Time Series Expansion Research Articles

CARMEL: Capturing spatio-temporal correlations via time-series sub-window imaging for home appliance classification

Energy management systems (EMS), as enablers of more efficient energy consumption, monitor and manage appliances to help residents be more energy efficient and thus more frugal. Recent appliance detection and identification techniques for such systems rely on machine learning. However, machine learning solutions for appliance classification on existing low-frequency household metering have not yet been thoroughly investigated. In this paper, we propose CARMEL, a new approach for identifying home appliances from load monitoring in building EMS based on a new data representation technique and a new model that leverages spatio-temporal correlations in the new representation. The proposed data representation technique performs dimensionality expansion of time series that scales linearly, rather than quadratically and, together with the proposed model, outperform the state of the art image transformation models by 5 percentage points. Evaluation on 5 different low-frequency household metering datasets, considering 29 appliances in total, shows that the proposed representation and the corresponding resource-aware deep learning architecture (1) achieve an average weighted F1 score of 0.92 and (2) require only 230 labeled samples and 3x fewer epochs to transfer to new households.

Research on the Application of Time Series in Financial Markets

In the current situation, the application of time series is extended to more fields. Macroeconomics has always been an important topic of concern for a country. Time series analysis of these data can obtain the relationship between various financial data, the law and trend of changes over time, abnormal changes, similar groups or different individuals, etc. Analysis, special investment opportunity exploration, etc. all have important reference value. Therefore, this paper discusses the application of time series in macroeconomics in different countries, China and the United States by reviewing several studies done by experts in the field of time series. The results show that the application of time series in the macroeconomics of China and the United States has reached a state of popularization. The research in this paper lays a theoretical foundation for the application and expansion of future time series. At the same time, the progress of time series analysis technology in other fields can also be used for reference by financial time series data mining technology.

Short-term PV power forecasting based on time series expansion and high-order fuzzy cognitive maps

Achieving short-term accurate photovoltaic power forecasting is of great significance to improve the efficiency of grid operation, especially in power stations where historical values of meteorological parameters are lagged or not recorded. Therefore, numerous studies have been presented to predict the intricate stochastic properties of photovoltaic power sequence in recent years. However, due to the limitation of algorithm performance and the effect of noise in the time series, previously proposed methods may not extract effective features from power data. Furthermore, most studies have only focused on point prediction, which ignores the uncertain information and unavoidable forecast bias. In this study, a hybrid framework based on fuzzy information granulation algorithm, improved variational mode decomposition technique, and high-order fuzzy cognitive maps is proposed to fill these gaps. Comparison experiments were set up using 5-minute photovoltaic power data from Alice Springs, Australia. The computational results not only demonstrate that the proposed framework significantly improves forecast accuracy of short-term photovoltaic power, but also achieves effective interval prediction by fuzzy information.

Extended disturbance observer for nonlinear system with time‐varying disturbance gain

SummaryIn control engineering, the disturbance is a major problem that deteriorates system robustness. To address this problem, a disturbance observer (DOB) has been proposed and developed. In particular, a general method of estimating high‐order disturbance, expressed as a time series expansion, was studied (H‐DOB). However, systems to which H‐DOB are applicable are limited to those in which disturbance gain is constant. This constraint degrades the generality of H‐DOB because applicable systems are limited. Therefore, by expanding to a system with a time‐varying disturbance gain, we propose a more general H‐DOB. The DOB proposed in this paper redesigns the dynamics of the observer based on the structure of the H‐DOB. The proposed DOB is applicable even if the system is highly nonlinear. This paper verifies the convergence of the proposed DOB through proof. Using this proof, the same characteristic error dynamics can be obtained, so the same design method can be applied. The simulation for the verification of the proposed method performs disturbance estimation of the extension system. This simulation proves that, compared to H‐DOB, the proposed DOB has good disturbance estimation performance.

