Non-stationary Data Research Articles

A fast clustering algorithm for evolving fuzzy classifier based on samples mean

Evolving models have shown great success in processing non-stationary data that change their characteristics over time. Motivated by elaborating a high-performance model for data classification, the present work proposes a new evolving fuzzy classifier. The proposed model, named evolving Fuzzy Mean Classifier (eFMC), has a low computational cost and is autonomous, i.e., no has user-defined parameters. The eFMC is based on fuzzy clustering structures, where the membership degree between the samples and the clusters is used to obtain the output. In the proposed approach, each class is represented by a cluster, and new clusters are created whenever a new class is discovered. The centers of the clusters are updated through the sample’s means calculated incrementally. Computational experiments were carried out to evaluate and compare the performance of the eFMC in terms of accuracy and processing time. Experimental results and comparisons against alternative state-of-the-art evolving classifiers show that the eFMC is accurate and fast, characteristics essential for adaptive classifiers, especially in online and real-time environments.

Quantifying reliability of liquefaction severity map developed from sparse cone penetration tests

The liquefaction potential index (LPI) is widely used for evaluating the severity of liquefaction manifestation at the ground surface (e.g., settlement, lateral spreading, sand boils, and crack) and for developing liquefaction severity maps. Over the last two decades, several methods, such as cumulative probability distribution of LPI and geostatistics-based LPI mapping, have been proposed to develop a liquefaction severity map from in situ tests (e.g., cone penetration tests, CPT), which are often sparsely performed in sites. These methods are either based on an assumption of statistical homogeneity within each geologic unit or a stationary Gaussian model. However, subsurface soils frequently show significant spatial variability and LPI data obtained at different geological units usually exhibit non-stationary characteristics. More importantly, existing methods offer little insight into the reliability level of the obtained liquefaction severity map. To address these issues, this study proposes a non-parametric and data-driven method for CPT-based liquefaction severity mapping and, for the first time ever, quantification of the liquefaction severity maps’ reliability level using the probability of mis-predicting liquefaction severity from the map. Both synthetic and real-life data are used to demonstrate and validate the proposed method. The illustration examples indicate that the proposed method can properly deal with non-stationary LPI data from different geological units and quantify the mis-prediction probability of liquefaction severity at each point of the map.

Leverage and Cook distance in regression with geostatistical data: methodology, simulation, and applications related to geographical information

Regression is often conducted assuming independent model errors. The detection of atypical values in regression (leverage and influential points) assumes independent errors. However, such independence could be unrealistic in geostatistics. In this article, we propose a methodology based on least squares and geostatistics to identify such values in spatial regression. Our procedure uses the hat matrix to detect leverage points. A modified Cook distance is employed to confirm whether these points are influential. The methodology is evaluated with stationary and non-stationary geostatistical data. We apply this methodology to real georeferenced data related to depth, dissolved oxygen, and temperature. First, an autoregressive model is fitted to depth data. Second, a regression between oxygen and temperature is estimated. In both models, spatial correlation is assumed to determine the parameters, leverage, and influential observations. Our methodology can be used in regression with geographical information to avoid misinterpreted results. Not considering this information may under- or over-estimate geographical indicators, such as the mean depth, which can affect the circulation of water masses or dissolved oxygen variability. Our results reveal that including spatial dependence to identify high leverage points is relevant and must be considered in any geostatistical analysis.

