Noise In Time Series Research Articles

LSTM-Autoencoder Based Detection of Time-Series Noise Signals for Water Supply and Sewer Pipe Leakages

The efficient management of urban water distribution networks is crucial for public health and urban development. One of the major challenges is the quick and accurate detection of leaks, which can lead to water loss, infrastructure damage, and environmental hazards. Many existing leak detection methods are ineffective, especially in complex and aging pipeline networks. If these limitations are not overcome, it can result in a chain of infrastructure failures, exacerbating damage, increasing repair costs, and causing water shortages and public health risks. The leak issue is further complicated by increasing urban water demand, climate change, and population growth. Therefore, there is an urgent need for intelligent systems that can overcome the limitations of traditional methodologies and leverage sophisticated data analysis and machine learning technologies. In this study, we propose a reliable and advanced method for detecting leaks in water pipes using a framework based on Long Short-Term Memory (LSTM) networks combined with autoencoders. The framework is designed to manage the temporal dimension of time-series data and is enhanced with ensemble learning techniques, making it sensitive to subtle signals indicating leaks while robustly dealing with noise signals. Through the integration of signal processing and pattern recognition, the machine learning-based model addresses the leak detection problem, providing an intelligent system that enhances environmental protection and resource management. The proposed approach greatly enhances the accuracy and precision of leak detection, making essential contributions in the field and offering promising prospects for the future of sustainable water management strategies.

Modeling random isotropic vector fields on the sphere: theory and application to the noise in GNSS station position time series

Modeling random isotropic vector fields on the sphere: theory and application to the noise in GNSS station position time series

Ai-driven innovations in greenhouse agriculture: Reanalysis of sustainability and energy efficiency impacts

In the context of greenhouse agriculture, the integration of Artificial Intelligence (AI) is evaluated for its potential to enhance sustainability and crop production efficiency. This study reanalyzes publicly available datasets, using advanced time series analysis and noise reduction techniques through seasonality detection and removal. This novel approach reveals trends more clearly, providing a detailed comparison between AI-driven methods and traditional agricultural practices. An extensive review of literature on AI applications in agriculture is conducted to establish a broad understanding of its current state and future prospects. The core focus is the Autonomous Greenhouses Challenge, an initiative where research teams apply AI technologies in real-world greenhouse settings. This challenge offers crucial data for a thorough assessment of AI’s practical impact. The analysis reveals that AI significantly reduces heating energy consumption, indicating a notable improvement in energy efficiency. However, reductions in CO2 emissions, along with improvements in electricity and water usage, are only marginal when compared to traditional farming methods. Similarly, enhancements in crop quality and profitability achieved through AI are found to be on par with conventional techniques. These findings highlight the dual nature of AI’s impact in greenhouse agriculture: it shows significant promise in some areas, while its effectiveness in other key sustainability aspects remains limited. The study emphasizes the need for further research and investment in technological advancements, as well as the importance of a robust data infrastructure. It also highlights the necessity of education and training in AI technologies for effective implementation in the agricultural sector. The results of this research aim to inform policymakers, researchers, and industry stakeholders about the mixed impacts of AI on sustainable greenhouse farming. By offering a comprehensive evaluation of the benefits and challenges of AI integration, this study contributes to the ongoing discussion on sustainable agricultural practices and provides insights into the future direction of AI in this field.

Development, Calibration and Validation of Time Series Analysis and Artificial Neural Network Joint Model for Urban Noise Prediction

Noise in large urban areas, which is mainly generated by road traffic and by the human activities carried out nearby and inside the area under study, is a relevant problem. The continuous exposure to high noise levels, in fact, can lead to several problems, largely documented in the scientific literature. The analysis and forecasting of the noise level in a given area are, then, fundamental for control and prevention, especially when field measurements present peculiar trends and slopes, which can be modeled with a Time Series Analysis approach. In this paper, a hybrid model is presented for the analysis and the forecasting of noise time series in urban areas: this technique is based on the application of a deterministic decomposition model followed in cascade by a predictor of the forecasting errors based on an artificial neural network. Two variants of the hybrid model have been implemented and presented. The time series used to calibrate and validate the model is composed of sound pressure level measurements detected on a busy road near the commercial port of an Italian city. The proposed hybrid model has been calibrated on a part of the entire time series and validated on the remaining part. Residuals and error analysis, together with a detailed statistical description of the simulated noise levels and error metrics describe in detail the method’s performances and its limitations.

