White Noise Perturbation Research Articles

Stochastic SIR Epidemiological Model With Two Levels of Severity

In this paper, we develop an epidemic model to analyze the spread of an infectious disease with two levels of severity within a population of varying size. Additionally, we examine the stability of the disease-free equilibrium.
 Such a model is suitable for the dynamics of COVID-19 disease spread. If the two types of infected individuals have different recovery rates, then there is no endemic equilibrium; only the disease-free equilibrium will be the subject of our study. We then study both the deterministic model and a stochastic version. The stochastic model is obtained by perturbing the contact rate using white noise. For the deterministic model, we have shown that if the basic reproduction number R_0 < 1, then the equilibrium state is globally asymptotically stable by using Lyapunov function. This implies that the disease will disappear, and the entire population will become susceptible. For the stochastic version, we demonstrate that the system admits a unique positive global solution that exists within a positively invariant domain. Under suitable conditions on the intensity of the white noise perturbations, we prove that the number of infectious individuals converge almost surely exponentially to zero and the disease-free equilibrium of system is stochastically asymptotically stable in the large provided. Finally, we give some numerical simulations to illustrate our theoretical results.

Continuous wave cavity ringdown spectroscopy incorporating with an off-axis arrangement, white noise perturbation, and optical re-injection

We present an ultra-sensitive continuous wave cavity ringdown spectroscopy (cw-CRDS) spectrometer to record high resolution spectra of reactive radicals and ions in a pulsed supersonic plasma. The spectrometer employs a home-made external cavity diode laser as the tunable light source, with its wavelength modulated by radio-frequency white noise. The ringdown cavity with a finesse of ∼105 is arranged with an off-axis alignment. The combination of the off-axis cavity and the white-noise perturbed laser yields quasi-continuum laser-cavity coupling without the need of mode matching. The cavity is further incorporated with an extra multi-pass cavity for optical re-injection of light reflected off the master cavity, which significantly increases the throughput power of the high-finesse cavity. A fast switchable semiconductor optical amplifier is used to modulate the cw laser beam to square wave pulses and to initialize timing controlled ringdown events, which are synchronized to the plasma pulses with an accuracy of ∼3 µs. The performance and potential of the cw-CRDS spectrometer are illustrated and discussed, based on the high resolution near-infrared spectroscopic detection of trace 13C13C radicals generated in a pulsed supersonic C2H2/Ar plasma with a pulse duration of ∼50 µs.

A large deviation principle for fluids of third grade

ABSTRACT This article establishes a large deviation principle for a non-Newtonian fluid of differential type, filling a two-dimensional non-axisymmetric bounded domain with slip boundary conditions. More precisely, we show that the solutions of small stochastic white noise perturbations of the third grade fluid equations converges to the deterministic solution, as the intensity of the noise goes to zero. Moreover, this convergence has an exponential rate given by a suitable rate function. To establish such asymptotic result, we follow the weak convergence approach introduced by Budhiraja, Dupuis and Ellis.

Fractional discrete Temimi–Ansari method with singular and nonsingular operators: applications to electrical circuits

The goal of this article is to present a recently developed numerical approach for solving fractional stochastic differential equations with a singular Caputo kernel and a nonsingular Caputo–Fabrizio and Atangana–Baleanu (ABC) kernel. The proposed method is based on the discrete Temimi–Ansari method, which is combined with three different numerical schemes that are appropriate for the new fractional derivative operators. The proposed technique is used to investigate the effects of Gaussian white-noise and Gaussian colored-noise perturbations on the potential source and resistance in fractional stochastic electrical circuits. The proposed method’s robustness and efficiency were demonstrated by comparing its results to those of the stochastic Runge–Kutta method (SRK). The valuable point in this article is that the resulting numerical scheme is able to combine two powerful methods that can be extended into more complex stochastic models. The comparison of different fractional derivatives using Mathematica 12 software has been obtained and the simulation results demonstrate the merit of the contributed method.

