White Noise Research Articles

Travelling Solitary Wave Solutions to Non-Gaussian χ-Wick-Type Stochastic Burgers’ Equation with Variable Coefficients

In this work, we obtain non-Gaussian (NG) stochastic solutions to χ-Wick-type stochastic (χ-Wk-TS) Burgers’ equations with variable coefficients. An Exp-function method, the connection between white noise theory and hypercomplex systems (HCSs), the χ-Wick product (χ-Wk-product) and an χ-Hermite transform (χ-Hr-transform) are proposed. We provide a new set of non-Gaussian solitary wave solutions (NG-SWSs) to Burgers’ equations with variable coefficients. NG white noise functional solutions (NG-WNFSs) to χ-Wk-TS Burgers’ equations with variable coefficients are shown. The symmetry coefficients of partial differential equations and the symmetrical properties of SPDEs are critical in determining the best solution.

Wireless Remote-Monitoring Technology for Wind-Induced Galloping and Vibration of Transmission Lines

In order to achieve wireless remote monitoring of wind-induced vibrations in power-transmission lines based on MEMS sensors, it is necessary to devise a method for reconstructing the wind swing curve, enabling the device’s real-time performance to promptly acquire, restore, and analyze data. Based on existing single-axis vibration-sensitive components, a measurement array using self-powered MEMS sensors and spacers has been designed. The Orthogonal Matching Pursuit (OMP) algorithm is selected to obtain displacement data collected by sensors installed on the transmission-line spacers. Leveraging the inherent sparsity of the data, a Gaussian white noise regularization matrix is chosen to establish the observation matrix. Through the algorithm, wind data curve reconstruction is achieved, enabling the reconstruction of large-span wind-induced vibration information without distortion. The experimental results demonstrate that when applying the orthogonal tracking algorithm in transmission-line curve reconstruction, sparsity is selected based on the sampling length, that is, the number of sensors installed on the spacers is determined by the span length; a portion of the observation values are selected to generate the observation matrix; and the wind galloping data curve of the transmission line is well restored.

Random transformations to improve mitigation of query-based black-box attacks

This paper proposes methods to upstage the best-known defences against query-based black-box attacks. These benchmark defences incorporate gaussian noise into input data during inference to achieve state-of-the-art performance in protecting image classification models against the most advanced query-based black-box attacks. Even so there is a need to improve upon them; for example, the widely benchmarked Random noise defense (RND) method has demonstrated limited robustness – achieving only 53.5% and 18.1% with a ResNet-50 model on the CIFAR-10 and ImageNet datasets, respectively – against the square attack, which is commonly regarded as the state-of-the-art black-box attack. Therefore, in this work, we propose two alternatives to gaussian noise addition at inference time: random crop-resize and random rotation of the input images. Although these transformations are generally used for data augmentation while training to improve model invariance and generalisation, their protective potential against query-based black-box attacks at inference time is unexplored. Therefore, for the first time, we report that for such well-trained models either of the two transformations can also blunt powerful query-based black-box attacks when used at inference time on three popular datasets. The results show that the proposed randomised transformations outperform RND in terms of robust accuracy against a strong adversary that uses a high budget of 100,000 queries based on expectation over transformation (EOT) of 10, by 0.9% on the CIFAR-10 dataset, 9.4% on the ImageNet dataset and 1.6% on the Tiny ImageNet dataset. Crucially, in two even tougher attack settings, that is, high-confidence adversarial examples and EOT-50 adversary, these transformations are even more effective as the margin of improvement over the benchmarks increases further.

The Noise of Our Daily Motion: General Spectral Characteristics of Human Mobility and Activity

In recent decades, a strong focus has emerged on exploring the scale-independent nature of our daily spatial motion. Similarly, heavy-tailed distributions have been observed for human locomotor activity, measured by actigraphs in medical fields. We recently proved that the raw acceleration data and also the activity signals calculated from them in diverse ways exhibit a general spectral characteristic; 1/f noise is observable above a certain cutoff frequency, while white noise and peaks corresponding to daily rhythms are visible at lower frequencies. We show that this pattern is strikingly similar to what we found earlier for GPS data and this similarity raises fundamental questions like what is the relation between human mobility and physical activity, what are the benefits of the analysis from this perspective, and how it helps us to better understand and model the scale-independent nature of human dynamics.

