Classification of process dynamics with Monte Carlo singular spectrum analysis

Singular systems (or singular spectrum) analysis (SSA) was originally proposed for noise reduction in the analysis of experimental data and is now becoming widely used to identify intermittent or modulated oscillations in geophysical and climatic time series. Progress has been hindered by a lack of effective statistical tests to discriminate between potential oscillations and anything but the simplest form of noise, that is, "white" (independent, identically distributed) noise, in which power is independent of frequency. The authors show how the basic formalism of SSA provides a natural test for modulated oscillations against an arbitrary "colored noise" null hypothesis. This test, Monte Carlo SSA, is illustrated using synthetic data in three situations: (i) where there is prior knowledge of the power-spectral characteristics of the noise, a situation expected in some laboratory and engineering applications, or when the "noise" against which the data is being tested consists of the output of an independently specified model, such as a climate model; (ii) where a simple hypothetical noise model is tested, namely, that the data consists only of white or colored noise; and (iii) where a composite hypothetical noise model is tested, assuming some deterministic components have already been found in the data, such as a trend or annual cycle, and it needs to be established whether the remainder may be attributed to noise. The authors examine two historical temperature records and show that the strength of the evidence provided by SSA for interannual and interdecadal climate oscillations in such data has been considerably overestimated. In contrast, multiple inter- and subannual oscillatory components are identified in an extended Southern Oscillation index at a high significance level. The authors explore a number of variations on the Monte Carlo SSA algorithm and note that it is readily applicable to multivariate series, covering standard empirical orthogonal functions and multichannel SSA.

Singular spectrum analysis (SSA) has recently been applied to various geodetic time series studies. As a data-adaptive method, SSA is capable of extracting signals with non-constant phase and amplitudes. Although SSA is a competent method in the presence of white noise, the contribution of colored noise, having semi-periodic behavior, degrades its performance. Parts of colored noise can be absorbed in the SSA eigenmodes, which specifies signals and hence resulting in spurious modulation or losing significant signals. Signals and colored noise are thus to be discriminated in the signal identification procedure. Monte Carlo SSA (MCSSA) in its original formulation, providing a significance test against the AR(1) noise null hypothesis, can be misinterpreted when other colored noise structures contribute to the series. We propose an algorithm for MCSSA that is not limited to the AR(1) noise hypothesis. It estimates the noise model parameters using LS-VCE and generates the surrogate data using the Cholesky decomposition. The algorithm is adapted to GPS position time series where the underlying noise is a combination of white noise and flicker noise. GPS position time series, postulated real situation, are first simulated to include annual and semiannual signals plus white and flicker noise. The results indicate that MCSSA can extract the annual and semiannual signals with 2.11 and 1.25 mm amplitudes (the global mean values) from 20-year-long time series, with 95% confidence level, if flicker noise is less than 17 and 13 $$ {\text{mm/year}}^{1/4} $$ , respectively. The longer the time series or the stronger the signals are, the higher these thresholds will be. This conclusion is also verified when applying MCSSA to the up component of GPS position time series of 347 JPL stations.

Process Monitoring and Fault Detection using Empirical Mode Decomposition and Singular Spectrum Analysis