On Infiltration and Infiltration Characteristic Times

AbstractIn his seminal paper on the solution of the infiltration equation, Philip (1969), https://doi.org/10.1016/b978-1-4831-9936-8.50010-6 proposed a gravity time, tgrav, to estimate practical convergence time and the time domain validity of his infinite time series expansion, TSE, for describing the transient state. The parameter tgrav refers to a point in time where infiltration is dominated equally by capillarity and gravity as derived from the first two (dominant) terms of the TSE. Evidence suggests that applicability of the truncated two‐term equation of Philip has a time limit requiring higher‐order TSE terms to better describe the infiltration process for times exceeding that limit. Since the conceptual definition of tgrav is valid regardless of the infiltration model used, we opted to reformulate tgrav using the analytic implicit model proposed by Parlange et al. (1982), https://doi.org/10.1097/00010694-198206000-00001 valid for all times and related TSE. Our derived gravity times ensure a given accuracy of the approximations describing transient states, while also providing insight about the times needed to reach steady state. In addition to the roles of soil sorptivity (S) and the saturated (Ks) and initial (Ki) hydraulic conductivities, we explored the effects of a soil specific shape parameter β, involved in Parlange's model and related to the type of soil, on the behavior of tgrav. We show that the reformulated tgrav (notably where F(β) is a β‐dependent function) is about three times larger than the classical tgrav given by . The differences between the classical tgrav,Philip and the reformulated tgrav increase for fine‐textured soils, attributed to the time needed to attain steady‐state infiltration and thus i + infiltration for inferring soil hydraulic properties. Results show that the proposed tgrav is a better indicator of time domain validity than tgrav,Philip. For the attainment of steady‐state infiltration, the reformulated tgrav is suitable for coarse‐textured soils. Still neither the reformulated tgrav nor the classical tgrav,Philip are suitable for fine‐textured soils for which tgrav is too conservative and tgrav,Philip too short. Using tgrav will improve predictions of the soil hydraulic parameters (particularly Ks) from infiltration data compared to tgrav,Philip.

Neural network disturbance observer with extended weight matrix for spacecraft disturbance attenuation

A modified neural network-based disturbance observer with high-accuracy estimation performance is fabricated for spacecraft attitude control in this paper. To reduce the approximation error of the neural network with a limited number of neurons for complex disturbances, the weight matrix of the neural network is extended into a time series expansion and updated by a modified back propagation algorithm. Thus, the high-order dynamics of the weight matrix can be reconstructed, and the disturbance estimation accuracy is improved. Then, by introducing an integral state of the lumped disturbance into the disturbance model and utilizing it as the virtual disturbance measurement, an improved neural network-based disturbance observer is designed. The proposed observer takes advantages of the nonlinear approximation capability of the neural network and the high-order dynamics estimation ability of the extended observer structure. To realize high-performance attitude control of a spacecraft, a composite controller based on the proposed observer is designed, and then tested by comparative simulations. Simulation results show that, the estimation error of the designed observer can be reduced by an order of magnitude than the traditional observers. It is suitable for high-performance disturbance attenuation of verities of applications.

MarineTools.temporal: A Python package to simulate Earth and environmental time series

The assessment of the uncertainty about the evolution of complex processes usually requires different realizations consisting of multivariate temporal signals of environmental data. However, it is common to have only one observational set. MarineTools.temporal is an open-source Python package for the non-stationary parametric statistical analysis of vector random processes suitable for environmental and Earth modelling. It takes a single timeseries of observations and allows the simulation of many time series with the same probabilistic behavior. The software generalizes the use of piecewise and compound distributions with any number of arbitrary continuous distributions. The code contains, among others, multi-model negative log-likely functions, wrapped-normal distributions, and generalized Fourier timeseries expansion. Its programming philosophy significantly improves the computing time and makes it compatible with future extensions of scipy.stats. We apply it to the analysis of freshwater river discharge, water currents, and the simulation of ensemble projections of sea waves, to show its capabilities.

Estimation of E-waste at micro level for reverse logistics: A case of Delhi

This study presents a method for estimating e-waste at the micro-level (ward-village level) using a real-life case of Delhi, India and an example of mobile phones. The study is motivated by the practical issues faced by the e-waste reverse logistics (RL) network, which requires micro-level estimation for various activities such as facility location, routing of vehicles, resource allocation, and capacity determination. Taking input as population, and product penetration, due to the unavailability of sales data at the micro-level, we propose an e-waste estimation approach based on the sales-stock-lifespan model. Considering product diffusion follows an 'S' shaped curve, the time-series expansion is modelled using the Gompertz curve and percentage change in mobile subscribers. We show that the waste from obsolete mobile phones increased exponentially from 2004 till 2019, i.e., 1147 in 2004–856483 in 2019, and is expected to be stable with less than 1% growth rate till 2030. We also show that Delhi will discard approximately 858611 mobile phones in the year 2020, and the top 5 e-waste generating wards-villages of Delhi will produce 13089, 6502, 5901, 5863, and 5742 obsolete mobile phones in 2020. The results of the study are of use for designing and operating the RL network.

