Random White Noise Research Articles

Development, validation, and application of a generic image-based noise addition method for simulating reduced dose computed tomography images.

Major efforts in computed tomography (CT) have been focused on reducing radiation dose to patients while maintaining adequate diagnostic quality. To that end, research tools have been developed to simulate reduced-dose images via either image-based or projection-based methods. The former is limited to fully capturing realistic texture, streak, and non-stationary characteristics of reduced dose, while the latter is impractical clinically. To develop and validate an image-based noise addition method that accounts for such attributes while being practical in clinical settings. A noise addition method was developed to add realistic noise in the image domain. The method first estimates the noise power spectrum (NPS) of CT images, which are also forward-projected to form synthetic projections. The projection data are supplemented with random white noise proportional to their attenuation values. The noise sinogram is then back-projected onto the image, filtered by the NPS, and scaled according to the desired dose reduction level. The tool was evaluated using both phantom images and patient data. The phantom images were acquired using a multi-sized image quality phantom (Mercury Phantom 3.0, Duke University), and a thorax anthropomorphic phantom (Lungman Phantom, Kyoto Kagaku) at different dose levels and reconstruction settings. The patient images consisted of two dose levels of various CT examinations and reconstruction settings. The simulated and real reduced-dose images were compared in terms of the noise magnitude and texture (i.e., NPS average frequency, NPS-fav). The utility of this methodology was also assessed for routine clinical use for CT protocol review. For the phantom images, the percent errors in the noise magnitude between the simulated images and the actual images of the Mercury Phantom and anthropomorphic phantom images were 3.34% and 3.50%, respectively. The difference in fav was 0.07mm-1 for the Mercury Phantom and 0.06mm-1 for the anthropomorphic phantom between the simulated and actual images. The average noise magnitude percent error between the simulated and actual patient images was 4.61% with noise texture judged to be visually comparable with some kernel dependencies. When implemented clinically, the tool proved practical to simplify the process of estimating radiation dose reduction for CT protocols, resulting in a 50% dose reduction of our multiple myeloma protocol. The method generated simulated CT images with realistic noise properties similar to images acquired at the same radiation exposure without needing access to raw projection data.

Transient shear banding during startup flow: Insights from nonlinear simulations

We study the dynamics of shear startup of Johnson–Segalman and non-stretching Rolie-Poly models using nonlinear simulations. We consider startup to shear rates in both monotonic and nonmonotonic regions of the constitutive curve. For the Johnson–Segalman model, which exhibits a shear stress overshoot during startup, our nonlinear simulations show that transient shear banding is absent regardless of whether the startup shear rate is in the monotonic or nonmonotonic regions of the constitutive curve. In the latter case, while there is clearly an inhomogeneity en route to the banded state, the magnitude of the extent of banding is not substantially large compared to that of the eventual banded state. Marked inhomogeneity in the velocity profile is predicted for the nonstretching Rolie-Poly model only if the solvent to solution viscosity ratio is smaller than O(10−3), but its occurrence does not appear to have any correlation with the stress overshoot during startup. The comparison of the present nonlinear results with the results obtained within the framework of linearized dynamics show that nonlinearities have a stabilizing effect and mitigate the divergence of perturbations (as predicted within the linearized dynamics) during shear startup. We argue that the neglect of inertia in the nonlinear simulations is not self-consistent if the solvent to solution viscosity ratio is very small, and that inertial effects need to be included in order to obtain physically realistic results. Furthermore, our study demonstrates a pronounced sensitivity of shear startup in the nonstretching Rolie-Poly model when a random white noise with zero mean is used as the initial perturbation. Finally, this study clearly emphasizes that stress overshoot during shear startup does not always result in transient shear banding, notwithstanding whether the shear rates is in the monotonic or nonmonotonic part of the constitutive curve.

