Scale Time Series Data Research Articles

A four-component mixing model reveals snowpack melting as early as March during the 2019 hydrological year in the Upper Ganga Basin

Ice and snow meltwater are important components of the glacier-fed Himalayan rivers that control the seasonal streamflow pattern. With the ongoing global warming, there remains significant uncertainty regarding how melting Himalayan glaciers will impact the water runoff. Here, we quantified the rainwater, ice meltwater, snow meltwater, and groundwater flow in the river using a δ18O, d, and Cl- -based 4-component hydro-geochemical mixing model. At a weekly resolution, we measured the stable water isotopes (18O/16O and 2H/1H, expressed as δ18O and δD), Cl- and Na+ near the river Alaknanda mouth, in the Upper Ganga Basin over one year (2018–2019). The weekly scale time-series geochemical record captured the subtle variability of ice and snow meltwater flow in the Alaknanda River. The two most significant observation was (i) an onset of snow meltwater was observed as early as in March during the study period contrary to our present understanding that the onset of snow meltwater usually happens in April, and (ii) a significant increase in ice and snow meltwater flow during the peak monsoon season. The early onset of snow meltwater runoff in the Himalayan rivers could be an important concern as this could potentially reduce the flow of snow meltwater during the early summer months when water demand is highest due to intense agricultural activities in the mountainous region. Similarly, an increase in ice meltwater runoff in the monsoon season increases the risks of major flood events. Since weekly scale time-series data of ice meltwater, snow meltwater, rainwater, and groundwater flow in glacier-fed Himalayan rivers over the entire hydrological year was largely missing, this study provides an important dataset to better understand the year-long dependency of the Himalayan rivers on the glaciers critical to improving the accuracy and predictive power of hydrologic models.

Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable

We construct a data-driven dynamical system model for a macroscopic variable the Reynolds number of a high-dimensionally chaotic fluid flow by training its scalar time-series data. We use a machine-learning approach, the reservoir computing for the construction of the model, and do not use the knowledge of a physical process of fluid dynamics in its procedure. It is confirmed that an inferred time-series obtained from the model approximates the actual one in each of various time-intervals, and that some characteristics of the chaotic invariant set mimic the actual ones. We investigate the appropriate choice of the delay-coordinate, especially the delay-time and the dimension, which enables us to construct a model having a relatively high-dimensional attractor easily.

Present and future perspectives of artificial intelligence: examples of mathematical approaches for analysis of disease dynamics

Artificial intelligence (AI) has been applied widely in medicine. For example, deep neural network-based deep learning is particularly effective for pattern recognition in static medical images. Additionally, dynamic time series data are analysed ubiquitously in biology and medicine, as in the application of BCR-ABL International Scale time series data measured from CML patients treated with tyrosine-kinase inhibitors. Nonlinear data analyses, rather than conventional deep learning, can be more powerful for this type of dynamic disease information. Here, I introduce our mathematical approaches that are applicable for disease dynamics, such as dynamical network biomarkers (DNB) and randomly distributed embedding (RDE), as examples of nonlinear data analyses. I also discuss the availability of neuroinspired and neuromorphic hardware systems, which we are developing for potential use in next-generation AI.

Multi-Scale Variation Prediction of PM2.5 Concentration Based on a Monte Carlo Method

Haze concentration prediction, especially PM2.5, has always been a significant focus of air quality research, which is necessary to start a deep study. Aimed at predicting the monthly average concentration of PM2.5 in Beijing, a novel method based on Monte Carlo model is conducted. In order to fully exploit the value of PM2.5 data, we take logarithmic processing of the original PM2.5 data and propose two different scales of the daily concentration and the daily chain development speed of PM2.5 respectively. The results show that these data are both approximately normal distribution. On the basis of the results, a Monte Carlo method can be applied to establish a probability model of normal distribution based on two different variables and random sampling numbers can also be generated by computer. Through a large number of simulation experiments, the average monthly concentration of PM2.5 in Beijing and the general trend of PM2.5 can be obtained. By comparing the errors between the real data and the predicted data, the Monte Carlo method is reliable in predicting the PM2.5 monthly mean concentration in the area. This study also provides a feasible method that may be applied in other studies to predict other pollutants with large scale time series data

