Singular Spectrum Research Articles

Rolling bearing faults identification based on multiscale singular value

To solve the vulnerability of singular value denoising to the effective number of singular value orders and influence of Hankel matrix structure, the paper has proposed a multiscale singular value denoising algorithm (M-SVD). Meanwhile, in concerning that when a fault of bearing occurs, the fault feature information contained in vibration signal tends to be weak and complex, the M-SVD method is blended with variational mode decomposition (VMD) algorithm in identification. Firstly, when bearing faults occur, raw vibration acceleration signals are decomposed using the superiority of VMD algorithm for non-stationary signal; in addition, considering that with the larger difference between singular values of signal, feature information will be more obvious, the method takes advantage of sensibility of variance to signal intensity and proposes to constitute Hankel matrix based on variance feature of signal. During the construction of Hankel matrix, the method to determine effective length of variance sequence (optimal scale) has been brought forward by sample entropy which is able to precisely measure the regularity of signal and detect the weak change of signal. Furthermore, component signals are denoised in line with reconstructed Hankel matrix and the spectrum of signals denoised are selected to describe fault characteristic information and judge the failure types. For the sake of verification of the accuracy and effectiveness of proposed method, the paper has analyzed and verified the data of rolling bearing in 3 different failure types and 2 different installation positions of accelerometers. The comparative analysis with classical singular value difference spectrum (SVDS) and singular value median decomposition (SVMD) denoising has further proved that presented VMD combined M-SVD method can effectively restrain noise while retaining fault characteristic information of signal. Therefore, the identification for rolling bearing fault types can be implemented, accurately.

Preservation of absolutely continuous spectrum for contractive operators

Contractive operators T T that are trace class perturbations of a unitary operator U U are treated. It is proved that the dimension functions of the absolutely continuous spectrum of T T , T ∗ T^* , and of U U coincide. In particular, if U U has a purely singular spectrum, then the characteristic function θ \theta of T T is a two-sided inner function, i.e., θ ( ξ ) \theta (\xi ) is unitary a.e. on T \mathbb {T} . Some corollaries to this result are related to investigations of the asymptotic stability of the operators T T and T ∗ T^* (the convergence T n → 0 T^n\to 0 and ( T ∗ ) n → 0 (T^*)^n\to 0 , respectively, in the strong operator topology). The proof is based on an explicit computation of the characteristic function.

Multi‐Step Forecasting for Household Power Consumption

AbstractIt is of great importance to build an accurate model for the multi‐step forecasting of household power consumption. In recent years, more and more researchers have focused on adopting hybrid models to execute forecasting due to the irregularity and nonlinearity of power data. However, existing forecasting models usually make predictions directly on original data. This paper introduces secondary decomposition algorithm used to decompose primal data. We use singular spectrum analysis (SSA) to decompose the original series into several subseries, utilize variational mode decomposition (VMD) optimized by whale optimization algorithm to decompose the subseries with the highest frequency into several intrinsic mode functions . Then all subseries obtained from SSA and VMD are fed into long short‐term memory model to get predictions. In order to confirm the validity of proposed model, this paper performs several experimental analyses. The results of experiments show that the proposed model effectively improves the accuracy of forecasting. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Periodic signal extraction of GNSS height time series based on adaptive singular spectrum analysis

Singular spectrum analysis is widely used in geodetic time series analysis. However, when extracting time-varying periodic signals from a large number of Global Navigation Satellite System (GNSS) time series, the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient. To improve the efficiency and accuracy of singular spectrum analysis, this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix. The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series, and the extraction efficiency of a single time series is six times that of singular spectrum analysis. The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites.

Detection and recognition of dim and small targets in sea clutter background based on polarization decomposition

The consideration of the polarization scattering characteristics of radar echo in the detection of small and dim targets in a sea clutter background leads to high detection probability and high recognition accuracy. In this study, a target detection method based on canonical polar decomposition (CPD) was developed. In particular, a polarization matrix T was constructed for the radar echo of each range bin; the absolute value A and phase [Formula: see text] of T were extracted; the diagonal elements of the characteristic matrix H were extracted and converted into the singular spectrum form; and the negative entropies [Formula: see text] and [Formula: see text] of the singular spectrum were calculated. We set [Formula: see text]; then, the negative entropy value [Formula: see text] of each range bin was obtained, and the range bin of the minimum value was identified, which was the target position. Thereafter, a seven-component scattering power decomposition (7SD) was performed on T. The basic scattering structure of the target was analyzed, and a polar feature description word (PFDW) was formed to recognize the target characteristics. The effectiveness of the proposed method was verified by using the sea clutter dataset obtained with the IPIX radar. The comparison with the statistical model-based method is also made for indicating the advantage of the proposed method.