Asymptotically autonomous robustness of random attractors for the stochastic wave lattice equations with random viscosity

In this paper, we focus on the asymptotic behavior of solutions to the non-autonomous stochastic wave lattice systems with random viscosity and multiplicative white noise. Under proper conditions, we first prove the existence and uniqueness of the pullback random attractors and then show their backward compactness in a weighted space. Finally, we establish the asymptotically autonomous robustness of pullback random attractors when the nonlinearity is bounded and the time-dependent forcing term converges to the time-independent counterpart.

Sensitivity of GNSS to vertical land motion over Europe: effects of geophysical loadings and common-mode errors

We perform a statistical sensitivity analysis on a parametric fit to vertical daily displacement time series of 244 European Permanent GNSS stations, with a focus on linear vertical land motion (VLM), i.e., station velocity. We compare two independent corrections to the raw (uncorrected) observed displacements. The first correction is physical and accounts for non-tidal atmospheric, non-tidal oceanic and hydrological loading displacements, while the second approach is an empirical correction for the common-mode errors. For the uncorrected case, we show that combining power-law and white noise stochastic models with autoregressive models yields adequate noise approximations. With this as a realistic baseline, we report improvement rates of about 14% to 24% in station velocity sensitivity, after corrections are applied. We analyze the choice of the stochastic models in detail and outline potential discrepancies between the GNSS-observed displacements and those predicted by the loading models. Furthermore, we apply restricted maximum likelihood estimation (RMLE), to remove low-frequency noise biases, which yields more reliable velocity uncertainty estimates. RMLE reveals that for a number of stations noise is best modeled by a combination of random walk, flicker noise, and white noise. The sensitivity analysis yields minimum detectable VLM parameters (linear velocities, seasonal periodic motions, and offsets), which are of interest for geophysical applications of GNSS, such as tectonic or hydrological studies.

Prospect and sustainability prediction of China's new energy vehicles sales considering temporal and spatial dimensions

The development prospect and sustainability of new energy vehicles (NEVs) are facing numerous challenges under the coupling influence of various factors, which has become a major strategic issue in the automotive industry research within China. Establishing a prediction method to forecast the development trends of NEVs under the complex conditions is of great significance. This paper comprehensively addresses the relevant factors influencing the sales of NEVs over temporal depth and spatial breadth, including random white noise and lag effect resulting from lag operators of influencing factors. A multivariate forecasting approach utilizing the ARIMA model and its optimized model, alongside the GBDT model were adopted to forecast NEV sales in China. The findings demonstrate that: 1) NEVs have exhibited a trend of rapid growth, but are still susceptible to random interference and lag effects caused by influencing factors. Key technology breakthroughs, accessibility of charging infrastructure, and national policy support remain as primary drivers of NEVs development; 2) The ARIM–IO–LSTM model achieved high prediction accuracy with a goodness-of-fit R2 exceeding 90%, outperforming the ARIMA and ARIMA-IO models by 23.586% and 20.790%, respectively, while the ARIMA-IO model improved accuracy by 5.126% compared to ARIMA. The method of model combination and outlier incorporation have proved to be practical solutions for strengthening model accuracy. 3) In the next 3–5 years, the NEV industry will enter a stage characterized by steady progress with an upward trend. Adapting the intensity, scope, and direction of policy support, coupled with achieving technological breakthroughs and enhancing infrastructure construction, are essential for sustaining industrial development and attaining desired objectives.

A new automatic geo-electric self-potential imaging technique for diverse sustainable development scenarios

This study introduces a rapid and efficient inversion algorithm designed for the interpretation of self-potential responses originating from mineralized and ore sources and hydrothermal activity, specifically addressing spherical, vertical, and horizontal cylindrical structures. The algorithm leverages local wavenumber and correlation imaging techniques to enhance accuracy in modeling. The correlation factor (Cf value) is crucial in this approach, calculated as the correlation between the local wavenumber of the measured self-potential field and that of the computed field. The algorithm identifies the maximum correlation Cf value (CF-max) as indicative of the optimal true model parameters. To validate the proposed algorithm, it was applied to three theoretical examples—one with contamination from regional background and another with multiple sources with and without different types of noises (random Gaussian and white Gaussian noises). Additionally, the approach was tested on three distinct real field cases related to mining, ore investigation and hydrothermal activity in India, Germany and USA. Through a comprehensive analysis of results from theoretical and real-world scenarios, including comparisons with different available data and literature information, the study concludes that the method is effective, applicable to multiple sources, accurate, and does not necessitate prior knowledge of the source shape. This algorithm presents a promising advancement in the field of self-potential interpretation for mineral exploration and geothermal exploration.

