When underwater degraded images meet logical stochastic resonance

Owing to light attenuation and high background noise, underwater images are significantly degraded, which hiders the development of underwater exploration. However, noise itself can be used to counter noise. In this paper, we apply logical stochastic resonance (LSR) to help detect weak objects from low-quality underwater images. On the basis of analysis of the physical character of underwater images, three models, namely basic dynamical system driven by Gaussian noise, basic dynamical system driven by Ornstein–Uhlenbeck (OU) noise, and dynamical system with extra delay loop, are chosen to study the performance of LSR-based object detection. The main workflow of LSR-based object detection is introduced. To analyze the performance of LSR, we perform explicit experiments and systematically discuss the interplay of additional noise with the system parameters. LSR is proven to be helpful in detecting weak objects from low-quality underwater images. Both OU noise and extra delay loop will help the whole system to maintain stability in a higher noisy background.     

Pattern discrimination and firing behavior of cold receptor model aided with noise

A method for characterizing and identifying firing patterns of neural spike trains is presented. Three characteristic variables defined at sequential moments, including two formal derivatives and the integration of the counting process, are introduced to reflect the temporal patterns of a spike train. This paper also examines how noise interacts with encoding mechanisms of neuronal stimulus in a cold receptor. From ISI series and bifurcation diagrams it is shown that there are considerable differences in interval distributions and impulse patterns caused by purely deterministic simulations and noisy simulations. The ISI-distance can be used as an effective and powerful way to measure the noise effects on spike trains quantitatively. It is found that spike trains observed in cold receptors can be more strongly affected by noise for low temperatures than for high temperatures in some aspects; meanwhile, spike train has greater variability with the noise intensity increasing.     

Turbulent travel speeds in nonlinear vehicle dynamics

Quarter car models of vehicles rolling on wavy roads lead to limit cycles of travel speed and acceleration with period doublings and bifurcation effects for appropriate driving force parameters. In case of narrow-banded road excitations, speed jumps occur, additionally. This has the consequence that the driving speed becomes turbulent. Bifurcation and jump effects vanish with growing vehicle damping. The same happens for increasing bandwidth of road excitations when, e.g., on flat highways there are no big road waves but only small noisy slope processes generated by rough road surfaces. The paper derives a new stability condition in mean. Numerical time integrations are stabilized by means of polar coordinates. Equivalently, Fourier series expansions are introduced in the angle domain. Phase portraits of travel speed and acceleration show new period-doublings of limit cycles when speed gets stuck before resonance. The paper extends these investigations to the stochastic case that road surfaces are random generated by filtered white noise. By means of Gaussian closure, a nonlinear mean speed equation is derived which includes the extreme cases of wavy roads and road noise.

     

Systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds

In almost all real-world application such as electric vehicles, system outputs are corrupted by various types of noises. Although the sliding mode controller is a popular controller in the electrical vehicle applications, it is vulnerable to the noisy signals, and even intensify its unwilling effects. In this paper, to eliminate process noise and stabilize the vehicle in noisy conditions, a minimum variance controller is utilized. It is shown that this controller is able to decrease the system output variance, optimally. Besides, it can track yaw rate and velocity reference inputs. Also stability condition is reached. Furthermore, decreasing control signal variance along with output variance is studied in this paper. Finally, the proposed approach is compared with sliding mode controller in noisy condition on four wheel drive electric vehicle which is simulated in MATLAB and CARSIM environments.     

The complete synchronization of Morris–Lecar neurons influenced by noise

The influence of noise on the complete synchronization in a Morris–Lecar (ML) model neuronal system is studied in this work. Two individual ML neurons with different initial conditions can discharge completely synchronously when the noise intensity is large enough, and for a smaller reversal potential (V _Ca), the uncoupled neuronal system could be induced to a complete synchronization state under smaller noise intensity. Two coupled ML neurons could be synchronized under very small noise intensity even in the case of weak coupling, the synchronization characteristics of the two coupled neurons are discussed by analyzing the Similarity Function (S(0)) of their membrane potentials, which proves that noise can promote the complete synchronization. The critical noise intensity (D _j ) to induce complete synchronization in coupled ML neurons will decrease with the increase of V _Ca. This result is helpful to study the synchronization and the code of a neural system.     

