Singular Spectrum Analysis Approach Research Articles

Singular Spectrum Analysis to Identify Excessive Rainfall

Indonesia is known for its excessive rainfall. Rainfall trends in an area have different characteristics. Differences in latitude, apparent motion of the sun, geographical position, topography, and the interaction of many forms of air circulation all contribute to this. Rainfall time series is essential for engineering planning, particularly for water infrastructure like irrigation, dams, urban drainage, ports, and wharves. Although meteorological technologies provide short-term rainfall predictions, long-term rainfall prediction is difficult and fraught with uncertainty. Unpredictability and seasonality can cause complex behavior in rainfall time series. This research utilizes the Singular Spectrum Analysis approach to extract trends; seasonality, cyclists, and noise can all be identified with potentially high accuracy.

Describing Polyps Behavior of a Deep-Sea Gorgonian, Placogorgia sp., Using a Deep-Learning Approach

Gorgonians play a fundamental role in the deep sea (below 200 m depth), composing three-dimensional habitats that are characterized by a high associated biodiversity and playing an important part in biogeochemical cycles. Here we describe the use of a benthic lander to monitoring polyps activity, used as a proxy of gorgonian feeding activity of three colonies of Placogorgia sp. Images cover a period of 22 days with a temporal resolution of 30 min. In addition, this seafloor observatory is instrumented with oceanographic sensors that allows continuous monitoring of the hydrographic conditions in the site. Deep-learning is used for automatic detection of the state of the polyps registered in the images. More than 1000 images of 3 large specimens of gorgonians are analyzed, annotating polyps as extended or retracted, using the semantic segmentation algorithm ConvNeXt. The segmentation results are used to describe the feeding patterns of this species. Placogorgia sp. shows a daily pattern of feeding conduct, depending on the hours of day and night. Using a Singular Spectrum Analysis approach, feeding activity is related to currents dynamics and Acoustic Doppler Current Profile (ADCP) return signal intensity, as proxy of suspended matter, achieving a linear correlation of 0.35 and 0.11 respectively. This is the first time that the behavior of the Placogorgia polyps, directly related to their feeding process, is described.

Singular spectrum analysis based structural damage identification in beams with multiple breathing cracks

This paper presents a generalized vibration-based multiple breathing crack localization technique in beams with an unknown number of cracks based on Singular Spectrum Analysis (SSA). Localization of multiple breathing cracks is a highly challenging inverse problem, as all these breathing cracks (more than two) might be in a similar state (either opening or closing state) at any particular time instant or in contrasting states (while some breathing cracks are opening, others in closing state) during vibration. The level of nonlinearity of vibration response is strongly dependent not only on each crack size, and location but also on the application of driving force along the cracked beam. The concept of varied input frequency excitation sources is employed in the present work for multiple breathing crack identification over the tedious traditional approach of varying input force application positions. The major advantage of using singular spectrum analysis in the present work is that it can reliably isolate and extract the very low-amplitude nonlinear sensitive components (super harmonics and intermodulation) being buried in the total response based on the pairwise eigenvalue property of harmonic components. Investigations have been carried out by varying the number, spatial locations, and also intensities of the breathing cracks. Sensitivities associated with measurement noise and also with limited sensors are also investigated. The results of both numerical and experimental investigations carried out in this paper concluded that the proposed SSA can effectively localize closely spaced or sparsely spaced (i.e.,, spatially far apart) multiple cracks in the beam. The proposed SSA approach is data-driven, works with limited sensors, and does not need reference healthy state measurements.

