Noise Term Research Articles

Scaled consensus for MASs with compound noises over Markovian switched topologies

AbstractThis article aims to address the stochastic scaled consensus issue in almost surely and mean square sense of stochastic multiagent systems (SMASs) with compound noises in a Markovian switching setting. At first, based on stochastic approximation technique and nearest‐neighbor interaction rules, the stochastic scaled consensus controller is built for SMASs in presence of multiplicative and additive noise by designing a time‐varying gain. Meanwhile, some consensus criterions of SMASs are addressed if the union of the graph and time‐varying gain fulfill some mild requirements. Furthermore, the scaled consensus means that the agents' state variables tend to a prescribed proportion rather than the common value, so this behavior can be seen as non‐convergent behavior. The difference with most of excellent literatures is that the coexistence of noncooperative behavior and multiplicative noise generates that it is not easy to transform the multiplicative noise term into the form of an error equation, which means that the Lyapunov methods cannot be directly utilized in our article. To cope with this, we first demonstrate the boundedness for each agent's state, and hence the convergence can be achieved. Finally, in order to reveal the efficiency of our proposed protocol, the corresponding example is given in the simulation part.

A Semidefinite Relaxation Approach for Mobile Target Localization Based on TOA and Doppler Frequency Shift Measurements

In this paper, we discuss mobile source localization using both time of arrival and Doppler frequency shift (TOA-DFS) measurements, where the source moves at a nonuniform velocity. To obtain the position of a mobile source, we first formulate the weighted least squares (WLS) problem by ignoring the second-order noise terms. Due to the non-convexity, we apply the convex relaxation technique to transform the problem into a semi-definite programming problem. However, ignoring the second-order noise terms is only reasonable in the case of small noise levels. In view of this, we then directly establish the maximum likelihood (ML) estimator based on the measurements model without ignoring the second-order noise terms. Since the ML estimator is a non-convex problem, we also propose implementable semidefinite relaxation (SDR) technique to tackle it. Finally, the Cramér-Rao lower bound (CRLB) analysis and results verify that the proposed methods based on the TOA-DFS measurements can significantly enhance localization accuracy.

Composite Patankar-Euler methods for positive simulations of stochastic differential equation models for biological regulatory systems.

Stochastic differential equations (SDE) are a powerful tool to model biological regulatory processes with intrinsic and extrinsic noise. However, numerical simulations of SDE models may be problematic if the values of noise terms are negative and large, which is not realistic for biological systems since the molecular copy numbers or protein concentrations should be non-negative. To address this issue, we propose the composite Patankar-Euler methods to obtain positive simulations of SDE models. A SDE model is separated into three parts, namely, the positive-valued drift terms, negative-valued drift terms, and diffusion terms. We first propose the deterministic Patankar-Euler method to avoid negative solutions generated from the negative-valued drift terms. The stochastic Patankar-Euler method is designed to avoid negative solutions generated from both the negative-valued drift terms and diffusion terms. These Patankar-Euler methods have the strong convergence order of a half. The composite Patankar-Euler methods are the combinations of the explicit Euler method, deterministic Patankar-Euler method, and stochastic Patankar-Euler method. Three SDE system models are used to examine the effectiveness, accuracy, and convergence properties of the composite Patankar-Euler methods. Numerical results suggest that the composite Patankar-Euler methods are effective methods to ensure positive simulations when any appropriate stepsize is used.

Using stochastic frontier analysis instead of data envelopment analysis in modelling investment performance

AbstractWe introduce methods to apply stochastic frontier analysis (SFA) to financial assets as an alternative to data envelopment analysis, because SFA allows us to fit a frontier with noisy data. In contrast to conventional SFA, we wish to deal with estimation risk, heteroscedasticity in noise and inefficiency terms. We investigate measurement error in the risk and return measures using a simulation–extrapolation method and develop residual plots to test model fit. We find that shrinkage estimators for estimation risk makes a striking difference to model fit, dealing with measurement error only improves confidence in the model, and the residual plots are vital for establishing model fit. The methods are important because they allow us to fit a frontier under the assumption that the risks and returns are not known exactly.