Separation of Water Level Change From Atmospheric Artifacts Through Application of Independent Component Analysis to InSAR Time Series

AbstractIn recent years, synthetic aperture radar (SAR) interferometry (InSAR) has emerged as a valuable tool for measuring water level change (WLC) to study hydrodynamic processes in coastal wetlands. However, the highly dynamic wet atmosphere conditions common in these areas have a significant impact on InSAR observations, producing errors in the derived values. Standard methods for estimating atmospheric noise in InSAR time series lack the spatial or temporal resolution needed to adequately correct for wet tropospheric delays. In this study, we utilize the Independent Component Analysis (ICA) signal decomposition technique to identify the likely WLC signal and eliminate atmospheric noise in a time series derived from rapid repeat measurements made with the L‐band uninhabited aerial vehicle synthetic aperture radar airborne instrument. The method compares in‐situ water level measurements with the independent components (IC) to identify the ICA components corresponding to WLC. The signal‐to‐noise ratio between the WLC after the ICA‐based filtering and in situ water level gauges used for validation reaches 16 dB compared to an average of 2.6 dB before filtering. The excluded IC are used to generate maps showing a time series of likely atmospheric features. The identified features in the maps generally correspond to atmospheric features identifiable in Next Generation Weather Radar (NEXRAD) S‐band ground weather radar reflectivity maps collected during the SAR acquisitions. The method is sufficiently general to be applied to any InSAR‐derived surface displacement time series.

Colored noise in GRACE total water storage time series: Its impact on trend significance in the Türkiye region and major world river basins

Temporal correlations are prevalent in most geophysical time series data, leading to what is known as colored noise, which become more apparent in the frequency domain rather than time domain. Neglecting this type of noise in modeling can result in underestimated standard errors for the parameters of the model used to analyze the time series. As a result, statistical tests misinterpret the significance of these parameters, such as the overall trend rate, because the “signal to noise” ratio becomes incorrectly larger than it should be. In this study, we investigate the temporal correlations in the time series data from the Gravity Recovery and Climate Experiment (GRACE) mission. GRACE and its successor mission GRACE Follow-On (GRACE-FO) have been successfully employed to monitor global total water storage anomalies over two decades since its initial launch in 2002. We primarily utilize monthly GRACE mascon (mass concentration) solutions provided by NASA Goddard Space Flight Center (GSFC), examining both regional and global scales. The power spectrum density of the residuals, calculated after applying standard harmonic regression to each mascon time series on Earth’s land, reveals an average spectral index of κ = −1. This indicates the predominance of flicker noise, one of the most common forms of colored noise in geodetic time series. Notably, the noise becomes more Brownian (κ < −1) in regions with intense hydrological events, while it tends to be more white noise (κ → 0) in areas with less water circulation compared to other land regions. This observation suggests that unmodelled hydrological events, such as droughts, floods, and ones associated with ice-melting, contribute to the residuals as colored noise in the time series. To account for this noise in our time series modeling, we primarily consider autoregressive (AR) moving average (MA) process, commonly known as ARMA, in addition to the standard variance component estimation for noise amplitudes. We focus on individual mascon blocks in the Türkiye Region and mascon solutions for 24 world’s major river basins. Our findings demonstrate that an ARMA(1,1) model is sufficient for describing the noise in these regions. The results underscore the importance of considering colored noise, as it leads to approximately three times larger standard errors for the overall trend rate. This substantially impacts the significance of the trend rates.

