Noise In Time Series Research Articles

Enhancement of chaotic hydrological time series prediction with real-time noise reduction using Extended Kalman Filter

Short-term prediction of hydrological time series using chaotic dynamical systems approach has gained popularity. However, noise can severely affect the prediction accuracy of any data driven modelling approach. Noise reduction processes attempted in chaotic hydrological time series analysis were later questioned by Elshorbagy et al. (2002) for their appropriateness for noise reduction processes. Only a few studies on noise reduction have appeared since then, and these too were limited to introducing new noise reduction methods.Most of the past studies on chaotic time series noise reduction shared a general perception that the noise reduced data trained models can give better predictions; they used off line noise reduction methods to obtain a ‘noise reduced data set’ which was then used to make prediction models. However, the results of this study showed that this was not necessarily true and often flawed, when the input data was noisier. Instead, noise-reduced data inputs, were shown to yield higher prediction accuracy even with noisy data trained models. Thus, the study showed a real need to use real-time noise reduction methods instead of off-line noise reduction methods that had previously been used.The Extended Kalman Filter (EKF), a popular nonlinear state estimation method from controls literature, was introduced as a real-time noise reduction method and its effectiveness was demonstrated on both synthetic chaotic time series and real river flow time series. EKF produced prediction improvement as high as 15%–40% on the benchmark time series with noise levels varying from 1% to 30%. Two river flow series, with low average flows, showed prediction improvement whereas three other flow series, with relatively large average flows, did not. Artificial Neural Network (ANN) models were used as the state-space models in EKF, and adopting them to time delays different from 1 unit was also demonstrated. The study demonstrated an ‘indirect’ validation method to verify the effectiveness of noise reduction when several interrelated time series were available; this was supported in observed discharge time series of the Ciliwung River in Jakarta, Indonesia.

Multipathing Rayleigh Waves From Long‐Distance Noise Cross Correlation Along an Ocean‐Continent Boundary (Alaska to California)

AbstractSeismic interferometry can reliably extract interstation surface waves in homogeneous or smooth media. We test the validity of this technique in the case of sharp lateral heterogeneity, by examining paths along the western edge of continental North America. After cross correlating several years of time series of ambient seismic noise, we extract interstation Rayleigh waves with different arrivals in the frequency of 0.04 to 0.06 Hz (periods 17 to 25 s). Using beamforming and seismic wavefield simulations, we show that the different Rayleigh wave arrivals are related to the oceanic and continental paths, respectively. This multipathing of Rayleigh waves that is identified from ambient noise is also identified from earthquakes. Our results demonstrate that seismic noise interferometry is capable of extracting realistic surface waves for complex structural paths such as along the continental margin of North America. Additional studies from other regions may demonstrate the potential for using multipathing surface waves within full waveform inversion.

On a class of estimation and test for long memory

This paper proposes a new analysis method of the estimation and test for long memory time series. We first introduce the definitions of the time scale series, strong variance scale exponent and weak variance scale exponent, and establish the mathematical equations for the variance scale exponents, with which the time series of the white noise, short memory and long memory can be accurately identified. Two statistics for the hypothesis tests of white noise, short memory and long memory time series are constructed, and the Monte Carlo performance for MSE of the weak variance scale exponent estimator and the empirical size and power of SLmemory statistic is subsequently demonstrated, giving practical recommendations of finite-sample. Finally, brief empirical examples are provided based on Sino–US stock index logarithmic return rate data.