Application of spectral analysis to the reservoir-triggered earthquakes in Three Gorges reservoir region, China

In the Three Gorges reservoir region, central China, seismic activity increased substantially after the reservoir impoundment in 2003 which continues till date. Previous studies show that these are reservoir-triggered earthquakes and various factors are responsible for the increase in seismic activity after the reservoir impoundment. However, these studies do not provide a comprehensive assessment of influence of reservoir water level variations on spatiotemporal distribution of earthquakes. In this study, we statistically analyze the influence of the water level variations on the increased seismic activity in the reservoir region for the period from May 2003 to April 2020, using the power spectrum and singular spectrum techniques. Our statistical analyses confirm the influence of long-term variations in the water level time series on the occurrence of earthquakes after the reservoir impoundment. The analysis also indicates a positive role of annual reservoir water level fluctuations in the total seismicity of the region. Depending on the cluster patterns and relationship with faults, the earthquakes of the Three Gorges reservoir region are divided into three seismic zones (A, B, and C). For zone C, both the power spectrum and singular spectrum analyses confirm the strong periodic influence of reservoir water level variations on the earthquakes. Increase in seismicity of zone B is only in the initial period but not in the later stages of water impoundment and our statistical analyses indicate that the seismicity of this zone is not directly related to the annual reservoir water level variations. This confirms the conjecture in the earlier studies that the seismicity of this zone is related to the collapse of coal mines present in the area in the initial stages of reservoir impoundment. For zone A, our statistical analyses do not show strong influence of the annual reservoir water level variations on the occurrence of earthquakes. We suggest that this is due to the contribution of various other factors along with reservoir impoundment in the occurrence of earthquakes in this zone, as also opined in some earlier studies.

Double grazing bifurcation route in a quasiperiodically driven piecewise linear oscillator.

Considering a piecewise linear oscillator with quasiperiodic excitation, we uncover the route of double grazing bifurcation of quasiperiodic torus to strange nonchaotic attractors (i.e., SNAs). The maximum displacement for double grazing bifurcation of the quasiperiodic torus can be obtained analytically. After double grazing of quasiperiodic orbits, the smooth quasiperiodic torus wrinkles increasingly with the continuous change of the parameter. Subsequently, the whole quasiperiodic torus loses the smoothness by becoming everywhere non-differentiable, which indicates the birth of SNAs. The Lyapunov exponent is adopted to verify the nonchaotic property of the SNA. The strange property of SNAs can be characterized by the phase sensitivity, the power spectrum, the singular continuous spectrum, and the fractal structure. Our detailed analysis shows that the SNAs induced by double grazing may exist in a short parameter interval between 1 T quasiperiodic orbit and 2 T quasiperiodic orbit or between 1 T quasiperiodic orbit and 4 T quasiperiodic orbit or between 1 T quasiperiodic orbit and chaotic motion. Noteworthy, SNAs may also exist in a large parameter interval after double grazing, which does not lead to any quasiperiodic or chaotic orbits.

GFR: Generic feature representations for class incremental learning

Class incremental learning (CIL) aims to continuously learn new classes while maintaining discrimination for old classes with sequentially coming data. Due to the lack of old-class samples, existing CIL methods fail to learn discriminative representations for both old and new classes simultaneously, resulting in a severe performance drop in old classes, which is the well-known catastrophic forgetting phenomenon. Different from most existing works, we facilitate CIL by learning generic feature representations that perform well in seen and unseen classes. Specifically, we prove that representations with a substantial number of significant singular values benefit CIL via better old knowledge reservation. However, the overly uniform singular value spectrum will hurt the discrimination of current tasks. Furthermore, we propose that increasing the embedding dimension can enhance the number of significant singular values and validate this assumption from two perspectives: adopting different pooling techniques and devising a wider network. Meanwhile, we also prove that satisfactory current task accuracy and old knowledge reservation can be achieved simultaneously. Finally, the simple yet effective generic feature representation regulation (GFR) is devised and incorporated into two baselines. Extensive experiments are conducted on CIFAR100, ImageNet-Subset, and ImageNet. The results show that the proposed method boosts the performance of both baselines with a large margin (2.00%-9.58% on CIFAR100, 0.68%-7.10% on ImageNet-Subset and 1.18%-5.04% on ImageNet) which outperforms existing SOTAs.