Modeling and forecasting multifractal wavelet scale: Western market versus eastern market

This leading primary study is about modeling multifractal wavelet scale time series data using multiple wavelet coherence (MWC), continuous wavelet transform (CWT) and multifractal detrended fluctuation analysis (MFDFA) and forecasting with vector autoregressive fractionally integrated moving average (VARFIMA) model. The data is acquired from Yahoo Finances!, which is composed of 1671 daily stock market of eastern (NIKKEI, TAIEX, KOPSI) and western (SP500, FTSE, DAX) markets. Once the co-movement dependencies on time-frequency space are determined with MWC, the coherent data is extracted out of raw data at a certain scale by using CWT. The multifractal behavior of the extracted series is verified by MFDFA and its local Hurst exponents have been calculated obtaining root mean square of residuals at each scale. This inter-calculated fluctuation function time series has been re-scaled and used to estimate the process with VARFIMA model and forecasted accordingly. The results have shown that the direction of price change is determined without difficulty and the efficiency of forecasting has been substantially increased using highly correlated multifractal wavelet scale time series data.

Linear optimization fusion model based on fuzzy C-means: Case study of energy efficiency evaluation in ethylene product plants

Ethylene production shares the common characteristics of different techniques and scales, high dimension and multi-correlation. However, the existing methods do not take the influence of the technology, scale and materials into account. In order to analyze the energy efficiency of ethylene plants better, this paper proposes a linear optimization fusion model based on fuzzy C-means (FCM) clustering. The FCM clustering is used to obtain the corresponding classification and clustering centers of the large scale time series data of the ethylene production process. Then the mean squares of time-series variables are calculated by various clustering centers. The multidimensional energy efficiency benchmarking of ethylene plants can be extracted by the fusion weighting vectors in linear optimization fusion model. The experimental results indicate that the proposed method intuitively reveals the running state and the operating level of ethylene plants and accurately identify the reason of energy consumption for improving energy efficiency.

Integrating age in the detection and mapping of incongruous patches in coffee (Coffea arabica) plantations using multi-temporal Landsat 8 NDVI anomalies

The development of cost-effective, reliable and easy to implement crop condition monitoring methods is urgently required for perennial tree crops such as coffee (Coffea arabica), as they are grown over large areas and represent long term and higher levels of investment. These monitoring methods are useful in identifying farm areas that experience poor crop growth, pest infestation, diseases outbreaks and/or to monitor response to management interventions. This study compares field level coffee mean NDVI and LSWI anomalies and age-adjusted coffee mean NDVI and LSWI anomalies in identifying and mapping incongruous patches across perennial coffee plantations. To achieve this objective, we first derived deviation of coffee pixels from the global coffee mean NDVI and LSWI values of nine sequential Landsat 8 OLI image scenes. We then evaluated the influence of coffee age class (young, mature and old) on Landsat-scale NDVI and LSWI values using a one-way ANOVA and since results showed significant differences, we adjusted NDVI and LSWI anomalies for age-class. We then used the cumulative inverse distribution function (α≤0.05) to identify fields and within field areas with excessive deviation of NDVI and LSWI from the global and the age-expected mean for each of the Landsat 8 OLI scene dates spanning three seasons. Results from accuracy assessment indicated that it was possible to separate incongruous and healthy patches using these anomalies and that using NDVI performed better than using LSWI for both global and age-adjusted mean anomalies. Using the age-adjusted anomalies performed better in separating incongruous and healthy patches than using the global mean for both NDVI (Overall accuracy=80.9% and 68.1% respectively) and for LSWI (Overall accuracy=68.1% and 48.9% respectively). When applied to other Landsat 8 OLI scenes, the results showed that the proportions of coffee fields that were modelled incongruent decreased with time for the young age category and while it increased for the mature and old age classes with time. We concluded that the method could be useful for the identification of anomalous patches using Landsat scale time series data to monitor large coffee plantations and provide an indication of areas requiring particular field attention.