The Accuracy of Frequency Estimation of Structure Vibration under Ambient Excitation: Problems, Causes, and Methods

Accurate identification of building structure frequencies forms the basis for damage detection. The structural dynamic response signal, under ambient excitation, can be transformed into a superposition of multiple single-frequency exponentially damped sinusoids combined with random white noise. However, the peak power spectrum of the response signal tends to exhibit line splitting, compromising the precision of frequency identification. This study examines the accuracy characteristics of the single-frequency free damping vibration signal (SFFDVS) and derives the Cramer–Rao lower bound for the frequency estimator. It thoroughly analyzes the factors influencing the accuracy of SFFDVS frequency identification. The study reveals that the primary cause of spectral line splitting is the random delay inherent in SFFDVS. Based on the maximum likelihood method (MLM), this research introduces the MLM algorithm for SFFDVS and provides a simulation analysis. The findings indicate that the MLM estimation algorithm for frequency parameters effectively addresses spectral line splitting and offers robust noise resistance and recognition accuracy.

Vibration reduction performance for the novel grounded inerter-based dynamic vibration absorber controlling a primary structure under random excitation

This paper investigates the control performance of a novel grounded inerter-based dynamic vibration absorber (GI-DVA) for random vibration reduction. First, the dynamics equations of the coupled system are written and the transfer function is obtained based on the Laplace transform. Then, assuming that the primary structure is under random white noise excitation, the displacement variance of the primary structure is calculated based on the exact definition of the H2 norm, by solving the Lyapunov equation. By imposing that the partial derivatives of the response variance of the primary structure with respect to the system parameters are simultaneously equal to zero, the optimum design values of the H2 optimized GI-DVA were derived numerically for given different mass ratio. It can be found that the optimal design parameters as the inerter-to-mass ratio, the stiffness ratio and the damping ratio increase, while the frequency ratio decreases with the increase in the mass ratio. Under the optimal conditions, the response analysis showed that the primary structure response controlled by the H2 optimized GI-DVA can decrease with the increase in the mass ratio, but is less sensitive to large mass ratios, and can be robust to the mistuning on the optimum design parameters. Then, the control performance evaluation is first performed in the frequency domain, which reveal that the dynamic response reduction capacity of the H2 optimized GI-DVA are significantly 62% and 48% superior to the H2 optimized classic DVA (CDVA) and high-performance passive nontraditional inerter-based DVA (NIDVA-C4), respectively. Furthermore, for the root mean square response evaluation ( H2 performance), the H2 optimized GI-DVA can provide significantly H2 performance 58% and 50% than the H2 optimized CDVA and NIDVA-C4, respectively. To obtain more realistic results, the time domain simulation is performed, which showed that the GI-DVA can provide significantly performance for random vibration reduction.

A time and ensemble equivalent linearization method for nonlinear systems under combined harmonic and random excitation

An Equivalent Linearization technique, termed an Equivalent Linearization Time and Ensemble Expectation (EL-TEE) approach, is used to develop an alternative method for estimating the response of a nonlinear oscillator to a combination of deterministic harmonic and random white noise excitation. The approach is based on applying equivalent linearization and averaging over the time period of one harmonic excitation cycle. This gives a set of coupled nonlinear equations that can be solved for the response averaged over time and across the ensemble. The primary advantages of the proposed method are its computational speed, ability to return physically meaningful linearization matrices and that it can be applied to a wide variety of nonlinearities. The method is applied to three example test systems: the well-known single degree of freedom Duffing oscillator; a single degree of freedom system with a displacement constraint imposing a discontinuous nonlinearity; and a multi degree of freedom oscillator with a localized polynomial nonlinearity that has also been examined experimentally. It is shown that the response predicted matches well with Monte Carlo results from direct time integration at a fraction of the computational cost, and the method is capable of reproducing key results observed experimentally.