REFINEMENT OF CONIFER GROWTH MODELS BASED ON TREE-RING CHRONOLOGIES OF THE NORTH OF WESTERN SIBERIA

The subject of this research is conifer growth model based on time-series of annual rings width. The article addresses processing of data and model update in respect of forest dendrology. The purpose of study is to update the conifer growth model due to expansion of time-series of tree-rings width in regards to conifer forests in Western Siberia. The method represents expansion of time-series due to the fact that some growth phases had not been taken into account. When measurements were taken at the height of 1.3 meters, the following phases were not considered: seedling, juvenile, immature and beginning of virginile phase. The authors carried out examination of a number of scans and core samples, as well as time-series received by other scientists and which are contained in the International Tree-Ring Data Bank. Based on the results of field studies, the authors recommend to add some zeroes to the beginning of time-series within the range of 10-15 years for pine-trees in the south of Western Siberia, depending on growth conditions; the range of 15-30 years in the north for larch-trees and pine-trees depending on soil and climate conditions and latitude. The sequence of data pre-processing operations for time-series, received by means of core sampling, is as follows: averaging out of radius gain in 2 (3) mutually perpendicular directions for one specimen, graphing of radius gain curve, adding to the beginning of time-series, its normalization, approximation by specified growth function. It is possible to build area growth function for the scans. For averaging out a group of model trees, the sequence of operations is as follows: synchronization of time-series by cross-correlation method, approximation by specified growth function. Methods and results of studies can be applied in forest sectors and oil and gas industries for monitoring of forest health conditions. The proposed method of curve growth model update will allow to define more precisely time intervals for efficient forest exploitation as well as to reconstruct digital models of conifer populations in the north of Western Siberia.

Modeling the Slant Wet Delays From One GPS Receiver as a Series Expansion With Respect to Time and Space: Theory and an Example of Application for the Tahiti Island

Traditionally, the modeling of the water vapor contents of the atmosphere is done through the estimation of precipitable water (PW)—the integrated value of the mass of water vapor over a vertical column expressed in millimeter equivalent height. This modeling method is justified by the fact that, to a high degree of approximation, the atmosphere can be seen as the stacking of horizontal layers, including water vapor, over distances larger than the height of the tropopause. Nevertheless, the cycle of the water vapor, the most prevalent of the greenhouse gases in the atmosphere, has a highly turbulent regime both in time and in space that the variations in PW cannot fully embrace. In this article, we explore the modeling method, as a series expansion in time and space, of the slant wet delays (SWDs) from one GPS receiver, as an extension of the usual modeling in zenith wet delays (ZWDs) and then PW values. In the first part, we assess, from a metrological point of view, the derivation of the SWDs computed from GPS carrier phase measurements, in the case of a very humid location, the tropical island of Tahiti, for a typical sample over the wet and dry seasons. In the second part, we introduce the series expansion of the SWDs, as seen from one GPS receiver, in terms of trigonometric functions of time and spherical harmonics of elevation and azimuth. This allows us to infer time and space correlations for the SWDs that are unreachable through the modeling of ZWD values alones. In a third part, to show that our approach also includes the zenith case, we make a comparison between the modeled SWDs in the zenith direction with wind velocities from a ground weather station and radiosonde soundings (RSs). The three main conclusions from our data case are: first, the SWDs are correlated in time by about four days, and in space, with an angular correlation distance of about 20°, both for the dry and wet seasons; second, the postfit residuals are almost uncorrelated with the SWDs from a temporal and spatial point of view, but with a diurnal component; third, there is a weak correlation between the SWDs and wind velocity, the pattern depends on the season.

Correlations between Socioeconomic Drivers and Indicators of Urban Expansion: Evidence from the Heavily Urbanised Shanghai Metropolitan Area, China

Rapid urban expansion resulting in increased impervious surfaces causes a series of urban environmental problems, e.g., the urban heat island and urban forest fragmentation. Urban expansion is a serious threat to human quality of life and living environments. It has been studied from a variety of aspects, but its driving factors and time series expansion characteristics (i.e., expansion intensity, pattern and direction) need to be better explained in order to devise more effective management strategies. This study examined how social and economic factors are linked in driving urban expansion. Based on multi-temporal aerial images, a rapid urban expansion period, 2000–2010, in Shanghai was analysed. The urban area expanded from 1770.36 to 2855.44 km2 in the period, with a mean annual expansion rate of 108.51 km2. Urban expansion in 2000–2005 (40.42%) was much faster than in 2005–2010 (14.86%), and its direction was southeast, southwest and south. The main pattern was edge expansion in both sub-periods. Social factors, especially population density, significantly affected urban expansion. These findings can help understand the urban expansion process and its driving factors, which has important implications for urban planning and management in Shanghai and similar cities.