A chaotic signal detection method based on the component permutation of the incomplete two-dimensional phase-space

Detection and identification of chaotic signal is very important in the chaotic time series analysis. It is not easy to distinguish chaotic time series from stochastic processes since they share some similar natures. The detection methods to capture and utilize the structure of state-space dynamics can be very effective. In practice, it is very hard to obtain full information about the structure, and accurate phase-space reconstruction from scalar time series data is also a real challenge. However, the chaotic signals also show fundamental dynamical structure in the incomplete two-dimensional phase-space for the reason that they are generated by the deterministic chaotic systems or maps. Based on the fact that the distribution of chaotic signals is quite different from that of the noise signals in the incomplete two-dimensional phase-space, a novel detection method, which depends on the component permutation of the incomplete two-dimensional phase-space, is proposed. The incomplete two-dimensional phase-space is first obtained through the time series. Then, the first component is sorted in the ascending order, and the second component is permutated accordingly. The permutated component shows more structure characteristics for chaotic signals because of the relation between these two components. But this phenomenon does not appear in the noise because these components are independent of each other. And then, the permutated component is segmented into several groups properly. Finally, the sample mean and sample variance of different groups are calculated to obtain the sequence of sample mean (SSM) and the sequence of sample variance (SSV). Meanwhile, by calculating the variance of the SSM and the mean of the SSV, the test statistic is obtained. Furthermore, it is proved that this test statistic follows the F distribution under the null hypothesis of Gaussian noise. The proposed method is first adopted for detecting the several chaotic signals under different data lengths in Gaussian noise conditions. The simulation results show that the proposed method can detect chaotic signals effectively under low signal-to-noise ratio and it also has a good robustness against noise compared with the permutation entropy test. The time consumptions of the proposed method under different data lengths are evaluated and also compared with the results of permutation entropy test, showing that the proposed method can detect chaotic signals quickly, and the time complexity is much lower than that of the permutation entropy test. The theoretical analysis and simulation results demonstrate that the proposed method not only outperforms the permutation entropy test with lower complexity, but also has a better robustness against noise.

A New Cost Function for Parameter Estimation of Chaotic Systems Using Return Maps as Fingerprints

Estimating parameters of a model system using observed chaotic scalar time series data is a topic of active interest. To estimate these parameters requires a suitable similarity indicator between the observed and model systems. Many works have considered a similarity measure in the time domain, which has limitations because of sensitive dependence on initial conditions. On the other hand, there are features of chaotic systems that are not sensitive to initial conditions such as the topology of the strange attractor. We have used this feature to propose a new cost function for parameter estimation of chaotic models, and we show its efficacy for several simple chaotic systems.

Application of joint permutations for predicting coupled time series

In this work, we introduce a model for predicting multivariate time series data. This model was obtained by partitioning the state space with joint permutations. We review the theoretical framework of the previous works, show a simple extension to multivariate data, and compare its performance to the previous model obtained by permutations for predicting scalar time series data.

Quasi-chaotic behaviors of narrow-band response of a non-deterministic resonant system: application to analysis of ship motion in irregular seas

This paper describes similarities between the narrow-band response of a resonant system excited by random inputs and low-dimensional chaos, with particular emphasis on the geometric characteristics of trajectories reconstructed in m-dimensional phase space from measured scalar time series data with a time-delay coordinate system. In this study, the time series data of ship roll angle in irregular waves were analyzed as an example of the narrow-band response of a resonant system. These time series data were measured by one of the authors in Tokyo Bay. The similarities between the narrow-band response of a resonant system excited by random inputs and low-dimensional chaos are verified by numerical simulation data.