Design and verifications of three building acoustic metamaterials for simultaneous noise insulation and ventilation

Ventilated acoustic metamaterials with simultaneous high noise insulation performance and sufficient ventilation aera are eagerly needed nowadays. Many acoustic metamaterials with high insulation capabilities are achieved at the expense of ventilation area of proposed configurations. Thus, there is a tradeoff between noise insulation capability and ventilation efficiency in metamaterial designing. Besides, most of the ventilated acoustic metamaterials are generally tested in impedance tubes, and they are seldom verified via building acoustic sound insulation laboratory testing. In this study, the traffic noise characteristics of two typical residential building away and nearby the main traffic road are measured, which both reveal that the traffic noises cover a broad frequency range of 200 Hz∼4000 Hz. Then, three ventilated acoustic metamaterials with the same out diameter (152.4 mm) but different ventilation areas (interior diameters of 29 mm, 60 mm, 100 mm) are investigated in detail via numerical simulations and experiments. The three metamaterials are fabricated with additive manufacturing techniques and their transmission loss performances are tested in impedance tubes firstly. Finally, their noise insulation performances are verified in the building acoustic sound insulation laboratory, where the acoustic excitation is white noise generated by a diffuse sound source and the sound transmitted into the receiving room is investigated. This study will pave a solid foundation for the applications of ventilated acoustic metamaterials.

Exploration of the normalized intradopant transition energy of GaAs quantum dot under the influence of noise

In this work the intradopant transition energy (IDTE) and the normalized intradopant transition energy (NIDTE) of GaAs quantum dot (QD) have been minutely explored. The QD contains Gaussian impurity as dopant. Gaussian white noise, applied via two different routes (additive and multiplicative), also becomes part of the QD confinement potential. Energy values are calculated using linear variational theory. The IDTE and NIDTE exhibit (depending on presence/absence of noise, mode of entrance of noise and the given physical parameter undergoing change) steady growth, steady fall, maximization, minimization and saturation. Throughout the entire study, the NIDTE plots efficiently highlight some weak features which IDTE plots fail to do and clearly announce their superiority over the IDTE plots in realizing the influences of various physical parameters. The findings of the study are expected to be quite relevant in elucidating the optical properties of low-dimensional nanostructures containing impurity and under the sway of noise.

Efficacy of fluoxetine and (R,S)-ketamine in attenuating conditioned fear behaviors in male mice

Post-traumatic stress disorder (PTSD) is caused by exposure to a traumatic or stressful event. Symptoms related to this disorder include persistent re-experiencing of memories and fear of generalization. Current pharmacological treatments for PTSD are insufficient, with fewer than 30% of patients reporting symptom remission. This study aims to determine the efficacy of acute (R,S)-ketamine and chronic fluoxetine (FLX) in reducing fear memory and fear generalization. In rodents, fear conditioning (FC) is commonly used in the literature to induce behaviors related to symptoms of PTSD, and the open field test (OFT) can assess anxiety and fear generalization behaviors during the exploration of a novel environment. In this study, FC consisted of a white noise cue stimulus and 4 inescapable foot shocks. Treatments began 4 hours after FC. Fear and anxiety behaviors were recorded during re-exposure to the FC stimuli at 24 hours and 2 weeks. The OFT was conducted 1 day before the last FC re-exposure. Results support the combined use of acute ketamine and chronic FLX as a treatment for reducing behaviors indicative of fear memory during re-exposure at 2 weeks, but not behaviors indicative of anxiety and fear generalization in the OFT. FLX alone was most effective in reducing behaviors related to fear generalization. This study contributes to the existing literature on pharmacological treatment for fear and anxiety behaviors relating to fear memory and fear generalization. Continued research is necessary to replicate results, optimize treatment protocols, and investigate the molecular adaptations to trauma and treatment. Significance StatementUp to 6% of people in the United States will develop PTSD within their lifetime, and less than half of those individuals will find relief from their symptoms given the current therapeutic options. This study offers preliminary support for the efficacy of ketamine and FLX in reducing PTSD-like behaviors induced by fear-conditioning in mice. Compared with current standard treatments, the results of the current study indicate the potential for a more effective therapeutic option for those with stress-related disorders, such as PTSD.