Dynamic Behavior of a Stochastic Avian Influenza Model with Two Strains of Zoonotic Virus

In this paper, a stochastic avian influenza model with two different pathogenic human–avian viruses is studied. The model analyzes the spread of the avian influenza virus from poultry populations to human populations in a random environment. The dynamic behavior of the stochastic avian influenza model is analyzed. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, under the condition of high pathogenic virus extinction, the persistence in the mean and extinction of the infected avian population with a low pathogenic virus is analyzed. Thirdly, the sufficient conditions for the existence and uniqueness of the ergodic stationary distribution in the stochastic avian influenza model are derived. We find the threshold of the stochastic model to determine whether the disease spreads when the white noise is small. The analysis results show that random white noise is effective for disease control. Finally, the theoretical results are verified by numerical simulation, and the numerical simulation analysis is carried out for the cases that cannot be theoretically deduced.

Physical layer secure key generation and distribution based on noise variances in optical fiber communications systems

Considering the key demand in the secure optical fiber communication, a key generation and distribution scheme based on random noise variances is proposed. The noise of optical communication systems is inevitable due to the influence of various factors. The additive noise that cannot be eliminated is random after digital signal processing, which ensures the randomness of the key. However, the range of system noise variances is small and the noise of links is exposed. A random Gaussian white noise is added at receivers, which increases the noise fluctuation and enhances security. Legitimate parties obtain secure keys by calculating the data inconsistency rate, where the consistency comes from the correlation of noise variances in adjacent time slots over a period of time. Experimental results demonstrate that the error-free key is obtained with the key generation rate of 1.6 Mbit/s over 105 km standard single-mode fiber. Moreover, the security analysis shows that the proposed key generation and distribution scheme can resist fiber-tapping attacks.

The Relationship of Time Span and Missing Data on the Noise Model Estimation of GNSS Time Series

Accurate noise model identification for GNSS time series is crucial for obtaining a reliable GNSS velocity field and its uncertainty for various studies in geodynamics and geodesy. Here, by comprehensively considering time span and missing data effect on the noise model of GNSS time series, we used four combined noise models to analyze the duration of the time series (ranging from 2 to 24 years) and the data gap (between 2% and 30%) effects on noise model selection and velocity estimation at 72 GNSS stations spanning from 1992 to 2022 in global region together with simulated data. Our results show that the selected noise model have better convergence when GNSS time series is getting longer. With longer time series, the GNSS velocity uncertainty estimation with different data gaps is more homogenous to a certain order of magnitude. When the GNSS time series length is less than 8 years, it shows that the flicker noise and random walk noise and white noise (FNRWWN), flicker noise and white noise (FNWN), and power law noise and white noise (PLWN) models are wrongly estimated as a Gauss–Markov and white noise (GGMWN) model, which can affect the accuracy of GNSS velocity estimated from GNSS time series. When the GNSS time series length is more than 12 years, the RW noise components are most likely to be detected. As the duration increases, the impact of RW on velocity uncertainty decreases. Finally, we show that the selection of the stochastic noise model and velocity estimation are reliable for a time series with a minimum duration of 12 years.

Uncovering block structures in large rectangular matrices

In this article, we proposed a conceptually simple, efficient, and easily implemented approach, named Block-structure Analysis on Rectangular Matrix (BARM), for learning the block structure in a large rectangular data matrix corrupted with random effects and white noise. With the possible unknown order of row or column variables, their group structures can be directly uncovered based on the singular values and singular vectors of the scaled data matrix. We also established the asymptotic properties of the proposed approach under regular conditions. Extensive experimental evaluations also demonstrate the reliability and robustness of the proposed approach.

