Multiplicative Noise Research Articles

The Impact of Noise on the Solution of the Stochastic Fractional Chiral Schrodinger Equation Forced by Multiplicative Noise in Ito Sense

The Impact of Noise on the Solution of the Stochastic Fractional Chiral Schrodinger Equation Forced by Multiplicative Noise in Ito Sense

Existence and Stability of Neutral Stochastic Impulsive and Delayed Integro-Differential System via Resolvent Operator

In this paper, we present the existence of a mild solution for a class of a neutral stochastic integro-differential system over a Hilbert space. Such systems are influenced by both multiplicative and fractional noise, alongside non-instantaneous impulses, with a Hurst index H in the interval (12,1). Additionally, the systems under consideration feature state-dependent delays (SDDs). To address this, we develop an approach to reformulate the neutral stochastic integro-differential system, incorporating SDDs and non-instantaneous impulses, into an equivalent fixed-point (FP) problem via an appropriate integral operator. By integrating stochastic analysis with the theory of resolvent operators, we employ Banach’s FP theorem to establish both the existence and uniqueness of the solution. Furthermore, we explore the Ulam–Hyers–Rassias stability of the system. Lastly, we provide illustrative examples to demonstrate the practical applicability of our results.

M-IPISincNet: An explainable multi-source physics-informed neural network based on improved SincNet for rolling bearings fault diagnosis

Timely and accurate diagnosis of bearing faults can effectively reduce the chance of accidents in equipment. However, deep learning methods are mostly completely dependent on data and lack interpretability. It is difficult to deal with the differences between real-time data and training data under changing working conditions and noisy environments. In this study, we proposed M-IPISincNet, an explainability multi-source physics-informed convolutional network based on improved SincNet. Rolling bearing fault diagnosis is realized by extracting fault features from vibration and current signals. Firstly, a physics-informed convolutional layer is designed based on inverse Fourier transform and bandpass filters. Fault features are extracted by multi-scale convolution and multi-layer nonlinear mapping. A DBN network is applied extract unsupervised hidden fusion features in the vibration and current signals. The proposed method is validated under the datasets of Paderborn University (PU) and Case Western Reserve University (CWRU), which proves that the proposed method has explainability, robustness and great accuracy under multiple working conditions and noises.

Sensing offset analysis and compensation of a capacitive displacement transducer for space inertial sensors

Abstract Capacitive displacement transducers play a crucial role in inertial sensors especially for space gravitational wave detection missions. One of the major requirements for the displacement transducer is to have a lower sensing offset. The sensing offset will adversely affect the accuracy of the absolute position measurement of the test mass, providing erroneous data to the drag-free controller and leading to spacecraft mispositioning. Additionally, the offset could introduce multiplicative noise to the sensing output and the closed loop output of the inertial sensor. The asymmetry of the sensing bridge within the front-end electronics has been identified as the primary source of these offsets. This paper analyzes the requirements of the main parameters in the sensing bridge. A method is proposed to reduce the sensing offset by utilizing differentiated resonant capacitors while maintaining the ability to tune the resonant frequency and ensure a sufficiently low sensing noise level. Experimental results show that this approach can effectively reduce the residual sensing offset to (−15.7 ± 5.0) ppm, which satisfies the stringent requirement for space inertial sensors in the TianQin mission.

On Asymptotic Behavior of Solutions of Linear Multidimensional Stochastic Differential Equations with Multiplicative Noise

On Asymptotic Behavior of Solutions of Linear Multidimensional Stochastic Differential Equations with Multiplicative Noise

Adaptive Linear Quadratic Control for Stochastic Discrete-Time Linear Systems With Unmeasurable Multiplicative and Additive Noises

Adaptive Linear Quadratic Control for Stochastic Discrete-Time Linear Systems With Unmeasurable Multiplicative and Additive Noises

Optical solitons for the concatenation model with differential group delay having multiplicative white noise by F–expansion approach

This study examines optical soliton solutions for the concatenation model, which includes differential group delay and white noise in both components. Through the F–expansion integration algorithm, an extensive spectrum of soliton solutions was found. It has been confirmed that white noise affects the phase of solitons along both components.