Counterfactuals for the Future

Counterfactuals are often described as 'retrospective,' focusing on hypothetical alternatives to a realized past. This description relates to an often implicit assumption about the structure and stability of exogenous variables in the system being modeled --- an assumption that is reasonable in many settings where counterfactuals are used. In this work, we consider cases where we might reasonably make a different assumption about exogenous variables; namely, that the exogenous noise terms of each unit do exhibit some unit-specific structure and/or stability. This leads us to a different use of counterfactuals --- a forward-looking rather than retrospective counterfactual. We introduce "counterfactual treatment choice," a type of treatment choice problem that motivates using forward-looking counterfactuals. We then explore how mismatches between interventional versus forward-looking counterfactual approaches to treatment choice, consistent with different assumptions about exogenous noise, can lead to counterintuitive results.

Versatile LiDAR-Inertial Odometry With SE(2) Constraints for Ground Vehicles

LiDAR SLAM has become one of the major localization systems for ground vehicles since LiDAR Odometry And Mapping (LOAM). Many extension works on LOAM mainly leverage one specific constraint to improve the performance, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> , information from on-board sensors such as loop closure and inertial state; prior conditions such as ground level and motion dynamics. In many robotic applications, these conditions are often known partially, hence a SLAM system can be a comprehensive problem due to the existence of numerous constraints. Therefore, we can achieve a better SLAM result by fusing them properly. In this paper, we propose a hybrid LiDAR-inertial SLAM framework that leverages both the on-board perception system and prior information such as motion dynamics to improve localization performance. In particular, we consider the case for ground vehicles, which are commonly used for autonomous driving and warehouse logistics. We present a computationally efficient LiDAR-inertial odometry method that directly parameterizes ground vehicle poses on SE(2). The out-of-SE(2) motion perturbations are not neglected but incorporated into an integrated noise term of a novel SE(2)-constraints model. For odometric measurement processing, we propose a versatile, tightly coupled LiDAR-inertial odometry to achieve better pose estimation than traditional LiDAR odometry. Thorough experiments are performed to evaluate our proposed method's performance in different scenarios, including localization for both indoor and outdoor environments. The proposed method achieves superior performance in accuracy and robustness.

Measurements and Modeling of a Monolithically Integrated Self-Spiking Two-Section Laser in InP

The self-spiking behavior of an integrated saturable absorber and gain section laser fabricated in an InP technology platform is analyzed. The gain, absorber and intensity dynamics are first inspected using the normalized Yamada model. This model shows excitable behavior as well as the relative refractory period, both of which are also present in biological neurons. Measurements of a two-section laser show irregular spike generation on the millisecond timescale, with a saturable absorber voltage controlled spike density. From our simulations, and from the quasi-random character and millisecond timescale at which these pulses occur, we conclude the laser is triggered by noise, an important characteristic in the operation of biological neurons. Simulations of the laser around the excitability threshold using a newly proposed model with an optical noise term show qualitatively similar self-spiking behavior as measured.

Constructive role of shot noise in the collective dynamics of neural networks.

Finite-size effects may significantly influence the collective dynamics of large populations of neurons. Recently, we have shown that in globally coupled networks these effects can be interpreted as additional common noise term, the so-called shot noise, to the macroscopic dynamics unfolding in the thermodynamic limit. Here, we continue to explore the role of the shot noise in the collective dynamics of globally coupled neural networks. Namely, we study the noise-induced switching between different macroscopic regimes. We show that shot noise can turn attractors of the infinitely large network into metastable states whose lifetimes smoothly depend on the system parameters. A surprising effect is that the shot noise modifies the region where a certain macroscopic regime exists compared to the thermodynamic limit. This may be interpreted as a constructive role of the shot noise since a certain macroscopic state appears in a parameter region where it does not exist in an infinite network.

Considerations for excess noise measurements of low-k-factor Sb-based avalanche photodiodes.

In applications where high sensitivity is required, the internal gain mechanism of avalanche photodiodes can provide a performance advantage relative to p-i-n photodiodes. However, this internal gain mechanism leads to an excess noise that scales with gain. This excess noise term can be minimized by using materials systems in which impact ionization is initiated primarily by one carrier type. Recently, two Sb-based materials systems, AlInAsSb and AlGaAsSb, have exhibited exceptionally low excess noise, particularly for III-V compound materials. There are four important considerations that can impact the excess noise measurements in such low-noise materials. These considerations deal with the excess noise factor calculation method, measurement RF frequency, measurement wavelength, and the gain calculation method. In this paper, each of these factors is discussed, and their implications on excess noise are considered.