Connectopic mapping techniques do not reflect functional gradients in the brain

Functional gradients, in which response properties change gradually across a brain region, have been proposed as a key organising principle of the brain. Recent studies using both resting-state and natural viewing paradigms have indicated that these gradients may be reconstructed from functional connectivity patterns via “connectopic mapping” analyses. However, local connectivity patterns may be confounded by spatial autocorrelations artificially introduced during data analysis, for instance by spatial smoothing or interpolation between coordinate spaces. Here, we investigate whether such confounds can produce illusory connectopic gradients. We generated datasets comprising random white noise in subjects’ functional volume spaces, then optionally applied spatial smoothing and/or interpolated the data to a different volume or surface space. Both smoothing and interpolation induced spatial autocorrelations sufficient for connectopic mapping to produce both volume- and surface-based local gradients in numerous brain regions. Furthermore, these gradients appeared highly similar to those obtained from real natural viewing data, although gradients generated from real and random data were statistically different in certain scenarios. We also reconstructed global gradients across the whole-brain – while these appeared less susceptible to artificial spatial autocorrelations, the ability to reproduce previously reported gradients was closely linked to specific features of the analysis pipeline. These results indicate that previously reported gradients identified by connectopic mapping techniques may be confounded by artificial spatial autocorrelations introduced during the analysis, and in some cases may reproduce poorly across different analysis pipelines. These findings imply that connectopic gradients need to be interpreted with caution.

Identifying the source for Fractional diffusion equations with Random Gaussian white noise

In this work, we study the problem of finding the source function of the inhomogeneous diffusion equations with conformable derivative c∂α t u−Δu = f(x), 0 < α < 1, associate with random noisy input data. This problem is ill-posed in the sense of Hadamard. In order to regulate the instablity of the solution, we applied the truncation method and estimated the error estimate between the exact solution and the regularized solution.

Optical Systems Identification through Rayleigh Backscattering.

We introduce a technique to generate and read the digital signature of the networks, channels, and optical devices that possess the fiber-optic pigtails to enhance physical layer security (PLS). Attributing a signature to the networks or devices eases the identification and authentication of networks and systems thus reducing their vulnerability to physical and digital attacks. The signatures are generated using an optical physical unclonable function (OPUF). Considering that OPUFs are established as the most potent anti-counterfeiting tool, the created signatures are robust against malicious attacks such as tampering and cyber attacks. We investigate Rayleigh backscattering signal (RBS) as a strong OPUF to generate reliable signatures. Contrary to other OPUFs that must be fabricated, the RBS-based OPUF is an inherent feature of fibers and can be easily obtained using optical frequency domain reflectometry (OFDR). We evaluate the security of the generated signatures in terms of their robustness against prediction and cloning. We demonstrate the robustness of signatures against digital and physical attacks confirming the unpredictability and unclonability features of the generated signatures. We explore signature cyber security by considering the random structure of the produced signatures. To demonstrate signature reproducibility through repeated measurements, we simulate the signature of a system by adding a random Gaussian white noise to the signal. This model is proposed to address services including security, authentication, identification, and monitoring.

Wind turbulence modeling for real-time simulation

This paper proposes a method to design a real-time wind turbulence simulator. The objective of such a simulator is to make dynamical models more accurate in order to develop more robust controls, especially in the case of mechanical systems operating outdoors such as tracking antennas. The models used to generate a random wind speed are based on the wind spectral characteristics rather than time domain ones. Indeed, turbulence is a stochastic and non-stationary process corresponding to the short-term component of wind and therefore is difficult to model in time domain. Wind spectral characteristics are described by the power spectral density whose approximation is used in the real-time simulator to reproduce wind behavior. The von Kármán model is the most commonly used model to approximate the power spectral density of wind turbulence. However, this model was originally designed for aircraft, and therefore for high altitudes and moving systems. In our case, tracking antennas are used under different conditions: low altitude and slow moving systems. This makes the von Kármán model less precise in middle and high range frequency. Consequently, there is a need in more accurately modeling wind turbulence under these specific conditions. As von Karman’s model expression uses fractional calculus, other models with the same range of parameter number are proposed to better approximate the wind power spectral density by using Cole-Cole and Davidson-Cole fractional models. The idea is to use shaping filters issued from these more precise fractional models to generate realistic random wind speed turbulence from a random white noise input. These filters are approximated by rational functions and their parameters are tuned in the same way as those of the von Kármán model with the same inputs (mean speed, standard deviation and length scale). If a rational model is sought, a very high number of parameters (more than six times) is needed to have the same precision as our proposed fractional Cole-Cole model which has only four parameters. Finally, an accurate turbulence wind speed generator is proposed.