含噪双稳杜芬振子矩方程的分岔与随机共振

研究了含噪声的双稳杜芬振子矩方程的分岔与随机共振的关系，并根据它们的关系, 从另 一个角度揭示了随机共振发生的机制. 首先在It?方程的基础上，导出了双稳杜芬振子在白噪声和弱周期信号作用下的矩方程，其次以噪声强度 为分岔参数分析了矩方程的分岔特性，再次分析了矩方程的分岔与双稳杜芬振子随机共振 之间的关系，最后根据该对应关系从另一种观点提出了双稳杜芬振子随机共振的机制，该 机制是由于以噪声强度为分岔参数的矩方程发生了分岔，而分岔使得原系统响应均值的能量分布发生了转移，使能 量向频率等于输入信号频率的分量处集中，使得弱信号得到了放大，随机共振发生了.     

Effects of non-Gaussian noise on logical stochastic resonance in a triple-well potential system

In this paper, we have investigated the phenomenon of logical stochastic resonance in a trip-well potential system driven by a colored non-Gaussian noise. The effects of a non-Gaussian noise on logical stochastic resonance have been discussed, and we have found that the reliability of the logic operation is dependent on the parameter q that indicates the departure from Gaussianity. The reliable region in the parameter plane of correlation time τ and noise strength D appears and expands with the decrease of q. Furthermore, it has been found that the reliable region in the plane (q,D) expands with the increase of noise color. The phenomenon can be explained successfully by the approach of Fokker–Planck equation.     

An adaptive vibrational resonance method based on cascaded varying stable-state nonlinear systems and its application in rotating machine fault detection

A weak character signal with low frequency can be detected based on the mechanism of vibrational resonance (VR). The detection performance of VR is determined by the synergy of a weak low-frequency input signal, an injected high-frequency sinusoidal interference and the nonlinear system(s). In engineering applications, there are many weak fault signals with high character frequencies. These fault signals are usually submerged in strong background noise. To detect these weak signals, an adaptive detection method for a weak high-frequency fault signal is proposed in this paper. This method is based on the mechanics of VR and cascaded varying stable-state nonlinear systems (VSSNSs). Partial background noise with high frequency is regarded as a special type of high-frequency interference and an energy source that protrudes a weak fault signal. In this way, high-frequency background noise is utilized in a VSSNS. To improve the detection ability, manually generated high-frequency interference is injected into another VSSNS. The VSSNS can be transformed into a monostable state, bistable state or tristable state by tuning the system parameters. The proposed method is validated by a simulation signal and industrial applications. The results show the effectiveness of the proposed method to detect a weak high-frequency character signal in engineering problems.

     

The influence of normal flow boundary conditions on spurious modes in finite element solutions to the shallow water equations

Finite element solutions of the primitive equation (PE) form of the shallow water equations are notorious for the severe spurious 2Δx modes which appear. Wave equation (WE) solutions do not exhibit these numerical modes. In this paper we show that the severe spurious modes in PE solutions are strongly influenced by essential normal flow boundary conditions in the coupled continuity-momentum system of equations. This is demonstrated through numerical examples that avoid the use of essential normal flow boundary conditions either by specifying elevation values over the entire boundary or by implementing natural flow boundary conditions in the weak weighted residual form of the continuity equation. Results from a series of convergence tests show that PE solutions are of nearly the same quality as WE solutions when spurious modes are suppressed by alternative specification of the boundary conditions. Network intercomparisons indicate that varying nodal support does not excite spurious modes in a solution, although it does enhance the spurious modes introduced when an essential normal flow boundary condition is used. Dispersion analysis of discrete equations for interior and boundary nodes offers an explanation of the observed solution behaviour. For certain PE algorithms a mixed situation can arise where the boundary nodes exhibit a monotonic (noise-free) dispersion relationship and the interior nodes exhibit a folded (noisy) dispersion relationship. We have found that the mixed situation occurs when all boundary nodes are specified elevation nodes (which are enforced as essential conditions in the continuity equation) or when specified flow boundary nodes are treated as natural boundary conditions in the continuity equation. In either case the effect is to generate a solution that is essentially free of noise. Apparently, the monotonic dispersion behaviour at the boundaries suppresses the otherwise noisy behaviour caused by the folded dispersion relation on the interior.     

拟可积哈密顿系统中噪声诱发的混沌运动

研究拟可积哈密顿系统在谐和与噪声激励联合作用下的混沌运动。通过对噪声性质的假定,并利用动力系统理论,给出了高维梅尔尼科夫方法应用于随机拟可积哈密顿系统的推广形式。根据这种推广的方法,研究了谐和与高斯白噪声激励联合使用下两自由度拟可积哈密顿系统 同宿分岔,得出了系统发生混沌运动的参数阈值,并由此讨论了噪声对系统的混沌运动的影响。蒙特-卡罗方法模拟、李雅普诺夫指数等数值结果表明,这种推广的方法是有效的。     

Moment Lyapunov exponent of three-dimensional system under bounded noise excitation

In the present paper,the moment Lyapunov exponent of a codimensional two-bifurcation system is evaluted,which is on a three-dimensional central manifold and subjected to a parametric excitation by the ...     