Role of impurity and thermal noise on the radiation sources in ITER using DT fuel

Abstract In this paper, the time evolution of bremsstrahlung radiation loss, plasma frequency and electron particles density and the relationship between these parameters and black body radiation are investigated. The model used in this work is based on numerical solution of particle and energy balance equations in ITER with DT fuel. The fusion reaction takes places in a plasma of deuterium and tritium heated to millions of degrees. It is expected that at this temperature, the thermal noise could have a significant effect on plasma behavior. This effect is considered in the solution of equations for the first time in this work. In order to attain a proper set of particle and energy balance equations, an appropriate thermal noise term is considered in the set of coupled differential equations. These equations are solved simultaneously by numerical methods. The results of the calculations for bremsstrahlung radiation loss, plasma frequency, intensity of blackbody radiation, absorption coefficient and quality factor show that in the absence of thermal noise blackbody radiation doesn’t occur but in the presence of thermal noise blackbody radiation occurs in times of 55.7 s and 42.73 s for two cases of considering and ignoring impurity respectively. As it can be seen that with the addition of impurities to the system, bremsstrahlung radiation and intensity of blackbody radiation increase while absorption coefficient and quality factor decrease.

On the Application of Non-Gaussian Noise in Stochastic Langevin Simulations

In light of recent advances in time-step independent stochastic integrators for Langevin equations, we revisit the considerations for using non-Gaussian distributions for the thermal noise term in discrete-time thermostats. We find that the desirable time-step invariance of the modern methods is rooted in the Gaussian noise, and that deviations from this distribution will distort the Boltzmann statistics arising from the fluctuation-dissipation balance of the integrators. We use the GJ stochastic Verlet methods as the focus of our investigation since these methods are the ones that contain the most accurate thermodynamic measures of existing methods. Within this set of methods we find that any distribution of applied noise, which satisfies the two first moments given by the fluctuation-dissipation theorem, will result in correct, time-step independent results that are generated by the first two moments of the system coordinates. However, if non-Gaussian noise is applied, undesired deviations in higher moments of the system coordinates will appear to the detriment of several important thermodynamic measures that depend especially on the fourth moments. The deviations, induced by non-Gaussian noise, become significant with the one-time-step velocity attenuation, thereby inhibiting the benefits of the methods. Thus, we conclude that the application of Gaussian noise is necessary for reliable thermodynamic results when using modern stochastic thermostats with large time steps.

Deep hierarchical generalized transformation models for spatio-temporal data with discrepancy errors

“Discrepancy error covariance” refers to the cross-covariance between the signal and the noise terms in an additive model. Traditionally, the signal and noise are assumed independent in additive models to avoid issues with confounding and non-identifiable expressions in the marginal likelihood. This assumption is made even in settings where it is known that discrepancy error covariances exists. Recently, a model has been proposed that allows for discrepancy error covariances that avoids issues with confounding. These models introduce a telescoping sum within the additive model’s expression such that the latent process of interest is dependent on other terms of the telescoping sum that are included as part of the noise. However, when evaluating the telescoping sum one obtains signal and noise terms that are independent, which avoids such concerns with confounding. The current model that allows for discrepancy error covariances only includes two terms in this telescoping sum, and consequently, a natural extension is to include more terms within the telescoping sum, which leads to a deep architecture to the statistical model. We refer to this model as the “deep hierarchical generalized transformation” (DHGT) model due to a relationship with the recently introduced hierarchical generalized transformation model. We show that the DHGT is extremely efficient to implement, and can allow for exact Bayesian implementation without the use of MCMC (i.e., we can sample directly from its posterior distribution). We illustrate the DHGT using a simulation and an analysis of the 2017 Haypress wildfire downloaded from the Geospatial Multi-Agency Coordination (GeoMAC) database. These illustrations show that discrepancy errors that arise from common model misspecifications in the spatio-temporal setting can be leveraged to improve prediction.

A dynamical study on stochastic reaction diffusion epidemic model with nonlinear incidence rate.