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.

Strategies for Producing Reliable Trends Forecasting of COVID-19 Pandemic in Malaysia using Dynamic Mode Decomposition

Dynamic Mode Decomposition (DMD) with time delay embedding is used to predict dynamic patterns in univariate time series. An important pattern that can be extracted using DMD is the trend or global change in a time series which is useful for producing reliable forecast. DMD utilizes the computationally effi cient singular value decomposition (SVD) to produce a low rank approximation of the linear operator that brings about the dynamic patterns in the time series. Trend in the time series is translated as dynamic modes of the operator with low frequencies. The time evolution of this low frequency pattern produces forecast of the time series. In this paper, we outline the strategies for extracting trend component from COVID-19 time series of Malaysia. It is discovered that, other than identifying modes with slow varying frequencies, we need to also resolve the time stamp delay, so that mean-square error of the reconstructed time series is minimal. Information of the magnitude and phase of DMD modes are useful to identify persistent patterns and remove nonstationary ones. We compare the performance of DMD with another SVD-based method which is the singular spectrum analysis (SSA) and our results highlight certain fundamental difference between these two methods. The forecasts from SSA tend to lean towards the direction of maximum variance, producing low reconstruction error but slow to detect sudden changes in the time series. On the other hand, forecasts from DMD captures the phases of dominant modes that dictates the overall global pattern, hence providing a better prediction of future dynamics of the time series.

FORECASTING THE NUMBER OF PASSENGER AT JENDERAL AHMAD YANI SEMARANG INTERNATIONAL AIRPORT USING HYBRID SINGULAR SPECTRUM ANALYSIS-NEURAL NETWORK (SSA-NN) METHOD

Transportation was an important sector of supporting the economic growth of a country. The impact of the Covid-19 2020 pandemic at Achmad Yani International Airport in Semarang resulted in the movement of the number of passengers decreasing quite drastically, but in mid-2020 the movement of the number of passengers had slowly increased. Forecasting was done to determine the flow of movement of the number of passengers in the future using the Hybrid Singular Spectrum Analysis (SSA)-Neural Network (NN) method. The SSA method was expected to be able to decompose various patterns in the data into trend, seasonality and noise. Furthermore, the NN method was used to analyze nonlinear patterns in the data. The results showed that the best method was a combination of the SSA method with a window length of 40 and the NN method with a 6-8-1 network architecture (6 input neurons, 8 hidden neurons and 1 output neuron) for the trend component, 11-15-1 (11 neurons input, 15 hidden neurons and 1 output neuron) for the seasonal component, and 10-15-1 (10 input neurons, 15 hidden neurons and 1 output neuron) for the noise component. The model produces a prediction error based on a MAPE value of 0.54% or an accuracy rate of 99.46%.

Rainfall Forcasting in Medan City Using Singular Spectrum Analysis (SSA)

Singular spectrum analysis is a time series analysis that can be used for data that has seasonal effects. Rainfall is one example that has a seasonal effect. High rainfall has an impact on natural disasters such as floods. Medan city is the capital city of North Sumatra province which has quite high rainfall and is a lowland area, so it has the potential for flooding. Rainfall forecasting can be done as disaster mitigation. The forecasting method used is SSA. The MAPE forecasting accuracy value obtained is 15.7% and the tracking signal is within tolerance limits so that it can be concluded that the forecasting is done well.

