Efficient and Adaptive Signal Denoising Based on Multistage Singular Spectrum Analysis

The increasing population growth in Pinrang Regency every year had an impact on increasing the need for food, especially rice production which was generally a staple food source in Pinrang Regency. so it was necessary to do a forecast to anticipate future food shortages. This study aimed to determine the yield of rice production in Pinrang Regency in 2021 and the level of accuracy of the method used. The results of the study obtained forecast for rice production in Pinrang Regency in 2021 using the Singular Spectrum Analysis (SSA) method, respectively from the first quarter to the third quarter of 33603 tons, 25988 tons, and 43234 tons with the level of forecasting accuracy based on standard MAPE value obtained by 4.97 %. The MAPE value obtained was less than 10 % and close to 0 %, meaning that the SSA method with windows length 9 and 7 groups were very accurate to be used to predict rice production in Pinrang Regency.

An application of Singular Spectrum Analysis(SSA) Method, based on a new elaborated tensorial approach of computation of singular values and left and right singular vectors of arbitrary non-square matrices, for time series is presented. All necessary calculations of singular values and both types (left and right) singular vectors are performed on the base of elaborated tensorial approach. It is showed that non parametric SSA can be efficiently used as a universal filter to separate Low and High frequencies components in long signals and time series.

As a maritime country strategically located along the world's leading transportation routes, Indonesia often faces increased ship accidents. Based on the Basarnas Statistics Book, ship accidents handled by Basarnas from 2021 to 2023 increased by 3%. This condition requires an effective forecasting method to carry out SAR operations to predict ship accidents in the Indonesian region in the future and assess the readiness and needs of Basarnas resources. This study compares the forecasting results obtained using the Singular Spectrum Analysis (SSA) and the Local Linear methods. Both methods do not require parametric assumptions. The data used in this study are divided into training data and test data. This data is secondary data obtained from the Basarnas Statistics Book. The training data in this study is the number of SAR operations from January 2021 to December 2022, while the testing data is from January 2023 to December 2023. From the analysis results, it is known that the method with the smallest MAPE is the Local Linear method with a MAPE of test data of 18.67% (good forecasting category), optimal bandwidth (h) = 4.299, and CV (h) = 231.39 where bandwidth is used to determine the level of smoothness of the estimate, while the CV (h) value is used to select the optimal bandwidth that minimizes the estimation error. At the same time, the SSA method has a MAPE of 40.27% (fair forecasting category). This shows that the Local Linear method provides a more accurate forecast of the number of SAR operations related to ship accidents in Indonesia. This research contributes to the SDGs to make Basarnas an effective and accountable institution and improve the planning and decision-making process in SAR operations through accurate forecasting research is relevant to accurate forecasting.

Microseismic (MS) monitoring technology has been widely used to monitor ground pressure disasters. However, the underground mining environment is complex and contains many types of noise sources. Furthermore, the traditional recognition method entails a complex process with low recognition accuracy for MS signals, so it is difficult to serve for the safe production of mines. Therefore, this study established a hybrid model combining the singular spectrum analysis (SSA) method, convolutional neural networks (CNN), and long short-term memory networks (LSTM). First, the principal components of monitoring signals were extracted with the SSA method, and then spatial and temporal features of monitoring signals were separately extracted with the CNN and LSTM. Based on actual field data collected from Xiadian Gold Mine, the hybrid model was compared with the CNN, LSTM, and back-propagation networks (BP), as well as commonly used recognition methods including the support vector machine (SVM), decision tree (DT), K-nearest neighbor (KNN), and linear discriminant analysis (LDA). The results show that the proposed hybrid model can accurately extract data features of monitoring signals and further improve MS signals' recognition performance. Furthermore, the recognition accuracy of mechanical signals in monitoring signals is particularly increased using the hybrid model, which avoids confusion with MS signals.

Window length is a very critical tuning parameter in Singular Spectrum Analysis (SSA) technique. For finding the optimal value of window length in SSA application, Periodogram analysis method with SSA for referencing on the selection of window length and confirm that the periodogram analysis can provide a good option for window length selection in the application of SSA. Several potential periods of Florida precipitation data are firstly obtained using periodogram analysis method. The SSA technique is applied to precipitation data with different window length as the period and experiential recommendation to extract the precipitation time series, which determines the leading components for reconstructing the precipitation and forecast respectively. A regressive model linear recurrent formula (LRF) model is used to discover physically evolution with the SSA modes of precipitation variability. Precipitation forecasts are deduced from SSA patterns and compared with observed precipitation. Comparison of forecasting results with observed precipitation indicates that the forecasts with window length of L=60 have the better performance among all. Our findings successfully confirm that the periodogram analysis can provide a good option for window length selection in the application of SSA and presents a detailed physical explanation on the varying conditions of precipitation variables.