CORROSIÓN POR HENDIDURA EN GRIETAS DEL AISI-410 USADO EN ALABES DE TURBINAS DE VAPOR

The blades of the last stage of steam turbines are subject to corrosive environment and cyclic load, which could lead to failures due to crack propagation and corrosion. Some turbine blades are made of materials like stainless steel AISI-410. In this paper the effect of temperature on corrosion crack propagation produced in a stainless steel AISI-410 type was studied. The cracked specimens were exposed in seawater during 5 days at two temperatures (25 °C and 90 °C) in static conditions. The corrosion was studied using the electrochemical noise technique (EN) and potentiodynamic polarization curves (PC). The electrochemical noise time series were used to analyze the changes in corrosion activity for AISI-410 under the mentioned experimental conditions determining the type and corrosion rate. The results showed that cracks were grown when exposed in seawater, especially at the higher temperature. Physical characterization obtained from SEM showed a great amount of corrosion products emerging from the cracks, observing a mixed corrosion type around the cracks: uniform and pitting. From the results, it is deduced that this corrosion attack may influence crevice corrosion, which eventually leads to stress corrosion cracking and corrosion fatigue.

Ocean ambient noise off Chennai due to very severe cyclonic storm Vardah

Ocean ambient noise during the passage of a very severe cyclonic storm, Vardah, in the Bay of Bengal has been studied and presented in this paper. A cyclone named Vardah formed near the Andaman and Nicobar Islands on December 6, 2016. The intensified cyclonic storm crossed the south-eastern coast of India in the afternoon hours (local time) of December 12, 2016. During the passage of this cyclone, ocean underwater ambient noise time series data were acquired from the shallow waters of the south-eastern coast of India. In this paper, the noises pertaining to heavy rain and light rain (drizzling) during the cyclonic event have been analysed along with the high wind noise, and the individual power spectra for both the noises have been estimated.

Is human atrial fibrillation stochastic or deterministic?-Insights from missing ordinal patterns and causal entropy-complexity plane analysis.

The mechanism of atrial fibrillation (AF) maintenance in humans is yet to be determined. It remains controversial whether cardiac fibrillatory dynamics are the result of a deterministic or a stochastic process. Traditional methods to differentiate deterministic from stochastic processes have several limitations and are not reliably applied to short and noisy data obtained during clinical studies. The appearance of missing ordinal patterns (MOPs) using the Bandt-Pompe (BP) symbolization is indicative of deterministic dynamics and is robust to brief time series and experimental noise. Our aim was to evaluate whether human AF dynamics is the result of a stochastic or a deterministic process. We used 38 intracardiac atrial electrograms during AF from the coronary sinus of 10 patients undergoing catheter ablation of AF. We extracted the intervals between consecutive atrial depolarizations (AA interval) and converted the AA interval time series to their BP symbolic representation (embedding dimension 5, time delay 1). We generated 40 iterative amplitude-adjusted, Fourier-transform (IAAFT) surrogate data for each of the AA time series. IAAFT surrogates have the same frequency spectrum, autocorrelation, and probability distribution with the original time series. Using the BP symbolization, we compared the number of MOPs and the rate of MOP decay in the first 1000 timepoints of the original time series with that of the surrogate data. We calculated permutation entropy and permutation statistical complexity and represented each time series on the causal entropy-complexity plane. We demonstrated that (a) the number of MOPs in human AF is significantly higher compared to the surrogate data (2.7 ± 1.18 vs. 0.39 ± 0.28, p < 0.001); (b) the median rate of MOP decay in human AF was significantly lower compared with the surrogate data (6.58 × 10-3 vs. 7.79 × 10-3, p < 0.001); and (c) 81.6% of the individual recordings had a rate of decay lower than the 95% confidence intervals of their corresponding surrogates. On the causal entropy-complexity plane, human AF lay on the deterministic part of the plane that was located above the trajectory of fractional Brownian motion with different Hurst exponents on the plane. This analysis demonstrates that human AF dynamics does not arise from a rescaled linear stochastic process or a fractional noise, but either a deterministic or a nonlinear stochastic process. Our results justify the development and application of mathematical analysis and modeling tools to enable predictive control of human AF.