Earthquake Magnitude and Frequency Forecasting in Northeastern Algeria using Time Series Analysis

This study uses two different time series forecasting approaches (parametric and non-parametric) to assess a frequency and magnitude forecasting of earthquakes above Mw 4.0 in Northeastern Algeria. The Autoregressive Integrated Moving Average (ARIMA) model encompasses the parametric approach, while the non-parametric method employs the Singular Spectrum Analysis (SSA) approach. The ARIMA and SSA models were then used to train and forecast the annual number of earthquakes and annual maximum magnitude events occurring in Northeastern Algeria between 1910 and 2019, including 287 main events larger than Mw 4.0. The SSA method is used as a forecasting algorithm in this case, and the results are compared to those obtained by the ARIMA model. Based on the root mean square error (RMSE) criterion, the SSA forecasting model appears to be more appropriate than the ARIMA model. The consistency between the observation and the forecast is analyzed using a statistical test in terms of the total number of events, denoted as N-test. As a result, the findings indicate that the annual maximum magnitude in Northeastern Algeria between 2020 and 2030 will range from Mw 4.8 to Mw 5.1, while between four and six events with a magnitude of at least Mw 4.0 will occur annually.

On the improvement of heart rate prediction using the combination of singular spectrum analysis and copula-based analysis approach.

In recent years, many people have been working from home due to the exceptional circumstances concerning the coronavirus disease 2019 (COVID-19) pandemic. It has also negatively influenced general health and quality of life. Therefore, physical activity has been gaining much attention in preventing the spread of Severe Acute Respiratory Syndrome Coronavirus. For planning an effective physical activity for different clients, physical activity intensity and load degree needs to be appropriately adjusted depending on the individual's physical/health conditions. Heart rate (HR) is one of the most critical health indicators for monitoring exercise intensity and load degree because it is closely related to the heart rate. Heart rate prediction estimates the heart rate at the next moment based on now and other influencing factors. Therefore, an accurate short-term HR prediction technique can deliver efficient early warning for human health and decrease the happening of harmful events. The work described in this article aims to introduce a novel hybrid approach to model and predict the heart rate dynamics for different exercises. The results indicate that the combination of singular spectrum analysis (SSA) and the Clayton Copula model can accurately predict HR for the short term.

Evaluation of the Consistency of Three GRACE Gap-Filling Data

The Gravity Recovery and Climate Experiment (GRACE) gravity mission has become a leading platform for monitoring temporal changes in the Earth’s global gravity field. However, the usability of GRACE data is severely limited by 11 months of missing data between the GRACE and GRACE Follow-on (GRACE-FO) missions. To date, several approaches have been proposed to fill this data gap in the form of spherical harmonic coefficients (an expression of the Earth’s gravity field, SHCs). However, systematic analysis to reveal the characteristics and consistency of the datasets produced by these latest gap-filling techniques is yet to be carried out. Here, three SHC gap-filling products are systematically analyzed and compared: (1) Combining high–low satellite-to-satellite tracking with satellite laser ranging (SLR) observations (QuantumFrontiers, QF), (2) SLR-based recovery incorporating the GRACE empirical orthogonal function decomposition model proposed by the Institute of Geodesy and Geoinformation at the University of Bonn (hereafter, denoted as IGG), and (3) applying the singular spectrum analysis approach (SSA). The results show that (1) the SHCs of the QF, IGG, and SSA data are consistent up to degree 12; (2) the IGG and SSA data give similar results over the 11 gap months, but the IGG shows a faster increase in the mean ocean water mass and the SSA appears to better capture the interannual variation in the terrestrial water storage; and (3) the noise level increases significantly in the high-degree terms (l > 16) of the QF data, so these data are only applicable for large-scale mass migration research. These results provide a reference for users to select a gap-filling product. Finally, we propose a new scheme based on the triple collocation method to derive a weight matrix to fuse these three datasets into a more robust solution.