Time series data can be reconstructed in terms of signal and noise components through Singular Spectrum Analysis method (SSA). In SSA, window length selection is important in ensuring that the signal and noise components are clearly separated. In general, the window length should be large enough but not greater than half of the observed time series data. However, different observed behaviour of a dataset might influence the selection of window length. In this study, we demonstrate the effect of window length on torrential rainfall time series data at three different scales in extracting the trend signals in rainfall data. The window lengths are compared using the classical SSA and another variation of SSA called iterative O-SSA. We use the minimum value of w-correlation to identify the window length that best measure clear separability between components. We found that a window length to the number of observed data of 6 shows a trend that fits well to the original rainfall time series data.

Background: Rice plays a central role in Indonesia's food security and inflation dynamics, making accurate price forecasts crucial for effective planning policies. In East Kalimantan, weekly rice prices represent a significant risk factor that needs to be closely monitored to anticipate potential risks to household welfare and regional inflation. Objective: To predict rice prices in East Kalimantan over the next eight periods using the SSA method. Methods: Singular Spectrum Analysis (SSA) to predict weekly rice prices. The SSA procedure includes embedding (window length L = 48), singular value decomposition, eigentriple clustering (trend: 1–2; seasonality: 3–35; disturbance: 36–48), diagonal averaging, and R-forecasting using the Linear Recursive Formula (LRF). Results: MAPE of 0.084% (in-sample) and 3.299% (out-sample). Estimates indicate that rice prices will remain in the range of IDR 15,500–16,500/kg during August–October 2025. Conclusion: The SSA is effective in capturing basic price components and producing reliable forecasts to support food reserve maintenance, distribution strategies, and inflation risk mitigation.

Indonesia is an archipelagic country where 2/3 of its territory is ocean. The vastness of Indonesia's oceans is expected to produce abundant sea products that can meet the needs of Indonesian consumers, especially fish. Adequacy of the amount of fish consumption can be assessed through the number of fish catch. Based on data at the Ministry of Marine Affairs and Fisheries in 2015, West Java has a low growth of fish consumption, 6.05% in 2010-2014. Therefore, it is necessary to forecast the results of fish catch for several years ahead so it can be known whether the provision of fish consumption will be fulfilled or not. One method that can be used is Singular Spectrum Analysis (SSA). The SSA method is a flexible method because it uses a nonparametric approach. That is, in its application, this method does not require the model specification of time series data, as well as parametric assumptions. Forecasting accuracy of a method is said to be good if it has a MAPE value less than 20%. MAPE of SSA method forecast is 6.19% so that SSA method is suitable for forecasting of capture fishery production in West Java Province. The forecast for fishery production in West Java Province in 2015 for the first, second, third, and fourth quarter were 53,978.49 Ton, 54,406.91 Ton, 50,889.11 Ton, and 56,896.96 Ton, respectively.

Complex control applications, such as robotics and aerospace engineering, often require nonlinear control strategies. In the backstepping, feedback linearization, and sliding mode control, online trajectory generation is a major requirement in improving the controller performance, leading to high precision tracking. Its purpose is to generate continuous and bounded trajectories that are derivatives of a rough input reference signal, such as steps and pulses. In this context, this paper proposes the use of a non-parametric filter based on the real- time Singular Spectrum Analysis (SSA) method for online trajectory generation. The SSA is highly adaptive to the behavior of signals, including non-stationary ones, through its spectral decomposition. Additionally, is more selective than a simple Finite Impulse Response (FIR) filter, commonly used for generating trajectories. It can identify and extract components, smooth, and denoise a signal. Some experimental results show that SSA can be used as trajectory filter, by successfully generating bounded derivatives from discontinuous input signals. Moreover, empirical adjustment of the fixed filter parameters resulted in similar responses as those obtained for a parametric trajectory filter. These findings provide a potential mechanism for further researches regarding complex and non-stationary signals.

Singular spectrum analysis (SSA) is a nonparametric spectral estimation method that decomposes time series signals into interpretable components. With the rise of big time series, the demand for effective and scalable SSA techniques has become increasingly urgent. In this paper, we propose a novel multiway extension of SSA, called higher-order multivariate SSA (HO-MSSA), specifically designed for multivariate and multichannel time series signal analysis via tensor decomposition. HO-MSSA utilizes time-delay embedding and tensor singular value decomposition to transform multichannel time series signals into trajectory tensors, which are then decomposed into elementary components in the Fourier domain, rather than the time domain as in traditional SSA methods. These components are grouped into disjoint subsets using spectral clustering, enabling the reconstruction of the underlying source signals. Experimental results demonstrate that HO-MSSA outperforms state-of-the-art SSA methods in various biomedical applications, including electromyography (EMG), electrocardiography (ECG), and electroencephalogram (EEG) signals. • A novel tensor-based multivariate singular spectrum analysis is introduced. • A new time embedding technique embeds time series into a higher dimension. • Tensor SVD is used to factorize the trajectory tensor of time series. • Spectral clustering detects and groups the underlying time series components.