Capturing resilience from phenotypic deviations: a case study using feed consumption and whole genome data in pigs

BackgroundIn recent years, interest has grown in quantifying resilience in livestock by examining deviations in target phenotypes. This method is based on the idea that variability in these phenotypes reflects an animal’s ability to adapt to external factors. By utilizing routinely collected time-series feed intake data in pigs, researchers can obtain a broad measure of resilience. This measure extends beyond specific conditions, capturing the impact of various unknown external factors that influence phenotype variations. Importantly, this method does not require additional phenotyping investments. Despite growing interest, the relationship between resilience indicators—calculated as deviations from longitudinally recorded target traits—and the mean of those traits remains largely unexplored. This gap raises the risk of inadvertently selecting for the mean rather than accurately capturing true resilience. Additionally, distinguishing between random phenotype fluctuations (white noise) and structural variations linked to resilience poses a challenge. With the aim of developing general resilience indicators applicable to commercial swine populations, we devised four resilience indicators utilizing daily feed consumption as the target trait. These include a canonical resilience indicator (BALnVar) and three novel ones (BAMaxArea, SPLnVar, and SPMaxArea), designed to minimize noise and ensure independence from daily feed consumption. We subsequently integrated these indicators with Whole Genome Sequencing using SLEMM algorithm, data from 1,250 animals to assess their efficacy in capturing resilience and their independence from the mean of daily feed consumption.ResultsOur findings revealed that conventional resilience indicators failed to differentiate from the mean of daily feed consumption, underscoring potential limitations in accurately capturing true resilience. Notably, significant associations involving conventional resilience indicators were identified on chromosome 1, which is commonly linked to body weight.ConclusionWe observed that deviations in feed consumption can effectively serve as indicators for selecting resilience in commercial pig farming, as confirmed by the identification of genes such as PKN1 and GYPC. However, the identification of other genes, such as RNF152, related to growth, suggests that common resilience quantification methods may be more closely related to the mean of daily feed consumption rather than capturing true resilience.

A method for signal components identification in acoustic signal with non-Gaussian background noise using clustering of data in time-frequency domain

This paper presents a novel method for fault detection in vibration/acoustic signals contaminated with non-Gaussian noise, specifically addressing the challenge of random impulsive and wideband disturbances in industrial measurements. While damage detection in Gaussian noise environments is well understood, high-amplitude non-cyclic impulsive disturbances arising from random aspects of industrial processes, such as non-uniform operations and random impacts, pose significant analytical challenges.The proposed method analyzes the distribution densities of spectral vectors derived from spectrograms. It considers a simple additive model consisting of the signal of interest (SOI) and Gaussian and non-Gaussian noise. Using the density-based spatial clustering algorithm (DBSCAN), the method isolates distinct classes of spectral vectors from the spectrogram, effectively separating different signal behaviors and extracting fault-related information. The effectiveness of the proposed method was validated using an envelope spectrum-based indicator (ENVSI) and successfully demonstrated on real signals from an industrial machine with a faulty bearing.

