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This paper describes an adaptive noise generator circuit suitable for on-chip simulations of stochastic chemical kinetics. The circuit uses amplified BJT white noise and adaptive low-pass filtering to emulate the power spectrum and auto-correlation of random telegraph signals (RTS) with Poisson-distributed level transitions. A current-mode implementation in the IHP 0.25 µm BiCMOS process shows excellent agreement with theoretical results from the Gillespie stochastic simulation algorithm over a 60 dB range in mean current levels (modeling molecule count numbers). The circuit has an estimated layout area of 0.01 mm2 and typically consumes 100 µA, which are 10× and 8× better, respectively, than prior implementations.

Piezoelectric energy harvesters are electromechanical systems, capable to convert ambient dispersed mechanical vibrations into usable electrical energy. They can be used for supplying power to sensors and actuators that are wireless connected, miniaturized and remote located. In this work, we analyze piezoelectric energy harvesters for mechanical vibrations in the frequency domain. White Gaussian and colored noise models for random vibrations are considered. The governing equations for the harvester are derived from mechanical properties, the characteristic relationships of piezoelectric materials, and circuit description of the electrical load. We show that the energy harvester can be modelled by cascade connected electromechanical two-ports, and that frequency domain methods are the perfect tool for analysis. Formulas for the harvested power and power efficiency are derived. We also show that application of matching networks reduces the impedance mismatch between the mechanical and the electrical parts, significantly increasing the harvested power and power efficiency. The matching network solution is compared to others, previously proposed solutions, such as application of power-factor correction. We show that the matching network offers nine times more average power and better power efficiency than the unmatched resistive load, and increases by more than 10% the harvested power and efficiency, with respect to the power-factor corrected solution.

In this paper, we study the asymptotic behavior of the quadratic variation for the class of AR(1) processes driven by white noise in the second Wiener chaos. Using tools from the analysis on Wiener space, we give an upper bound for the total-variation speed of convergence to the normal law, which we apply to study the estimation of the model’s mean-reversion. Simulations are performed to illustrate the theoretical results.

In the missile-borne Strapdown Inertial Navigation System/Global Navigation Satellite System (SINS/GNSS) integrated navigation system, due to the factors such as the high dynamics, the signal blocking by obstacles, the signal intefereces, etc., there always exist pulse interferences or measurement information interruptions in the satellite receiver, which make nonstationary measurement process. The traditional Kalman Filter (KF) can tackle the state estimation problem under Gaussian white noise, but its performance will be significantly reduced under non-Gaussian noises. In order to deal with the non-Gaussian conditions in the actual missile-borne SINS/GNSS integrated navigation systems, a Maximum Versoria Criterion Extended Kalman Filter (MVC-EKF) algorithm is proposed based on the MVC and the idea of M-estimation, which assigns a smaller weight to the anomalous measurements so as to suppress the influence of anomalous measurements on the state estimation while maintaining a relatively low calculation cost. Finally, the integrated navigation simulation experiments prove the effectiveness and robustness of the proposed algorithm.

Speaker Recognition is a challenging topic in Speech Processing research area. The various models proposed have succeeded in achieving a fairly high level of accuracy in this research. However, the level of Speaker Recognition accuracy is not yet maximized because the small dataset is a problem that is still being faced at this time, causing overfitting and biased data samples. This work proposes a Data Augmentation strategy using Adding White Noise techniques, Pitch Shifting, and Time Stretching, which are processed using a Deep Neural Network to produce a new model in speaker recognition as an approach called as DA-DNN7L. The Data Augmentation approach is used as a solution to increase the limited data quantity of Indonesian ethnic speakers, while the seven layer DNN is an architecture that provides the best accuracy performance compared to other multilayer approach models, besides that the 7 layer approach used in several other studies achieves a high degree of accuracy. Research that has been carried out using the best performance seven-layer Deep Neural Network Data Augmentation strategy resulted in an accuracy rate of 99.76% and a loss of 0.05 in the 70%:30% split ratio and the addition of 400 augmentation data. After seeing the performance of this model, it can be concluded that Data Augmentation Deep Neural Network can improve the speaker's recognition performance using the Indonesian ethnic dataset.