The current study deals with the stochastic reaction-diffusion epidemic model numerically with two proposed schemes. Such models have many applications in the disease dynamics of wildlife, human life, and others. During the last decade, it is observed that the epidemic models cannot predict the accurate behavior of infectious diseases. The empirical data gained about the spread of the disease shows non-deterministic behavior. It is a strong challenge for researchers to consider stochastic epidemic models. The effect of the stochastic process is analyzed. So, the SIR epidemic model is considered under the influence of the stochastic process. The time noise term is taken as the stochastic source. The coefficient of the stochastic term is a Borel function, and it is used to control the random behavior in the solutions. The proposed stochastic backward Euler scheme and the proposed stochastic implicit finite difference scheme (IFDS) are used for the numerical solution of the underlying model. Both schemes are consistent in the mean square sense. The stability of the schemes is proven with Von-Neumann criteria and schemes are unconditionally stable. The proposed stochastic backward Euler scheme converges toward a disease-free equilibrium and does not converge toward an endemic equilibrium but also possesses negative behavior. The proposed stochastic IFD scheme converges toward disease-free equilibrium and endemic equilibrium. This scheme also preserves positivity. The graphical behavior of the stochastic SIR model is much similar to the classical SIR epidemic model when noise strength approaches zero. The three-dimensional plots of the susceptible and infected individuals are drawn for two cases of endemic equilibrium and disease-free equilibriums. The efficacy of the proposed scheme is shown in the graphical behavior of the test problem for the various values of the parameters.

Tool Degradation Prediction Based on Semimartingale Approximation of Linear Fractional Alpha-Stable Motion and Multi-Feature Fusion

Tool wear will reduce workpieces’ quality and accuracy. In this paper, the vibration signals of the milling process were analyzed, and it was found that historical fluctuations still have an impact on the existing state. First of all, the linear fractional alpha-stable motion (LFSM) was investigated, along with a differential iterative model with it as the noise term is constructed according to the fractional-order Ito formula; the general solution of this model is derived by semimartingale approximation. After that, for the chaotic features of the vibration signal, the time-frequency domain characteristics were extracted using principal component analysis (PCA), and the relationship between the variation of the generalized Hurst exponent and tool wear was established using multifractal detrended fluctuation analysis (MDFA). Then, the maximum prediction length was obtained by the maximum Lyapunov exponent (MLE), which allows for analysis of the vibration signal. Finally, tool condition diagnosis was carried out by the evolving connectionist system (ECoS). The results show that the LFSM iterative model with semimartingale approximation combined with PCA and MDFA are effective for the prediction of vibration trends and tool condition. Further, the monitoring of tool condition using ECoS is also effective.

Spontaneous emission noise resilience of coupled nanolasers

We investigate the spontaneous emission noise resilience of the phase-locked operation of two delay-coupled nanolasers. The system is modeled by semi-classical Maxwell–Bloch rate equations with stochastic Langevin-type noise sources. Our results reveal that a polarization dephasing time of two to three times the cavity photon lifetime maximizes the system’s ability to remain phase-locked in the presence of noise-induced perturbations. The Langevin noise term is caused by spontaneous emission processes which change both the intensity auto-correlation properties of the solitary lasers and the coupled system. In an experimental setup, these quantities are measurable and can be directly compared to our numerical data. The strong parameter dependence of the noise tolerance that we find may show possible routes for the design of robust on-chip integrated networks of nanolasers.

Second-generation time-delay interferometry

Time-Delay Interferometry (TDI) is the data processing technique that cancels the large laser phase fluctuations affecting the heterodyne Doppler measurements made by unequal-arm space-based gravitational wave interferometers. The space of all TDI combinations was first derived under the simplifying assumption of a stationary array, for which the three time-delay operators commute. In this model, any element of the TDI space can be written as a linear combination of four TDI variables, the generators of the "first-generation" TDI space. To adequately suppress the laser phase fluctuations in a realistic array configuration, the rotation of the array and the time-dependence of the six inter-spacecraft light-travel-times have to be accounted for. In the case of the Laser Interferometer Space Antenna (LISA), a joint ESA-NASA mission characterized by slowly time varying arm-lengths, it has been possible to identify data combinations that, to first order in the inter-spacecraft velocities, either exactly cancel or suppress the laser phase fluctuations below the level identified by the noise sources intrinsic to the heterodyne measurements (the so called "secondary" noises). Here we reanalyze the problem of exactly canceling the residual laser noise terms linear in the inter-spacecraft velocities. We find that the procedure for obtaining elements of the $2^{\rm nd}$-generation TDI space can be generalized in an iterative way. This allows us to "lift-up" the generators of the $1^{\rm st}$-generation TDI space and construct elements of the higher order TDI space.

