Probability Distribution Of Noise Research Articles

Analysis and Modeling of Geodetic Data Based on Machine Learning

Abstract This paper underscores the significance of earth deformation observation in analyzing earth tide curves and predicting earthquakes, positioning it as a cornerstone of Earth observation technology. We delve into the critical task of detecting and diagnosing anomalies in geodetic data. Utilizing Python for data preprocessing, our approach identifies missing values, categorizes them by their spatial occurrence, and employs spline interpolation and autoregressive prediction methods for data imputation. This process ensures the integrity of the dataset for subsequent analysis and modeling, reinforcing the precision and reliability of geodetic data analysis in Earth science research. For problem I To expand the data set, we propose three models. Model I: Adding gaussian noise to the data. Model II: Resample the data. Model III: Using machine learning methods to learn the internal laws of the data and predict itself to generate new data. For each model, we discuss its advantages and disadvantages. Finally, we structurally fuse the three models to complete data enhancement. For problem II To extract the noise, we use DB4 wavelet transform to denoise the data set and extract the noise. Then we make descriptive statistics on the noise distribution, and use Laplace distribution to fit the probability distribution of noise, and finally get the accurate noise distribution. For problem III We start from the time domain and frequency domain to extract the features of the data. First, 17 features are extracted in the time domain, then the discrete fourier transform algorithm is used to transform the data into frequency domain data, and 13 are extracted. Therefore, we encode each data as a feature vector with a length of 30. We first use the decision tree as the baseline model to establish the recognition model to select the features. Logistic Regression, KNN, Naive Bayes and SVM are used to establish the recognition model. Finally, we use the Voting ensemble learning method to fuse the model, achieving an accuracy of 86% on the test set.

Variational Bayesian Inference for Robust Identification of PWARX Systems With Time-Varying Time-Delays.

This article presents a robust variational Bayesian (VB) algorithm for identifying piecewise autoregressive exogenous (PWARX) systems with time-varying time-delays. To alleviate the adverse effects caused by outliers, the probability distribution of noise is taken to follow a t -distribution. Meanwhile, a solution strategy for more accurately classifying undecidable data points is proposed, and the hyperplanes used to split data are determined by a support vector machine (SVM). In addition, maximum-likelihood estimation (MLE) is adopted to re-estimate the unknown parameters through the classification results. The time-delay is regarded as a hidden variable and identified through the VB algorithm. The effectiveness of the proposed algorithm is illustrated by two simulation examples.

Motional consensus of self-propelled particles

The motional consensus of self-propelled particles is studied in both noise-free cases and cases with noise by the standard Vicsek model. In the absence of noise, we propose a simple method, using grid-based technique and defining the normalized variance of the ratio of the number of particles locally to globally, to quantitatively study the movement pattern of the system by the spatial distribution of the particles and the degree of aggregation of particles. It is found that the weaker correlation of velocity leads to larger degree of aggregation of the particles. In the cases with noise, we quantify the competition between velocity alignment and noise by considering the difference of the variety of order parameter result from the velocity alignment and noise. The variation of the effect of noise on motional consensus is non-monotonic for the change of the probability distribution of noise from uniform to non-uniform. Our results may be useful and encourage further efforts in exploring the basic principles of collective motion.

Integrated Navigation Method of Aerospace Vehicle Based on Rank Statistics

The large dynamic and high-speed flight of aerospace vehicle will bring unpredictable conditions to its navigation system, resulting in that its system random noise probability distribution will no longer meet the preconditions of Gaussian distribution preset by the existing filter algorithm, thus reducing the accuracy of the navigation system. So, it is very important to propose an effective method to solve the filter problem of the navigation system in non-Gaussian distribution to improve the accuracy of the navigation system. Therefore, an integrated navigation method of aerospace vehicle based on rank statistics (LRF) has been proposed in this paper. Firstly, based on the flight characteristics of aerospace vehicles, an accurate gravity calculation model has been established to improve the accuracy of system modelling. Then, the state equation and measurement equation of integrated navigation system have been established. In combination with the rank filter algorithm as well as the determined weights, sampling points are calculated and nonlinearly propagated through the transition matrix to achieve an accurate estimation about the predicted values of the state quantities and measurement quantities and the covariance matrix. In turn, it simulates the probability distribution of the system state effectively. Therefore, when the system random noise probability distribution of the aerospace vehicle does not meet the Gaussian distribution due to various interference factors in the actual flight process, the algorithm can simulate the probability distribution of the actual system to the greatest extent, to improve the accuracy of the integrated navigation system and enhance the reliability of the navigation system ultimately.

