Types Of Random Noise Research Articles

LINEAR FRACTAL INTERPOLATION FUNCTION FOR DATA SET WITH RANDOM NOISE

Fractal interpolation is a contemporary technique to approximate numerous scientific experiments and natural phenomena. For data sets in [Formula: see text], the simplest and easy-to-handle fractal interpolation functions (FIFs) are linear. In this study, we estimate probability distributions of linear FIFs for data sets with various types of random noise. In order to evaluate the distribution of any linear FIF associated with a prescribed data set having Student’s t-distributed noise, we develop a technique to approximate the distribution of a linear combination of independent generalized Student’s t-distributed random variables. In addition, we provide some statistical properties and numerical approximations of these linear fractal functions.

Wavelet Based Denoising of the Simulated Chest Wall Motion Detected by SFCW Radar

Low power and compact radars have emerged with the development of electronic technology. This has enabled the use of radars in indoor environments and the realization of many applications. The detection, tracking and classification of human movements by radar are among the remarkable applications. Contactless detection of human vital signs improves the quality of life of patients being kept under observation and facilitates the work of experts. In this study, it was simulated that the movement of the chest wall was modeled and detected by the SFCW radar. Gaussian, Rician and uniformly distributed random noise types were added to the modeled chest motion at different levels. The noisy signal obtained at the receiver is denoised with different mother wavelet functions and the performances of these functions are presented comparatively.

Integration of weighted LS-SVM and manifold learning for fuzzy modeling

Abstract In this paper, a robust fuzzy modeling method is proposed for strongly nonlinear systems in the presence of noise and/or outliers. The proposed method integrates the advantages of the fuzzy structure, the manifold learning, and the weighted least squares support vector machine (LS-SVM). First, the Gustafson–Kessel clustering algorithm (GKCA) is applied to split the training data set into several subsets to determine the fuzzy rules and premise parameters. Then, a new objective function is constructed based on the fuzzy structure, the weighted LS-SVM, and the manifold regularization, which takes into account robustness and the intrinsic geometry of the data. A solving method is further developed, from which the fuzzy model is achieved and can effectively approximate a nonlinear system with various types of random noise. The proposed method is applied to an artificial case as well as a practical hydraulic actuator, demonstrating its effectiveness in modeling of a nonlinear system even under noise.

Angle measurement uncertainty statistical distribution of pulsed laser quadrant photodetector

As a positionsensitive detector, laser quadrant photodetector(QPD) is widely used in the areas such as laser guidance, laser radar and space optical communication. In the echoed laser pulse detection mode, the laser pulse signal arrived at the QPD photosensitive surface is changed in pulse amplitude, pulse width and pulse waveform due to the influences of target characteristic, atmospheric transmission and other complex factors. In addition, there are random noises in QPD itself and the signal processing circuit. These factors will have an uncertainty effect on the angle measurement accuracy of the QPD. However, the study on the statistical distribution of digital angle measurement of pulsed laser QPD has not been carried out so far. To investigate this angle measurement statistical distribution, the channel of laser angle measurement circuit and the echoed laser spot on QPD photosensitive surface should be modeled first. A measurable signal model in one quadrant of QPD processing circuit channel is established based on the type of random noise and the type of desired ideal signal. The random noise model is considered to be a Gaussian distribution, and the ideal laser pulse signal is considered to have the Gaussian or inverted parabolic distribution in the time domain. Taking into account the QPD symmetry, the statistical distributions of angle measurement value αy for five different spot centers are calculated by the Monte Carlo simulation method within the range θ0∈[0,π/4], under the conditions of different signal distribution types in the time domain, different total peak powers of the spots, different ideal signal widths at half maximum, and different standard deviations of equivalent noise voltage probability density. Simulation results show that the statistical distribution of the measured angle αy value is a normal distribution, and is influenced by the above-mentioned conditions, especially by the signaltonoise ratio in one quadrant. QPD possesses higher angular accuracy as the spot center is closer to the axis center. While the spot center is not closer to the axis center, the mean of statistical distribution of the QPD measurement angle αy is always less than the ideal angle measurement value. Therefore, in order to improve the angle measurement accuracy of the pulsed laser QPD for digital purpose, laser pulse transmit power should be increased, or the noise of each circuit channel of QPD should be reduced, or the laser pulse width should be increased by modulating appropriately.