Effect of removing the common mode errors on linear regression analysis of noise amplitudes in position time series of a regional GPS network & a case study of GPS stations in Southern California

The analysis of the correlations between the noise in different components of GPS stations has positive significance to those trying to obtain more accurate uncertainty of velocity with respect to station motion. Previous research into noise in GPS position time series focused mainly on single component evaluation, which affects the acquisition of precise station positions, the velocity field, and its uncertainty. In this study, before and after removing the common-mode error (CME), we performed one-dimensional linear regression analysis of the noise amplitude vectors in different components of 126 GPS stations with a combination of white noise, flicker noise, and random walking noise in Southern California. The results show that, on the one hand, there are above-moderate degrees of correlation between the white noise amplitude vectors in all components of the stations before and after removal of the CME, while the correlations between flicker noise amplitude vectors in horizontal and vertical components are enhanced from un-correlated to moderately correlated by removing the CME. On the other hand, the significance tests show that, all of the obtained linear regression equations, which represent a unique function of the noise amplitude in any two components, are of practical value after removing the CME. According to the noise amplitude estimates in two components and the linear regression equations, more accurate noise amplitudes can be acquired in the two components.

A multiscale time-space approach to analyze and categorize the precipitation fluctuation based on the wavelet transform and information theory concept

AbstractThe present study proposed a time-space framework using discrete wavelet transform-based multiscale entropy (DWE) approach to analyze and spatially categorize the precipitation variation in Iran. To this end, historical monthly precipitation time series during 1960–2010 from 31 rain gauges were used in this study. First, wavelet-based de-noising approach was applied to diminish the effect of noise in precipitation time series which may affect the entropy values. Next, Daubechies (db) mother wavelets (db5–db10) were used to decompose the precipitation time series. Subsequently, entropy concept was applied to the sub-series to measure the uncertainty and disorderliness at multiple scales. According to the pattern of entropy across scales, each cluster was assigned an entropy signature that provided an estimation of the entropy pattern of precipitation in each cluster. Spatial categorization of rain gauges was performed using DWE values as input data to k-means and self-organizing map (SOM) clustering techniques. According to evaluation criteria, it was proved that k-means with clustering number equal to 5 with Silhouette coefficient=0.33, Davis–Bouldin=1.18 and Dunn index=1.52 performed better in determining homogenous areas. Finally, investigating spatial structure of precipitation variation revealed that the DWE had a decreasing and increasing relationship with longitude and latitude, respectively, in Iran.

Low-quality multivariate spatio-temporal serial data preprocessing

As the accumulation of spatio-temporal data, the low-quality problems of multivariate spatio-temporal data become clear and mainly present that numerous missing data, high noise of time series and great different spatial scale of spatiotemporal data. Aimed at the low-quality problems of multivariate spatio-temporal series, we propose three methods to process them, firstly, using improved non-local means (NLM) algorithm and nonlinear regression analysis method to achieve incomplete data imputation; secondly, using NLM algorithm to deal with Gaussian white noise in time series; thirdly, using the Gaussian pyramid method to zoom the spatial scale for multivariate spatial data. Besides, we compare with traditional methods using quantitative evaluation indices to measure the performance, including K-nearest and wavelet threshold. The experimental simulations indicate that the interpolating accuracy of the two proposed algorithms are higher than K-nearest neighbor algorithm and the effect of denoising using NLM algorithm is obviously better than wavelet threshold method. The experiment results further indicate that the Gaussian pyramid method effectively achieves spatial scale transformation of multivariate spatial data and keeps the local detail characteristics of spatial data with better visual expression effect.