The Rayleigh Problem (Random Flights) is Everywhere Redux

The phase noise problem (or Rayleigh problem) occurs in all aspects of radar. It is an effect that a radar engineer or physicist always has to take into account as part of a design or in an attempt to characterize the physics of a problem such as reverberation. Normally, the mathematical difficulties of phase noise characterization are avoided by assuming the phase noise probability distribution function (PDF) is uniformly distributed, and the Central Limit Theorem (CLT) is invoked to argue that the superposition of relatively few random components obey the CLT and hence the superposition can be treated as a normal distribution. By formalizing the characterization of phase noise for an individual random variable, the summation of identically distributed random variables is the product of multiple characteristic functions (CF). The product of the CFs for phase noise has a CF that can be analyzed to understand the limitations CLT when applied to phase noise.

An improved sparse identification of nonlinear dynamics with Akaike information criterion and group sparsity.

A crucial challenge encountered in diverse areas of engineering applications involves speculating the governing equations based upon partial observations. On this basis, a variant of the sparse identification of nonlinear dynamics (SINDy) algorithm is developed. First, the Akaike information criterion (AIC) is integrated to enforce model selection by hierarchically ranking the most informative model from several manageable candidate models. This integration avoids restricting the number of candidate models, which is a disadvantage of the traditional methods for model selection. The subsequent procedure expands the structure of dynamics from ordinary differential equations (ODEs) to partial differential equations (PDEs), while group sparsity is employed to identify the nonconstant coefficients of partial differential equations. Of practical consideration within an integrated frame is data processing, which tends to treat noise separate from signals and tends to parametrize the noise probability distribution. In particular, the coefficients of a species of canonical ODEs and PDEs, such as the Van der Pol, Rössler, Burgers’ and Kuramoto–Sivashinsky equations, can be identified correctly with the introduction of noise. Furthermore, except for normal noise, the proposed approach is able to capture the distribution of uniform noise. In accordance with the results of the experiments, the computational speed is markedly advanced and possesses robustness.

Асимптотически робастный инвариантный алгоритм демодуляции DPSK-сигналов при воздействии внешних помех с априорно неопределенными параметрами

The study aims at synthesizing an asymptotically robust invariant demodulation algorithm for DPSK signals with arbitrary modulation multiplicity used in aircraft communication systems and observed against the background of noise with an unknown probability distribution and a noise complex with a priori uncertain parameters. The analysis of the efficiency of the proposed algorithm is carried out by a computer simulation modeling. The algorithm implies automatic detection and rejection of narrowband pulse noise. This type of interference is typical for radio-navigation systems. It has been shown that the narrowband pulse noise should be eliminated if the signal-to-interference ratio becomes less than -10 dB. The use of the asymptotic robustness principle ensures the stability of the algorithm characteristics to changes in the character of the noise probability distribution density. It was found that the joint application of narrowband pulse interference elimination and the asymptotically robust approach provides reliable demodulation performance both when receiving against the background Gaussian noise and under the action of pulse interference and noise with "heavy tails". In addition, it has been shown that the use of signals with differential phase modulation, direct sequence spread spectrum, and the sidelobe levels of less than 10% effectively suppresses interference caused by multipath signal propagation.

Feature-guided regularization parameter selection in sparse de-noising for fault diagnosis

Using the sparse and redundant representation model to de-noise vibration signals is an effective method for mechanical fault diagnosis. The selection of the regularization parameter in the sparse de-noising algorithm plays a vital role in reconstructing fault features. The current choices, however, are primarily based on fixed-form parameters derived under the assumption of additive white noise or based on the “trial and error” method. As a result, the extracted de-noised signals often fail to show fault features. To solve this difficulty, a self-adaptive regularization parameter selection strategy is proposed, which directly measures the significance of fault features in sparse de-noised signals. Firstly, the entire solution path is obtained by the computationally efficient least angle regression (LARS) algorithm. Besides, a feature presence probability index (FP) is well designed to measure the significance of fault features in the reconstructed signal envelope demodulation spectrum. Accordingly, with the help of the maximal FP indicator, the optimal regularization parameter and LARS solution is determined. The proposed method is not limited by noise probability distributions; therefore, it shows the superiority of extracting fault features in both the simulation and experimental data analysis.