A remaining useful life prediction method based on PSR-former

The non-linear and non-stationary vibration data generated by rotating machines can be used to analyze various fault conditions for predicting the remaining useful life(RUL). It offers great help to make prognostic and health management(PHM) develop. However, the complexity of the mechanical working environment makes the vibration data collected easily affected, so it is hard to form an appropriate health index(HI) to predict the RUL. In this paper, a PSR-former model is proposed including a Phase space reconstruction(PSR) layer and a Transformer layer. The PSR layer is utilized as an embedding to deepen the understanding of vibration data after feature fusion. In the Transformer layer, an attention mechanism is adopted to give different assignments, and a layer-hopping connection is used to accelerate the convergence and make the structure more stable. The effectiveness of the proposed method is validated through the Intelligent Maintenance Systems (IMS) bearing dataset. Through analysis, the prediction accuracy is judged by the parameter RMSE which is 1.0311. Some state-of-art methods such as LSTM, GRU, and CNN were also analyzed on the same dataset to compare. The result indicates that the proposed method can effectively establish a precise model for RUL predictions.

ANALISIS FAKTOR-FAKTOR YANG MEMPENGARUHI IMPOR MINYAK BUMI MENTAH INDONESIA

Crude oil is an important source of energy in every country, especially in industrialists. This energy can drive the manufacturing sector of a country to get the desired output. It can be seen that this crude oil is one of the main commodities imported by Indonesia from year to year and imports of petroleum are relatively high. This study aims to analyze the factors affecting imports of crude oil in Indonesia in 2001-2020 using gravity with the variables Price, Exchange Rate, Production and Foreign Exchange Reserves. The research location was conducted in Indonesia because this research discussed the determinants of Indonesian crude oil imports. The type of data used in this research is secondary data. The analytical method in this study is the Error Correction Model used to overcome the problem of non-stationary data. The results of this study The price of crude oil, exchange rates, production, and foreign exchange simultaneously affect imports of crude oil in Indonesia. Crude oil prices, production, and foreign exchange reserves partially have a positive and significant effect both in the long and short term on the import of crude oil in Indonesia. While the exchange rate has no effect in the long term, it has a positive and significant effect in the short term on imports of crude oil in Indonesia.

DISCOVERING CLUSTERING PATTERNS FROM E-COUNTER DATA STREAMS

Abstract. Clustering data streams has gained popularity in recent years due to their potential of generating relevant information for planning building automation, evaluating energy efficiency scenarios, and simulating emergency protocols in indoor spaces. In this paper, a Data Stream Affinity Propagation (DSAP) clustering algorithm is proposed for analyzing indoor localization data generated from e-counters systems. The data streams are a sequence of potentially infinite and non-stationary data points, arriving continuously where random access to the data is not feasible and storing all the arriving data is impractical. The DSAP model is developed based on a two-phase approach (i.e., online and offline clustering phases) using the landmark time window model. It is non-parametric in the sense of not requiring any prior knowledge about the number of clusters and their respective labels. The validation and performance of the DSAP model is evaluated using real-world data streams from a behavioural experiment aimed at finding new spatio-temporal patterns in stair usage due to an educational intervention campaign.

Recurrence measures and transitions in stock market dynamics

The financial markets are understood as complex dynamical systems whose dynamics is analysed mostly using nonstationary and brief data sets from stock markets. For such data sets, the most reliable method of analysis is the one based on recurrence plots and recurrence networks, constructed from the data sets over the period of study. In this study, we do a comprehensive analysis of the complexity of the underlying dynamics of 26 markets around the globe using recurrence based measures. We also examine trends during the transitions as revealed from these measures by the sliding window analysis along the time series during the Global Financial Crisis (GFC) of 2008 and compare that with changes during the most recent pandemic related lock down. We show that the measures derived from recurrence patterns can be used to capture the nature of transitions in stock market dynamics. Thus, our study indicates that the transition in the dynamics prior to GFC is due to increasing stochasticity as seen from the recurrence measures. We also find that the markets have not stabilised after the 2020 pandemic and may possibly approach a crisis in recent future. Further the markets that go together during GFC are responding differently during the pandemic indicating that the underlying causes and mechanisms can be different.

