Multichannel Singular Spectrum Analysis Research Articles

The Study on Anomalies of the Geomagnetic Topology Network Associated with the 2022 Ms6.8 Luding Earthquake

On 5 September 2022, the Ms 6.8 Luding earthquake occurred at 29.59°N and 102.08°E in China. To investigate the variations in geomagnetic signals before the earthquake, this study analyzes the geomagnetic data from nine stations around the epicenter. First, we apply the Multi-channel Singular Spectrum Analysis to reconstruct the periodic components of the geomagnetic data from multiple stations. Second, we employ K-means clustering to rule out the possibility of occasional anomalies caused by a single station. Subsequently, we construct a geomagnetic topology network considering the remaining stations. Network centrality is defined as a measure of overall network connectivity, where the higher the correlation between multiple stations, the greater the network centrality. Finally, we examine the network centrality 45 days before and 15 days after the Luding earthquake. The results show that several anomalies in network centrality are extracted about one week before the earthquake. We further validate the significance of the anomalies in terms of time as well as space and verify the utility of the centrality anomalies through the SEA technique. The anomalies are found to have a statistical correlation with the earthquake event. We consider that this study provides a new way and a novel observational perspective for earthquake precursor analysis of ground-based magnetic data.

Establishing and modeling the causality relationship of hydro-climatic and land cover change variables with water quality over Lake Tana, Ethiopia

Lakes, the most widespread inland water bodies in the globe, are highly susceptible to change in trophic state due to external factors. Changing hydro-climatic conditions and land cover changes (LCC) can cause lake water quality deterioration. This study establishes the quantitative relationship between variability in the water quality index and changes in hydro-climatic and LCC variables. Water quality is represented by the Forel-ule index (FUI) whereas the hydro-climatic variables considered in this study are lake bottom layer temperature (lblt), lake total layer temperature (ltlt), precipitation, runoff, evaporation, lake skin temperature (lskt), surface wind speed and air temperature. The LCC is quantified by lower and higher level leaf area index (Lv-lai and Hv-lai). FUI has a positive relationship with surface wind speed, precipitation, runoff, ltlt, lblt, and LCC and a negative relationship with evaporation, lskt, and air temperature with 95% confidence level over most parts of the Lake. The temporal correlation is also apparent from the long-term trend pattern. A significant decreasing trend is observed in FUI and lake bottom layer temperature (lblt). In contrast, an insignificant increasing trend is observed in air temperature and lake skin temperature (lskt). The changes in LCC, runoff, precipitation, and surface wind speed is insignificant between 2000 and 2020. Moreover, the phase composites of FUI and hydro-climatic and LCC variables derived from multichannel singular spectrum analysis (MSSA) show strong seasonal modulation of water quality by hydro-climatic and LCC variables. The annual cycle represented by the first two eigenmodes (except wind speed which is represented by the second and third eigenmodes) accounts for between 27.41% (wind speed) to 52.32% (precipitation) of the total joint spatiotemporal variability of FUI and the driving variables. The convergent cross-mapping (CCM) analysis shows that cross-map skill (ρ2) is increased with increasing library length (L) and time delay (τ), which suggests significant causal effects of hydro-climatic and LCC variables on FUI and the lagged causation is consistent with maximum values of ρ2. The significant feedback of FUI to changes in hydro-climatic and LCC variables shows the possibility of hindcast/forecast of the historical/future status of water quality from hydro-climatic and LCC variables. As a result, a multivariate nonlinear regression model (MNWQFM) is developed to forecast the lake water quality index from the hydro-climatic and LCC variables. The model has high performance with R2 of 83.6% and root means square error (RMSE) of 0.15 in FUI.

Filling the gap between GRACE and GRACE follow-on observations based on principal component analysis