Bifurcations in a birhythmic biological system with time-delayed noise

We study the effects of recycled noise on the dynamics of a birhythmic biological system. This noise is generated by the superposition of a primary Gaussian white noise source with a second component (its replicas delayed of time τ). We find that under the influence of this kind of noise, the dynamics of the birhythmic biological system can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary probability distribution. Analytical results are obtained following the quasiharmonic assumption through the Langevin and Fokker–Planck equations. Comparing the analytical and numerical results, we find good agreement when the frequencies of both attractors are equal, while the predictions of the analytic estimates deteriorate when the two frequencies depart. We also find that the increase of noise intensity leads to coherence resonance.     

The non‐reflective interface: an innovative forcing technique for computational acoustic hybrid methods

The present article concerns a commonly used methodology for the numerical simulation of acoustic emission and propagation phenomena. We consider the so‐called multi‐stage hybrid acoustic approach, in which a given noise problem is simulated via a sequence of weakly coupled computations of noise generation and acoustic propagation stages, wherein the simulation of the propagation stage is based on advanced Computational AeroAcoustics (CAA) techniques. The paper introduces an original forcing technique, namely, the Non‐Reflective Interface (NRI), to enable the transfer of an acoustic signal from an a priori noise generation stage into a CAA‐based acoustic propagation phase. Unlike most existing forcing techniques, the NRI is non‐reflective (or anechoic) in nature and, therefore, can properly handle the backscattering effects arising during the noise propagation stage. This attribute makes the NRI‐based weak‐coupling procedure and the associated CAA‐based hybrid approach compatible with a larger variety of realistic noise problems (such as those involving installed configurations in wind tunnel experiments, for instance). The NRI technique is first validated via several test cases of increasing complexity and is then applied to two aerodynamic noise problems. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.     

Experimental study of vortex–structure interaction noise radiated from rod–airfoil configurations

Vortex–structure interaction noise radiated from an airfoil embedded in the wake of a rod is investigated experimentally in an anechoic wind tunnel by means of a phased microphone array for acoustic tests and particle image velocimetry (PIV) for the flow field measurements. The rod–airfoil configuration is varied by changing the rod diameter (D), adjusting the cross-stream position (Y) of the rod and the streamwise gap (L) between the rod and the airfoil leading edge. Two noise control concepts, including “air blowing” on the upstream rod and a soft-vane leading edge on the airfoil, are applied to control the vortex–structure interaction noise. The motivation behind this study is to investigate the effects of the three parameters on the characteristics of the radiated noise and then explore the influences of the noise control concepts. Both the vortex–structure interaction noise and the rod vortex shedding tonal noise are analysed. The acoustic test results show that both the position and magnitude of the dominant noise source of the rod–airfoil model are highly dependent on the parameters considered. In the case where the vortex–structure interaction noise is dominant, the application of the air blowing and the soft vane can effectively attenuate the interaction noise. Flow field measurements suggest that the intensity of the vortex–structure interaction and the flow impingement on the airfoil leading edge are suppressed by the control methods, giving a reduction in noise.     

Lower Semicontinuity Properties of Functionals with Free Discontinuities

This paper is concerned with functionals with free discontinuities, considered as depending on the set variable. A splitting operation divides the sets in which the functional takes low values in the union of a noise part and a macroscopic part. Then we show lower semicontinuity results on the limit of the macroscopic parts by Hausdorff distance, along minimizing sequences.     