Application of singular spectrum analysis method to forecast rice production in west sumatra

The imbalance between the population and rice production will cause various negative impacts such as food crisesand increasing poverty, so forecasting needs to be done to maintain food availability in the future. This study aimsdetermine the results of rice production in West Sumatra Province for 12 periods in 2023 using the SA method. Basedon the results of the analysis, rice production in 2023 for 12 periods tends to decrease compared to the previous year.Forecasting rice production using the SSA method with L=21 can be said to be accurate with a MAPE obtained of17.69%.

Hybrid quantum singular spectrum decomposition for time series analysis

Classical data analysis requires computational efforts that become intractable in the age of Big Data. An essential task in time series analysis is the extraction of physically meaningful information from a noisy time series. One algorithm devised for this very purpose is singular spectrum decomposition (SSD), an adaptive method that allows for the extraction of narrow-banded components from non-stationary and non-linear time series. The main computational bottleneck of this algorithm is the singular value decomposition (SVD). Quantum computing could facilitate a speedup in this domain through superior scaling laws. We propose quantum SSD by assigning the SVD subroutine to a quantum computer. The viability for implementation and performance of this hybrid algorithm on a near term hybrid quantum computer is investigated. In this work, we show that by employing randomized SVD, we can impose a qubit limit on one of the circuits to improve scalibility. Using this, we efficiently perform quantum SSD on simulations of local field potentials recorded in brain tissue, as well as GW150914, the first detected gravitational wave event.

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.

A hybrid model for online short-term tidal energy forecasting

A hybrid model is proposed for the short-term online prediction of tidal currents. The harmonic residual analysis (HRA) model is designed to augment the numerical schemes employed by tidal energy installations by forecasting the residual error of existing methods. Using a combination of techniques from Information and Fractal Theory, a novel component selection criterion for singular spectrum analysis (SSA) is used to remove true noise from the residual time series and to decompose the signal into components that are appropriate for linear-recurrent forecasting (LRF) and high order fuzzy time series (HOFTS) respectively. The performance of the HRA method is evaluated using a combination of simulated and real data from sites in the United Kingdom and the United States. Results demonstrate the model’s viability for 6-minute and 1-hour forecast horizons across sites exhibiting variable degrees of non-linearity. Empirical analysis of the resultant tidal energy forecast verifies the superior accuracy and reliability of the HRA method when compared with existing numerical schemes. Simulated data from three sites at the Pentland Firth, UK is also provided to facilitate further study of the site’s power generation characteristics and to allow for direct model performance comparisons.

Detection of Anomalies in Natural Complicated Data Structures Based on a Hybrid Approach

A hybrid approach is proposed to detect anomalies in natural complicated data structures with high noise levels. The approach includes the application of an autoencoder neural network and singular spectrum analysis (SSA) with an adaptive anomaly detection algorithm (AADA) developed by the authors. The autoencoder is the quintessence of the representation learning algorithm, and it projects (selects) data features. Here, under-complete autoencoders are used. They are a product of the development of the principal component method and allow one to approximate complex nonlinear dependencies. Singular spectrum analysis decomposes data through the singular decomposition of matrix trajectories and makes it possible to detect the data structure in the noise. The AADA is based on the combination of wavelet transforms with threshold functions. Combinations of different constructions of wavelet transformation with threshold functions are widely applied to tasks relating to complex data processing. However, when the noise level is high and there is no complete knowledge of a useful signal, anomaly detection is not a trivial problem and requires a complex approach. This paper considers the use of adaptive threshold functions, the parameters of which are estimated on a probabilistic basis. Adaptive thresholds and a moving time window are introduced. The efficiency of the proposed method in detecting anomalies in neutron monitor data is illustrated. Neutron monitor data record cosmic ray intensities. We used neutron monitor data from ground stations. Anomalies in cosmic rays can create serious radiation hazards for people as well as for space and ground facilities. Thus, the diagnostics of anomalies in cosmic ray parameters is quite topical, and research is being carried out by teams from different countries. A comparison of the results for the autoencoder + AADA and SSA + AADA methods showed the higher efficiency of the autoencoder + AADA method. A more flexible NN apparatus provides better detection of short-period anomalies that have complicated structures. However, the combination of SSA and the AADA is efficient in the detection of long-term anomalies in cosmic rays that occur during strong magnetic storms. Thus, cosmic ray data analysis requires a more complex approach, including the use of the autoencoder and SSA with the AADA.