This paper deals with the stability problem of T-S fuzzy systems (TSFSs) with hybrid communication delays (HCDs). Compared with traditional communication delays, HCDs with Bernoulli distributed white noise sequences not only involve probabilistic discrete time-varying delays but also random additive time-varying delays (ATVDs). Based on the delay-product-type function (DPTF) and the second derivative method, a novel Lyapunov-Krasovskii functional (LKF) is developed, which fully considers the information of various communication delays. Moreover, by using novel integral inequalities and stochastic analysis theory, new stabilization criteria are established. Meanwhile, the desired fuzzy state feedback controller with HCDs and parallel distributed compensation (PDC) is designed by solving a set of linear matrix inequalities (LMIs). In the end, the usefulness of the obtained theoretical results is illustrated through two numerical simulation examples.

Doppler ultrasound techniques are currently employed in several industrial, consumer, and biomedical applications. They are implemented in electronic systems of different complexity: from simple low-cost embedded boards to high-end echographs. The development, implementation, and periodic verification of such systems involve complex tests carried out through flow-rigs and phantoms. Unfortunately, these hydraulic circuits are affected by several issues, like the huge dimensions and the lack of an accurate reference for the velocity distribution developed by the fluid. In this work we present an innovative Flow Emulator Board (FEB). The FEB is compact and does not need moving fluids or pumps. Moreover, it produces a signal that mimics a programmable velocity profile with known characteristics. The FEB can replace the flow-rigs in most of the tests where Pulsed Wave Doppler (PWD) methods and PWD electronics systems are involved. The presented experiments show that the proposed FEB synthetizes arbitrary flow velocity profiles with programmable clutter, white noise, propagation attenuation, and sample volume extension; and show how FEB is employed for testing an industrial sensor and a research echograph.

Identifiability of linear dynamic networks requires the presence of a sufficient number of external excitation signals. The problem of allocating a minimal number of external signals for guaranteeing generic network identifiability in the full measurement case has been recently addressed in the literature. Here we will extend that work by explicitly incorporating the situation that some network modules are known, and thus are fixed in the parametrized model set. The graphical approach introduced earlier is extended to this situation, showing that the presence of fixed modules reduces the required number of external signals. An algorithm is presented that allocates the external signals in a systematic fashion.

Comparing with traditional stochastic differential equations (SDEs) involving white noise, random differential equations (RDEs) with colored noise are claimed to have more practical meaning. This paper considers the event-triggered adaptive tracking control for RDE systems with coexisting parametric uncertainties and severe nonlinearities. Combining a tracking error-based dynamic gain with a relative threshold event triggered control mechanism (ETCM), the tracking control problem for the random systems is solved without Zeno behavior. The tracking error can be rendered small enough by tuning design parameters. First, a series of adaptive control laws are designed by using backstepping technique. Then, two special cases are considered and the main results are extended to MIMO systems. Finally, a simulation example confirms the validity of the results. To the best of the authors knowledge, this paper serves as the first attempt of event-based control for RDE systems.

We study nonlinear parabolic stochastic partial differential equations with Wick-power and Wick-polynomial type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fujita equation, the stochastic Fisher-KPP equation and the stochastic FitzHugh-Nagumo equation among many others. By implementing the theory of $C_0-$semigroups and evolution systems into the chaos expansion theory in infinite dimensional spaces, we prove existence and uniqueness of solutions for this class of SPDEs. In particular, we also treat the linear nonautonomous case and provide several applications featured as stochastic reaction-diffusion equations that arise in biology, medicine and physics.

The thermodynamic Cucker–Smale model (TCS model) describes dynamic consistency caused by different temperatures between multi-agent particles. This paper studies the flocking behaviors of the TCS model with multiplicative white noise under hierarchical leadership. First, we introduce the corresponding model of two particles. Then, by using mathematical induction and considering the properties of differential functions, it is proved that, under certain conditions, the group can achieve flocking. Finally, we verify the conclusion through numerical simulation results. Similarly, this paper studies the above model with perturbation functions.

Stochastic partial differential equations have wide applications in various fields of science and engineering. This paper addresses the optical stochastic solitons and other exact stochastic solutions through birefringent fibers for the Biswas–Arshed equation with multiplicative white noise using the modified extended mapping method. This model contains many kinds of soliton solutions, which are always symmetric or anti-symmetric in space. Stochastic bright soliton solutions, stochastic dark soliton solutions, stochastic combo bright–dark soliton solutions, stochastic combo singular-bright soliton solutions, stochastic singular soliton solutions, stochastic periodic solutions, stochastic rational solutions, stochastic Weierstrass elliptic doubly periodic solutions, and stochastic Jacobi elliptic function solutions are extracted. The constraints on the parameters are considered to guarantee the existence of these stochastic solutions. Furthermore, some of the selected solutions are described graphically to demonstrate the physical nature of the obtained solutions.