Reliability analysis of controlled structures based on probabilistic active controller

The reliability of controlled structures has been a subject of considerable concern in recent years. The present study investigated the effects of a probabilistic fuzzy logic controller (PFLC) as an intelligent controller and a linear quadratic regulator (LQR) controller as a classic controller on the reliability of a structure. Monte Carlo reliability analysis has been used to determine the reliability of the controlled structures. A single-degree-of-freedom (SDOF) system and multiple-degree-of-freedom (MDOF) structures with different tendon arrangements were considered. The structures were subjected to random Gaussian white noise as excitation and the variables considered were random Gaussian samples with a dispersion coefficient of 10%. The probability of failure could be estimated by PFLC at up to 10-5 as the threshold level increased in MDOF structures. Moreover, the results indicate that PFLC was more accurate than the LQR controller for a lower probability of failure because the associated limit state function includes stochastic uncertainty.

Closed form expressions for H2 optimal control of negative stiffness and inerter-based dampers for damped structures

This study presents the H2 optimal control of negative stiffness and inerter-based dampers as supplemental dampers to a damped single degree of freedom system (SDOF). In total, five different negative stiffness and inerter combinations have been studied, viz., a negative stiffness damper (NSD), three negative stiffness inerter dampers (NSIDs) and a tuned inerter damper (TID). NSIDs are novel energy dissipation devices consisting of negative stiffness dampers (NSD) and inerter mechanisms. H2 optimal control minimises the root mean square (RMS) of structural response under random/stochastic excitations. The ground acceleration excitation is modelled as a stationary random white noise process. The equations of motion for the SDOF system with different supplemental dampers are written in a state space form, and corresponding closed-form expressions for the optimal parameters are arrived at. The closed-form expressions for NSD, NSIDs and TID are arrived at by a two-stage process: First, by using the numerical search technique for calculating the minima of the H2 norm. Second, using the results of the corresponding numerical search, a sequence of fitting curve schemes is employed to arrive at various closed-form expressions. The closed-form expressions are more straightforward to use. Finally, the comparative seismic performance of the base-isolated (BI) structure with the proposed optimal dampers is obtained under the set near fault (NF) and far-field (FF) ground motions. The time history analysis shows that the H2 optimal control is very efficient in response control of the base-isolated structures. In particular, optimally designed NSIDs outperform the NSD and TID as a control device to a base-isolated structure. Hence, the performance of both NSD and TID as the supplemental damper is enhanced by adding the inerter mechanism.

Instability analysis and regularization approximation to the forward/backward problems for fractional damped wave equations with random noise

Considered herein is the forward/backward problems for fractional damped wave equations utt+α(−Δ)s1ut+β(−Δ)s2u=F(u,x,t) subject to the random Gaussian white noise initial and final data. First of all, we construct the mild solutions to forward/backward problems under all cases for parameters α, β, s1 and s2, and then investigate their stability and instability properties in the sense of Hadamard. Secondly, we propose the regularized solutions by using the Fourier truncation method and establish well-posedness for regularized solutions in above unstable cases. Thirdly, we derive some error estimates between the exact solutions and their regularized solutions in E‖⋅‖22-norm, and theoretically characterize the Fourier truncation approximation effect from regularized solutions to exact solutions. Finally, we give a series of numerical examples used to illuminate the regularization approximation effect of above method.