Laser ultrasonic inspection of surface and subsurface defects in materials based on deep learning

ABSTRACT Laser ultrasonic testing is an advanced non-destructive testing with high frequency and fast detection speed. However, most laser ultrasonic testing characterises defects by manually extracting the features of signals. To address this, deep learning is introduced to identify defects intelligently. Firstly, theoretical models based on finite elements are built to study the the surface and subsurface defects’ effects on surface acoustic wave (SAW) propagation. Experimental studies are also conducted on 5 samples with surface defects and 15 with subsurface defects. Then, Gaussian white noise is added to both simulation and experimental signals to expand the data set and imitate the complex conditions. The wavelet transform images of the reflected and transmitted signal are combined into a data set for training the convolutional neural network (CNN). The subsurface defects’ data set is similarly augmented. Finally, a total of 40,000 surface defect and 21,000 subsurface defect data are collected and split into training, test, and validation sets (6:2:2 ratio). The CNN accurately classifies surface defect penetration depth (minimum error 5.87%), while subsurface defect widths are determined with transfer learning (minimum error 5.6%). It proves that it is feasible to classify and identify defects by combining the laser ultrasonic method with deep learning.

Element-wise and recursive solutions for the power spectral density of biological stochastic dynamical systems at fixed points

Stochasticity plays a central role in nearly every biological process, and the noise power spectral density (PSD) is a critical tool for understanding variability and information processing in living systems. In steady state, many such processes can be described by stochastic linear time-invariant (LTI) systems driven by Gaussian white noise, whose PSD is a complex rational function of the frequency that can be concisely expressed in terms of their Jacobian, dispersion, and diffusion matrices, fully defining the statistical properties of the system's dynamics at steady state. Here, we arrive at compact, element-wise solutions of the rational function coefficients for the auto- and cross-spectrum that enable the explicit analytical computation of the PSD in dimensions n=2,3,4. We further present a recursive Leverrier-Faddeev-type algorithm for the exact computation of the rational function coefficients. Crucially, both solutions are free of matrix inverses. We illustrate our element-wise and recursive solutions by considering the stochastic dynamics of neural systems models, namely, FitzHugh-Nagumo (n=2), Hindmarsh-Rose (n=3), Wilson-Cowan (n=4), and the stabilized supralinear network (n=22), as well as an evolutionary game-theoretic model with mutations (n=5,31). We extend our approach to derive a recursive method for calculating the coefficients in the power-series expansion of the integrated covariance matrix for interacting spiking neurons modeled as Hawkes processes on arbitrary directed graphs. Published by the American Physical Society 2024

A cost-effective load side management solution based on power line carrier communication i-PLCC.

Conventional power systems are almost at the verge of their existence and are quickly being replaced by modern, especially smarter alternatives. Rapid and wide deployment of Load side management, which is a smarter and modern way to ensure efficient and economical use of power, is a classic example. However, there are several challenges which need to be addressed before it can be realized as a commercially viable solution. Suitable communication method, called "Home Area Networks", is a mandatory requirement which should be cost effective, robust and with ability to simultaneously handle large number of devices. Due to various inherent issues, communication protocols commonly used now-a-days, are not fully capable to address the requirements of HANs. Power Line Carrier Communications (PLCC) can be a suitable and efficient alternative of quick realization of HANs. In this paper, various aspects of PLCC have been analyzed for use in HANs. Modulation methods, materials, physical parameters and effect of noise have been analyzed. The paper evaluates performance and effectiveness of FSK modulation with aluminum transmission medium for PLC within a residential environment, focusing on the tradeoffs between distance, transmission medium diameter, and type of transmission medium, and cable gauge, which can degrade the performance of PLCC. A novel simulation model has been presented incorporating RLCG (Resistance, Inductance, Capacitance, and Conductance) tools and additive white Gaussian noise (AWGN). Performance parameter have been comprehensively analyzed of implementation using aluminum as a communication medium. This paper discusses cost effectiveness of PLCC by replacing copper by aluminum as the transmission medium. The study reveals that aluminum cables must be twice the size of copper cable in order to achieve same communication distances. Higher carrier frequencies in FSK modulation increase noise susceptibility, consequently reducing achievable communication distances. Cables with smaller diameters results in lower transmission ranges. These results highlight the trade-offs involved in implementing FSK for in-home PLCC (iPLCC). The study highlights how crucial it is to take these trade-offs into account while developing and refining FSK-based iPLCC systems for use in smart homes.