Abstract 052: Central Gain For Sympathetic Outflow Is Increased In Postural Tachycardia Syndrome

White noise perturbations using neck suction (NS) can be applied to identify open loop transfer function in a closed loop baroreflex system. It allows an estimation of central arc transfer function (H1) which represents how afferent baroreceptor information is translated into sympathetic outflow and peripheral arc transfer function (H2) which describes how muscle sympathetic nerve activity (MSNA) affects blood pressure (BP). We hypothesize that patients with postural tachycardia syndrome (POTS) have elevated central gain compared to healthy controls (CONT). We recorded raw MSNA and continuous finger BP during randomized NS (0 to -50 mmHg, 0.03-0.3 Hz) and controlled breathing at 0.25 Hz for 6 minutes in 10 female POTS and 9 female CONT. Both groups were matched for age (28.4±2.1 vs. 31.9±3.0 p=0.80) and BMI (23.0±0.7 vs 24.5±1.0, p=0.25). We derived the continuous spike rate using wavelet-based denoising. We estimated median central gain in H1 and peripheral gain in H2 for low (LF: 0.04-0.15 Hz) and high (HF: 0.15-0.4 Hz) frequency ranges (Figure). We found that POTS have significantly higher central gain in LF range (2.44±0.38 vs 1.53±0.24 spikes/s/mmHg, p=0.028, MN±SE) but not in HF range (9.02±3.02 vs. 5.06±0.52 spikes/s/mmHg, p=0.604). Median peripheral gains were comparable in LF (0.68±0.15 vs 0.58±0.09 mmHg/spikes/s, p>0.99) and HF ranges (0.18±0.02 vs 0.21±0.03 mmHg/spikes/s, p=0.497). Our results indicate that POTS have higher recruitment of neural sympathetic spike activity during BP oscillations in the LF range. This could explain why higher sympathetic activation/modulation and greater BP fluctuations in the LF range are found during upright in POTS.

Emergent behaviors of the Justh-Krishnaprasad model with uncertain communications

We study stochastic alignment of the Justh-Krishnaprasad(J-K) model under a multiplicative noise. Justh and Krishnaprasad proposed a planar Newtonian particle model for an ensemble of flocking agents moving with a unit speed, where the dynamics of the heading angles (of velocities) is governed by a generalized Kuramoto-type model with a communication weight. In this paper, we are interested in the random perturbation of the communication weight, which is represented by a multiplicative noise. Unlike the additive white noise perturbation, the multiplicative one is known not to violate collective behaviors. We present sufficient conditions leading to the nematic alignment of velocities in terms of the system parameters and initial data. Our analysis begins with the two-body system, where it turns out to be stable under the effect of noise, showing that the nematic alignment occurs when the communication is sufficiently strong with respect to the noise strength. For the general many-body system with a corresponding condition, we showed the accumulation of heading angles modulo π/2 and the stochastic stability of nematic alignment under the assumption of the constant communication weight, which suggests a strong evidence for the nematic alignment. This analysis is done by transporting the system into a similar form to the stochastic Kuramoto model, where we refined the order parameter analysis in order to extend local stochastic stability results to the whole circle of heading angles. We present several numerical simulations and compare them with analytical results.

Comparison of Perturbation Strategies for the Initial Ensemble in Ocean Data Assimilation with a Fully Coupled Earth System Model

It is widely recognized that the initial ensemble describes the uncertainty of the variables and, thus, affects the performance of ensemble-based assimilation techniques, which is investigated in this paper with experiments using the Community Earth System Model (CESM) and the Data Assimilation Research Testbed (DART) assimilation software. Five perturbation strategies involving adding noises of different patterns and with/without extra integration are compared in the observation system simulation experiments framework, in which the SST is assimilated with the ensemble adjustment Kalman filter method. The comparison results show that for the observed variables (sea surface temperature), the differences in the initial ensemble lead to different rate of convergence in the assimilation, but all experiments reach convergence after three months. However, other variables (sea surface height and sea surface salinity) are more sensitive to the initial ensemble. The analysis of variance results reveal that the white-noise perturbation scheme has the largest RMSE. After excluding the effect of the white noise perturbation scheme, it can be found that the difference in the effect of different initial ensembles on the SSH with only assimilated SST is concentrated in the region of the Antarctic Circumpolar Current, which is related to the spread of the covariance between the SSH and the SST.