On the interference arising from random spatial fields of interferers utilizing multiple subcarriers

Effective symbol detection, channel estimation and decoding of channel codes require an accurate characterization of the noise probability distribution. In many systems, notably the internet of things, noise is largely in the form of interference, arising from a massive number of simultaneous transmissions from uncoordinated devices. Obtaining the probability distribution of the interference is a challenging problem due to the use of non-orthogonal multiple access schemes over several subcarriers (leading to multivariate statistical models) and the heavy-tailed nature of the interference due to the random locations of devices. In this paper, we derive a novel tractable characterization of the interference probability distribution based on an application of Sklar’s theorem to develop a combination of alpha-stable and t-copula dependence models. We demonstrate that this formulation produces an accurate statistical modeling framework that admits efficient parameter estimation methods. As an illustration of the utility of our models, we develop a simple-to-implement nonlinear receiver when a binary signal is transmitted over all subcarriers by the desired transmitter, which is effective in a range of scenarios and can significantly outperform existing approaches.

Automatic differentiation to simultaneously identify nonlinear dynamics and extract noise probability distributions from data

The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from time-series data. As with all system identification methods, noisy measurements compromise the accuracy and robustness of the model discovery procedure. In this work we develop a variant of the SINDy algorithm that integrates automatic differentiation and recent time-stepping constrained motivated by Rudy et al (2019 J. Computat. Phys. 396 483–506) for simultaneously (1) denoising the data, (2) learning and parametrizing the noise probability distribution, and (3) identifying the underlying parsimonious dynamical system responsible for generating the time-series data. Thus within an integrated optimization framework, noise can be separated from signal, resulting in an architecture that is approximately twice as robust to noise as state-of-the-art methods, handling as much as 40% noise on a given time-series signal and explicitly parametrizing the noise probability distribution. We demonstrate this approach on several numerical examples, from Lotka-Volterra models to the spatio-temporal Lorenz 96 model. Further, we show the method can learn a diversity of probability distributions for the measurement noise, including Gaussian, uniform, Gamma, and Rayleigh distributions.

Understanding and planning shared micro-mobility

The prediction and evaluation of expressway traffic noise is essential work of environmental management. A Monte Carlo simulation method for instantaneous sound levels is introduced according to the characteristics of free-flow traffic on expressways. The sound power levels of light and heavy vehicles are measured by field experiments, and a probability model of vehicle noise emission is established. Noise under different traffic volumes and distances is simulated by the Monte Carlo method. A probability distribution model of traffic noise with traffic volume and distance as parameters is given. A comparison of the calculated results and measured data shows that the proposed model can effectively predict the probability distribution of traffic noise and can be used to predict common traffic noise indicators. The prediction errors are less than 3 dB(A) for Leq, L10, L50, and L90; less than 1.3 dB(A) for σ; and less than 13 dB(A) for TNI.

A probability distribution prediction method for expressway traffic noise

The prediction and evaluation of expressway traffic noise is essential work of environmental management. A Monte Carlo simulation method for instantaneous sound levels is introduced according to the characteristics of free-flow traffic on expressways. The sound power levels of light and heavy vehicles are measured by field experiments, and a probability model of vehicle noise emission is established. Noise under different traffic volumes and distances is simulated by the Monte Carlo method. A probability distribution model of traffic noise with traffic volume and distance as parameters is given. A comparison of the calculated results and measured data shows that the proposed model can effectively predict the probability distribution of traffic noise and can be used to predict common traffic noise indicators. The prediction errors are less than 3 dB(A) for Leq, L10, L50, and L90; less than 1.3 dB(A) for σ; and less than 13 dB(A) for TNI.

Point-kinetics neutron noise modeling and analysis via probabilistic finite state automata

This paper addresses two issues for safety & performance analysis of nuclear reactors; these issues are: (i) Modeling of the neutron noise process, which is constructed as stochastic differential equations by augmenting deterministic dynamic models of point kinetics, thermal hydraulics, and mechanical vibrations in the reactor core, and (ii) Time-series analysis of nuclear reactor internals for early-stage anomaly detection by making use of the neutron noise model. The model is used to generate an ensemble of time series of neutron noise under both normal and anomalous operating conditions, where an anomaly in the postulated probability distribution of neutron noise is caused by abnormal vibration of the fuel assembly. A symbolic time series analysis (STSA) tool, called probabilisitc finite state automata (PFSA), has been selected to detect the anomalies, if any. The PFSA method symbolizes a time-series and then encodes the resulting symbol string into a state transition probability matrix, which is both stochastic and ergodic by construction. The discrimination function for anomaly detection is built upon the residual error of the principal (left) eigenvector of the state transition probability matrix, which is also the state probability vector of the PFSA. The accuracy of the proposed analysis and its capability for online anomaly detection is demonstrated by simulation on a low-order dynamic model of a 2,500 MWt PWR of the Three-Mile-Island type.