Deterring Deepfake Attacks with an Electrical Network Frequency Fingerprints Approach

With the fast development of Fifth-/Sixth-Generation (5G/6G) communications and the Internet of Video Things (IoVT), a broad range of mega-scale data applications emerge (e.g., all-weather all-time video). These network-based applications highly depend on reliable, secure, and real-time audio and/or video streams (AVSs), which consequently become a target for attackers. While modern Artificial Intelligence (AI) technology is integrated with many multimedia applications to help enhance its applications, the development of General Adversarial Networks (GANs) also leads to deepfake attacks that enable manipulation of audio or video streams to mimic any targeted person. Deepfake attacks are highly disturbing and can mislead the public, raising further challenges in policy, technology, social, and legal aspects. Instead of engaging in an endless AI arms race “fighting fire with fire”, where new Deep Learning (DL) algorithms keep making fake AVS more realistic, this paper proposes a novel approach that tackles the challenging problem of detecting deepfaked AVS data leveraging Electrical Network Frequency (ENF) signals embedded in the AVS data as a fingerprint. Under low Signal-to-Noise Ratio (SNR) conditions, Short-Time Fourier Transform (STFT) and Multiple Signal Classification (MUSIC) spectrum estimation techniques are investigated to detect the Instantaneous Frequency (IF) of interest. For reliable authentication, we enhanced the ENF signal embedded through an artificial power source in a noisy environment using the spectral combination technique and a Robust Filtering Algorithm (RFA). The proposed signal estimation workflow was deployed on a continuous audio/video input for resilience against frame manipulation attacks. A Singular Spectrum Analysis (SSA) approach was selected to minimize the false positive rate of signal correlations. Extensive experimental analysis for a reliable ENF edge-based estimation in deepfaked multimedia recordings is provided to facilitate the need for distinguishing artificially altered media content.

Modeling and forecasting of principal minerals production

Although coal reserves are abundant in Pakistan, still share of gas and oil is about 65% in the energy mix. Pakistan, despite being a mineral-enriched country, is facing an alarming situation as its power generation is based on foreign exchange. The mineral sector of Pakistan is dominated by four principal minerals which are gas, oil, gypsum, and coal, while gypsum being a source of reclamation and poverty reduction. There is a strong need to analyze and forecast the production of these four principal minerals to cope up with emerging challenges. Data contains 114 observations from the period of July 2005 to December 2014, measured in terms of metric tonnes (MT). In parametric models, Box-Jenkins (B-J) methodology, a regression model with auto-regressive errors (ARAR), and Holt-Winter (HW) method are used to model. In nonparametric models, univariate singular spectrum analysis (SSA) and multivariate SSA (MSSA) modeling approach are applied. Data is split into train and test data in order to specify a suitable model for forecasting. Root Mean Square Error (RMSE), Mean Absolute Percentage Error, and Theil’s U statistic are utilized as the measure of accuracy. For gas and coal, HW model is a suitable model to forecast. For gypsum and oil, Auto-regressive Integrated Moving Average (Box Jenkins ARIMA) and MSSA provide more accurate predictions, respectively. The forecasts for gas and gypsum as compared to 2014 are expected to be approximately 11 % and 45 %, respectively, more in 2020. In 2020, the forecasts of oil are expected to be eight times more than in 2014. The production of coal in 2020 is expected to decrease 12 % than in 2014. There is a strong need to optimize the production of coal by providing incentives for exploration and mining. The stakeholders should make serious efforts to bring the production of coal at an optimum level such as by providing modern equipment and high incentives to promote coal mining and exploration.

Forecasting the COVID-19 Pandemic in Saudi Arabia Using a Modified Singular Spectrum Analysis Approach: Model Development and Data Analysis

