We explored the predictive performance of the model with regard to monthly runoff in the upper Heihe River Basin, China, and compared its performance with other single and hybrid models. The results show that the proposed model has obvious advantages in terms of the performance of point prediction and interval prediction compared to several comparative models. The Nash–Sutcliffe efficiency coefficient (NSE) of the prediction results reached 0.96, and the coverage of the interval prediction reached 0.967 and 0.908 at 95% and 90% confidence intervals, respectively. Therefore, the proposed model is feasible for simulating the monthly runoff of this watershed.

Regional forecasting of significant wave height and mean wave period using EOF-EEMD-SCINet hybrid model

Most studies only focus on single-point wave forecasting, while regional wave forecasting has more important significance for ocean engineering construction, navigation safety and disaster warning. To solve the problems of high computational cost and poor performance of regional wave forecasting models, a novel hybrid model for regional significant wave height (SWH) and mean wave period (MWP) forecasting, called EOF-EEMD-SCINet, is proposed by combining empirical orthogonal functions (EOF) analysis, ensemble empirical mode decomposition (EEMD) and sample convolution and interaction network (SCINet). After determining the optimal input steps, the number of intrinsic mode functions (IMFs) and the decomposition method, the forecasting performance of the model for SWH and MWP with lead times of 24, 48 and 72 h is evaluated based on SWH, MWP, wind speed (WSPD), significant height of first swell partition (SWH1) and significant height of wind waves (SHWW) in the South China Sea (SCS). The results show that the proposed model can not only accurately forecast the changes in SWH and MWP with time, but also has a high forecasting precision for regional waves, which is superior to other models. In addition, the increase of wave lead time has less negative effect on the forecasting performance of the proposed model compared to other models. As the lead time changes from 24 h to 72 h, the mean absolute error (MAE) of SWH increases by less than 6 cm, and the MAE of MWP changes around 0.04 s. Besides, EOF-EEMD-SCINet has enormous advantage in terms of efficiency. EOF-EEMD-SCINet is a model that can simultaneously forecast regional SWH and MWP with high precision.

A fault diagnosis method for building electrical systems based on the combination of variational modal decomposition and new mutual dimensionless

The fault diagnosis of building electrical systems are of great significance to the safe and stable operation of modern intelligent buildings. In this paper, it has many problems, such as various fault types, inconspicuous fault characteristics, uncertainty of fault type and mode, irregularity, unstable signal, large gap between fault data classes, small gap between classes and nonlinearity, etc. A method of building electrical system fault diagnosis based on the combination of variational mode decomposition and mutual dimensionless indictor (VMD-MDI) and quantum genetic algorithm-support vector machine (QGA-SVM) is proposed. Firstly, the method decomposes the original signal through variational modal decomposition to obtain the optimal number of Intrinsic Mode Function(IMF) containing fault feature information. Secondly, extracts the mutual dimensionless indicator for each IMF. Thirdly, the optimal penalty coefficient C of the support vector machine and the parameter gamma (gamma) in the radial basis kernel function are selected by the quantum genetic algorithm. Finally, SVM optimized by the QGA is used to identify and classify the faults. By applying the proposed method to the experimental platform data of building electrical system, and compared with the traditional feature extraction method Empirical Mode Decomposition (EMD), Singular Value Decomposition(SVD), Local Mean Decomposition(LMD). And compared with traditional SVM, Genetic Algorithm optimized Support Vector Machine (GA-SVM), One-Dimensional Convolutional Neural Network (1DCNN) for fault classification methods. The experimental results show that the method has better effect and higher accuracy in fault diagnosis and classification of building electrical system. Its average test accuracy can reach 91.67%.

Electricity Load and Price Forecasting Using a Hybrid Method Based Bidirectional Long Short-Term Memory with Attention Mechanism Model