Stochastic modulational instability in the nonlinear Schrödinger equation with colored random dispersion

We study modulational instability (MI) in optical fibers with random group-velocity dispersion (GVD). We consider Gaussian and dichotomous colored stochastic processes. We resort to different analytical methods (namely, the cumulant expansion and the functional approach) and assess their reliability in estimating the MI gain of stochastic origin. If the power spectral density (PSD) of the GVD fluctuations is centered at null wave number, we obtain low-frequency MI sidelobes which converge to those given by a white-noise perturbation when the correlation length tends to 0. If instead the stochastic processes are modulated in space, one or more MI sidelobe pairs corresponding to the well-known parametric resonance (PR) condition can be found. A transition from small and broad sidelobes to peaks nearly indistinguishable from PR-MI is predicted, in the limit of large perturbation amplitudes and correlation lengths of the random process. We find that the cumulant expansion provides good analytical estimates for small PSD values and small correlation lengths, when the MI gain is very small. The functional approach is rigorous only for the dichotomous processes, but allows us to model a wider range of parameters and to predict the existence of MI sidelobes comparable to those observed in homogeneous fibers of anomalous GVD.

Stationary distribution of a stochastic predator–prey model with hunting cooperation

In this paper, we propose a stochastic predator–prey model with hunting cooperation and nonlinear perturbation of white noise. The sufficient criteria for the existence of a unique ergodic stationary distribution are established by constructing suitable Lyapunov functions. It reveals that the white noise has a significant impact on the dynamical behavior of the model.

Atypical exit events near a repelling equilibrium

We consider exit problems for small, white noise perturbations of a dynamical system generated by a vector field and a domain containing a critical point with all positive eigenvalues of linearization. We prove that, in the vanishing noise limit, the probability of exit through a generic set on the boundary is asymptotically polynomial in the noise strength with exponent depending on the mutual position of the set and the flag of the invariant manifolds associated with the top eigenvalues. Furthermore, we compute the limiting exit distributions conditioned on atypical exit events of polynomially small probability and show that the limits are Radon–Nikodym equivalent to volume measures on certain manifolds that we construct. This situation is in sharp contrast with the large deviation picture where the limiting conditional distributions are point masses.

Data Assimilation Using WRFDA Over the Terminal Area of Rio de Janeiro

Abstract The impact of the data assimilation process of air temperature and relative humidity from surface meteorological stations and sounding at airports in the terminal area of Rio de Janeiro is evaluated using the Weather Research and Forecast Data Assimilation system. Synthetic data of temperature, relative humidity and wind are generated in the locations of airport sensors by applying a white-noise perturbation in the forecast data. Results show a positive overall impact of the assimilation process with the removal of part of the noise in the observation data but keeping the effect of local conditions in the later timesteps of the simulation. In addition, with the assimilation process there is a global reduction of the error between the analysis data and the observation data. In the future, a neural network will be trained to emulate the data assimilation process to speed-up the assimilation process in the WRF model.

Stochastic approach for noise analysis and parameter estimation for RC and RLC electrical circuits

‎The main focus of this paper is to examine the effects of Gaussian white noise and Gaussian colored noise perturbations on the voltage of RC and RLC electrical circuits‎. ‎For this purpose‎, ‎the input voltage is assumed to be corrupted by the white noise and the charge is observed at discrete time points‎. ‎The deterministic models will be transferred to stochastic differential equations and these models will be solved analytically using Ito's lemma‎. ‎Random colored noise excitations‎, ‎more close to real environmental excitations‎, ‎so Gaussian colored noise is considered in these electrical circuits‎. ‎Scince there is not always a closed form analytical solution for stochastic differential equations‎, ‎then these models will be solved numerically based on the Euler‎- ‎maruyama scheme‎. ‎The parameter estimation for these stochastic models is investigated using the least square estimator when the parameters are missing data that it is a concern in electrical engeineering‎. ‎Finally‎, ‎some numerical simulations via Matlab programming are carried out in order to show the efficiency and accuracy of the present work‎.