MDCNet: Long-term time series forecasting with mode decomposition and 2D convolution

Long-term time series forecasting is widely used in various real-world applications, such as weather, traffic, energy, healthcare, etc. Recently, time series decomposition techniques have been adopted in many mainstream forecasting models, such as the prevalent Transformer-based models, to help capture sophisticated temporal patterns and achieve success in several benchmark tasks. However, conventional decomposition algorithms are often based on simple operations or limited to specific fields, and therefore are not effective and applicable enough, especially for complex time series. In this paper, we propose Mode Decomposition and 2D Convolutional Network (MDCNet), a structure-simple yet effective forecasting architecture based on a more effective decomposition method and a multi-frequency time series feature extraction network with multi-scale 2D convolution. Specifically, we first introduce a Variational Mode Decomposition Block to discover intricate time patterns, which decompose time series into trend components and stationary modal components at different main frequencies. Then, we design a Trend Prediction Block and an Intrinsic Mode Functions Prediction Block to capture global correlation and hidden dependencies within different main frequencies, respectively. Furthermore, a Frequency Enhancement Module is designed to further reduce the impact of noise in long-term time series. Experiments on eight benchmark datasets show that MDCNet significantly reduces the error of the previous state-of-the-art method by 15.1% and 11.5% for multivariate and univariate time series, respectively.

Characterizing Colored Noise Time Series Patterns with Deep Learning Models

Characterizing Colored Noise Time Series Patterns with Deep Learning Models

Anatomy of the spatiotemporally correlated noise in GNSS station position time series

Anatomy of the spatiotemporally correlated noise in GNSS station position time series

Selection of noise models for GNSS coordinate time series based on model averaging algorithm

In the field of global navigation satellite system (GNSS) time series noise analysis, appropriately modeling the noise components plays an important role in determining the velocity of GNSS sites and quantifying the uncertainty associated with the velocity estimation. Over the years, researchers have focused on only one optimal noise model, while other noise models that show similar performance to the optimal model have been ignored. We investigated whether these ignored noise models can be made use of to describe the noise in the GNSS time series after applying a model averaging algorithm. The experimental data were derived from 28 International GNSS Service (IGS) sites in the California region of the United States and 110 IGS sites worldwide. The results showed that for the GNSS time series of 28 IGS sites in the California, 79%, 68%, and 75% of the site components can be applied the model averaging algorithm in the east/north/up (E/N/U) directions, respectively. Based on it, the east direction showed the best performance, with 50% of the site components obtaining more conservative velocity uncertainty after applying the model averaging algorithm compared to the optimal noise model. For GNSS time series of 110 IGS stations worldwide, the model averaging algorithm demonstrates excellent performance in all the E/N/U directions. In the E/N/U directions, 86%, 94%, and 57% of the site components can apply the model averaging algorithm. Building upon this, 77%, 65%, and 62% of the site components achieve more conservative velocity uncertainty in the E/N/U directions compared to the optimal noise model. To fully validate the feasibility of the model averaging algorithm, we also tested GNSS time series of varying lengths and different thresholds of the model averaging algorithm. In summary, the model averaging algorithm performs exceptionally well in the noise analysis of GNSS time series. It helps prevent overly optimistic estimation results.

Enhancing Sea Level Rise Estimation and Uncertainty Assessment from Satellite Altimetry through Spatiotemporal Noise Modeling