高斯色噪声和谐波激励共同作用下耦合SD振子的混沌研究

耦合SD振子作为一种典型的负刚度振子, 在工程设计中有广泛应用. 同时高斯色噪声广泛存在于外界环境中, 并可能诱发系统产生复杂的非线性动力学行为, 因此其随机动力学是非线性动力学研究的热点和难点问题. 本文研究了高斯色噪声和谐波激励共同作用下双稳态耦合SD振子的混沌动力学, 由于耦合SD振子的刚度项为超越函数形式, 无法直接给出系统同宿轨道的解析表达式, 给混沌阈值的分析造成了很大的困难. 为此, 本文首先采用分段线性近似拟合该振子的刚度项, 发展了高斯色噪声和谐波激励共同作用下的非光滑系统的随机梅尔尼科夫方法. 其次, 基于随机梅尔尼科夫过程, 利用均方准则和相流函数理论分别得到了弱噪声和强噪声情况下该振子混沌阈值的解析表达式, 讨论了噪声强度对混沌动力学的影响. 研究结果表明, 随着噪声强度的增大混沌区域增大, 即增大噪声强度更容易诱发耦合SD振子产生混沌. 当阻尼一定时, 弱噪声情况下混沌阈值随噪声强度的增加而减小; 但是强噪声情况下噪声强度对混沌阈值的影响正好相反. 最后, 数值结果表明, 利用文中的方法研究高斯色噪声和谐波激励共同作用下耦合SD振子的混沌是有效的.本文的结果为随机非光滑系统的混沌动力学研究提供了一定的理论指导.      

Secure communication in wireless sensor networks based on chaos synchronization using adaptive sliding mode control

Due to resource constraints in wireless sensor networks and the presence of unwanted conditions in communication systems and transmission channels, the suggestion of a robust method which provides battery lifetime increment and relative security is of vital importance. This paper considers the secure communication in wireless sensor networks based on new robust adaptive finite time chaos synchronization approach in the presence of noise and uncertainty. For this purpose, the modified Chua oscillators are added to the base station and sensor nodes to generate the chaotic signals. Chaotic signals are impregnated with the noise and uncertainty. At first, we apply the modified independent component analysis to separate the noise from the chaotic signals. Then, using the adaptive finite-time sliding mode controller, a control law and an adaptive parameter-tuning method is proposed to achieve the finite-time chaos synchronization under the noisy conditions and parametric uncertainties. Synchronization between the base station and each of the sensor nodes is realized by multiplying a selection matrix by the specified chaotic signal which is broadcasted by the base station to the sensor nodes. Simulation results are presented to show the effectiveness and applicability of the proposed technique.     

Nonlinear filters for chaotic oscillatory systems

This paper examines and contrasts the feasibility of joint state and parameter estimation of noise-driven chaotic systems using the extended Kalman filter (EKF), ensemble Kalman filter (EnKF), and particle filter (PF). In particular, we consider the chaotic vibration of a noisy Duffing oscillator perturbed by combined harmonic and random inputs ensuing a transition probability density function (pdf) of motion which displays strongly non-Gaussian features. This system offers computational simplicity while exhibiting a kaleidoscope of dynamical behavior with a slight change of input and system parameters. An extensive numerical study is undertaken to contrast the performance of various nonlinear filtering algorithms with respect to sparsity of observational data and strength of model and measurement noise. In general, the performance of EnKF is better than PF for smaller ensemble size, while for larger ensembles PF outperforms EnKF. For moderate measurement noise and frequent measurement data, EKF is able to correctly track the dynamics of the system. However, EKF performance is unsatisfactory in the presence of sparse observational data or strong measurement noise.     

The effects of initial perturbation to mixing-layer noise

The far-field noise radiated from mixing layers is determined by the near-field flow dynamics which is sensitive to the initial perturbation of instability introduced physically or numerically. This study focuses on the effects of the phase delay in two initial perturbations, one at the fundamental wave number and the other at its subharmonic both calculated from linear instability analysis, on the sound generation in mixing layers. When different phase delays φ₁ changing from zero to 2π is applied on the fundamental mode, we observe different vortex merging processes (e.g. vortex pairing or tearing). The strong nonlinear interaction in the merging process generates most of the noise from mixing layers. There shows a pattern in a period of 2π for the response of far-field sound to the change of φ₁. Similar effects on the dynamics and acoustics can be achieved by adding different phase delays φ₂ to the subharmonic mode instead, however, the response repeats in a period of only π for φ₂. The effects of the combination of different phase delays to other parameters, including the amplitude and wave number for each perturbations, are also investigated. All the results indicate a critical role of nonlinearity in the sound generation mechanism of mixing layers.     

Effect of noise on erosion of safe basin in power system

We study the effect of Gaussian white noise on erosion of safe basin in a simple model of power system whose safe basin is integral in the absence of noise. The stochastic Melnikov method is first applied to predict the onset of basin erosion when the noise excitation is present in system. And then the eroded basins are simulated according to the necessary restrictions for the system’s parameters. It is found that for the noisy power system when the noise intensity σ is greater than a threshold, basin erosion occurs and as σ is further increased basin erosion is aggravated. These studies imply that random noise excitation can induce and enhance the basin erosion in the power system.