Reconstructing time series and their uncertainty from observations with universal noise

AbstractA new approach is presented for the reconstruction of time series and other (y,x) functions from observables with any type of stochastic noise. In particular, noise may exist in both dependent and independent variables, i.e., y and x, or t, and may even be correlated between these variables. This situation occurs in many areas of the geosciences when the independent time variable is itself the result of a measurement process, such as in paleo– sea level estimation. Uncertainty in the recovered time series is quantified in probabilistic terms using Bayesian changepoint modeling. The main contribution of the paper is the derivation of a new form of integrated likelihood function which can measure the data fit for a curve to (y,t) observables contaminated by any type of random noise. Closed form expressions are found for the special case of correlated Gaussian data noise and curves built from the sum of piecewise linear polynomials. The technique is illustrated by estimating relative sea level variations, over the last five glacial cycles, from a data set of 1928 δ18O measurements. Comparisons are also made with other techniques including those that assume an error free “independent” variable. Experiments illustrate several benefits of accounting for timing errors. These include allowing rigorous uncertainty information of both time‐dependent signals and their gradients. Derivatives of the integrated likelihood function are also given, which allow implementation of likelihood maximization. The new likelihood function better reflects real errors in data and can improve recovery of the estimated time series.

Dempster–Shafer theory-based robust least squares support vector machine for stochastic modelling

Noise can be produced from various types of sources with different spectral distributions. This often causes the least squares support vector machine (LS-SVM) to be less effective since the LS-SVM is sensitive to noisy data. In this work, a Dempster–Shafer (D–S) theory-based robust LS-SVM is proposed, which has a more reliable modelling performance under various noise regimes. A distributed LS-SVM is first developed to construct the evidence data set. Fuzzy clustering is then used to construct an evidence base from the data. D–S theory is further used to fuse different pieces of evidence to derive the parameters for the construction of a robust LS-SVM. This robust model can represent the original system well even in the presence of different types of random noise. Case studies are presented to demonstrate the effectiveness of the proposed LS-SVM approach.

Statistical errors in interferometry with least-squares algorithms and large step sizes

This paper investigates statistical errors in determining peak positions of interference fringes with the least-squares algorithms when the phase-shifting step sizes are 2π/3, π/2, and 2π/5. Two types of random noises are considered, which are called intensity noise and position noise. With these large step sizes, the statistical errors obtained from simulated measurements are compared with the theoretical results published in Ref. [11]. The effects of the wavelength and the amplitude on the statistical errors are investigated. A discrepancy between the simulation results and the theoretical results has been observed, that is, when the step size was π/2, the statistical errors caused by position noise have shown strong peak-position dependence, which cannot be explained by Eq. (16) given in Ref. [11]. A new equation is given to account for the simulation results.

Random errors for the measurement of central positions in white-light interferometry with the least-squares method.

This paper analyzes the effect of random noise on the measurement of central positions of white-light correlograms with the least-squares method. Measurements of two types of central positions, the central position of the envelope (CPE) and the central position of the central fringe (CPCF), are investigated. Two types of random noise, intensity noise and position noise, are considered. Analytic expressions for random error due to intensity noise (REIN) and random error due to position noise (REPN) are derived. The theoretical results are compared with the random errors estimated from computer simulations. Random errors of CPE measurement are compared with those of CPCF measurement. Relationships are investigated between the random errors and the wavelength of the light source. The REPN of CPCF measurement has been found to be independent of the wavelength of the light source and the amplitude of the central fringe.

Random errors in interferometry with the least-squares method

This investigation analyzes random errors in interferometric surface profilers using the least-squares method when random noises are present. Two types of random noise are considered here: intensity noise and position noise. Two formulas have been derived for estimating the standard deviations of the surface height measurements: one is for estimating the standard deviation when only intensity noise is present, and the other is for estimating the standard deviation when only position noise is present. Measurements on simulated noisy interferometric data have been performed, and standard deviations of the simulated measurements have been compared with those theoretically derived. The relationships have also been discussed between random error and the wavelength of the light source and between random error and the amplitude of the interference fringe.