<p>The North Atlantic Oscillation (NAO) index describes the hemispheric meridional oscillation of atmospheric masses above near Iceland and the subtropical Atlantic regions. In specific, NAO index indicates the differences in atmospheric pressure patterns between the two regions. Strong positive NAO index values relate to significant pressure differences, exposing US East and Northern Europe to warmer weather conditions, and Southern Europe to colder weather conditions. Negative NAO index values indicate weaker pressure differences, exposing US East and Northern Europe to cold weather, and Southern Europe to warm weather. A significant portion of the Atlantic sector climate is associated with NAO index and its variability. Historically, NAO index values were in a positive trend between 1970s and 1980s. Highest positive values were reported in the early 1990s. By that time, it was suggested that NAO index positive trends contributed significantly to the global warming signal. Most recently, research outputs from climate model predictions suggest that NAO index values will be more at the positive phase as a result of strong global warming signal. In a warmer climate the overall number of storms is predicted to decrease but storms will be more intense. However, more research is needed to understand variability trends in NAO index and to what extent they might be attributed to climate change impacts. Hence referred in here as NAO natural and non-natural, or else, climate change related variability trends. This study investigated the NAO variability trends by use of Singular Spectrum Analysis (SSA) and SSA based Entropy index. SSA is a statistical mechanics tool used to study the non-linear behavioral characteristics in complex geophysical, meteorological and climatic systems, monitored by time series data. The main objective of this analysis is to reveal the evolution of the NAO index dynamical system and convey information about the changing dynamics of the system. By use of SSA Entropy based index, the chaotic behavior of NAO index is studied. An SSA entropy based chaotic descriptor might entail information of the non-natural variability trend for NAO index values. Also the same descriptor might prove capable of defining a historical milestone of when this NAO variability trend started changing in an unpredictable- non natural- way owed to climate change forcing factors. NAO Index data are extracted from Climatic Research Unit, University of East Anglia from 1979-2018. SSA Phase space reconstruction by method of delays has been applied first to characterize the statistical and chaotic behavior of NAO patterns, by calculating variability and inconsistency descriptors. Phase space reconstruction allows analyzing time series data within the dynamics systems theory context. Following that, reconstructed attractor from the NAO observed time series allowed to build an approximation of the unknown observed states. Results revealed a highly variable and inconsistent behavior in NAO patterns over time. SSA Entropy based index investigation is currently underway to further understand the nature of inconsistency revealed in NAO patterns. Further research is expected to establish wind and wave storm patterns connections with NAO index patterns, through transfer dynamics concepts.</p>

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.

Missing values in time series data is a well-known and important problem which many researchers have studied extensively in various fields. In this paper, a new nonparametric approach for missing value imputation in time series is proposed. The main novelty of this research is applying the [Formula: see text] norm-based version of Singular Spectrum Analysis (SSA), namely [Formula: see text]-SSA which is robust against outliers. The performance of the new imputation method has been compared with many other established methods. The comparison is done by applying them to various real and simulated time series. The obtained results confirm that the SSA-based methods, especially [Formula: see text]-SSA can provide better imputation in comparison to other methods.

Singular Spectrum Analysis (SSA) is an effective method of decomposition of time series for separating key components in data, such as trends, seasonality, and noise. This study aims to analyze the role of Hankel matrix in the SSA embedding process and how window length (L) selection can affect the effectiveness of component separation in data time series. In this study, the data used includes public data that can be influenced by seasonal factors and unexpected events, such as natural disasters or regulatory changes. The research process begins with the data preprocessing stage, followed by the embedding stage to form a matrix used in decomposition with Singular Value Decomposition (SVD). To evaluate the similarity of separate components, w-correlation is used. The results show that the selection of optimal window lengths, in the range of N/4 < L < N/2 is very important to maintain a balance between temporal information and matrix dimensions. With the right window selection, the embedding process in SSA can be more effective in separating the trending, seasonal, and noise components in the data pattern. By understanding the structure of the Hankel matrix and selecting the right parameters, the embedding process in SSA can be more effective in separating the components of the time series and preserving temporal information.

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.

Neurocontrol of a multi-effect batch distillation pilot plant based on evolutionary reinforcement learning

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.

A 38 m long sediment core (MD992201) retrieved from a water depth of 290 m from the leeward margin of the Great Bahama Bank (GBB; 25°53·49′N, 79°16·34′W) has been investigated for changes in aragonite content. The core covers the Mid to Late Holocene (the past 7230 yr). Sediment lightness (L*‐values) was used as a proxy for aragonite content, based on a high linear correlation (R = 0·93) between the X‐ray diffraction derived aragonite content and L*‐values. The resulting time resolution of the L*‐values derived aragonite content ranges from 1 yr at the base of the core to 4 yr at the top. Detailed time series analysis using Monte Carlo Singular Spectrum Analysis and spectral analysis (Lomb–Scargle Fourier transform) identifies the presence of seven signals with varying amplitudes and wavelengths that could be traced throughout the past 5500 yr. During the first ∼1600 yr of sedimentation the aragonite record is dominated by the initial flooding of the flat‐topped GBB. Superimposed on a multimillennial signal, related to Holocene sea‐level changes, a millennial‐scale fluctuation and five quasi‐periodic oscillations were detected (∼1·3–2 kyr, ∼500–600 yr, ∼380 yr, ∼260 yr, ∼200 yr and ∼100 yr period). Comparisons with other proxies (e.g. tree ring‐Δ14C, 10Be and δ18O in ice cores) provides information on the origin and dynamics of the individual signals. The analysis shows that the ∼200 yr and ∼100 yr signals can be attributed to solar forcing. The ∼260 yr, ∼380 yr and the ∼500–600 yr quasi‐periodic signals are found to be of climatic origin, whereas the millennial scale fluctuations remain enigmatic, although solar forcing mechanisms seem likely. The data show that variability of solar output as well as past oceanographic and atmospheric changes have modulated the Mid to Late Holocene climate, which in turn controlled sediment input variations found in the Holocene wedge leeward of the GBB. Although these periplatform sediments have a rather uniform appearance, they still contain a large variety of subtle sedimentary variations.