Singular spectrum analysis (SSA) is a nonparametric method for separating time series data into a sum of small numbers of interpretable components (signal + noise). One of the steps of the SSA method, which is referenced to Embedding, is extremely sensitive to contamination of outliers which are often founded in time series analysis. To reduce the effect of outliers, SSA based on Singular Spectrum Decomposition (SSD) method is proposed. In this article, the ability of SSA based on SSD and basic SSA are compared in time series reconstruction in the presence of outliers. It is noteworthy that the matrix norm used in Basic SSA is the Frobenius norm or L 2-norm. There is a newer version of SSA that is based on L 1-norm and called L 1-SSA. It was confirmed that L 1-SSA is robust against outliers. In this regard, this research is also introduced a new version of SSD based on L 1-norm which is called L 1-SSD. A wide empirical study on both simulated and real data verifies the efficiency of basic SSA based on SSD and L 1-norm in reconstructing the time series where polluted by outliers.

A structural health monitoring system has been installed in a typical Tibetan timber building to measure the structural strains. In this paper, the singular spectrum analysis (SSA) is used for both the long-term and short-term forecasting on the structural strain variations. The optimal parameters of the SSA are selected according to the minimum mean square error of the prediction. In the 3 months forecasting, sequential prediction of 1 month could be achieved with the best result. For the 1 day forecasting, the data length in the forecasting model should not be less than 10 days. Results show that the SSA method could effectively forecast the long-term trend and the short-term fluctuation of the strains. The SSA is found slightly superior for both the long-term and short-term forecasting compared with results from the autoregressive integrated moving average (ARIMA) model.

Early studies have shown evidence of the seismo-ionospheric perturbations prior to large earthquakes. Due to dynamic complexity in the ionosphere, the identification of precursory ionospheric changes is quite challenging. In this study, we analyze the total electron content (TEC) in the global ionosphere map and investigate the TEC changes prior to M ≥ 6.0 earthquakes in the Chinese Mainland during 1998–2013 to identify possible seismo-ionospheric precursors. Singular spectrum analysis is applied to extract the trend and periodic variations including diurnal and semi-diurnal components, which are dominated by solar activities. The residual ΔTEC which is mainly composed of errors and possible perturbations induced by earthquakes and geomagnetic activities is further investigated, and the root-mean-square error is employed to detect anomalous changes. The F10.7 and Dst index is also used as criterion to rule out the anomalies when intense solar or geomagnetic activities occur. Our results are consistent with those of previous studies. It is confirmed that the negative anomalies are dominant 1–5 days before the earthquakes at the fixed point (35°N, 90°E) during 0600–1000 LT. The anomalies are more obvious near the epicenter area. The singular spectrum analysis method help to establish a more reliable variation background of TEC and thus may improve the identification of precursory ionospheric changes.

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.

In singular spectrum analysis, which is applied to signal extraction, it is of critical importance to select the number of components correctly in order to accurately estimate the signal. In the case of a low-rank signal, there is a challenge in estimating the signal rank, which is equivalent to selecting the model order. Information criteria are commonly employed to address these issues. However, singular spectrum analysis is not aimed at the exact low-rank approximation of the signal. This makes it an adaptive, fast, and flexible approach. Conventional information criteria are not directly applicable in this context. The paper examines both subspace-based and information criteria, proposing modifications suited to the Hankel structure of trajectory matrices employed in singular spectrum analysis. These modifications are initially developed for white noise, and a version for red noise is also proposed. In the numerical comparisons, a number of scenarios are considered, including the case of signals that are approximated by low-rank signals. This is the most similar to the case of real-world time series. The criteria are compared with each other and with the optimal rank choice that minimizes the signal estimation error. The results of numerical experiments demonstrate that for low-rank signals and noise levels within a region of stable rank detection, the proposed modifications yield accurate estimates of the optimal rank for both white and red noise cases. The method that considers the Hankel structure of the trajectory matrices appears to be a superior approach in many instances. Reasonable model orders are obtained for real-world time series. It is recommended that a transformation be applied to stabilize the variance before estimating the rank.