BackgroundInfectious disease is one of the main issues that threatens human health worldwide. The 2019 outbreak of the new coronavirus SARS-CoV-2, which causes the disease COVID-19, has become a serious global pandemic. Many attempts have been made to forecast the spread of the disease using various methods, including time series models. Among the attempts to model the pandemic, to the best of our knowledge, no studies have used the singular spectrum analysis (SSA) technique to forecast confirmed cases.ObjectiveThe primary objective of this paper is to construct a reliable, robust, and interpretable model for describing, decomposing, and forecasting the number of confirmed cases of COVID-19 and predicting the peak of the pandemic in Saudi Arabia.MethodsA modified singular spectrum analysis (SSA) approach was applied for the analysis of the COVID-19 pandemic in Saudi Arabia. We proposed this approach and developed it in our previous studies regarding the separability and grouping steps in SSA, which play important roles in reconstruction and forecasting. The modified SSA approach mainly enables us to identify the number of interpretable components required for separability, signal extraction, and noise reduction. The approach was examined using different levels of simulated and real data with different structures and signal-to-noise ratios. In this study, we examined the capability of the approach to analyze COVID-19 data. We then used vector SSA to predict new data points and the peak of the pandemic in Saudi Arabia.ResultsIn the first stage, the confirmed daily cases on the first 42 days (March 02 to April 12, 2020) were used and analyzed to identify the value of the number of required eigenvalues (r) for separability between noise and signal. After obtaining the value of r, which was 2, and extracting the signals, vector SSA was used to predict and determine the pandemic peak. In the second stage, we updated the data and included 81 daily case values. We used the same window length and number of eigenvalues for reconstruction and forecasting of the points 90 days ahead. The results of both forecasting scenarios indicated that the peak would occur around the end of May or June 2020 and that the crisis would end between the end of June and the middle of August 2020, with a total number of infected people of approximately 330,000.ConclusionsOur results confirm the impressive performance of modified SSA in analyzing COVID-19 data and selecting the value of r for identifying the signal subspace from a noisy time series and then making a reliable prediction of daily confirmed cases using the vector SSA method.

Peer Review of “Forecasting the COVID-19 Pandemic in Saudi Arabia Using a Modified Singular Spectrum Analysis Approach: Model Development and Data Analysis”

Peer Review of “Forecasting the COVID-19 Pandemic in Saudi Arabia Using a Modified Singular Spectrum Analysis Approach: Model Development and Data Analysis”

Author’s Responses to Peer Reviews of “Forecasting the COVID-19 Pandemic in Saudi Arabia Using a Modified Singular Spectrum Analysis Approach: Model Development and Data Analysis”

Author’s Responses to Peer Reviews of “Forecasting the COVID-19 Pandemic in Saudi Arabia Using a Modified Singular Spectrum Analysis Approach: Model Development and Data Analysis”

Peer Review of “Forecasting the COVID-19 Pandemic in Saudi Arabia Using a Modified Singular Spectrum Analysis Approach: Model Development and Data Analysis”

Peer Review of “Forecasting the COVID-19 Pandemic in Saudi Arabia Using a Modified Singular Spectrum Analysis Approach: Model Development and Data Analysis”

Application of Singular Spectrum Analysis in Deep-Ocean Tide Reconstruction and Prediction

This study utilized the Singular Spectrum Analysis (SSA) approach to perform time series orthogonalization and demonstrated its use by analyzing vertical tidal acceleration and sea level time series from different deep-ocean locations. This method quantifies astronomical variations by using decomposed vertical tidal acceleration to reconstruct and predict deep-ocean tide. The results show that each decomposed vertical tidal acceleration can be associated with the decomposed sea level having at least 5 astronomical variations. Their associated energies can also be used to diagnose the change of the oceanic tide response to tidal acceleration. Performance evaluation also shows that this method can give comparable reconstruction accuracy and slightly better prediction accuracy compared to the harmonic analysis-based method. It is indicated that the proposed method is accurate enough to be applied in a tsunami detection algorithm. The results also indicate that the proposed method is stable enough to provide unpropagated prediction residuals.

Modified Sliding Singular Spectrum Analysis-Based Noncontact-Type Detection of Separated Instrument in Root Canal Therapy Using Low-Frequency Ultrasonic Pattern Transceiver Design