Application of Metaheuristic Algorithms and ANN Model for Univariate Water Level Forecasting

With the rapid development of machine learning (ML) models, the artificial neural network (ANN) is being increasingly applied for forecasting hydrological processes. However, researchers have not treated hybrid ML models in much detail. To address these issues, this study herein suggests a novel methodology to forecast the monthly water level (WL) based on multiple lags of the Tigris River in Al-Kut, Iraq, over ten years. The methodology includes preprocessing data methods, and the ANN model optimises with a marine predator algorithm (MPA). In the optimisation procedure, to decrease uncertainty and expand the predicting range, the slime mould algorithm (SMA-ANN), constriction coefficient-based particle swarm optimisation and chaotic gravitational search algorithms (CPSOCGSA-ANN), and particle swarm optimisation (PSO-ANN) are applied to compare and validate the MPA-ANN model performance. Analysis of results revealed that the data pretreatment methods improved the original data quality and selected the ideal predictors’ scenario by singular spectrum analysis and mutual information methods, respectively. For example, the correlation coefficient of the first lag improved from 0.648 to 0.938. Depending on various evaluation metrics, MPA-ANN tends to forecast WL better than SMA-ANN, PSO-ANN, and CPSOCGSA-ANN algorithms with coefficients of determination of 0.94, 0.81, 0.85, and 0.90, respectively. Evidence shows that the proposed methodology yields excellent results, with a scatter index equal to 0.002. The research outcomes represent an additional step towards evolving various hybrid ML techniques, which are valuable to practitioners wishing to forecast WL data and the management of water resources in light of environmental shifts.

The Geometry of Feature Space in Deep Learning Models: A Holistic Perspective and Comprehensive Review

As the field of deep learning experiences a meteoric rise, the urgency to decipher the complex geometric properties of feature spaces, which underlie the effectiveness of diverse learning algorithms and optimization techniques, has become paramount. In this scholarly review, a comprehensive, holistic outlook on the geometry of feature spaces in deep learning models is provided in order to thoroughly probe the interconnections between feature spaces and a multitude of influential factors such as activation functions, normalization methods, and model architectures. The exploration commences with an all-encompassing examination of deep learning models, followed by a rigorous dissection of feature space geometry, delving into manifold structures, curvature, wide neural networks and Gaussian processes, critical points and loss landscapes, singular value spectra, and adversarial robustness, among other notable topics. Moreover, transfer learning and disentangled representations in feature space are illuminated, accentuating the progress and challenges in these areas. In conclusion, the challenges and future research directions in the domain of feature space geometry are outlined, emphasizing the significance of comprehending overparameterized models, unsupervised and semi-supervised learning, interpretable feature space geometry, topological analysis, and multimodal and multi-task learning. Embracing a holistic perspective, this review aspires to serve as an exhaustive guide for researchers and practitioners alike, clarifying the intricacies of the geometry of feature spaces in deep learning models and mapping the trajectory for future advancements in this enigmatic and enthralling domain.

Multidimensional Analysis of Precursor Information of Rockburst during Loading and Unloading of Deep Diorite

At present, rockburst disasters cannot be predicted accurately, and the prevention and control of deep underground engineering disasters are significantly challenging. To explore the evolution law of precursory information of rockburst instability, the rockburst test of diorite was conducted with high confining pressure and different unloading rates (0.1 MPa/s, 0.3 MPa/s, 0.5 MPa/s, 0.7 MPa/s, and 0.9 MPa/s). Multidimensional analysis is carried out by evaluating deformation features, fast Fourier transform (FFT), energy entropy, singular spectrum entropy, and power spectrum entropy. The results show that Poisson’s ratio is hook-shaped before rockburst, the elastic modulus is in the shape of a step, ringing count and energy surge after a quiet period, three-dimensional law of 0.98 σ c ~ σ c stress location space shows a large red ball distribution along the shear plane, b value fluctuates in the low-value range, and low-frequency high amplitude and high-frequency low amplitude fluctuate in a large range after 300 s, with frequent abnormal fluctuations of the energy spectrum entropy, the singular spectrum entropy, and the power spectrum entropy curve. The above research results can be considered the evolution law of rockburst precursor information, which enriches the theoretical method of explosion disaster prediction.