The accuracy of forecasting short- or medium-term electricity loads and prices is critical in the energy market. The amplitude and duration of abnormally high prices and load spikes can be detrimental to retailers and production systems. Therefore, predicting these spikes to effectively manage risk is critical. In this paper, a novel hybrid method that combines ensemble empirical mode decomposition (EEMD) algorithm and a bidirectional long short-term memory with attention mechanism (BiLSTM-AM) model is proposed to predict electricity loads and prices. A simple approach is proposed to determine the number of intrinsic mode functions (IMFs) that decompose raw data using EEMD to avoid overdecomposition, irrelevant components, and high computational cost. Each selected mode is then modeled with BiLSTM-AM to obtain a predicted sequence. These sequences are summed and then reverted to obtain the final predicted value. The proposed method is validated using two datasets (PMJ and Australian Energy Market Operator) with different time intervals to demonstrate the generality and robustness of the forecasts, especially in temporal valley or peak forecasting. The results show that the proposed method outperforms other methods in prediction accuracy and spike-capturing ability, with EEMD reducing the mean absolute percentage error (MAPE) by 53%, 54%, and 60%, respectively. In the three forecast periods, the average MAPE and R ̲ 2 are 0.097 and 0.92, respectively. Furthermore, we use Kolmogorov-Smirnov predictive accuracy (KSPA) test and model confidence set (MCS) test to validate the superiority of the proposed model. The results demonstrate its suitability, reliability, and performance in short- and medium-term forecasting.

A novel denoising method for non‐linear and non‐stationary signals

Signal denoising is a crucial step in signal analysis. Various procedures have been attempted by researchers to remove the noise while preserving the effective components of the signal. One of the most successful denoising methods currently in use is the variational mode decomposition (VMD). Unfortunately, the effectiveness of VMD depends on the appropriate selection of the decomposition level and the effective modes to be reconstructed, and, like many other traditional denoising methods, it is often ineffective when the signal is non-linear and non-stationary. In view of these problems, this study proposes a new denoising method that consists of three steps. First, an improved VMD method is used to decompose the original signal into an optimal number of intrinsic mode functions (IMFs). Second, the energy variation ratio function is applied to distinguish between the effective and non-effective IMFs. Third, the valuable components are retained while the useless ones are removed, and the denoised signal is obtained by reconstructing the useful IMFs. Simulations and experiments on various noisy non-linear and non-stationary signals demonstrated the superior performance of the proposed method over existing denoising approaches.

Use of Holo-Hilbert spectral analysis to reveal the amplitude modulation features of faulty rolling bearing signals

Time-frequency analysis (TFA) is a powerful tool for vibration signal analysis. However, it cannot comprehensively reflect the cross-scale coupling relationship between amplitude-modulated (AM) and frequency-modulated (FM) characteristics of the vibration signal collected from faulty rolling bearings. To address this shortcoming, the Holo-Hilbert spectral analysis (HHSA) method with combining the masking empirical mode decomposition (Masking-EMD) for signal separation is introduced to completely describe the internal modulation characteristics of faulty rolling bearing. In HHSA, first, the initial vibration signal of faulty rolling bearing is decomposed into numbers of intrinsic mode functions (IMFs) to extract its time-varying FM and AM characteristics. Next, the instantaneous frequency and the instantaneous amplitude of each IMF are estimated, respectively. Then, each first-layer IMF is decomposed into a series of IMFs with AM characteristics via reusing Masking-EMD. Finally, the FM and AM components are combined with their instantaneous modulation energy to realize the three-dimensional Holo-Hilbert spectrum (HHS). The simulation and experiment results illustrate that the introduced method can completely reveal the AM characteristics of non-linear vibration signals and the corresponding carrier frequency range.

Composite fault diagnosis for rolling bearing based on parameter-optimized VMD

Variational mode decomposition (VMD) is a recently introduced adaptive signal analysis method, which is widely used in fault diagnosis of rotating machinery due to its excellent noise reduction performance. But it is often used to realize a single fault diagnosis of the bearing. In this paper, a feasible solution based on the parameter-optimized VMD is introduced to realize the composite fault diagnosis of bearing whose fault components are located in different frequency bands, and without combining with other methods. First, the kurtosis value of the envelope signal is used as an indicator to determine the optimal mode number. Then, after the mode number is determined, the penalty factor is optimized by the same indicator. Then, the original signal is decomposed into the sum of a certain number of intrinsic mode functions (IMFs), each IMF has a different frequency band. Then, the IMFs are sorted in descending order of the envelope signal kurtosis value, and the IMFs with significantly smaller indicator values are removed. Finally, in accordance with the sequence of the reserved IMF components, the power spectrum analysis of the envelope is performed on each IMF to realize the feature extraction of bearing composite faults. Simulation analysis and actual case analysis prove the robustness and feasibility of the presented solution.