SUMMARY The Gravity Recovery and Climate Experiment (GRACE) and its successor, GRACE Follow-On (GRACE-FO), have revolutionized the approach to monitoring global mass variations. However, the presence of several gaps, notably the continuous 11-month gap between the two missions, has generated a disruption in observations and hindered the analysis and application of the data. To address this problem, we have proposed a spectral domain gap-filling approach based on principal component analysis (PCA). Our simulation experiments demonstrate that the PCA gap-filling technique has significant potential to successfully reconstruct global mass variation and accurately capture real signals for most basins with an accuracy of less than 2 cm. When applied to actual missing data, our methodology delivers highly consistent results with previously published filling approaches, such as singular spectrum analysis and improved multichannel singular spectrum analysis method, for most of the global basins. Noteworthy, in the case of the Nelson basin, our PCA gap-filling method outperforms other methods in capturing seasonal signals and the return to a normal level of the terrestrial water storage changes in 2018. A comparison in the spectral domain indicates that the accuracy of the PCA-filling output is comparable to the original GRACE(-FO) data. Moreover, our method exhibits high generality, allowing for direct application to continuous GRACE(-FO) data without other additional data processing and without differentiating the types of missing data. Therefore, the proposed PCA gap-filling method offers exciting opportunities to guarantee the continuity of global mass change observations and benefit subsequent applications that require continuous data records.

A GPS multipath mitigation method in coordinate-domain considering the effects of gross errors and missing data

Multipath is a significant obstacle to achieving high-precision deformation monitoring using the Global Positioning System (GPS) technique. Sidereal filtering (SF) can mitigate GPS multipath effects based on the multipath models derived from historical measurements, but its practical application in complex scenarios is still challenging due to unavoidable gross errors and missing data problems. In this paper, an improved SF algorithm is proposed that accurately extracts multipath immune to the effects of gross errors and missing values in historical measurements, aiming to obtain accurate displacements in a harsh environment. Specifically, a gross error detection method is first developed based on the dynamic time warping (DTW) algorithm to filter gross errors. Then, we adopt the multichannel singular spectrum analysis (MSSA) algorithm to extract initial multipath errors. Finally, we propose a weighted fusion (WF) algorithm to eliminate the impact of missing values and obtain the final multipath sequences. Extensive experiments with datasets collected from a real-world landslide, including both stable and sliding stations, demonstrate the effectiveness of our proposed method. Results show that compared with the traditional SF method, our proposed method can effectively mitigate the effects of gross errors and missing values on multipath modeling, with the multipath filtering accuracy improving by approximately 12% and 21% for stable and sliding scenarios, respectively.

Coupling VMD and MSSA denoising for dam deformation prediction

The measured data of dams in complex environments are influenced by factors such as external forcing and instrumentation errors and inevitably contain noise, which makes accurately predicting dam deformation challenging. Traditional denoising methods suffer from both excessive denoising and incomplete denoising, resulting in limited improvement in prediction accuracy. To better address these problems, this paper proposes a denoising method that combines adaptive variational modal decomposition (VMD) with improved multichannel singular spectrum analysis (MSSA). The algorithm denoises the decomposed subsequence while accounting for the covariance between the subsequence and extracts valid information from the residual sequences. A concrete panel rockfill dam is used as an example for validation. The results show that the proposed algorithm effectively preserves the intrinsic components and coupling relationships between the decomposed subsequence. Based on machine learning models with different sensitivities to noise, the prediction accuracy of the proposed denoising algorithm model is better than that of the traditional denoising algorithm model. It is more suitable for deformation prediction modelling in complex situations involving actual dams, which further enhances the generalization ability of the prediction model.

Combining unsupervised deep learning and Monte Carlo dropout for seismic data reconstruction and its uncertainty quantification

Many methods, such as multichannel singular spectrum analysis (MSSA) and deep seismic prior (DSP), have been developed for seismic data reconstruction, but they do not quantify the uncertainty of reconstructed traces, relying on the subjective visual inspection of results. Our goal is to quantify the reconstructed uncertainty while recovering missing traces. We develop a framework including an unsupervised deep-learning-based seismic data reconstruction method and the existing Monte Carlo dropout method to achieve this goal. The only information required by our framework is the original incomplete data. A convolutional neural network trained on the original nonmissing traces can simultaneously denoise and reconstruct seismic data. For uncertainty quantification, the Monte Carlo dropout method treats the well-known dropout technique as Bayesian variational inference. This refers to the fact that the dropout technique can be regarded as an approximation to the probabilistic Gaussian process and thus can be used to obtain an approximate distribution (Bernoulli variational distribution) of the posterior distribution. The reconstructed result and uncertainty of the trained model are yielded through multiple Monte Carlo dropout simulations. The analysis of the reconstructed uncertainty quantifies the confidence to use reconstructed traces. Tests on synthetic and field data illustrate that our framework outperforms the MSSA and DSP methods on reconstructed accuracy and quantifies the reconstructed uncertainty as an objective benchmark to guide decision making.