In root canal therapy, breakage of the instrument in the root canal is the most common problem which may lead to failure of the treatment. The live localization of the separated instrument from root canal is a major challenge. The radiographic imaging and cone beam computed tomography (CBCT)-based detection methods are proposed by various researchers. In this article, a novel approach (noncontact type) is proposed which uses ultrasonic signal for detection and continuous localization of the separated instrument in the root canal. The ultrasonic signal is transmitted in the root canal using 20-80-kHz ultrasonic pattern generator designed using dental gel without directly touching the ultrasound probe to the tooth (noncontact type). The signals from tooth are received by the designed ultrasonic sensor using dental gel again as interface and then analyzed using sliding singular spectrum analysis (SSSA) approach to extract the information about the position of the separated instrument. The detected position of the separated instrument is displayed in real-time on the screen in a doctor-friendly form. The design has been tested on extracted teeth and human jaws at Maulana Azad Institute of Dental Sciences, Delhi, India. This novel approach demonstrates an efficiency of approximately 87% and provides an ultraeconomical solution. The results show that this approach reduces the efforts to detect the position of the separated instrument without the loss of tooth anatomy and helps doctor extract the broken instrument out of root canal.

Effectiveness analysis of bio-electronic stimulation therapy to Parkinson’s diseases via joint singular spectrum analysis and discrete fourier transform approach

This paper studies the effectiveness of applying the bio-electronic stimulation therapy to suppress the syndromes of the Parkinson’s diseases. Here, eight patients suffering from the Parkinson’s diseases are invited for performing the investigation. The patients wear the wearable devices before and after applying the bio-electronic stimulation therapy for acquiring the corresponding resting tremor signals. First, the DC means of these signals are removed. Then, these zero mean signals are normalized to the unit energy signals. Second, the singular spectrum analysis is performed and the sets of singular spectrum analysis components are obtained. Next, the singular spectrum analysis components corresponding to the voluntary movements and the noises from various sources are removed. Third, the fast Fourier transforms are computed on the sums of the rest of singular spectrum analysis components. Then, the signal components between 3 Hz and 8 Hz are extracted out. Next, the energies of the signal components are computed for performing the analysis. The computer numerical simulation results show that the energies of the tremors after applying the bio-electronic stimulation therapy are lower than those before applying the bio-electronic stimulation therapy for all these eight patients. Compare to the processing without performing the singular spectrum analysis, the energies of the tremors after applying the bio-electronic stimulation therapy are lower than those before applying the bio-electronic stimulation therapy only for seven patients. This verifies that the singular spectrum analysis approach is effective for performing the analysis and the bio-electronic stimulation therapy is effective for suppressing the syndromes of the Parkinson’s diseases.

Water table variations in Atacama Desert alluvial fans: discussion of “Evidence of short-term groundwater recharge signal propagation from the Andes to the central Atacama Desert: a singular spectrum analysis approach”*

ABSTRACT Using a statistical approach, Scheihing attempts to demonstrate the direct influence of recharge events in the Precordillera and the Andean Piedmont on water table variations in downstream alluvial fans. The author “unquestionably” discards the existence of ephemeral recharge processes in alluvial fans although they are frequently impacted by major floods. However, the author does not consider previous publications about recharge processes in arid alluvial fans, the hydraulic setting of the Pampa del Tamarugal Aquifer (PTA) and anthropogenic pressure changes in the PTA. Because the sustainable management of groundwater resources in drylands depends on a good understanding of hydrogeological processes, we propose a thorough reinterpretation of the short- and long-term PTA water table variations addressed by the author. In this comment, we illustrate the limits of the sole use of a statistical approach for characterizing both recharge processes and factors controlling the water table variations in the Atacama Desert.

Suppressing the Spikes in Electroencephalogram via an Iterative Joint Singular Spectrum Analysis and Low-Rank Decomposition Approach.