Long term solar-terrestrial records from sediments: carbon isotopes in planktonic foraminifera during the last millennium

Smart factories and big data are important factors in the Fourth Industrial Revolution. Smart factories aim for automation and integration; however, the most important part is the application of data. Despite extensive research on the maintenance and quality management of big data-based production equipment, industrial data gathered for analysis contain more normal data than abnormal data. In addition, a significant amount of energy is expended in the data pre-processing process to analyze the acquired data. Therefore, to maintain production equipment and quality management, data classification technology that allows easy data analysis by classifying abnormal data into normal data is required. In this paper, we propose an abnormal data classification architecture for cycle data sets gathered from production facilities through SSA-CAE along with data storage methods for each product unit. SSA-CAE is a hybrid technique that combines singular spectrum analysis (SSA) techniques that are effective in reducing noise in time series data with convolutional auto encoder (CAE) that have performed well in time series.

In contemporary agricultural practices, greenhouses serve as a critical component of infrastructure, where soil temperature plays a vital role in enhancing pest management and regulating crop growth. However, achieving precise greenhouse environmental control continues to pose a significant challenge. In this context, the present study proposes ReSSA-iTransformer, an advanced predictive model engineered to accurately forecast soil temperatures within greenhouses across diverse temporal scales, encompassing both long-term and short-term horizons. This model capitalizes on the iTransformer time-series forecasting framework and integrates Singular Spectrum Analysis (SSA) to decompose environmental variables, thereby augmenting the extraction of pivotal features, such as soil temperature. Furthermore, to mitigate the prevalent distribution shift issues inherent in time-series data, Reversible Instance Normalization (RevIN) is incorporated within the model architecture. ReSSA-iTransformer is adept at executing multi-step forecasts for both extended and immediate future intervals, thereby offering comprehensive predictive capabilities. Empirical evaluations substantiate that ReSSA-iTransformer surpasses conventional models, including LSTM, Informer, and Autoformer, across all assessed metrics. Specifically, it attained R2 coefficients of 98.51%, 97.03%, 97.26%, and 94.83%, alongside MAE values of 0.271, 0.501, 0.648, and 1.633 for predictions at 3 h, 6 h, 24 h, and 48 h intervals, respectively. These results highlight the model’s superior accuracy and robustness. Ultimately, ReSSA-iTransformer not only provides dependable soil temperature forecasts but also delivers actionable insights, thereby facilitating enhanced greenhouse management practices.

Effectively forecasting the failure data in the maintenance stage is essential in many reliability planning and scheduling activities. Although a number of data‐driven techniques have been applied to cope with this issue and achieved noteworthy performance, the reliability prediction problem is still not fully explored, especially for applying the hybridization methods. In this paper, we introduce a hybrid model which integrates singular spectrum analysis (SSA) and support vector machines regression (SVR) to forecast the failure time series data gathered from the maintenance stage of the Boeing 737 aircraft. Two significant components recognized as the trend and fluctuation are extracted from the original failure time series data by using the techniques of SSA and noise test, and the two components are associated with the inherent and operational reliability, respectively. Then two models named as trend‐SSA and fluctuation‐SVR are individually developed to conduct the tasks of modeling and forecasting the two components. Furthermore, the optimal parameters of the hybrid model are obtained efficiently by a stepwise grid search method. The performance of the presented model is measured against other unitary models such as Holt‐Winters, autoregressive integrated moving average, multiple linear regression, group method of data handling, SSA, and SVR, as well as their hybridizations. The comparison results indicate that the proposed model outperforms other techniques and can be utilized as a promising tool for reliability forecast applications. Copyright © 2016 John Wiley & Sons, Ltd.