An Antijamming Method Based on Multichannel Singular Spectrum Analysis and Affinity Propagation for UWB Ranging Sensors

Ultra-wideband impulse radio system has received extensive attention due to their high resolution and poor interception possibility. But the specific electromagnetic threat posed by its complex work environment cannot be ignored. In all kinds of active jamming signals, smart noise jamming plays an important role in modern radar electronic warfare, and most traditional anti-jamming methods have less suppression effect. In this paper, the mechanism of smart noise jamming on the UWB ranging sensor is discussed first. On this basis, an anti-smart noise jamming method based on multichannel singular spectrum analysis and kurtosis characteristic is proposed. Experiments show that smart noise jamming is more threatening to the UWB system than other noise modulation jamming. And the improved algorithm proposed in this paper can suppress the jamming better. After the anti-jamming processing, the average detection probability can reach more than 95%. Meanwhile, the method is improved by adding the affinity propagation (AP) clustering algorithm to solve the underdetermined signal separation problem in the case of compound jamming. The advantage is that it does not have to estimate the number of signals first. Even if the SJR is -10 dB, the waveform similarity between the separation signal and the source signal can reach 0.7 or more.

Data‐Driven Gap Filling and Spatio‐Temporal Filtering of the GRACE and GRACE‐FO Records

AbstractGravity Recovery And Climate Experiment and Follow On (GRACE/‐FO) global monthly measurements of Earth's gravity field have led to significant advances in quantifying mass transfer. However, a significant temporal gap between missions hinders evaluating long‐term mass variations. Moreover, instrumental and processing errors translate into large non‐physical North‐South stripes polluting geophysical signals. We use Multichannel Singular Spectrum Analysis (M‐SSA) to overcome both issues by exploiting spatio‐temporal information of Level‐2 GRACE/‐FO solutions, filtered using the DDK7 decorrelation and a new complementary filter, built based on the residual noise between fully processed data and a parametric fit to observations. Using an iterative M‐SSA on Equivalent Water Height (EWH) time series processed by Center of Space Research, GeoForschungsZentrum, Institute of Geodesy at Graz University of Technology, and Jet Propulsion Laboratory, we replace missing data and outliers to obtain a combined evenly sampled solution. Then, we apply M‐SSA to retrieve common signals between each EWH time series and its same‐latitude neighbors to further reduce residual spatially uncorrelated noise. Comparing GRACE/‐FO M‐SSA solution with Satellite Laser Ranging and Swarm low‐degree Earth's gravity field and hydrological model demonstrates its ability to satisfyingly fill missing observations. Our solution achieves a noise level comparable to mass concentration (mascon) solutions over oceans (3.0 mm EWH), without requiring a priori information nor regularization. While short‐wavelength signals are challenging to capture using highly filtered spherical harmonics or mascons solutions, we show that our technique efficiently recovers localized mass variations using well‐documented mass transfers associated with reservoir impoundments.

Three dimensional seismic data reconstruction based on truncated nuclear norm

The rank reduction method is widely used to reconstruct three dimensional (3D) seismic data. The traditional multichannel singular spectrum analysis (MSSA) utilizes truncated singular value decomposition (TSVD) to approximately solve the rank function of the block Hankel structure matrix constructed by frequency slices of seismic data. However, the TSVD algorithm discards all nonzero singular values except a few largest singular values and ignores the useful seismic information in small nonzero singular values. To further utilize the seismic data information contained in these small singular values, this paper proposes a method to recover 3D seismic data with truncated nuclear norm (TNN). The proposed method imposes different constraints on large singular values and small singular values. Essentially, the TNN is closer to the rank function than the TSVD. Finally, the proposed model is addressed by the alternating direction method of multipliers, and closed-form solutions are used to update the optimization variables. The experimental results demonstrate that the proposed method achieves superior reconstruction results than the traditional MSSA method.

Irregularly sampled seismic data interpolation with self-supervised learning

Supervised convolutional neural networks (CNNs) are commonly used for seismic data interpolation, in which a recovery network is trained over corrupted (input)/complete (label) pairs. However, the trained model always suffers from poor generalization when the target test data are significantly different from the training data sets. To address this issue, we have developed a self-supervised deep learning method for interpolating irregularly missing traces, which uses only the corrupted seismic data for training. This approach is based on the receptive field characteristic of CNNs, and the training pairs are extracted from the corrupted seismic data through a random trace mask. After network training, all target data are recovered using the trained model. This self-supervised learning interpolation (SSLI) method can be easily integrated into commonly used CNNs. Synthetic and field examples demonstrate that SSLI not only significantly outperforms traditional multichannel singular spectrum analysis and unsupervised deep seismic prior methods but also competes with supervised learning methods.