A geodetic matched filter search for slow slip with application to the Mexico subduction zone

AbstractSince the discovery of slow slip events, many methods have been successfully applied to model obvious transient events in geodetic time series, such as the widely used network strain filter. Independent seismological observations of tremors or low‐frequency earthquakes and repeating earthquakes provide evidence of low‐amplitude slow deformation but do not always coincide with clear occurrences of transient signals in geodetic time series. Here we aim to extract the signal corresponding to slow slips hidden in the noise of GPS time series, without using information from independent data sets. We first build a library of synthetic slow slip event templates by assembling a source function with Green's functions for a discretized fault. We then correlate the templates with postprocessed GPS time series. Once the events have been detected in time, we estimate their duration T and magnitude Mw by modeling a weighted stack of GPS time series. An analysis of synthetic time series shows that this method is able to resolve the correct timing, location, T, and Mw of events larger than Mw 6 in the context of the Mexico subduction zone. Applied on a real data set of 29 GPS time series in the Guerrero area from 2005 to 2014, this technique allows us to detect 28 transient events from Mw 6.3 to 7.2 with durations that range from 3 to 39 days. These events have a dominant recurrence time of 40 days and are mainly located at the downdip edges of the Mw&gt;7.5 slow slip events.

Electrochemical noise analysis of Ti-15Mo alloy samples exposed to Hanks solution: association between milling time and corrosion resistance

AbstractThe aim of this work was to evaluate the corrosion resistance of Ti15Mo alloys prepared with different milling times (0, 3, 5 and 8 hours) and exposed to Hanks solution. The alloys of Ti-15Mo were prepared by mechanical milling under an Ar atmosphere. SPEX 8000M was connected to a hardened steel container with 13 mm (Ø) balls as milling media, using alternate cycles of 30 minutes milling and 30 min resting. Milling time longer than 8 hours using Ti alloys were avoided to prevent oxidation. The electrochemical noise time series of current (I) and voltage (V) were used to calculate the Rn corrosion index = voltage SD / current SD; SD = standard deviation. Rn was calculated from the original data and also from data after drift removal with two fitting procedures: cubic polynomial (degree 3) and moving average. A significant inverse association (p &lt; 0.05, Spearman’s correlation analysis) between milling time and Rn was found in time series fitted by a polynomial, which indicates higher corrosion resistance among samples prepared with longer milling times. The recurrence plot analysis showed that the fitting method also influenced the dynamical behaviour of these time series.

Microtremor Response of a Mass Movement in Federal District of Brazil

The present study provides a brief description of the ambient noise recorded at a slow moving mass movement in Ribeirao Contagem Basin. The area is an interesting natural laboratory as river detachment processes in a number of diferent stages can be identiied and are easily accessible. We investigate the site dynamic characteristics of the study area by recording ambient noise time-series at nine points, using portable nine three-component short period seismometers. The time-series are processed to give both horizontal to vertical spectral ratio (HVSR) curves as well as time-frequency plots of noise power spectral density (SPD). The HVSR curves illustrate and quantify aspects of site resonance efects due to the local geological setting. Probability density function (PDF) shows that noise level lies well between new high noise model (NHNM) and new lower noise model (NLNM) and their probabilities are higher above 2 Hz. HVSR curves present a uniform lithologically controlled peak at 2 Hz. Directional properties of the waveield are determined by beamforming method. The f-k analysis results in the E-W component show that at 5 Hz phase velocities are close to 1700 m/s while at 10 Hz dropped to 250 m/s. We observed that between 5 and 16 Hz the incoming waveield arrive from 260 degrees. Further studies will apply a detailed noise analysis for relating the dynamics of the landslide (which can be retriggered by river erosion as well as rainfalls and seismic shaking) to possible changes in detectable physical properties.

A Simple Test for White Noise in Functional Time Series

We propose a new procedure for white noise testing of a functional time series. Our approach is based on an explicit representation of the L2‐distance between the spectral density operator and its best (L2‐)approximation by a spectral density operator corresponding to a white noise process. The estimation of this distance can be easily accomplished by sums of periodogram kernels, and it is shown that an appropriately standardized version of the estimator is asymptotically normal distributed under the null hypothesis (of functional white noise) and under the alternative. As a consequence, we obtain a very simple test (using the quantiles of the normal distribution) for the hypothesis of a white noise functional process. In particular, the test does not require either the estimation of a long‐run variance (including a fourth order cumulant) or resampling procedures to calculate critical values. Moreover, in contrast to all other methods proposed in the literature, our approach also allows testing for ‘relevant’ deviations from white noise and constructing confidence intervals for a measure that measures the discrepancy of the underlying process from a functional white noise process.