Antiforensics of Speech Resampling Using Dual‐Path Strategy

Resampling is an operation to convert a digital speech from a given sampling rate to a different one. It can be used to interface two systems with different sampling rates. Unfortunately, resampling may also be intentionally utilized as a postoperation to remove the manipulated artifacts left by pitch shifting, splicing, etc. To detect the resampling, some forensic detectors have been proposed. Little consideration, however, has been given to the security of these detectors themselves. To expose weaknesses of these resampling detectors and hide the resampling artifacts, a dual‐path resampling antiforensic framework is proposed in this paper. In the proposed framework, 1D median filtering is utilized to destroy the linear correlation between the adjacent speech samples introduced by resampling on low‐frequency component. And for high‐frequency component, Gaussian white noise perturbation (GWNP) is adopted to destroy the periodic resampling traces. The experimental results show that the proposed method successfully deceives the existing resampling forensic algorithms while keeping good perceptual quality of the resampled speech.

Stability analysis of a SIR epidemic model with random parametric perturbations

This paper is concerned with a SIR model for the spread of an epidemic amongst a population of individuals with random additive perturbations of the transmission rate. Recently, many papers are devoted to the case of the Gaussian white noise perturbation. However, this model violates the condition of positivity of the transmission rate. In the paper we consider three models of the random perturbation which do not change this condition. The two of them are the telegraphic noise, trichotomous noise and the third is the bounded noise. Explicit conditions of the amost sure asymptotic stability of disease-free equilibrium state are obtained in the case of the first two models. An efficient numerical procedure is proposed for the construction of stability charts in the case of bounded noise. The effect of random perturbations on the stability behavior of disease-free equilibrium is discussed. Some transient mean-square properties of the SIR stochastic epidemic model are also presented.

A Study of the Effects of Anthropogenic Gaseous Emissions on the Microphysical Properties of Landfalling Typhoon Nida (2016) over China

Using the Weather Research and Forecasting model with chemistry module (WRF-Chem), Typhoon Nida (2016) was simulated to investigate the effects of anthropogenic gaseous emissions on the vortex system. Based on the Multi-resolution Emission Inventory for China (MEIC), three certain experiments were conducted: one with base-level emission intensity (CTRL), one with one-tenth the emission of SO2 (SO2_C), and one with one-tenth the emission of NH3 (NH3_C). Results show that the simulations reasonably reproduced the typhoon’s track and intensity, which were slightly sensitive to the anthropogenic gaseous emissions. When the typhoon was located over the ocean, a prolonged duration of raindrop growth and more precipitation occurred in CTRL run. The strongest updraft in CTRL is attributed to the maximum latent heating through water vapor condensation. During the landfalling period, larger (smaller) differential reflectivities in the main-core of the vortex were produced in NH3_C (SO2_C) run. Such opposite changes of raindrop size distributions may lead to stronger (weaker) rainfall intensity, and the ice-related microphysical processes and the relative humidity in low troposphere were two possible influential factors. Moreover, additional ten-member ensemble results in which white noise perturbations were added to the potential temperature field, indicated that the uncertainty of thermodynamic field in the current numerical model should not be ignored when exploring the impacts of aerosol on the microphysics and TC precipitation.

Application of White Noise Perturbation in Wavelength Modulated Off-Axis Integrated Cavity Spectroscopy

Application of White Noise Perturbation in Wavelength Modulated Off-Axis Integrated Cavity Spectroscopy

The Role of Multiscale Interaction in Tropical Cyclogenesis and Its Predictability in Near-Global Aquaplanet Cloud-Resolving Simulations