Improving Consistency of GNSS-IR Reflector Height Estimates between Different Frequencies Using Multichannel Singular Spectrum Analysis

Previous studies of GNSS-IR mainly focused on the legacy L1C signal; the potential of modernized signals (L2C and L5Q) has not yet been fully exploited. In this paper, we applied the Multichannel Singular Spectrum Analysis (M-SSA) method to extract common interference patterns from different frequencies simultaneously. The three-frequency (L1C, L2C, and L5Q) signal-to-noise ratio (SNR) measurements from a total of 840 satellite rising and setting arcs, occurring between day of year 250 to 279 in year 2020 and 2021, were used. By comparing GNSS-IR reflector heights obtained from the original and M-SSA-reconstructed SNR time series, we found that M-SSA significantly improves the between-frequency consistency, as shown by an increase in the values of R-squared of linear regression from (0.69, 0.67, 0.89) to (0.95, 0.96, 0.98), and a decrease in RMSE from (0.10 m, 0.10 m, 0.06 m) to (0.04 m, 0.04 m, 0.02 m) for S1C-S2C, S1C-S5Q, and S2C-S5Q pair, respectively. Our results validate (1) the effectiveness of the M-SSA method in extracting common interference patterns from multi-frequency SNR time series, and (2) the superiority of modernized civil signals L2C and L5Q over the legacy L1C signal in GNSS-IR studies. We also emphasize the important role that the L5 signal will play in future GNSS-IR research because of its compatibility and interoperability among different satellite navigation systems.

Dynamical data mining captures disc–halo couplings that structure galaxies

ABSTRACTStudying coupling between different galactic components is a challenging problem in galactic dynamics. Using basis function expansions (BFEs) and multichannel singular spectrum analysis (mSSA) as a means of dynamical data mining, we discover evidence for two multicomponent disc–halo dipole modes in a Milky-Way-like simulated galaxy. One of the modes grows throughout the simulation, while the other decays throughout the simulation. The multicomponent disc–halo modes are driven primarily by the halo, and have implications for the structural evolution of galaxies, including observations of lopsidedness and other non-axisymmetric structure. In our simulation, the modes create surface density features up to 10 per cent relative to the equilibrium model stellar disc. While the simulated galaxy was constructed to be in equilibrium, BFE + mSSA also uncovered evidence of persistent periodic signals incited by aphysical initial conditions disequilibrium, including rings and weak two-armed spirals, both at the 1 per cent level. The method is sensitive to distinct evolutionary features at and even below the 1 per cent level of surface density variation. The use of mSSA produced clean signals for both modes and disequilibrium, efficiently removing variance owing to estimator noise from the input BFE time series. The discovery of multicomponent halo–disc modes is strong motivation for application of BFE + mSSA to the rich zoo of dynamics of multicomponent interacting galaxies.

Identification and Removal of Reaction Wheel Interference From In‐Situ Magnetic Field Data Using Multichannel Singular Spectrum Analysis

AbstractIn situ magnetic field measurements are critical to our understanding of a variety of space physics phenomena including field‐aligned currents and plasma waves. Unfortunately, high‐fidelity magnetometer measurements are often degraded by stray magnetic fields from the host spacecraft, its subsystems, and other instruments. One dominant source of magnetic interference on many missions are reaction wheels—spinning platters of varying rates used to control spacecraft attitude. This manuscript presents a novel approach to the mitigation of reaction wheel interference on magnetometer measurements aboard spacecraft where multiple magnetometer sensors are deployed. Specifically, multichannel singular spectrum analysis is employed to decompose multiple time series simultaneously. A technique for automatic component selection is proposed that classifies the decomposed signals into common geophysical signals and disparate locally generated signals enabling the robust estimation and removal of the local interference without requiring any assumptions about its characteristics or source. The utility of this proposed method is demonstrated empirically using in situ data from the CASSIOPE/Swarm‐Echo mission, and a data interval with near‐constant background field was shown to have its local reaction wheel interference reduced from 1.90 nT RMS, for the uncorrected outboard sensor, to 0.21 nT RMS (an 89.0% reduction). This technique can be generalized to arrays of more than two sensors, and should apply to additional types of magnetic interference.