Noise Reduction Based on CEEMDAN-ICA and Cross-Spectral Analysis for Leak Location in Water-Supply Pipelines

Due to the leakage vibration signal of the water-supply pipeline is easily interfered with by background noise, which leads to a significant leakage location error of time delay estimation. The complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and independent component analysis (ICA) combined noise reduction method based on cross-spectral analysis is proposed and applied to leak location of water supply pipelines. Firstly, determine the frequency band range of the source leakage signal by cross-spectral analysis of the leakage vibration signal. At the same time, the leakage vibration signal is decomposed into a finite number of intrinsic mode functions (IMFs) using CEEMDAN. Then, the IMF components are filtered according to the effective amplitude ratio criterion, and the filtered components are reconstructed into a virtual noise channel. Finally, the leakage vibration signal and virtual noise channel are unmixed using FastICA to obtain the best estimate of the source leakage signal, which is used to estimate time delay using cross-correlation for determining the leak location. Simulation and experimental results show that the proposed method effectively improves the signal-to-noise ratio (SNR) and time delay estimation accuracy, and reduces leak location error. Compared with cross-correlation, CEEMDAN-ICA based on correlation coefficients, and CEEMDAN based on cross-spectral analysis, the average relative positioning error of the proposed method is respectively reduced by 11.07%, 9.7%, and 1.8%. In addition, the superiority of the proposed method compared with other state-of-the-art noise reduction methods is verified by comparative experiments.

Vibration signal analysis of a rotor-bearing system through wavelet transform and empirical mode decomposition

Vibration analysis is widely used for the monitoring of the health of rotating machinery. There are different methods to interpret the vibration signals like time-domain analysis and frequency domain analysis, where the conventional Fast Fourier Transform (FFT) method is applied. FFT has been used successfully to extract stationary parameters from the frequency domain data. Complex machines normally consist of many parts and their vibration response contains many non-stationary signals and nonlinear signals. The objective of this research is to explore the feasibility of utilizing the wavelet transform (WT) and empirical mode decomposition (EMD) to efficiently decompose the sophisticated vibration signals of a rotor-bearing system into a finite number of intrinsic mode functions so that the fault characteristics of the rotor-bearing system can be analysed. A test rig of a rotor-bearing system was used to perform the experiments, and the vibration signals were recorded through NI-DAQ system. Vibration signals received from the test rig were analyzed using MATLAB software to present the useful information. The analysis result showed that the proposed approach is capable of diagnosing the faults of the rotor-bearing system.

A Short-Term Wind Speed Forecasting Model Based on EMD/CEEMD and ARIMA-SVM Algorithms

In order to ensure the driving safety of vehicles in windy environments, a wind monitoring and warning system is widely used, in which a wind speed prediction algorithm with better stability and sufficient accuracy is one of the key factors to ensure the smooth operation of the system. In this paper, a novel short-term wind speed forecasting model, combining complementary ensemble empirical mode decomposition (CEEMD), auto-regressive integrated moving average (ARIMA), and support vector machine (SVM) technology, is proposed. Firstly, EMD and CEEMD are used to decompose the measured wind speed sequence into a finite number of intrinsic mode functions (IMFs) and a decomposed residual. Each of the IMF subseries has better linear characteristics. The ARIMA algorithm is adopted to predict each of the subseries. Then, a new subseries is reconstructed using the sum of the predicted errors of all subseries. The high nonlinear features of the reconstructed error subseries are modeled using SVM, which is suitable to process nonlinear data. Finally, the superposition of all prediction results is performed to obtain the final predicted wind speed. To verify the stability and accuracy of the model, two typhoon datasets, measured from the south coast of China, are used to test the proposed methods. The results show that the proposed hybrid model has a better predictive ability than single models and other combined models. The root mean squared errors (RMSEs) of the hybrid model for the three wind speed datasets are 0.839, 0.529, and 0.377, respectively. The combination of CEEMD with ARIMA contributes most of the prediction performance to the hybrid model. It is feasible to apply the hybrid model to wind speed prediction.