SU-E-J-146: Time Series Prediction of Lung Cancer Patients' Breathing Pattern Based on Nonlinear Dynamics.

Prediction methods for breathing patterns, which are crucial to deal with system latency in treatments of moving lung tumors using state-space methodologies based on non-linear dynamics are contrasted to linear predictive methods. In our previous work we established that breathing patterns can be described as a 5-6 dimensional nonlinear, stationary and deterministic system that exhibits sensitive dependence on initial conditions. In this work, nonlinear prediction methods are used to predict the short-term evolution of the respiratory system for 3 patients. Single step and N-point multi step prediction are performed for sampling rates of 5Hz, 10Hz, and 30Hz. We compare the employed nonlinear prediction methods with respect to prediction accuracy to Infinite Impulse Response (IIR) prediction filters. The simplest form of local prediction is finding similar segments of scalar time series data in a higher dimensional embedding space. Hence, we predict the future value x(t)of N-time steps ahead by simply finding the average of nearest neighbor points to the point x(t) in the past and using them to estimate x(t+N), yielding a local average model (LAM). Local linear models (LLM) which are linear autoregressive models that hold only for a region around the target point formed by the nearest neighbor points is combined with a set of linear regularization techniques to solve ill-posed regression problems are also implemented. For all sampling frequencies, both single step and N-point multi step prediction results obtained using LAM and LLM with regularization methods are better than IIR prediction filters for the selected sample patients. The use of non-linear prediction methods for predicting the breathing pattern of lung cancer patients may lead to improved, robust and accurate long-term prediction to account for system latencies.

An application of ARIMA model to predict submicron particle concentrations from meteorological factors at a busy roadside in Hangzhou, China

In order to investigate the effect of meteorological factors on submicron particle (ultrafine particle (UFP) and particulate matter 1.0 (PM1.0)) concentrations under busy traffic conditions, a model study was conducted in Hangzhou, a city with a rapid increase of on-road vehicle fleet in China. A statistical model, Autoregressive Integrated Moving Average (ARIMA), was used for this purpose. ARIMA results indicated that barometric pressure and wind velocity were anti-correlated and temperature and relative humidity were positively correlated with UFP number concentrations and PM1.0 mass concentrations (p<0.05). These data suggest that meteorological factors are significant predictors in forecasting roadside atmospheric concentrations of submicron particles. The findings provide baseline information on the potential effect of meteorological factors on UFP and PM1.0 levels on a busy viaduct with heavy traffic most of the day. This study also provides a framework that may be applied in future studies, with large scale time series data, to predict the impact of meteorological factors on submicron particle concentrations in fast-developing cities, in China.

A Visualization and Level-of-Detail Control Technique for Large Scale Time Series Data

本論文では, 対話的な詳細度制御によって大規模時系列データの可視化を実現する一手法を提案する．本手法では時系列データを表す折れ線グラフをクラスタリングし, 各クラスタの中心に近いグラフのみを表示する．これにより, グラフの表示本数を低減することで表示結果の煩雑さを抑え, かつデータ全体の特徴を逃さない表示を実現する．また本手法は, 詳細度制御後の可視化結果画面から, ユーザが着目したグラフをインタラクティブに選択するための, ユーザインタフェースを併せ持つ．これを用いることでユーザは, 選択したグラフと同じクラスタ内にあるグラフを表示させることができる．よって, ユーザが着目した特徴をもつデータについて, 対話的に詳細度を再制御できる．著者らは, 日本全国の気温データに提案手法を適用し可視化を試みた．本論文では, 詳細度制御とグラフ選択のインタフェースの利用により気象現象を解析した例を紹介する．