The expected acceleration in sea level rise (SLR) throughout this century poses significant threats to coastal cities and low-lying regions. Since the early 1990s, high-precision multi-mission satellite altimetry (SA) has enabled the routine measurement of sea levels, providing a continuous 30-year record from which the mean sea level rise (global and regional) and its variability can be computed. The latest reprocessed product from CMEMS span the period from 1993 to 2020, and have enabled the acquisition of accurate sea level data within the coastal range of 0–20 km. In order to fully utilize this new dataset, we establish a global virtual network consisting of 184 virtual SA stations. We evaluate the impact of different stochastic noises on the estimation of the velocity of the sea surface height (SSH) time series using BIC_tp information criterion. In the second step, the principal component analysis (PCA) allows the common mode noise in the SSH time series to be mitigated. Finally, we analyzed the spatiotemporal characteristics and accuracy of sea level change derived from SA. Our results suggest that the stochasticity of the SSH time series is not well described by a combination of random, flicker, and white noise, but is best described by an ARFIM/ARMA/GGM process. After removing the common mode noise with PCA, about 96.7% of the times series’ RMS decreased, and most of the uncertainty associated with the computed SLR decreased. We confirm that the spatiotemporal correlations should be accounted for to yield trustworthy trends and reliable uncertainties. Our estimated SLR is 2.75 ± 0.89 mm/yr, which aligns closely with recent studies, emphasizing the robustness and consistency of our method using virtual SA stations. We additionally introduce open-source software (SA_Tool V1.0) to process the SA data and reduce noise in surface height time series to the community.

Weighted Compressive Sensing Applied to Seismic Interferometry: Wavefield Reconstruction Using Prior Information

Abstract Seismic interferometry is widely used for passive subsurface investigation using seismic noise. The technique requires much storage for long noise records to suppress interferometric noise, which consists of spurious arrivals that do not correspond to the inter-receiver surface waves. Such long recordings may not be available in practice. Compressive sensing (CS), which is a wavefield reconstruction technique operating on incomplete data, may increase the availability, and reduce storage limitations of long noise time series. Using a numerical example of a linear array surrounded by sources and the Fourier basis for a sparse transform, we show that inter-receiver wavefields can be recovered at the locations where seismometers are unavailable, reducing the storage required for interferometry. We propose and develop a weighted CS algorithm that helps suppress the spurious arrivals by incorporating a priori information about the arrivals of surface waves that can be expected.

How do wavelength correlations affect transmission spectra? Application of a new fast and flexible 2D Gaussian process framework to transiting exoplanet spectroscopy

The use of Gaussian processes (GPs) is a common approach to account for correlated noise in exoplanet time series, particularly for transmission and emission spectroscopy. This analysis has typically been performed for each wavelength channel separately, with the retrieved uncertainties in the transmission spectrum assumed to be independent. However, the presence of noise correlated in wavelength could cause these uncertainties to be correlated, which could significantly affect the results of atmospheric retrievals. We present a method that uses a GP to model noise correlated in both wavelength and time simultaneously for the full spectroscopic dataset. To make this analysis computationally tractable, we introduce a new fast and flexible GP method that can analyse 2D datasets when the input points lie on a (potentially non-uniform) 2D grid - in our case a time by wavelength grid - and the kernel function has a Kronecker product structure. This simultaneously fits all light curves and enables the retrieval of the full covariance matrix of the transmission spectrum. Our new method can avoid the use of a `common-mode' correction, which is known to produce an offset to the transmission spectrum. Through testing on synthetic datasets, we demonstrate that our new approach can reliably recover atmospheric features contaminated by noise correlated in time and wavelength. In contrast, fitting each spectroscopic light curve separately performed poorly when wavelength-correlated noise was present. It frequently underestimated the uncertainty of the scattering slope and overestimated the uncertainty in the strength of sharp absorption peaks in transmission spectra. Two archival VLT/FORS2 transit observations of WASP-31b were used to compare these approaches on real observations. Our method strongly constrained the presence of wavelength-correlated noise in both datasets, and significantly different constraints on atmospheric features such as the scattering slope and strength of sodium and potassium features were recovered.

A new denoising approach based on mode decomposition applied to the stock market time series: 2LE-CEEMDAN.