The novelty and the contribution of this paper consists of applying an iterative joint singular spectrum analysis and low-rank decomposition approach for suppressing the spikes in an electroencephalogram. First, an electroencephalogram is filtered by an ideal lowpass filter via removing its discrete Fourier transform coefficients outside the wave band, the wave band, the wave band, the wave band and the wave band. Second, the singular spectrum analysis is performed on the filtered electroencephalogram to obtain the singular spectrum analysis components. The singular spectrum analysis components are sorted according to the magnitudes of their corresponding eigenvalues. The singular spectrum analysis components are sequentially added together starting from the last singular spectrum analysis component. If the variance of the summed singular spectrum analysis component under the unit energy normalization is larger than a threshold value, then the summation is terminated. The summed singular spectrum analysis component forms the first scale of the electroencephalogram. The rest singular spectrum analysis components are also summed up together separately to form the residue of the electroencephalogram. Next, the low-rank decomposition is performed on the residue of the electroencephalogram to obtain both the low-rank component and the sparse component. The low-rank component is added to the previous scale of the electroencephalogram to obtain the next scale of the electroencephalogram. Finally, the above procedures are repeated on the sparse component until the variance of the current scale of the electroencephalogram under the unit energy normalization is larger than another threshold value. The computer numerical simulation results show that the spike suppression performance based on our proposed method outperforms that based on the state-of-the-art methods.

A heuristic singular spectrum analysis method for suspended sediment concentration time series contaminated with multiplicative noise

This paper proposes a heuristic singular spectrum analysis (SSA) approach to extract signals from suspended sediment concentration (SSC) time series contaminated by multiplicative noise, in which multiplicative noise is converted to approximate additive noise by multiplying with the signal estimate of the time series. Therefore both the signal and noise components need to be recursively estimated. Since the converted additive noise is heterogeneous, a weight factor is introduced according to the variance of additive noise. The proposed heuristic SSA approach is employed to process the SSC series in San Francisco Bay compared to the traditional SSA and homomorphic log-transformation SSA approach. By using our heuristic SSA approach, the first 10 principal components derived can capture 96.49% of the total variance with the fitting error of 6.17 mg/L, better than those derived by traditional SSA approach and homomorphic log-transformation SSA approach that catch 88.97% and 87.35% of the total variance with the fitting errors of 14.47 mg/L and 15.03 mg/L, respectively. Therefore, our heuristic SSA approach can extract more signals than traditional SSA and homomorphic log-transformation SSA approach. Furthermore, the results from the simulation cases show that all the mean root mean squared errors and mean absolute errors derived by our heuristic SSA are smaller than the traditional and homomorphic log-transformation SSA, which indicate that the extracted signals by heuristic SSA approach are much closer to the real signals than those by the other two approaches. Therefore it can be conclude that our heuristic SSA approach performs better in extracting signals from SSC time series contaminated with multiplicative noise.

Linear phase properties of the singular spectrum analysis components for the estimations of the RR intervals of electrocardiograms

Denoising is the first step in both the QRS complex detection and the beat classification. However, infinite impulse response filters usually exhibit nonlinear phase responses. As a result, the group delays of the output signals based on the infinite impulse response filtering are different at different time instants. This causes the inaccuracies of the estimations of the RR intervals of the electrocardiograms. In this paper, the denoising is performed based on the singular spectrum analysis approach. The linear phase properties of the singular spectrum analysis components are investigated. Finally, the RR intervals of the denoised electrocardiograms are estimated and those obtained based on the infinite impulse response filtering approach are compared. The computer numerical simulation results show that the estimation performance based on the singular spectrum analysis approach outperforms that based on the infinite impulse response filtering approach.

Iterative deblending of simultaneous-source data using smoothed singular spectrum analysis

Simultaneous-source acquisition helps the field crews obtain a faster seismic data recording by allowing multiple sources to be fired simultaneously. However, the simultaneous source ignition causes strong interferences in the recorded data, which greatly affects the subsequent seismic data processing and imaging workflows. An effective separation of simultaneous sources is considered as the key in successfully utilizing the simultaneous-source acquisition technology. In this paper, we propose a novel smoothed singular spectrum analysis (SSA) approach to remove blending noise in an iterative inversion manner. Compared with the traditional SSA approach, the smoothed SSA approach applies a Gaussian smoothing operator onto the Hankel matrix in the frequency domain, and can attenuate more blending noise than the traditional SSA method. We use both synthetic and field data examples to demonstrate the successful performance of the proposed method.