A temporal dependency feature in lower dimension for lung sound signal classification

Respiratory sounds are expressed as nonlinear and nonstationary signals, whose unpredictability makes it difficult to extract significant features for classification. Static cepstral coefficients such as Mel-frequency cepstral coefficients (MFCCs), have been used for classification of lung sound signals. However, they are modeled in high-dimensional hyperspectral space, and also lose temporal dependency information. Therefore, we propose shifted delta -cepstral coefficients in lower-subspace (SDC-L) as a novel feature for lung sound classification. It preserves temporal dependency information of multiple frames nearby same to original SDC, and improves feature extraction by reducing the hyperspectral dimension. We modified EMD algorithm by adding a stopping rule to objectively select a finite number of intrinsic mode functions (IMFs). The performances of SDC-L were evaluated with three machine learning techniques (support vector machine (SVM), k-nearest neighbor (k-NN) and random forest (RF)) and two deep learning algorithms (multilayer perceptron (MLP) and convolutional neural network (cNN)) and one hybrid deep learning algorithm combining cNN with long short term memory (LSTM) in terms of accuracy, precision, recall and F1-score. We found that the first 2 IMFs were enough to construct our feature. SVM, MLP and a hybrid deep learning algorithm (cNN plus LSTM) outperformed with SDC-L, and the other classifiers achieved equivalent results with all features. Our findings show that SDC-L is a promising feature for the classification of lung sound signals.

Multi-step ahead wind speed prediction based on a two-step decomposition technique and prediction model parameter optimization

Accurate and reliable wind speed prediction is essential for the exploitation and utilization of the wind energy. In this paper, a novel hybrid multi-step wind speed prediction model is proposed based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), robust local mean decomposition (RLMD), and improved whale optimization algorithm (IWOA), and long-term and short-term memory network (LSTM). CEEMDAN is utilized to decompose the wind speed series into a number of intrinsic mode functions, and the RLMD is used to the second step decompose the most non-stationary intrinsic mode function into a series of product functions. After the two-step decomposition, a group of new subsequences is formed. The long-term and short-term memory network (LSTM) prediction model is constructed for every subsequence and an improved whale optimization algorithm (IWOA) is used to optimize key parameters affecting the prediction performance of the LSTM model. And at last, the subsequence prediction results are superimposed to provide the final prediction results. The effectiveness and advancement of the proposed hybrid model is verified by employing wind speed data from two different wind farms. And according to the experimental results and comparison, it can be found that the proposed model can provide better performance than the seven compared models.

A heart sound classification method based on complete ensemble empirical modal decomposition with adaptive noise permutation entropy and support vector machine

Heart sound signal is a kind of physiological signal with nonlinear and nonstationary features. In order to improve the accuracy and efficiency of the phonocardiogram (PCG) classification, a new method was proposed by means of support vector machine (SVM) in which the complete ensemble empirical modal decomposition with adaptive noise (CEEMDAN) permutation entropy was as the eigenvector of heart sound signal. Firstly, the PCG was decomposed by CEEMDAN into a number of intrinsic mode functions (IMFs) from high to low frequency. Secondly, the IMFs were sifted according to the correlation coefficient, energy factor and signal-to-noise ratio. Then the instantaneous frequency was extracted by Hilbert transform, and its permutation entropy was constituted into eigenvector. Finally, the accuracy of the method was verified by using a hundred PCG samples selected from the 2016 PhysioNet/CinC Challenge. The results showed that the accuracy rate of the proposed method could reach up to 87%. In comparison with the traditional EMD and EEMD permutation entropy methods, the accuracy rate was increased by 18%-24%, which demonstrates the efficiency of the proposed method.

A modified EMD method for detecting and mitigating narrow-band RFI in SAR data

ABSTRACT The empirical mode decomposition (EMD) based method for mitigating radio frequency interference (RFI) has the capability of removing narrow-band RFI and the advantage of easy-to-implement. The signals are decomposed by EMD into a finite number of intrinsic mode functions (IMFs) in a pulse-by-pulse manner, and then the IMFs corresponding to the RFI are subtracted to achieve interference mitigation. However, useful signals will be lost by using this method, which reduces the synthetic aperture radar (SAR) imaging quality. In this letter, a modified EMD method is proposed to tackle this problem. Firstly, the interferences of the echoes are detected through the relative energy ratio. Secondly, echoes containing RFI are decomposed into many IMFs via EMD. These IMFs are transformed into time-frequency (TF) domain via short-time Fourier transform (STFT), and then IMFs corresponding to RFI are screened out via the robust bisecting k-means algorithm. Finally, the RFIs in TF domain are located with the robust OTSU algorithm and mitigated by a notch operation. Experimental results of real SAR data with simulated RFIs demonstrate the effectiveness and superiority of the proposed method.