Time series, including noise, non-linearity, and non-stationary properties, are frequently used in prediction problems. Due to these inherent characteristics of time series data, forecasting based on this data type is a highly challenging problem. In many studies within the literature, high-frequency components are commonly excluded from time series data. However, these high-frequency components can contain valuable information, and their removal may adversely impact the prediction performance of models. In this study, a novel method called Two-Level Entropy Ratio-Based Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (2LE-CEEMDAN) is proposed for the first time to effectively denoise time series data. Financial time series with high noise levels are utilized to validate the effectiveness of the proposed method. The 2LE-CEEMDAN-LSTM-SVR model is introduced to predict the next day's closing value of stock market indices within the scope of financial time series. This model comprises two main components: denoising and forecasting. In the denoising section, the proposed 2LE-CEEMDAN method eliminates noise in financial time series, resulting in denoised intrinsic mode functions (IMFs). In the forecasting part, the next-day value of the indices is estimated by training on the denoised IMFs obtained. Two different artificial intelligence methods, Long Short-Term Memory (LSTM) and Support Vector Regression (SVR), are utilized during the training process. The IMF, characterized by more linear characteristics than the denoised IMFs, is trained using the SVR, while the others are trained using the LSTM method. The final prediction result of the 2LE-CEEMDAN-LSTM-SVR model is obtained by integrating the prediction results of each IMF. Experimental results demonstrate that the proposed 2LE-CEEMDAN denoising method positively influences the model's prediction performance, and the 2LE-CEEMDAN-LSTM-SVR model outperforms other prediction models in the existing literature.

Determining Which Sine Wave Frequencies Correspond to Signal and Which Correspond to Noise in Eye-Tracking Time-Series.

The Fourier theorem states that any time-series can be decomposed into a set of sinusoidal frequencies, each with its own phase and amplitude. The literature suggests that some frequencies are important to reproduce key qualities of eye-movements ("signal") and some of frequencies are not important ("noise"). To investigate what is signal and what is noise, we analyzed our dataset in three ways: (1) visual inspection of plots of saccade, microsaccade and smooth pursuit exemplars; (2) analysis of the percentage of variance accounted for (PVAF) in 1,033 unfiltered saccade trajectories by each frequency band; (3) analyzing the main sequence relationship between saccade peak velocity and amplitude, based on a power law fit. Visual inspection suggested that frequencies up to 75 Hz are required to represent microsaccades. Our PVAF analysis indicated that signals in the 0-25 Hz band account for nearly 100% of the variance in saccade trajectories. Power law coefficients (a, b) return to unfiltered levels for signals low-pass filtered at 75 Hz or higher. We conclude that to maintain eyemovement signal and reduce noise, a cutoff frequency of 75 Hz is appropriate. We explain why, given this finding, a minimum sampling rate of 750 Hz is suggested.

Investigation of background noise in the GNSS position time series using spectral analysis – A case study of Nepal Himalaya

Investigation of background noise in the GNSS position time series using spectral analysis – A case study of Nepal Himalaya

Characterizing High Rate GNSS Velocity Noise for Synthesizing a GNSS Strong Motion Learning Catalog

Data-driven approaches to identify geophysical signals have proven beneficial in high dimensional environments where model-driven methods fall short. GNSS offers a source of unsaturated ground motion observations that are the data currency of ground motion forecasting and rapid seismic hazard assessment and alerting. However, these GNSS-sourced signals are superposed onto hardware-, location- and time-dependent noise signatures influenced by the Earth’s atmosphere, low-cost or spaceborne oscillators, and complex radio frequency environments. Eschewing heuristic or physics based models for a data-driven approach in this context is a step forward in autonomous signal discrimination. However, the performance of a data-driven approach depends upon substantial representative samples with accurate classifications, and more complex algorithm architectures for deeper scientific insights compound this need. The existing catalogs of high-rate (≥1Hz) GNSS ground motions are relatively limited. In this work, we model and evaluate the probabilistic noise of GNSS velocity measurements over a hemispheric network. We generate stochastic noise time series to augment transferred low-noise strong motion signals from within 70 kilometers of strong events (≥ MW 5.0) from an existing inertial catalog. We leverage known signal and noise information to assess feature extraction strategies and quantify augmentation benefits. We find a classifier model trained on this expanded pseudo-synthetic catalog improves generalization compared to a model trained solely on a real-GNSS velocity catalog, and offers a framework for future enhanced data driven approaches.

Data-driven modeling of noise time series with convolutional generative adversarial networks ∗ ∗U.S. government work not protected by U.S. copyright.