Learning Nonstationary Time-Series With Dynamic Pattern Extractions

The era of information explosion had prompted the accumulation of a tremendous amount of time-series data, including stationary and nonstationary time-series data. State-of-the-art algorithms have achieved a decent performance in dealing with stationary temporal data. However, traditional algorithms that tackle stationary time-series do not apply to nonstationary series like Forex trading. This article investigates applicable models that can improve the accuracy of forecasting future trends of nonstationary time-series sequences. In particular, we focus on identifying potential models and investigate the effects of recognizing patterns from historical data. We propose a combination of the seq2seq model based on recurrent neural network, along with an attention mechanism and an enriched set features extracted via dynamic time warping and zigzag peak valley indicators. Customized loss functions and evaluating metrics have been designed to focus more on the predicting sequence’s peaks and valley points. Our results show that our model can predict 4-h future trends with high accuracy in the Forex dataset, which is crucial in realistic scenarios to assist foreign exchange trading decision making. We further provide evaluations of the effects of various loss functions, evaluation metrics, model variants, and components on model performance.

An ensemble LSTM-based AQI forecasting model with decomposition-reconstruction technique via CEEMDAN and fuzzy entropy.

Air quality affects people’s daily life. Air quality index (AQI) is an essential indicator for controlling air pollution and ensuring public health, whose accurate forecasting can provide timely air pollution warnings and remind people to take protective measures against air pollution in advance. To address this issue, this paper developed a new ensemble learning model for AQI forecasting. In this study, (1) the signal decomposition technique complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is introduced to decompose the nonlinear and nonstationary AQI history data series into several more regular and more stable subseries firstly. (2) Fuzzy entropy (FE) is selected as the feature indicator to recombine the subseries with similar trends to avoid the problem of over-decomposition and reduce the computing time. (3) An ensemble long short-term memory (LSTM) neural network is established to forecast each reconstructed subseries, whose values are superimposed to predict the AQI value eventually. To validate the predicting performance of the proposed model, daily AQI data of Wuhan, China, dating from January 1, 2019, to February 28, 2022, is used as the experiment case. And comparative analysis is made between the proposed model and other common-used forecasting models. Benchmarking results of the numerical study demonstrate that the proposed model is superior to the other forecasting models with better AQI prediction accuracy.

Reliability-driven time series data analysis in multiple-level deep Learning methods utilizing soft computing methods

This paper introduces a novel method for mining data & information retrieval using series data for the duration. A multi-resolution S transformis viewed as a stage-adjusted transform of wavelet/a parameter window low period. Fourier-transform is used to recover significant characteristics from nonstationary duration series data with electricity-network disruptions. In pattern classification of disturbance waveform information, and incorporated Learning Vector Quantization neural-network & different feed-forward neural-network designs were employed afterwardextending required characteristics from the period of series-data.A fuzzy Multilayer perceptron accepts other connectionist systems and therefore is utilized in the final phase of encoding information inside the linking weights to produce fuzzy disturbance rules pattern inference. With energy signal time series data, a pattern classification performance of 99% was attained. Utilizing the new measurement processes, the data-driven information retrieval was displayed. A method proposed in this research is generically used to mine for information similarities in either duration of the series data pattern.

Steady-State Data Baseline Model for Nonstationary Monitoring Data of Urban Girder Bridges

In bridge structural health monitoring systems, an accurate baseline model is particularly important for identifying subsequent structural damage. Environmental and operational loads cause nonstationarity in the strain monitoring data of urban girder bridges. Such nonstationary monitoring data can mask damage and reduce the accuracy of the established baseline model. To address this problem, a steady-state data baseline model for bridges is proposed. First, for observable effects such as ambient temperature, a directional projection decoupling method for strain monitoring data is proposed, which can reduce the nonstationary effect of ambient temperature, and the effectiveness of this method is proven using equations. Second, for unobservable effects such as traffic load, a k-means clustering method for steady state of traffic loads is proposed; using this method, which can divide the steady and nonsteady states of traffic loads and reduce the nonstationary effect of traffic loads on strain monitoring data, a steady-state baseline model is established. Finally, the effectiveness of the steady-state baseline model is verified using an actual bridge. The results show that the proposed baseline model can reduce the error caused by nonstationary effects, improve the modelling accuracy, and provide useful information for subsequent damage identification.