Dynamical analysis and fault detection application of a time-delayed multi-stable stochastic resonance system driven by white correlated noises.

Bearing fault diagnosis is a crucial means to ensure the normal operation of machinery, reduce maintenance costs, enhance equipments safety and extend the service life of bearings. However, the noise interference in input signals often affects the effective extraction of bearing fault signals. In this paper, a time-delay multi-stable stochastic resonance (SR) system driven by white correlated noises is proposed. Firstly, the expressions of the steady-state probability density (SPD) function and the mean first passage time (MFPT) is derived. Simultaneously, we delve into the influences of various system parameters, including multiplicative noise intensity, additive noise intensity, noise correlated strength, time-delay, and time-delay feedback intensity, on the dynamical behavior exhibited by particles within the system. Then, according to the signal-to-noise ratio (SNR) formula, the paper investigates the impact of system parameters on the SNR. It is found that the ease of SR occurrence is directly related to the system parameters. Finally, the experimental results demonstrate that the proposed method exhibits superior performance in detecting faults compared with the classical bistable SR system and the quad-stable SR system.

Fast and Accurate Numerical Integration of the Langevin Equation with Multiplicative Gaussian White Noise.

A univariate stochastic system driven by multiplicative Gaussian white noise is considered. The standard method for simulating its Langevin equation of motion involves incrementing the system's state variable by a biased Gaussian random number at each time step. It is shown that the efficiency of such simulations can be significantly enhanced by incorporating the skewness of the distribution of the updated state variable. A new algorithm based on this principle is introduced, and its superior performance is demonstrated using a model of free diffusion of a Brownian particle with a friction coefficient that decreases exponentially with the kinetic energy. The proposed simulation technique proves to be accurate over time steps that are an order of magnitude longer than those required by standard algorithms. The model used to test the new numerical technique is known to exhibit a transition from normal diffusion to superdiffusion as the environmental temperature rises above a certain critical value. A simple empirical formula for the time-dependent diffusion coefficient, which covers both diffusion regimes, is introduced, and its accuracy is confirmed through comparison with the simulation results.

Coupling by change of measure for conditional McKean–Vlasov SDEs and applications

The couplings by change of measure are applied to establish log-Harnack inequality(equivalently the entropy-cost estimate) for conditional McKean–Vlasov SDEs and derive the quantitative conditional propagation of chaos in relative entropy for mean field interacting particle system with common noise. For the log-Harnack inequality, two different types of couplings will be constructed for non-degenerate conditional McKean–Vlasov SDEs with multiplicative noise. As to the quantitative conditional propagation of chaos in relative entropy, the initial distribution of interacting particle system is allowed to be singular with that of limit equation. The above results are also extended to conditional distribution dependent stochastic Hamiltonian system.

Stability of stochastic difference equations with multiplicative and additive fading noise

In this paper, the effects of multiplicative and additive fading stochastic perturbations on the solutions of stochastic difference equations are studied, in which the strength of fading stochastic perturbations is square summable. Different from the existing research, this paper mainly studies the influence of two kinds of stochastic perturbations on the stability of the system, and applies the Lyapunov functional method, the asymptotic mean square trivial sufficiency conditions are obtained for the solutions of stochastic difference equations which based on the influence of multiplicative and additive fading noises. At the same time, the conditions of stochastic perturbation fading rate are obtained. Finally, the above conditions are verified by numerical simulation examples, and the results of numerical simulation show that: (1) the additive perturbations have less influence on the system than the multiplicative perturbations; (2) the fading stochastic perturbations can make the system reach a stable state in a faster time.

Generation of squeezed vacuum state in the millihertz frequency band

The detection of gravitational waves has ushered in a new era of observing the universe. Quantum resource advantages offer significant enhancements to the sensitivity of gravitational wave observatories. While squeezed states for ground-based gravitational wave detection have received marked attention, the generation of squeezed states suitable for mid-to-low-frequency detection has remained unexplored. To address the gap in squeezed state optical fields at ultra-low frequencies, we report on the first direct observation of a squeezed vacuum field until Fourier frequency of 4 millihertz with the quantum noise reduction of up to 8.0 dB, by the employment of a multiple noise suppression scheme. Our work provides quantum resources for future gravitational wave observatories, facilitating the development of quantum precision measurement.