Co-estimation of lithium-ion battery state-of-charge and state-of-health based on fractional-order model

Accurate estimation of lithium-ion battery state of charge and state of health has been the focus of research in battery management systems. Effectively improving the estimation accuracy of battery state parameters is crucial for the safe and stable driving of electric vehicles. In this paper, based on the fractional-order model, a multi-scale cooperative estimation method based on the dual adaptive Unscented Kalman filter is proposed. Firstly, according to the fast and slow time-varying characteristics of the measured parameters, the dual filters perform state estimation of SOC and SOH according to different time scales, alternately updating the information parameters by nesting them with each other and optimizing the noise terms with an adaptive algorithm. Meanwhile, the influence of temperature on the battery parameters is considered, and experimental analysis of the battery is carried out using a variety of different temperatures and operating conditions, as well as the accuracy and stability of the algorithm are verified by simulation. The experimental and simulation results show that the co-estimation method has good accuracy and robustness in both high and low-temperature environments.

On hypothesis testing in latent class and finite mixture stochastic frontier models, with application to a contaminated normal-half normal model

Latent class and finite mixture stochastic frontier models have been proposed as a means of allowing either for technological heterogeneity or more flexible distributions of noise and inefficiency. As in the wider literature on latent class and finite mixture models, we are interested in class enumeration, particularly testing against homogeneity. We apply a modified likelihood ratio test for homogeneity in a stochastic frontier setting, based on established results for non-Gaussian latent class and finite mixture models, and provide evidence from Monte Carlo experiments which suggest the applicability of results regarding a modified likelihood ratio test to the stochastic frontier setting. We demonstrate an application to testing a model with a contaminated normal noise term against a model with a normally distributed noise term, finding that the former is preferred, with significant implications for efficiency prediction.

Detrending and Denoising of Industrial Oscillation Data

Industrial oscillation recordings are often corrupted by underlying nonstationary trend and noisy artifacts, which can occlude features of interest and complicate subsequent oscillation detection and diagnosis. However, there are considerably fewer techniques available in the literature for systematically removing both trend and noise terms from the oscillation measurements. To cater for the general detrending and denoising needs of oscillatory signals, this paper proposes an integrated framework featuring the following steps: (i) The ensemble empirical mode decomposition is first adopted to decompose the industrial single-loop data into several Intrinsic Mode Functions (IMFs). (ii) To eliminate the trend term, a surrogate-based nonstationarity testing algorithm is implemented to automatically identify and remove the requisite IMFs. (iii) By applying canonical correlation analysis on the remained IMFs, the noise-dependent components can be further isolated, which finally yields the detrended and denoised oscillation data. We conducted performance comparison study through extensive simulations and industrial examples. The results demonstrate that the proposed work is a promising tool for industrial oscillation data preprocessing.

Oscillating Behavior of a Compartmental Model with Retarded Noisy Dynamic Infection Rate

Our study is based on an epidemiological compartmental model, the SIRS model. In the SIRS model, each individual is in one of the states susceptible (S), infected (I) or recovered (R), depending on its state of health. In compartment R, an individual is assumed to stay immune within a finite time interval only and then transfers back to the S compartment. We extend the model and allow for a feedback control of the infection rate by mitigation measures which are related to the number of infections. A finite response time of the feedback mechanism is supposed that changes the low-dimensional SIRS model into an infinite-dimensional set of integro-differential (delay-differential) equations. It turns out that the retarded feedback renders the originally stable endemic equilibrium of SIRS (stable focus) to an unstable focus if the delay exceeds a certain critical value. Nonlinear solutions show persistent regular oscillations of the number of infected and susceptible individuals. In the last part we include noise effects from the environment and allow for a fluctuating infection rate. This results in multiplicative noise terms and our model turns into a set of stochastic nonlinear integro-differential equations. Numerical solutions reveal an irregular behavior of repeated disease outbreaks in the form of infection waves with a variety of frequencies and amplitudes.