Order pattern recurrence for the analysis of complex systems

In this paper, order pattern recurrence plot (OPRP) and order pattern recurrence quantification analysis (OPRQA) are proposed to quantify recurrence characteristics of complex systems. The method uses the recurrence of order patterns in symbolic sequence to explore the order structure of the original data, in which the color of the symbol is employed to distinguish different order patterns. The main advantage of the approach is its robustness with respect to non-stationary data and low requirements for the length of the required time series. The method is demonstrated to be effective in synthetic data and real data. As demonstrated in simulation models, the conclusion is that the method can not only make a distinction between chaotic system and random noise but also quantify various bifurcation transition scenarios like period doubling or other phenomena associated with chaos-to-chaos transitions in logistic map. In empirical analysis, this approach helps observe the different performance of the time series before, during and after the financial crisis. In addition, differences of stocks between developing countries and developed countries are reflected in OPRP and quantified by the corresponding OPRQA. The proposed method brings together recurrence plots and symbolic dynamics to empower researchers with effective means to visualize and quantify complex behavior in dynamic system.

AI-Based Prediction of Capital Structure: Performance Comparison of ANN SVM and LR Models.

Capital structure is an integral part of the corporate finance that sources the funds to finance growth and operations. Managers always have to maintain value of the firm to be higher than the cost of capital in order to maximize the shareholders wealth. Empirical studies have used sources of finance like debt and equity as variables of capital structure. A choice between debt and equity finance analyzes the firm's ability to perform under the financially constrained environment to attain the sustainable growth. Therefore, it gives rise to a dire need to estimate the cost of capital precisely. We examined the capital structure of top ten market capitalization of the stock markets included in MSCI Emerging index with the use of artificial neural networks, support vector regression, and linear regression in forecasting methods. The capital structure is measured as the proportion of total debt over total equity (Tang et al., 1991). Other financial ratios such as profitability, liquidity, solvent, and turnover ratios were considered as drivers of the capital structure. Applying logistic and hyperbolic tangent activation functions, it was concluded that ANN has a great potential of replacing other traditional forecasting models with the nonstationary data. This research contributes with a new dimension for estimation through different activation functions. There is a possibility of ANN dominance as compared to the other models applied for predictability in financial markets.

Fleet-based early fault detection of wind turbine gearboxes using physics-informed deep learning based on cyclic spectral coherence

The development of a reliable and automated condition monitoring methodology for the detection of mechanical failures in rotating machinery has garnered much interest in recent years. Thanks to the rise in popularity of machine learning techniques, the number of purely data-driven approaches that try to tackle the issue of vibration-based condition monitoring has also drastically improved. Instead of directly using the vibration measurement data as input to a machine learning model, this work first exploits the cyclostationary characteristics inherent to vibration waveforms originating from rotating machinery. The proposed methodology first estimates the two-dimensional cyclic spectral coherence map of a vibration signal in order to decompose the cyclic modulations on the cyclic and carrier frequency plane. While this provides an effective tool to visualize any potential modulation signatures of faulty gears or bearings, it does not allow for easy inspection over time due to its dimensions. To tackle this issue, this paper proposes an unsupervised deep learning approach to wield this vast amount of data as a tool for detecting persistent changes in the modulation characteristics of the vibration signals. In the first phase, a deep autoencoder learns to reconstruct predictions of the cyclic coherence maps based on unlabeled healthy vibration data and the machine operating conditions. Two post-processing steps improve the predictions by mitigating frequency shifts and outlier or noisy measurements. Lastly, the residual error between the predicted and the actual coherence map is then aggregated and employed for further alarming based on thresholds. The autoencoder model is trained using five years of gearbox vibration data from five different wind turbines. The methodology is then validated on two faulty and eight healthy turbines. The results confirm that the proposed approach can deliver clear indications of failure for the faulty turbine while being completely devoid of any significant alarm trends for the healthy turbines. Thanks to the combination of highly effective cyclostationary signal processing with deep learning while using the operating conditions, the proposed methodology can detect and track incipient mechanical faults from non-stationary vibration data of rotating machinery. Lastly, it is important to emphasize that the proposed method is capable of learning the healthy behavior on one turbine and predicting the expected behavior on another turbine.