Field PMU Test and Calibration Method– Part I: General Framework and Algorithms for PMU Calibrator

Laboratory testing of phasor measurement units (PMUs) guarantees their performance under laboratory conditions. However, many factors may cause PMU measurement problems in actual power systems, resulting in the malfunction of PMU-based applications. Therefore, field PMUs need to be tested and calibrated to ensure their performance and data quality. In this paper (Part I), a general framework for the field PMU test and calibration in different scenarios is proposed. This framework consists of a PMU calibrator and an analysis center, where the PMU calibrator provides the reference values for PMU error analysis. Two steps are implemented to ensure the calibrator accuracy for complex field signals: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\textcircled{1}$</tex> by analyzing the frequency-domain probability distribution of random noise, a Fourier-transform-based signal denoising method is proposed to improve the anti-interference capability of the PMU calibrator; and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\textcircled{2}$</tex> a general synchrophasor estimation method based on complex bandpass filters is presented for accurate synchrophasor estimations in multiple scenarios. Simulation and experimental test results demonstrate that the PMU calibrator has a higher accuracy than that of other calibrator algorithms and is suitable for field PMU test. The analysis center for evaluating the performance of field PMUs and the applications of the proposed field PMU test system are provided in detail in Part II of the next-step research.

Learning Data Consistency and its Application to Dynamic MR Imaging.

Magnetic resonance (MR) image reconstruction from undersampled k-space data can be formulated as a minimization problem involving data consistency and image prior. Existing deep learning (DL)-based methods for MR reconstruction employ deep networks to exploit the prior information and integrate the prior knowledge into the reconstruction under the explicit constraint of data consistency, without considering the real distribution of the noise. In this work, we propose a new DL-based approach termed Learned DC that implicitly learns the data consistency with deep networks, corresponding to the actual probability distribution of system noise. The data consistency term and the prior knowledge are both embedded in the weights of the networks, which provides an utterly implicit manner of learning reconstruction model. We evaluated the proposed approach with highly undersampled dynamic data, including the dynamic cardiac cine data with up to 24-fold acceleration and dynamic rectum data with the acceleration factor equal to the number of phases. Experimental results demonstrate the superior performance of the Learned DC both quantitatively and qualitatively than the state-of-the-art.

Scattering Model-Based Frequency-Hopping RCS Reconstruction Using SPICE Methods

RCS reconstruction is an important way to reduce the measurement time in anechoic chambers and expand the radar original data, which can solve the problems of data scarcity and a high measurement cost. The greedy pursuit, convex relaxation, and sparse Bayesian learning-based sparse recovery methods can be used for parameter estimation. However, these sparse recovery methods either have problems in solving accuracy or selecting auxiliary parameters, or need to determine the probability distribution of noise in advance. To solve these problems, a non-parametric Sparse Iterative Covariance Estimation (SPICE) algorithm with global convergence property based on the sparse Geometrical Theory of Diffraction (GTD) model (GTD–SPICE) is employed for the first time for RCS reconstruction. Furthermore, an improved coarse-to-fine two-stage SPICE method (DE–GTD–SPICE) based on the Damped Exponential (DE) model and the GTD model (DE–GTD) is proposed to reduce the computational cost. Experimental results show that both the GTD–SPICE method and the DE–GTD–SPICE method are reliable and effective for RCS reconstruction. Specifically, the DE–GTD–SPICE method has a shorter computational time.