Improving solution availability and temporal consistency of an optimal-estimation physical retrieval for ground-based thermodynamic boundary layer profiling

Abstract. Thermodynamic profiles in the atmospheric boundary layer can be retrieved from ground-based passive remote sensing instruments like infrared spectrometers and microwave radiometers with optimal-estimation physical retrievals. With a high temporal resolution on the order of minutes, these thermodynamic profiles are a powerful tool to study the evolution of the boundary layer and to evaluate numerical models. In this study, we describe three recent modifications to the Tropospheric Remotely Observed Profiling via Optimal Estimation (TROPoe) retrieval framework, which improve the availability of valid solutions for different atmospheric conditions and increase the temporal consistency of the retrieved profiles. We present methods to enhance the availability of valid solutions retrieved from infrared spectrometers by preventing overfitting and by adding information from an additional spectral band in high-moisture environments. We show that the characterization of the uncertainty of the input and the choice of spectral infrared bands are crucial for retrieval performance. Since each profile is retrieved independently from the previous one, the time series of the thermodynamic variables contain random uncorrelated noise, which may hinder the study of diurnal cycles and temporal tendencies. By including a previous retrieved profile as input to the retrieval, we increase the temporal consistency between subsequent profiles without suppressing real mesoscale atmospheric variability. We demonstrate that these modifications work well at midlatitudes, polar and tropical sites, and for retrievals based on infrared spectrometer and microwave radiometer measurements.

Design of a Differential Chaotic Shift Keying Communication System Based on Noise Reduction with Orthogonal Double Bit Rate

In this paper, a differential chaotic shift keying communication system based on noise reduction with orthogonal double bit rate (NR-ODBR-DCSK) is proposed. The system incorporates Walsh orthogonalization at the transmitter side to orthogonalize the information signals so that two mutually orthogonal signals can be superimposed. At the receiving end, because the principle of orthogonal signals is used, it achieves the characteristic of double information transmission rate for information signal transmission while avoiding the problem of chaotic synchronization. In addition, the system employs a noise reduction transmission mechanism, which reduces the noise variance in the received signal, further reducing the BER of the system and thus improving the performance of the communication system. By analyzing the signal format of the system, the transmitter and receiver structures of the communication system are designed. Subsequently, theoretical analyses and simulations in an additive white Gaussian noise (AWGN) channel demonstrate the good performance of the system, including a low bit error rate (BER) and a good data-energy to bit-energy ratio (DBR). Finally, a simulation test of the NR-ODBR-DCSK system for a semi-physical communication system was carried out using two USRP devices to verify the experimental feasibility of the system. The simulation analysis results show that comparative analyses with conventional DCSK and SR-DCSK systems highlight the superior performance of the NR-ODBR-DCSK system.

On statistical zonostrophic instability and the effect of magnetic fields

Zonal flows are mean flows in the east–west direction, which are ubiquitous on planets, and can be formed through ‘zonostrophic instability’: within turbulence or random waves, a weak large-scale zonal flow can grow exponentially to become prominent. In this paper, we study the statistical behaviour of the zonostrophic instability and the effect of magnetic fields. We use a stochastic white noise forcing to drive random waves, and study the growth of a mean flow in this random system. The dispersion relation for the growth rate of the expectation of the mean flow is derived, and properties of the instability are discussed. In the limits of weak and strong magnetic diffusivity, the dispersion relation reduces to manageable expressions, which provide clear insights into the effect of the magnetic field and scaling laws for the threshold of instability. The magnetic field mainly plays a stabilising role and thus impedes the formation of the zonal flow, but under certain conditions it can also have destabilising effects. Numerical simulation of the stochastic flow is performed to confirm the theory. Results indicate that the magnetic field can significantly increase the randomness of the zonal flow. It is found that the zonal flow of an individual realisation may behave very differently from the expectation. For weak magnetic diffusivity and moderate magnetic field strengths, this leads to considerable variation of the outcome, that is whether zonostrophic instability takes place or not in individual realisations.