The Research on Risk Distribution and Evolution of Deep Foundation Pit Construction Adjacent to Existing Tunnels Based on Complex Network

The construction of deep foundation pits adjacent to existing subway tunnels faces enormous challenges, and once a safety accident occurs, there are often mass injuries that cause substantial economic losses. However, there are many shortcomings and defects in the traditional methods of assessing the safety of the pit itself and the existing tunnel in the construction of the deep foundation pit adjacent to existing tunnels. This study establishes an optimized complex network-based dynamic risk assessment model to dynamically assess the overall risk of deep foundation pits in adjacent existing tunnels systematically, solving the challenges of inaccurate risk assessment and inaccurate description of correlations between nonstationary time series data. In this study, we first divide the monitoring data into time windows and describe the correlation between nonstationary time-series monitoring data within each window based on the MF-DCCA method and the threshold method, and establish the adjacency matrix to prepare for the establishment of an optimized complex network model. Secondly, based on the adjacency matrix, a complex network model under different time windows is constructed, and risk assessment indexes are established through the topological parameters of the complex network model to explore the evolution of risk in time and space, so as to realize the risk distribution and quantitative evolution assessment of the system which is deep foundation pit adjacent to existing subway tunnels. Finally, the proposed method is tested by taking the Nanning underground comprehensive utilization project as an example. The results show that this method can quantify the risk of the construction of deep foundation pits adjacent to existing tunnels more effectively than the traditional method to describe the evolution law better. It has important guiding significance for strengthening the safety risk monitoring and safety management of the construction system of deep foundation pits adjacent to existing tunnels.

Nonstationary data stream classification with online active learning and siamese neural networks✩

We have witnessed in recent years an ever-growing volume of information becoming available in a streaming manner in various application areas. As a result, there is an emerging need for online learning methods that train predictive models on-the-fly. A series of open challenges, however, hinder their deployment in practice. These are, learning as data arrive in real-time one-by-one, learning from data with limited ground truth information, learning from nonstationary data, and learning from severely imbalanced data, while occupying a limited amount of memory for data storage. We propose the ActiSiamese algorithm, which addresses these challenges by combining online active learning, siamese networks, and a multi-queue memory. It develops a new density-based active learning strategy which considers similarity in the latent (rather than the input) space. We conduct an extensive study that compares the role of different active learning budgets and strategies, the performance with/without memory, the performance with/without ensembling, in both synthetic and real-world datasets, under different data nonstationarity characteristics and class imbalance levels. ActiSiamese outperforms baseline and state-of-the-art algorithms, and is effective under severe imbalance, even only when a fraction of the arriving instances’ labels is available. We publicly release our code to the community.

A Stock Price Forecasting Model Integrating Complementary Ensemble Empirical Mode Decomposition and Independent Component Analysis