Experimental detection of train wheel defects using wayside vibration signal processing

While many studies have been used onboard monitoring methods to detect train wheel defects, this paper aims to extract damage features from vibrational signals obtained by the wayside monitoring system. To provide an appropriate tool for the decomposition of experimental nonstationary vibration signals containing impacts, an analytical amplitude-based signal decomposition method is provided. A two-axle motor car with a flat wheel defect is studied at different operating conditions. Vibrational signals arising from wheel-rail interactions are gathered by the Wayside Data Collection Setup (WDCS) with five piezoelectric accelerometers. The tests are performed at the constant speeds of 10, 20, 30, and 40 km/h. The acquired signals are decomposed by the Multi-channel Singular Spectrum Analysis (MSSA) into the contributing components. Based on the results, increases in the amplitudes of the second reconstructed components (RCs) of the vibrational signals sensed by all the accelerometers can be observed at a specific time instance as a repeating pattern. Similar patterns are obtained at different motor car positions relative to the measurement area, as well as different motor car speeds. To verify the consistency of the second RCs, the crest factors are obtained for all the angular positions. The results show sudden increases in the crest factor at a fixed angular position that indicate the existence of a defect at that specific angular position of the wheel.

Random noise attenuation of ocean bottom seismometers based on a substep deep denoising autoencoder

AbstractOcean bottom seismometer data usually contain a large amount of random noise, which seriously reduces the signal‐to‐noise ratio of the data and affects subsequent imaging. Hence, random noise attenuation is one of the most essential steps in ocean bottom seismometer data processing. In this paper, a novel approach is proposed to attenuate the marine seismic random noise of ocean bottom seismometers based on a six‐dense‐layer denoising autoencoder. We input the domain data into the denoising autoencoder, the encoder compresses the signal and noise and extracts the main features and the decoder finally reconstructs the denoised data with the same dimension as the input. In this approach, because few raw labelled examples are available, we first constructed the pretraining, training and test data sets by patch processing. Then, we pretrained the encoder based on clean synthetic seismic data through unsupervised learning and pretrained the decoder based on noisy synthetic seismic data through supervised learning. Next, the pretrained model was fine‐tuned with the encoder–decoder on a raw seismic data set in an unsupervised manner. Finally, we used the model to attenuate the random noise in raw ocean bottom seismometer data for testing. Synthetic and raw examples are used to compare the deconvolution, multichannel singular spectrum analysis, deep denoising autoencoder and substep deep denoising autoencoder approaches. Experimental tests demonstrate that the proposed method has higher processing efficiency and precision.

3-D Data Interpolation and Denoising by an Adaptive Weighting Rank-Reduction Method Using Multichannel Singular Spectrum Analysis Algorithm

Addressing insufficient and irregular sampling is a difficult challenge in seismic processing and imaging. Recently, rank reduction methods have become popular in seismic processing algorithms for simultaneous denoising and interpolating. These methods are based on rank reduction of the trajectory matrices using truncated singular value decomposition (TSVD). Estimation of the ranks of these trajectory matrices depends on the number of plane waves in the processing window; however, for the more complicated data, the rank reduction method may fail or give poor results. In this paper, we propose an adaptive weighted rank reduction (AWRR) method that selects the optimum rank in each window automatically. The method finds the maximum ratio of the energy between two singular values. The AWRR method selects a large rank for the highly curved complex events, which leads to remaining residual errors. To overcome the residual errors, a weighting operator on the selected singular values minimizes the effect of noise projection on the signal projection. We tested the efficiency of the proposed method by applying it to both synthetic and real seismic data.

Three-Dimensional Seismic Data Reconstruction Based on Fully Connected Tensor Network Decomposition