Stability domains in flow–structure interaction and influence of random noises

The article treats the general aeroelastic stability of slender engineering structures with regards to parametric and additive noises. Conditions of a dynamic stability loss and subsequent detailed analysis of stability domains are significantly influenced by random noises accompanying nonconservative and gyroscopic forces. The final influence of random forces onto the form of the stability domain can be both negative or positive. Response properties of a system located on a stability boundary together with tendencies in its neighborhood due to both types of random noises are presented and interpreted from a physical point of view. Theoretical analysis motivated by wind tunnel tests and results of experimental investigation are presented. They can be used for explanations of several effects observed so far experimentally but remaining without theoretical explanation until now.

Image discrimination models predict detection in fixed but not random noise

By means of a two-interval forced-choice procedure, contrast detection thresholds for an aircraft positioned on a simulated airport runway scene were measured with fixed and random white-noise masks. The term fixed noise refers to a constant, or unchanging, noise pattern for each stimulus presentation. The random noise was either the same or different in the two intervals. Contrary to simple image discrimination model predictions, the same random noise condition produced greater masking than the fixed noise. This suggests that observers seem unable to hold a new noisy image for comparison. Also, performance appeared limited by internal process variability rather than by external noise variability, since similar masking was obtained for both random noise types.

Search for finite dimensional attractors in atmospheric turbulence

The question is investigated whether the dynamics of turbulent wind fields in the atmospheric boundary layer can be satisfactorily described by a low-dimensional deterministic system. Special emphasis is laid on the detection of a possibly existing, underlying strange attractor. Fast response wind measurements of an ultrasonic anemometer with a sampling rate of 21 Hz were carried out over periods of several days in the near surface boundary layer. The correlation dimension of the resulting time series, several million data points long, is estimated by means of the Grassberger-Procaccia algorithm. No sign of a low dimensional attractor can be detected. By comparison with different types of random noise, the existence of an attractor with dimension lower than six can be excluded in the present data sets.

Finite correlation dimension for stochastic systems with power-law spectra

We discuss a counter-example to the traditional view that stochastic processes lead to a non-convergence of the correlation dimension in computed or measured time series. Specifically we show that a simple class of “colored” random noises characterized by a power-law power spectrum have a finite and predictable value for the correlation dimension. These results have implications on the experimental study of deterministic chaos as they indicate that the soie observation of a finite fractal dimension from the analysis of a time series is not sufficient to infer the presence of a strange attractor in the system dynamics. We demonstrate that the types of random noises considered herein may be given an interpretation in terms of their fractal properties. The consequent exploitation of the non-Gaussian behavior of these random noises leads us to the introduction of a new time series analysis method which we call multivariate scaling analysis. We apply this approach to characterize several “global” properties of random noise.

Learning from noisy examples

The basic question addressed in this paper is: how can a learning algorithm cope with incorrect training examples? Specifically, how can algorithms that produce an “approximately correct” identification with “high probability” for reliable data be adapted to handle noisy data? We show that when the teacher may make independent random errors in classifying the example data, the strategy of selecting the most consistent rule for the sample is sufficient, and usually requires a feasibly small number of examples, provided noise affects less than half the examples on average. In this setting we are able to estimate the rate of noise using only the knowledge that the rate is less than one half. The basic ideas extend to other types of random noise as well. We also show that the search problem associated with this strategy is intractable in general. However, for particular classes of rules the target rule may be efficiently identified if we use techniques specific to that class. For an important class of formulas—the k-CNF formulas studied by Valiant—we present a polynomial-time algorithm that identifies concepts in this form when the rate of classification errors is less than one half.

Learning From Noisy Examples

The basic question addressed in this paper is: how can a learning algorithm cope with incorrect training examples? Specifically, how can algorithms that produce an “approximately correct” identification with “high probability” for reliable data be adapted to handle noisy data? We show that when the teacher may make independent random errors in classifying the example data, the strategy of selecting the most consistent rule for the sample is sufficient, and usually requires a feasibly small number of examples, provided noise affects less than half the examples on average. In this setting we are able to estimate the rate of noise using only the knowledge that the rate is less than one half. The basic ideas extend to other types of random noise as well. We also show that the search problem associated with this strategy is intractable in general. However, for particular classes of rules the target rule may be efficiently identified if we use techniques specific to that class. For an important class of formulas – the k-CNF formulas studied by Valiant – we present a polynomial-time algorithm that identifies concepts in this form when the rate of classification errors is less than one half.