Study on four disturbance observers for FO-LTI systems

This paper addresses the problem of designing disturbance observer for fractional order linear time invariant U+0028 FO-LTI U+0029 systems, where the disturbance includes time series expansion disturbance and sinusoidal disturbance. On one hand, the reduced order extended state observer U+0028 ROESO U+0029 and reduced order cascade extended state observer U+0028 ROCESO U+0029 are proposed for the case that the system state can be measured directly. On the other hand, the extended state observer U+0028 ESO U+0029 and the cascade extended state observer U+0028 CESO U+0029 are presented for another case when the system state cannot be measured directly. It is shown that combination of ROCESO and CESO can achieve a highly effective observation result. In addition, the way how to tune observer parameters to ensure the stability of the observers and reduce the observation error is presented in this paper. Finally, numerical simulations are given to illustrate the effectiveness of the proposed methods.

Inhomogeneous quenches in a free fermionic chain: Exact results

We consider the non-equilibrium physics induced by joining together two tight-binding fermionic chains to form a single chain. Before being joined, each chain is in a many-fermion ground state. The fillings (densities) in the two chains might be different. We present a number of exact results, focusing on two-point correlators and the Loschmidt echo (return probability). For the non-interacting case, we identify through an exact derivation the regime in which a semiclassical ansatz is valid. We present a number of analytical results beyond semiclassics, such as the approach to the non-equilibrium steady state and the appearance of Tracy-Widom distributions at the front of the light cone. The light cone behavior is quantified through a series expansion in time, and this description is shown to be valid for interacting systems as well. Results on the Loschmidt echo, presented for finite and zero interactions, illustrate that the physics is different from both local and global quenches.

Phase shift formulation for N-light-pulse atom interferometers: application to inertial sensing

We report on an original and simple formulation of the phase shift in N-light-pulse atom interferometers. We consider atomic interferometers based on two-photon transitions (Raman transitions or Bragg pulses). Starting from the exact analytical phase shift formula obtained from the atom optics ABCD formalism, we use a power series expansion in time of the position of the atomic wave packet with respect to the initial condition. The result of this expansion leads to a formulation of the interferometer phase shift where the leading coefficient in the phase terms up to T^k dependences (k >= 0) in the time separation T between pulses, can be simply expressed in terms of a product between a Vandermonde matrix, and a vector characterizing the two-photon pulse sequence of the interferometer. This simple coefficient dependence of the phase shift reflects very well the atom interferometer's sensitivity to a specific inertial field in the presence of multiple gravito-inertial effects. Consequently,we show that this formulation is well suited when looking for selective atomic sensors of accelerations, rotations, or photon recoil only, which can be obtained by simply zeroing some specific coefficients. We give a theoritical application of our formulation to the photon recoil measurement.

Separation of the atmospheric variability into non-Gaussian multidimensional sources by projection pursuit techniques

We develop an expansion of space-distributed time series into statistically independent uncorrelated subspaces (statistical sources) of low-dimension and exhibiting enhanced non-Gaussian probability distributions with geometrically simple chosen shapes (projection pursuit rationale). The method relies upon a generalization of the principal component analysis that is optimal for Gaussian mixed signals and of the independent component analysis (ICA), optimized to split non-Gaussian scalar sources. The proposed method, supported by information theory concepts and methods, is the independent subspace analysis (ISA) that looks for multi-dimensional, intrinsically synergetic subspaces such as dyads (2D) and triads (3D), not separable by ICA. Basically, we optimize rotated variables maximizing certain nonlinear correlations (contrast functions) coming from the non-Gaussianity of the joint distribution. As a by-product, it provides nonlinear variable changes ‘unfolding’ the subspaces into nearly Gaussian scalars of easier post-processing. Moreover, the new variables still work as nonlinear data exploratory indices of the non-Gaussian variability of the analysed climatic and geophysical fields. The method (ISA, followed by nonlinear unfolding) is tested into three datasets. The first one comes from the Lorenz’63 three-dimensional chaotic model, showing a clear separation into a non-Gaussian dyad plus an independent scalar. The second one is a mixture of propagating waves of random correlated phases in which the emergence of triadic wave resonances imprints a statistical signature in terms of a non-Gaussian non-separable triad. Finally the method is applied to the monthly variability of a high-dimensional quasi-geostrophic (QG) atmospheric model, applied to the Northern Hemispheric winter. We find that quite enhanced non-Gaussian dyads of parabolic shape, perform much better than the unrotated variables in which concerns the separation of the four model’s centroid regimes (positive and negative phases of the Arctic Oscillation and of the North Atlantic Oscillation). Triads are also likely in the QG model but of weaker expression than dyads due to the imposed shape and dimension. The study emphasizes the existence of nonlinear dyadic and triadic nonlinear teleconnections.