An exponential stochastic Runge–Kutta type method of order up to 1.5 for SPDEs of Nemytskii-type

Abstract For the approximation of solutions for stochastic partial differential equations, numerical methods that obtain a high order of convergence and at the same time involve reasonable computational cost are of particular interest. We therefore propose a new numerical method of exponential stochastic Runge–Kutta type that allows for convergence with a temporal order of up to $\frac{3}/{2}$ and that can be combined with several spatial discretizations. The developed family of derivative-free schemes is tailored to stochastic partial differential equations of Nemytskii-type, i.e., with pointwise multiplicative noise operators. We prove the strong convergence of these schemes in the root mean-square sense and present some numerical examples that reveal the theoretical results.

Heavy-Tail Phenomenon in Decentralized SGD

Recent theoretical studies have shown that heavy-tails can emerge in stochastic optimization due to ‘multiplicative noise’, even under surprisingly simple settings, such as linear regression with Gaussian data. While these studies have uncovered several interesting phenomena, they consider conventional stochastic optimization problems, which exclude decentralized settings that naturally arise in modern machine learning applications. In this paper, we study the emergence of heavy-tails in decentralized stochastic gradient descent (DE-SGD), and investigate the effect of decentralization on the tail behavior. We first show that, when the loss function at each computational node is twice continuously differentiable and strongly convex outside a compact region, the law of the DE-SGD iterates converges to a distribution with polynomially decaying (heavy) tails. To have a more explicit control on the tail exponent, we then consider the case where the loss at each node is a quadratic function, and show that the tail-index can be estimated as a function of the step-size, batch-size, and the topological properties of the network of the computational nodes. Then, we provide theoretical and empirical results showing that DE-SGD has heavier tails than centralized SGD. We also compare DE-SGD to disconnected SGD where nodes distribute the data but do not communicate. Our theory uncovers an interesting interplay between the tails and the network structure: we identify two regimes of parameters (stepsize and network size), where DE-SGD can have lighter or heavier tails than disconnected SGD depending on the regime. Finally, to support our theoretical results, we provide numerical experiments conducted on linear regression and neural networks that suggest the heavier tails is correlated with better generalization in the decentralized setting.

The impact of receiver arrays on suppressing seismic speckle scattering noise caused by the meter-scale near-surface heterogeneity

Managing seismic scattering noise in geophysical surveying, especially from near-surface heterogeneity, presents significant challenges. We revisit the role of receiver arrays in mitigating such noise in regions with near-surface meter-scale heterogeneity. Moving beyond traditional approaches that focus on suppressing coherent noise from near-surface arrivals and random ambient noise, our research highlights the substantial impact of speckle scattering noise. This noise, resulting from near-ballistic scattering on small-scale heterogeneities, introduces considerable trace-to-trace variability in phase and amplitude, complicating data processing. By integrating a novel model of random multiplicative noise with sophisticated statistical techniques, we determine the efficacy of array stacking in significantly reducing this type of noise and decreasing the dispersion of phase and amplitudes. Our analytical and numerical analyses reveal a notable trend: the reduction in phase and amplitude spread amplifies with the array size. A key finding of our study is the identification of a [Formula: see text] law for phase spread reduction, analogous yet distinct from the well-known [Formula: see text] law observed in amplitude attenuation of additive ambient noise. In our context, this law implies that the standard deviation of residual phase disturbances diminishes in proportion to [Formula: see text], where N denotes the array size. This insight holds particular significance for smaller arrays, such as those with nine receivers commonly used in desert environments.