The measurement of muddy seabed properties using ambient noise coherence

The autonomous passive acoustic lander Deep Sound was deployed five times during the Seabed Characterization Experiment and collected ambient noise data on four hydrophones, arranged in a inverted “T” shape, with three spaced in the horizontal and two in the vertical. The lander was deployed with the bottom-most phones approximately 30 cm above the seafloor, recording over an acoustic bandwidth of 5 Hz–30 kHz. Pressure time series, vertical and horizontal noise coherence (directionality), and the local temperature and conductivity were recorded continuously for periods of 9 hours. Wind-driven surface ambient noise coherence was used to estimate bulk acoustic seabed properties. An analytical Pekeris-waveguide noise model was fitted to the data in order to determine the bulk sound speed, density, and frequency dependent attenuation in the bottom fluid half-space. [Research supported by ONR.]

Evenly spaced Detrended Fluctuation Analysis: Selecting the number of points for the diffusion plot

Detrended Fluctuation Analysis (DFA) has become a widely-used tool to examine the correlation structure of a time series and provided insights into neuromuscular health and disease states. As the popularity of utilizing DFA in the human behavioral sciences has grown, understanding its limitations and how to properly determine parameters is becoming increasingly important. DFA examines the correlation structure of variability in a time series by computing α, the slope of the logSD–logn diffusion plot. When using the traditional DFA algorithm, the timescales, n, are often selected as a set of integers between a minimum and maximum length based on the number of data points in the time series. This produces non-uniformly distributed values of n in logarithmic scale, which influences the estimation of α due to a disproportionate weighting of the long-timescale regions of the diffusion plot. Recently, the evenly spaced DFA and evenly spaced average DFA algorithms were introduced. Both algorithms compute α by selecting k points for the diffusion plot based on the minimum and maximum timescales of interest and improve the consistency of α estimates for simulated fractional Gaussian noise and fractional Brownian motion time series. Two issues that remain unaddressed are (1) how to select k and (2) whether the evenly-spaced DFA algorithms show similar benefits when assessing human behavioral data. We manipulated k and examined its effects on the accuracy, consistency, and confidence limits of α in simulated and experimental time series. We demonstrate that the accuracy and consistency of α are relatively unaffected by the selection of k. However, the confidence limits of α narrow as k increases, dramatically reducing measurement uncertainty for single trials. We provide guidelines for selecting k and discuss potential uses of the evenly spaced DFA algorithms when assessing human behavioral data.

Multiscale Poincaré plot analysis of time series from laser speckle contrast imaging data

The monitoring of microvascular blood flow is of importance for research and clinical purposes because, for some pathologies as diabetes, the microcirculation may be affected long before organ dysfunctions are diagnosed. Laser speckle contrast imaging (LSCI) is gaining an increased interest to monitor microvascular blood flow (peripheral cardiovascular data). However, in spite of this and by opposition to central cardiovascular data as electrocardiograms, very few studies have been conducted on the analysis of LSCI through scales. We therefore propose to process LSCI data with a multiscale approach relying on Poincare plots. For this purpose, we first study multiscale Poincare (MSP) plots of simulated signals (synthetic white and 1/f noise time series). Then, MSP plots of LSCI time series recorded in 24 healthy volunteers are generated and analyzed. Furthermore, this analysis on real-life data is also conducted to study the role played by age on the results. Thus, the subjects were divided into two age groups: 13 young subjects (mean age = 23.8 ± 3.2 years old) and 11 elderly subjects (mean age = 56.9 ± 6.7 years old). Our results show properties that may reveal a weak fractal structure for LSCI data. Moreover, we find no statistical difference (p ≥ 0.05) for the descriptors of MSP plots between the two age groups. MSP plots may become a simple-to-implement visualization tool to provide new insights into biomedical data across scales.