In recent years, due to the non-stationary behavior of data samples, modeling and forecasting the stock price has been challenging for the business community and researchers. In order to address these mentioned issues, enhanced machine learning algorithms can be employed to establish stock forecasting algorithms. Accordingly, introducing the idea of “decomposition and ensemble” and the theory of “granular computing”, a hybrid model in this paper is established by incorporating the complementary ensemble empirical mode decomposition (CEEMD), sample entropy (SE), independent component analysis (ICA), particle swarm optimization (PSO), and long short-term memory (LSTM). First, aiming at reducing the complexity of the original data of stock price, the CEEMD approach decomposes the data into different intrinsic mode functions (IMFs). To alleviate the cumulative error of IMFs, SE is performed to restructure the IMFs. Second, the ICA technique separates IMFs, describing the internal foundation structure. Finally, the LSTM model is adopted for forecasting the stock price results, in which the LSTM hyperparameters are optimized by synchronously utilizing the PSO algorithm. The experimental results on four stock prices from China stock market reveal the accuracy and robustness of the established model from the aspect of statistical efficiency measures. In theory, a useful attempt is made by integrating the idea of “granular computing” with “decomposition and ensemble” to construct the forecasting model of non-stationary data. In practice, the research results will provide scientific reference for the business community and researchers.

Coarse-to-fine condition identification for wide-range non-stationary processes driven by coupled condition indicators

Frequent changes in operating conditions would result in wide-range non-stationarity and bring significant challenges to tracking data characteristics for industrial processes. Commonly, those changes are closely related to some coupled condition indicators (CIs). Therefore, this paper explores the synergy of coupled CIs on process characteristics and proposes a coarse-to-fine condition identification (CFCI) strategy to identify condition modes for process monitoring. Firstly, the coarse-level identification probes into the distribution of augmented CIs using the density-based clustering algorithm and then restores the time-wise non-stationary data into condition-wise new analysis units. Secondly, the fine-level identification is performed with canonical variate analysis (CVA) on new analysis units to obtain fine-scale condition modes by exploring the influences of the coupled CIs on process characteristics. In this way, process data can be automatically divided into fine-grained condition modes with the concurrent evaluation of CIs and the changing law of process characteristics under the synergy of coupled CIs. Specifically, the CFCI strategy naturally builds the links between process data and coupled CIs, which also provides explicit physical interpretations for the recognized condition modes. Finally, local models resorting to CVA are rationally constructed to present comprehensive monitoring of different condition modes. The validity of the proposed method has been empirically demonstrated against other related methods through an industrial process.

Statistical disclosure and economic growth: What is the nexus?

Although the benefits of information for the quality of economic decisions have been highlighted by numerous theoretical studies, only a few empirical studies have investigated the relevance of statistics for the economy. It is particularly surprising that no previous empirical study has researched the existence of a causal link running from statistical disclosure to long-run economic growth. Our research investigates the existence of this nexus in a panel of 105 countries. We applied methodologies for non-stationary panel data in order to assess the long-run causality. We found that data availability was causing long-run economic growth in all income level groups but in the high income one. However, the higher certainty about a positive causality was found in middle income nations. This is true because bidirectional causality was found in poor nations, where it is possible that statistical production demand more resources than it may generate by boosting economic growth. With regard to short-run causality, it was only found in middle income nations. Finally, we find that the publication of the indicators in the World Bank’s World Development Indicators database is in fact relevant for economic growth.

Adaptive Broad Echo State Network for Nonstationary Time Series Forecasting

Time series forecasting provides a vital basis for the control and management of various systems. The time series data in the real world are usually strongly nonstationary and nonlinear, which increases the difficulty of reliable forecasting. To fully utilize the learning capability of machine learning in time series forecasting, an adaptive broad echo state network (ABESN) is proposed in this paper. Firstly, the broad learning system (BLS) is used as a framework, and the reservoir pools in the echo state network (ESN) are introduced to form the broad echo state network (BESN). Secondly, for the problem of information redundancy in the reservoir structure in BESN, an adaptive optimization algorithm for the BESN structure based on the pruning algorithm is proposed. Thirdly, an adaptive optimization algorithm of hyperparameters based on the nonstationary test index is proposed. In brief, the structure and hyperparameter optimization algorithms are studied to form the ABESN based on the proposed BESN model in this paper. The ABESN is applied to the data forecasting of air humidity and electric load. The experiments show that the proposed ABESN has a better learning ability for nonstationary time series data and can achieve higher forecasting accuracy.