Automated Data-Driven Selection of the Hyperparameters for Total-Variation-Based Texture Segmentation

Penalized least squares are widely used in signal and image processing. Yet, it suffers from a major limitation since it requires fine-tuning of the regularization parameters. Under assumptions on the noise probability distribution, Stein-based approaches provide unbiased estimator of the quadratic risk. The Generalized Stein Unbiased Risk Estimator is revisited to handle correlated Gaussian noise without requiring to invert the covariance matrix. Then, in order to avoid expansive grid search, it is necessary to design algorithmic scheme minimizing the quadratic risk with respect to regularization parameters. This work extends the Stein’s Unbiased GrAdient estimator of the Risk of Deledalle et al. (SIAM J Imaging Sci 7(4):2448–2487, 2014) to the case of correlated Gaussian noise, deriving a general automatic tuning of regularization parameters. First, the theoretical asymptotic unbiasedness of the gradient estimator is demonstrated in the case of general correlated Gaussian noise. Then, the proposed parameter selection strategy is particularized to fractal texture segmentation, where problem formulation naturally entails inter-scale and spatially correlated noise. Numerical assessment is provided, as well as discussion of the practical issues.

Research on seismic wave first arrival Picking Based on improved U-Net

For the current problem of low accuracy of seismic wave phase pickup, this paper proposes a method based on the improved U-Net seismic wave P-wave and S-wave first-to-arrival pickup. Firstly, in order to reduce the impact of pre-processing operations such as filtering, the 20,000 three-component seismic waveform data will be normalized as input. Secondly, in order to reduce the loss of information during the seismic waveform extraction and increase the amount of information of effective features at the starting point, the Residual Unit is added to the encoder part of U-Net only, instead of adding it to the decoder part. In order to reduce the loss of high frequency information of seismic waveform, convolution operation is used instead of pooling operation. Finally, the probability distributions of P-wave, S-wave and noise are used as the output. The results show that the accuracy of the first-to-arrival pickup of P-wave is 93% and the accuracy of the first-to-arrival pickup of S-wave is 90% of the test set. The improved U-Net increased 30.9% and 6.2% in P-wave accuracy, 7.6% and 2.8% in S-wave accuracy, 39.6% and 4.0% in the P-wave recall, and 41.5% and 4.7% in the S-wave recall, respectively, compared with the conventional STA/LTA and U-Net. The improved U-Net outperforms the other two models in both evaluation metrics of recall and accuracy. The research results of this paper are of great practical significance in the localization of earthquakes, the interpretation of the earthquake gestation mechanism, and the prevention and mitigation of earthquakes.

Kepler Data Analysis: Non-Gaussian Noise and Fourier Gaussian Process Analysis of Stellar Variability

Abstract We develop a statistical analysis model of Kepler stellar flux data in the presence of planet transits, non-Gaussian noise, and stellar variability. We first develop a model for the Kepler noise probability distribution in the presence of outliers, which make the noise probability distribution non-Gaussian. We develop a signal likelihood analysis based on this probability distribution, in which we model the signal as a sum of the star variability and planetary transits. We argue that these components need to be modeled together if optimal signal is to be extracted from the data. For the stellar variability model we develop an optimal Gaussian process analysis using a Fourier-based Wiener filter approach, where the power spectrum is non-parametric and learned from the data. We develop high dimensional optimization of the objective function, where we jointly optimize all the model parameters, including thousands of star variability modes, and planet transit parameters. We apply the method to Kepler-90 data and show that it gives a better match to the stellar variability than the existing methods, and robustly handles noise outliers. As a consequence, the planet radii have a higher value than what the existing methods give, including splines and celerite.

First Arrival Time Identification Using Transfer Learning With Continuous Wavelet Transform Feature Images

In our work, the deep learning technique has been used to develop an automatic method for identifying the first arrival times of seismic waves. This method introduces transfer learning to train a deep neural network, given a limited number of continuous wavelet transform (CWT) feature images as input. The application of the CWT for feature extraction, aimed at detecting abrupt changes in the amplitude, phase, and frequency produced by first arrivals as a whole rather than any single characteristic, provides the most informative images. First, we apply the CWT to each seismic trace to obtain the CWT feature images and split them into a set of subimages. Then, a pretrained convolutional neural network (CNN) is fine-tuned with limited labeled subimages. The resulting model can be used to predict probability distributions of noise, first-break, and post first-break. Finally, the first arrival times are extracted from the peaks of the probability distributions. We have tested the performance of the method using vibroseis, dynamite, and air gun shot records, which include various types of seismic waves and noise. More accurate and robust results can be obtained with the proposed method compared with the short-time and long-time average (STA/LTA) algorithm and the adaptive multiband picking algorithm (AMPA).