A weighted EMD-based prediction model based on TOPSIS and feed forward neural network for noised time series

In line with the decomposition-and-reconstitution principle, the empirical mode decomposition (EMD)-based modeling framework has been a widely used alternative for non-linear, non-stationary time series prediction to decompose an original time series into different sub-series that can be identified, separately predicted, and then recombined for aggregate forecasting. However, in many cases, recombination has been found to adversely affect prediction accuracy. To address this problem, this study incorporates a feed forward neural network (FNN) into the EMD-based forecasting framework and brings forward the weighted recombination strategy to allow for one step ahead forward prediction. To justify and compare the effectiveness of the proposed model, four non-linear, non-stationary data series are applied and benchmarked using four well-established prediction model recombination methods. The results show that the proposed weighted EMD-based forecasting model observably improves forecast validity. This approach also has great promise for intricate and noise disturbed irregular and highly volatile time series predictions.

Information flow in a network of dispersed signalers-receivers

I consider a stochastic model of multi-agent communication in regular network. The model describes how dispersed animals exchange information. Each agent can initiate and transfer the signal to its nearest neighbors, who may pass it farther. For an external observer of busy networks, signaling activity may appear random, even though information flow actually thrives. Only when signal initiation and transfer are at low levels do spatiotemporal autocorrelations emerge as clumping signaling activity in space and pink noise time series. Under such conditions, the costs of signaling are moderate, but the signaler can reach a large audience. I propose that real-world networks of dispersed signalers-receivers may self-organize into this state and the flow of information maintains their integrity.

Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations

Fluctuation Analysis (FA) and specially Detrended Fluctuation Analysis (DFA) are techniques commonly used to quantify correlations and scaling properties of complex time series such as the observable outputs of great variety of dynamical systems, from Economics to Physiology. Often, such correlated time series are analyzed using the magnitude and sign decomposition, i.e., by using FA or DFA to study separately the sign and the magnitude series obtained from the original signal. This approach allows for distinguishing between systems with the same linear correlations but different dynamical properties. However, here we present analytical and numerical evidence showing that FA and DFA can lead to spurious results when applied to sign and magnitude series obtained from power-law correlated time series of fractional Gaussian noise (fGn) type. Specifically, we show that: (i) the autocorrelation functions of the sign and magnitude series obtained from fGns are always power-laws; However, (ii) when the sign series presents power-law anticorrelations, FA and DFA wrongly interpret the sign series as purely uncorrelated; Similarly, (iii) when analyzing power-law correlated magnitude (or volatility) series, FA and DFA fail to retrieve the real scaling properties, and identify the magnitude series as purely uncorrelated noise; Finally, (iv) using the relationship between FA and DFA and the autocorrelation function of the time series, we explain analytically the reason for the FA and DFA spurious results, which turns out to be an intrinsic property of both techniques when applied to sign and magnitude series.

Analysis of marginal ice zone noise events: Revisited

Acoustic transients observed in a noise time series, called noise events, are believed to be the major contributor to Arctic Ocean ambient noise. Underwater ambient noise data from the Marginal Ice Zone Experiment 1984 (MIZEX84), at frequencies between 20 and 2000 Hz, are studied. Results show that temporal and spatial distribution of events are characterized by clustering and seem to depend on environmental conditions such as swells and ice concentration. Event densities increase as f at frequencies below 200 Hz, decrease as f −1 at frequencies above 300 Hz, and reach a maximum at frequencies between 200 and 300 Hz. The change in trend may indicate a transition in the source mechanism for frequencies below 200 Hz and above 300 Hz. The noise source can be modeled as octo-pole which is the best fit from the noise data. [Work supported by Office of Naval Research, and completed under Prof. Ira Dyer's supervision in Massachusetts Institute of Technology in 1990.]