Abstract Tropical cyclogenesis (TCG) is a multiscale process that involves interactions between large-scale circulation and small-scale convection. A near-global aquaplanet cloud-resolving model (NGAqua) with 4-km horizontal grid spacing that produces tropical cyclones (TCs) is used to investigate TCG and its predictability. This study analyzes an ensemble of three 20-day NGAqua simulations, with initial white-noise perturbations of low-level humidity. TCs develop spontaneously from the northern edge of the intertropical convergence zone (ITCZ), where large-scale flows and tropical convection provide necessary conditions for barotropic instability. Zonal bands of positive low-level absolute vorticity organize into cyclonic vortices, some of which develop into TCs. A new algorithm is developed to track the cyclonic vortices. A vortex-following framework analysis of the low-level vorticity budget shows that vertical stretching of absolute vorticity due to convective heating contributes positively to the vorticity spinup of the TCs. A case study and composite analyses suggest that sufficient humidity is key for convective development. TCG in these three NGAqua simulations undergoes the same series of interactions. The locations of cyclonic vortices are broadly predetermined by planetary-scale circulation and humidity patterns associated with ITCZ breakdown, which are predictable up to 10 days. Whether and when the cyclonic vortices become TCs depend on the somewhat more random feedback between convection and vorticity.

Numerical Investigation on Aero-optical Reduction for Supersonic Turbulent Mixing Layer

The tangential injection flow commingled with the mainstream could be abstracted as mixing layer, and profound importance is attached to aero-optical reduction for film-cooling target-seeking vehicles in engineering application. Leveraging the in-house code based on explicit fifth-order Weighted Compact Nonlinear Scheme and ray-tracing method, the supersonic mixing layer is numerically simulated to investigate the effect of inflow disturbance on large-scale structure growth and aero-optical reduction. The vortex growth would be stimulated somewhere when the frequency of inflow perturbation added is close to the local characteristic most unstable value. Based on such cognition, different techniques of super-harmonic and sub-harmonic disturbance are employed for effective aero-optical suppression schemes in the following research. The sub-harmonic one without phase shift shows such ability in the whole turbulent region, and additional perturbation of white noise is also promising for better control consequence.

Assessing the Impact of Stochastic Perturbations in Cloud Microphysics using GOES-16 Infrared Brightness Temperatures

AbstractIn this study, infrared brightness temperatures (BTs) are used to examine how applying stochastic perturbed parameter (SPP) methodology to the widely used Thompson–Eidhammer cloud microphysics scheme impacts the cloud field in high-resolution forecasts. Modifications are made to add stochastic perturbations to three parameters controlling cloud generation and dissipation processes. Two five-member ensembles are generated, one using the microphysics parameter perturbations (SPP-MP) and another where white noise perturbations were added to potential temperature fields at initialization time (Control). The impact of the SPP method was assessed using simulated and observed GOES-16 BTs. This analysis uses pixel-based and object-based methods to assess the impact on the cloud field. Pixel-based methods revealed that the SPP-MP BTs are slightly more accurate than the Control BTs. However, too few pixels with a BT lower than 270 K result in a positive bias compared to the observations. A negative bias compared to the observations is observed when only analyzing lower BTs. The spread of the ensemble BTs was analyzed using the continuous ranked probability score differences, with the SPP-MP ensemble BTs having less (more) spread during May (January) compared to the Control. Object-based analysis using the Method for Object-Based Diagnostic Evaluation revealed the upper-level cloud objects are smaller in the SPP-MP ensemble than the Control but a lower bias exists in the SPP-MP BTs compared to the Control BTs when overlapping matching objects. However, there is no clear distinction between the SPP-MP and Control ensemble members during the evolution of objects, Overall, the SPP-MP perturbations result in lower BTs compared to the Control ensemble and more cloudy pixels.

Experimental Verification of Fault Identification for Overactuated System With a Scaled-Down Electric Vehicle

The experimental verification of the optimal input design method for fault identification is performed using a scaled-down overactuated electric vehicle. In the previous study, online fault identification was achieved by utilizing all the characteristics of an overactuated system (Park and Park, 2016). The perturbation input signal for the actuator fault identification can be applied to the faulty actuators to suppress most of the control performance loss. The scaled-down vehicle contains four independent driving motors and four independent wheel steering motors to model an extremely overactuated system. The lateral velocity and yaw rate are estimated using the state observer to realize feedback control, and the cornering stiffness is determined based on the estimated values. Experimental verification is performed using steady state cornering maneuvers with sudden actuator faults. The experiments with the scaled-down vehicle support the performance of the optimal input design method. When sensor noise and modeling uncertainties exist, the results from our method were much more precise than the results obtained using the conventional white noise perturbation input signal.