FRUITS Time 大規模時系列データの詳細度制御を利用した可視化

大規模時系列データの詳細度制御を利用した可視化 内田悠美子,伊藤貴之 (お茶の水女子大学大学院 人間文化創成科学研究科) FRUITS Time: A visualization technique using level of detail control for large scale time series data Yumiko UCHIDA and Takayuki ITOH ABSTRACT This paper presents a technique for visualizing large scale time series data. This technique represents variation over time in data as line charts. We cannot figure out feature of time series data, when we draw the data which contain a large amount of elements as line charts in one display. To solve this problem, this technique uses a level-of-detail control technique. The technique applies a clustering technique based on shapes of charts, and selects representative line charts for each cluster. It displays only representative charts for level-of-detail control. Moreover, the technique can interactively control level-of-detail on the display. We suppose there are various applications of the technique since we can figure out which the chart has interesting behaviors from the visualization result applying level-of-detail control. This paper shows the visualization result of volume data obtained from weather simulation and observed temperature data throughout Japan as examples of results of the proposed technique.

TIME SERIES ANALYSIS IN RECONSTRUCTED STATE SPACES

Concepts for the analysis of observed scalar time series data in reconstructed vector valued phase spaces are reviewed. Originally exclusively designed for data from deterministic chaotic systems, phase space methods were recently extended to usage for nonlinear stochastic and for nonstationary processes.

Reconstructions and predictions of nonlinear dynamical systems: a hierarchical Bayesian approach

An attempt is made to reconstruct model nonlinear dynamical systems from scalar time series data via a hierarchical Bayesian framework. Reconstruction is performed by fitting given training data with a parameterized family of functions without overfitting. The reconstructed model dynamical systems are compared with respect to (approximated) model marginal likelihood, which is a natural Bayesian information criterion. The best model is selected with respect to this criterion and is utilized to make predictions. The results are applied to two problems: (i) chaotic time series prediction and (ii) building air-conditioning load prediction. The former is a very good class of problems for checking the abilities of prediction algorithms for at least two reasons. First, since no linear dynamical systems can admit chaotic behavior, an algorithm must capture the nonlinearities behind the time series. Second, chaotic dynamical systems are sensitive to initial conditions. More precisely, the error grows exponentially with respect to time so that crispness of capturing nonlinearities is also important. Experimental results appear to indicate that the proposed scheme can capture difficult nonlinearities behind the chaotic time series data. The latter class of problems (air conditioning load prediction) is motivated by a great amount of demand for reducing CO/sub 2/ emissions associated with electric power generation. The authors won a prediction competition using the proposed algorithm; therefore, it appears to be reasonably sound.

Synchronization and control of spatiotemporal chaos using time-series data from local regions.

In this paper we show that the analysis of the dynamics in localized regions, i.e., sub-systems can be used to characterize the chaotic dynamics and the synchronization ability of the spatiotemporal systems. Using noisy scalar time-series data for driving along with simultaneous self-adaptation of the control parameter representative control goals like suppressing spatiotemporal chaos and synchronization of spatiotemporally chaotic dynamics have been discussed. (c) 1998 American Institute of Physics.

Control of spatiotemporal chaos: A study with an autocatalytic reaction-diffusion system

The characterization of chaotic spatiotemporal dynamics has been studied for a representative nonlinear autocatalytic reaction mechanism coupled with diffusion. This has been carried out by an analysis of the Lyapunov spectrum in spatiallylocalised regions. The linear scaling relationships observed in the invariant measures as a function of thesub-system size have been utilized to assess the controllability, stability and synchronization properties of the chaotic dynamics. The dynamical synchronization properties of this high-dimensional system has been analyzed using suitable Lyapunov functionals. The possibility of controlling spatiotemporal chaos for relevant objectives using available noisy scalar time-series data with simultaneous self-adaptation of the control parameter(s) has also been discussed.

Recognizing determinism in a time series.

A quantitative measure of determinism in a recurrent time series is developed. Specifically, scalar time series data are used to form a vector series in reconstructed phase space. A statistic is then developed to measure the observed ``continuity'' of the vector series. The statistic is used as a measure of determinism. Several examples are included to demonstrate the effectiveness of the method.