Robust License Plate Recognition in OCC-Based Vehicle Networks Using Image Reconstruction

With the help of traffic lights and street cameras, optical camera communication (OCC) can be adopted in Internet of Vehicles (IoV) applications to realize communication between vehicles and roadside units. However, the encoded light emitted by these OCC transmitters (LED infrastructures on the roadside and/or LED-based headlamps embedded in cars) will generate stripe patterns in image frames captured by existing license-plate recognition systems, which seriously degrades the accuracy of the recognition. To this end, we propose and experimentally demonstrate a method that can reduce the interference of OCC stripes in the image frames captured by the license-plate recognition system. We introduce an innovative pipeline with an end-to-end image reconstruction module. This module learns the distribution of images without OCC stripes and provides high-quality license-plate images for recognition in OCC conditions. In order to solve the problem of insufficient data, we model the OCC strips as multiplicative noise and propose a method to synthesize a pairwise dataset under OCC using the existing license-plate dataset. Moreover, we also build a prototype to simulate real scenes of the OCC-based vehicle networks and collect data in such scenes. Overall, the proposed method can achieve a recognition performance of 81.58% and 79.35% on the synthesized dataset and that captured from real scenes, respectively, which is improved by about 31.18% and 24.26%, respectively, compared with the conventional method.

Weak convergence rates for temporal numerical approximations of the semilinear stochastic wave equation with multiplicative noise

AbstractIn this work we establish weak convergence rates for temporal discretisations of stochastic wave equations with multiplicative noise, in particular, for the hyperbolic Anderson model. For this class of stochastic partial differential equations the weak convergence rates we obtain are indeed twice the known strong rates. To the best of our knowledge, our findings are the first in the scientific literature which provide essentially sharp weak convergence rates for temporal discretisations of stochastic wave equations with multiplicative noise. Key ideas of our proof are a sophisticated splitting of the error and applications of the recently introduced mild Itô formula. We complement our analytical findings by means of numerical simulations in Python for the decay of the weak approximation error for SPDEs for four different test functions.

Consensus for discrete-time second-order multi-agent systems in the presence of noises and semi-Markovian switching topologies

In this paper, we focus on the control problem of mean square consensus for second-order continuous-time multi-agent systems with multiplicative noises under Markovian switching topologies. A new Lyapunov function based on the Laplacian matrix of the corresponding union topology of all possible topologies is designed for the stochastic stability analysis of consensus. Applying matrix theory and stochastic stability for stochastic differential equations, we can analyze the consensus problem of the considered systems with the designed Lyapunov function. In addition, we present the sufficient conditions of the mean square consensus exponentially for the considered stochastic systems. Finally, we give an simulation example to numerically validate our theoretical results.

Existence and Regularity of Random Attractors for Stochastic Evolution Equations Driven by Rough Noise

AbstractThis work establishes the existence and regularity of random pullback attractors for parabolic partial differential equations with rough nonlinear multiplicative noise under natural assumptions on the coefficients. To this aim, we combine tools from rough path theory and random dynamical systems. An application is given by partial differential equations with rough boundary noise, for which flow transformations are not available.

The LIFE SILENT project's approach to sustainable noise mitigation

The main objective of the LIFE SILENT PROJECT is the development of sustainable and eco-friendly solutions to mitigate noise in complex urban environments, where multiple and diverse noise sources, mainly roads and railways, coexist across densely populated areas. Mitigating noise in such environments generally excludes the use of solutions that might interfere with the urban context, such as noise barriers. This is mainly due to the proximity of receivers to the noise source, which reduces the visibility of the surroundings and air circulation, leading to microclimatic modifications and social opposition. This is why noise mitigation measures acting directly on the source are recommended, such as low-noise pavements for roads, and dampers, rail grinding, and silent brakes for railways. However, these solutions suffer from either durability issues or high implementation costs. Thus, an improvement is necessary. In the LIFE SILENT project, innovative and sustainable low-noise and long-lasting pavements, as well as low-height noise barriers will be developed and demonstrated in a real test environment. Additionally, procedures will be established to facilitate their synergistic implementation, providing transport infrastructure owners and managers with solid information to support their widespread adoption. In this paper, a general overview of the LIFE SILENT project is given.