Principal nonlinear dynamical modes of climate variability.

We suggest a new nonlinear expansion of space-distributed observational time series. The expansion allows constructing principal nonlinear manifolds holding essential part of observed variability. It yields low-dimensional hidden time series interpreted as internal modes driving observed multivariate dynamics as well as their mapping to a geographic grid. Bayesian optimality is used for selecting relevant structure of nonlinear transformation, including both the number of principal modes and degree of nonlinearity. Furthermore, the optimal characteristic time scale of the reconstructed modes is also found. The technique is applied to monthly sea surface temperature (SST) time series having a duration of 33 years and covering the globe. Three dominant nonlinear modes were extracted from the time series: the first efficiently separates the annual cycle, the second is responsible for ENSO variability, and combinations of the second and the third modes explain substantial parts of Pacific and Atlantic dynamics. A relation of the obtained modes to decadal natural climate variability including current hiatus in global warming is exhibited and discussed.

Modeling for Control [About This Issue

Summarizes the articles included in this issue of the publication.

Handling uncertainty in bivariate quantile estimation – An application to flood hazard analysis in the Mekong Delta

Summary The hydrological load causing flood hazard is in many instances not only determined by peak discharge, but is a multidimensional problem. While the methodology for multivariate frequency analysis is well established, the estimation of the associated uncertainty is rarely studied. In this paper, a method is developed to quantify the different sources of uncertainty for a bivariate flood frequency analysis. The method is exemplarily developed for the Mekong Delta (MD), one of the largest and most densely populated river deltas worldwide. Floods in the MD are the basis for the livelihoods of the local population, but they are also the major hazard. This hazard has, however, not been studied within the frame of a probabilistic flood hazard analysis. The nature of the floods in the MD suggests a bivariate approach, because the societal flood severity is determined by both peak discharge and flood volume. The uncertainty caused by selection of statistical models and parameter estimation procedures are analyzed by applying different models and methods. For the quantification of the sampling uncertainty two bootstrapping methods were applied. The developed bootstrapping-based uncertainty estimation method shows that large uncertainties are associated with the estimation of bivariate flood quantiles. This uncertainty is much larger than the model selection and fitting uncertainty. Given the rather long data series of 88 years, it is concluded that bivariate flood frequency analysis is expected to carry significant uncertainty and that the quantification and reduction of uncertainty merit greater attention. But despite this uncertainty the proposed approach has certainly major advantages compared to a univariate approach, because (a) it reflects the two essential aspects of floods in this region, (b) the uncertainties are inherent for every bivariate frequency analysis in hydrology due to the general limited length of observations and can hardly be avoided, and (c) a framework for the quantification of the uncertainties is given, which can be used and interpreted in the hazard assessment. In addition it is shown by a parametric bootstrapping experiment how longer observation time series can reduce the sampling uncertainty. Based on this finding it is concluded that bivariate frequency analyses in hydrology would greatly benefit from discharge time series augmented by proxy or historical data, or by causal hydrologic expansion of time series.

Transient Flows of Newtonian Fluid through a Rectangular Microchannel with Slip Boundary

We study the transient flow of a Newtonian fluid in rectangular microchannels taking into account boundary slip. An exact solution is derived by using the separation of variables in space and Fourier series expansion in time. It is found that, for different forms of driving pressure field, the effect of boundary slip on the flow behavior is qualitatively different. If the pressure gradient is constant, the flow rate is almost linearly proportional to the slip parameterlwhenlis large; if the pressure gradient is in a waveform, as the slip parameterlincreases, the amplitude of the flow rate increases until approaching a constant value whenlbecomes sufficiently large.

Observation of a Class of Disturbance in Time Series Expansion for Fractional Order Systems

This paper is concerned with the problem of designing disturbance observer for fractional order systems, of which the disturbance is in time series expansion. The stability of a special observer with the selected nonlinear weighted function and transient dynamics function is rigorously analyzed for slowly varying disturbance. In addition, the result is also extended to estimate slope forms disturbance and higher order disturbance of fractional order systems. The efficacy of the proposed method is validated through numerical examples.