Rank-reduction approaches assume that seismic data in the frequency-space domain is of low-rank after a specific pre-transformation. The presence of noise or missing traces will increase the rank; therefore, seismic data can be denoised and recovered via rank-reduction techniques. The iterative weighted project onto the convex set (POCS) framework can be used for noise attenuation and data reconstruction simultaneously. Multichannel singular spectrum analysis (MSSA) is a classic 3D seismic data reconstruction algorithm that rearranges the temporal frequency slices of the data with missing traces into a block Hankel matrix, and then uses randomized singular value decomposition (RSVD) to interpolate slices. To further improve the efficiency and precision of 3D seismic data reconstruction, we introduce the fully connected tensor network (FCTN) decomposition over the Hankel tensor of the frequency slices. We show that our novel rank-reduction method estimates fewer parameters than MSSA, yielding more accurate and robust results. Moreover, FCTN decomposes a fourth-order tensor into four factor contractions, which breaks the limitations that traditional tensor decomposition methods such as CANDECOMP/PARAFAC (CP) and Tucker decomposition cannot establish the connections between different factors, and are less effective at characterizing relationships. The newly proposed approach does not require singular value decomposition (SVD), leading to an overall reduction in computational complexity. Synthetic and field examples are used to compare the performance of our method with MSSA, and our numerical results reveal the better performance of the proposed FCTN decomposition method for seismic data with large gaps or a high missing ratio.

Diffraction separation and imaging using ensemble empirical mode decomposition and multichannel singular spectrum analysis

AbstractSeismic diffracted wavefield has substantial potential for high‐resolution subsurface imaging of discontinuous geological structures; however, they are often masked by higher amplitude reflection, thus requiring separation. According to the low‐rank nature of a seismic wavefield, the diffracted wavefield can be extracted using the rank‐reduction method. The traditional low‐rank diffraction separation suffers from a threshold selection problem, especially for field data. To improve threshold accuracy, we propose a method in the common‐offset or poststack domains based on the f–x ensemble empirical mode decomposition and multichannel singular spectrum analysis. We demonstrate that such decomposition allows the determination of the diffraction threshold according to the difference between the singular values of the data before and after it. Synthetic and field data examples prove that the decomposition can effectively predict and suppress the horizontal reflected signal, while attenuating the energy of the dipping reflected signal. The following multichannel singular spectrum analysis suppresses the dipping reflection and separates the diffraction according to the precise threshold obtained earlier. The proposed method effectively improves the accuracy of the diffraction threshold selection, enhances diffraction and attenuates reflection, resulting in an enhanced image of small‐scale geological structures.

Прогнозирование динамики пробега локомотивов с учетом влияния неисправностей и модернизаций узлов

Purpose: To improve planning system for depot and factory repairs and for locomotive up-grades in the conditions of new rolling stock delivery on the basis of life-cycle contract by the way of the development and application of mathematical model for prognosing average daily and linear runs given the impact on run of technical-technological, seasonal and random fac-tors as well as defects, limiting junctions, and their upgrading. Methods: To achieve the set goal realization, the impact assessment for non-productive downtime of new locomotives at repairs as a result of clearing of junction defects and an equipment and of downtime in wait-ing for planned repairs on dynamics of average daily and linear runs was carried out. Based on the method of multidimensional spectral singular analysis and the prognosis of time series Multi-Channel Singular Spectrum Analysis, the mathematical model on run prognosis which algorithm for, has been embodied in integrated programming environment Visual Studio (2019) on C++ programming codes. Results: Run determination method given junction and equipment possible defects and given being planned upgrading has been proposed. Practical importance: In the conditions of life-cycle contract application which frames in, the participa-tion of locomotives and their components manufacturers in the technical support of supplied products throughout their entire service-life is implied, the usage of the proposed model at re-pair program monthly, quarterly and annual planning, would reduce the downtime in waiting for putting into a repair position on account of more accurate forecast, rationally distributed repairs, materials, stock of linear equipment between service manufactures.

Integrated fault diagnosis of rolling bearings based on improved multichannel singular spectrum analysis and frequency–spatial domain decomposition

Extensive fault information can be obtained from the vibration signals of rotating machines with faulty rolling bearings. However, the diagnosis of compound faults is challenging because of their easy mix-ups, which can lead to faulty diagnosis and judgment. This study improves the multichannel singular spectrum analysis (MSSA) by using convex optimization. In addition, an integrated fault diagnosis technology for rolling bearings using an improved MSSA and frequency–spatial domain decomposition was developed. This approach involves two primary stages: signal preprocessing and fault diagnosis. The proposed method was tested to diagnose faults in the rolling bearings of pellet mills. Signal preprocessing can significantly improve the quality of a vibration signal and preserve modal information that characterizes a fault. Fault diagnosis identifies the modal parameters entirely and accurately from the reconstructed vibration signal, and determines the degree of damage. The proposed method can aid in the robust diagnosis of faulty rolling bearings under severe operating conditions.