Random noise arising from physical processes is an inherent characteristic of measurements and a limiting factor for most signal processing and data analysis tasks. Given the recent interest in generative adversarial networks (GANs) for data-driven modeling, it is important to determine to what extent GANs can faithfully reproduce noise in target data sets. In this paper, we present an empirical investigation that aims to shed light on this issue for time series. Namely, we assess two general-purpose GANs for time series that are based on the popular deep convolutional GAN architecture, a direct time-series model and an image-based model that uses a short-time Fourier transform data representation. The GAN models are trained and quantitatively evaluated using distributions of simulated noise time series with known ground-truth parameters. Target time series distributions include a broad range of noise types commonly encountered in physical measurements, electronics, and communication systems: band-limited thermal noise, power law noise, shot noise, and impulsive noise. We find that GANs are capable of learning many noise types, although they predictably struggle when the GAN architecture is not well suited to some aspects of the noise, e.g. impulsive time-series with extreme outliers. Our findings provide insights into the capabilities and potential limitations of current approaches to time-series GANs and highlight areas for further research. In addition, our battery of tests provides a useful benchmark to aid the development of deep generative models for time series.

A Time Series Data Regression Analysis based on B-spline Basis Expansion and Distance Covariance Weighted Stacking Framework

Aiming at the problem of time series data regression prediction, this paper proposed a methodology for time series prediction based on data augmentation and cosine similarity weighted model average in the case where the predictor and response variable is a time series and the continuous scalar respectively. The constructed method deals with the problems of high dimension and noise of time series through B-spline basis expansion in which Blending algorithm was used to enhance the correlation information between B-spline basis coefficients and response variables, so as to further reduce the influence of noise on prediction models. Next, the cosine similarity model average is used to capture the unknown latent model structure between characteristic and response variables to improve the prediction accuracy of the model. The proposed method can effectively balance the bias and variance of the prediction model. In addition, the regression method in the technique is model-free. The analysis of actual data shows that the proposed method has certain advantages compared with those existing. Eventually, the method can be extended to forecasting applications in the fields of stock price prediction, social science, medicine and so on.

The 95 per cent confidence interval for the mean sea-level change rate derived from tide gauge data

SUMMARYTide gauge (TG) data are crucial for assessing global sea-level and climate changes, coastal subsidence and inundation. Mean sea-level (MSL) time-series derived from TG data are autocorrelated. The conventional ordinary least-squares regression method provides reasonable estimates of relative sea-level (RSL) change rates (linear trends) but underestimates their uncertainties. In order to cope with the autocorrelation issue, we propose an approach that uses an ‘effective sample size’ (${N}_{\mathrm{ eff}}$) to estimate the uncertainties (±95 per cent confidence interval, or 95 per cent CI for short). The method involves decomposing the monthly MSL time-series into three components: a linear trend, a periodic component and a noise time-series. The ${N}_{\mathrm{ eff}}$ is calculated according to the autocorrelation function (ACF) of the noise time-series. We present an empirical model that fits an inverse power-law relationship between 95 per cent CI and time span (T) based on 1160 TG data sets globally distributed, where $95\ \mathrm{ per}\ \mathrm{ cent}\,\mathrm{ CI} = 179.8{T}^{ - 1.29}$. This model provides a valuable tool for projecting the optimal observational time span needed for the desired uncertainty in sea-level rise rate or coastal subsidence rate from TG data. It suggests that a 20-yr TG time-series may result in a 3–5 mm yr−1 uncertainty (95 per cent CI) for the RSL change rate, while a 30-yr data set may achieve about 2 mm yr−1 uncertainty. To achieve a submillimetre per year (&amp;lt; 1 mm yr−1) uncertainty, approximately 60 yr of TG observations are needed. We also present a Python module (TG_Rate_95CI.py) for implementing the methodology. The Python module and the empirical model have broad applications in global sea-level rise and climate change studies, and coastal environmental and infrastructure planning, as well as Earth science education.