Gaussian fluctuations of spatial averages of a system of stochastic heat equations

. We consider a system of d non-linear stochastic heat equations driven by an m-dimensional space-time white noise on R + × R . In this article, we study the asymptotic behavior of spatial averages over large intervals [ − R , R ] . We establish a rate of convergence to a multivariate normal distribution in the Wasserstein distance and a functional central limit theorem.

Numerical ergodicity of a full‐discrete exponential Euler scheme for stochastic Burgers–Huxley equation

In this paper, we mainly complete the research on approximate study of invariant measures for one‐dimensional stochastic Burgers–Huxley equations driven by additive Gaussian noise. A fully discretization scheme is proposed based on the spectral Galerkin method and the exponential Euler scheme in both spatial and temporal directions, respectively. Moreover, we establish the unique ergodicity for both the spatial semi‐discretization and the full discretization of numerical solutions, along with providing rigorous error estimations for invariant measures under approximate conditions. Some numerical experiments are presented to verify the theoretical findings.

Robust joint estimation of sideslip angle and tire lateral force for distributed drive electric vehicle

Accurate estimation of vehicle sideslip angle (SA) and tire lateral force (TLF) is essential for the effective functioning of vehicle active safety control systems. However, effective estimation of SA and TLF using low-cost on-board sensors is a major challenge. In this paper, a robust joint estimation method of SA and TLF for distributed drive electric vehicle (DDEV) is proposed. Adaptive sliding-mode observer (ASMO) is used to estimate the TLF and is used as the input to the subsequent filter. Maximum correntropy criterion (MCC) is introduced to improve the robustness of the unscented Kalman filter (UKF) under mixed Gaussian noise, and the maximum correntropy unscented Kalman filter (MCUKF) algorithm is composed to estimate SA. The effectiveness of the proposed ASMO and MCUKF joint estimation method is verified by Simulink/Carsim joint simulation experiments. The experimental results show that compared with the existing methods, the estimation method proposed in this paper effectively improves the estimation accuracy and robustness of SA and TLF under the mixed Gaussian environment, which is of great significance for the improvement of vehicle active safety.

Modal Parameter Identification of Jacket-Type Offshore Wind Turbines Under Operating Conditions

Operational modal analysis (OMA) is essential for long-term health monitoring of offshore wind turbines (OWTs), helping identifying changes in structural dynamic characteristics. OMA has been applied under parked or idle states for OWTs, assuming a linear and time-invariant dynamic system subjected to white noise excitations. The impact of complex operating environmental conditions on structural modal identification therefore requires systematic investigation. This paper studies the applicability of OMA based on covariance-driven stochastic subspace identification (SSI-COV) under various non-white noise excitations, using a DTU 10 MW jacket OWT model as a basis for a case study. Then, a scaled (1:75) 10 MW jacket OWT model test is used for the verification. For pure wave conditions, it is found that accurate identification for the first and second FA/SS modes can be achieved with significant wave energy. Under pure wind excitations, the unsteady servo control behavior leads to significant identification errors. The combined wind and wave actions further complicate the picture, leading to more scattered identification errors. The SSI-COV based modal identification method is suggested to be reliably applied for wind speeds larger than the rated speed and with sufficient wave energy. In addition, this method is found to perform better with larger misalignment of wind and wave directions. This study provides valuable insights in relation to the engineering applications of in situ modal identification techniques under operating conditions in real OWT projects.

Mean random dynamical systems and random attractors of stochastic Hopfield neural models with locally Lipschitz noise and time delay

In this paper, we investigate the long term dynamical behaviour of stochastic Hopfield neural network models driven by white noise with time delay, where the nonlinear drift and diffusion terms are both locally Lipschitz continuous. We establish the global-in-time solvability of these systems with locally Lipschitz continuous nonlinear drift and diffusion terms by using mean square uniform estimates of solutions. Furthermore, we demonstrate that the mean random dynamical system generated by the solution operators possesses a unique weak pullback mean random attractor in the Hilbert space L 2 ( Ω ~ , F ι ; l 2 ) × L 2 ( Ω ~ , F ι ; L 2 ( ( − ϱ , 0 ) , l 2 ) ) .