This paper investigates an uncommon technique by using the influence of the random function (Weiner process function), on a two-temperature problem, at the free surface of the semiconducting medium, by using the photo-thermoelasticity theory. Using the Silicon material as an example of a semiconducting medium under the influence of a magnetic field, the novel model can be formulated. To make the problem more logical, the randomness of the Weiner process function is aged to the governing stochastic equation. A combining stochastic process with the boundary of the variables is studied. In this case, the stochastic and deterministic solutions were obtained for all physical quantities. The additional noise is regarded as white noise. The problem is investigated according to a two-dimensional (2D) deformation. The normal mode method can be used mathematically to obtain numerically the deterministic, stochastic, and variance solutions of all physical quantities. Three sample paths are obtained by making a comparison between the stochastic and deterministic distributions of the field variables. The impacts of adding randomization to the boundary conditions are highlighted. The numerical results are shown graphically and discussed in consideration of the two-temperature parameter effect.

The current paper recovers dispersive optical solitons in birefringent fibers that are modeled by the Schrödinger–Hirota equation with differential group delay and white noise. Itô Calculus conducts the preliminary analysis. The G′/G-expansion approach and the enhanced Kudryashov’s scheme gave way to a wide spectrum of soliton solutions with the white noise component reflected in the phase of the soliton.

This paper examines the role of the main character’s youngest son, Wilder, in Don Delilo’s White Noise. The protagonist, Jack, is increasingly “bewildered” by the fear of death. The way Jack is easily influenced by the words of people around him, and the power of suggestion, contrasts with his son’s lack of language, and his happy existence. In the novel, DeLillo suggests that this “white noise,” which surrounds Wilder, is the key to processing the fear of death. Instead of being “bewildered” we should “be Wilder.”, 10

A time-domain jitter estimation methodology considering process-voltage-temperature (PVT) variations of the single-ended ring oscillator (SERO) at an early stage of design is presented for near-threshold voltage (NTV) regime where nonlinearities dominates. For the first time, the model accounts for the jitter due to the over/undershoot region which is critical in the NTV regime. Further, the model uses effective drive current, Ieff model. The Ieff is obtained considering the regions of device operation, instead of using only saturation current for jitter calculation. A time-domain jitter model is developed by considering the change in transition threshold points (TTPs) whose relative values are supply independent and Ieff of each region with the PVT variation, design parameters, and with the introduction of noise in the circuit. The model analyzes the effects of random (white noise) and deterministic (supply, substrate) noise in the NTV regime. This approach is physics/topologybased and is valid for different technologies. Post-layout simulations have been performed on parasitic extracted netlist using CADENCE and HSPICE in STM 65nm CMOS Process Design Kit (PDK) to validate the jitter model in the NTV regime.

Aerodynamic loading is one of the most dominating environmental excitations of Floating Wind Turbines (FWTs) and plays an important role in the FWT dynamics. In this study, we developed a model Spar-type FWT and then constructed a dedicated experiment apparatus to reveal the aerodynamic loading effects. As for the floater motion, the wind loading serves as an external exciting force, as well as potential damping source and equivalent added mass item. To take all these roles into account, we proposed a concept of aerodynamic loading effect. The presence of aerodynamic loading effect is validated by free decay tests and white noise wave tests. Results show that the aerodynamic loading effect alters the natural frequencies and damping ratios of the FWT system. We suggest the FWT designers refer to the altered natural frequencies when designing the floater and the FWT controllers. We experimentally observed that the increased aerodynamic loading tends to suppress the pitch resonance vibration while amplifies the resonance vibration at surge frequency. Besides, the nacelle motions, blade loads, and the tower dynamics, are all significantly impacted by the aerodynamic loading effect. The presented results are potentially helpful for optimizing FWTs and developing advanced FWT controllers.

This paper describes a frequency-domain method for the identification of multi-input control equivalent turbulence input models. Such models can be identified from flight data gathered in specific ...

This article inspects the problem of robust synchronization for uncertain Markovian jumping complex interconnected neural networks with randomly occurring uncertainties and time delays. The uncertainties considered here occur randomly and are assumed to follow certain mutually uncorrelated Bernoulli distributed white noise sequences. The presence of sensor faults may cause degradation or even instability of the entire network. Therefore, control laws are designed with sensor faults to ensure the controlled synchronization of the complex interconnected neural networks. Three types of fault-tolerant controls are designed based on the Lyapunov stability theory and adaptive schemes which include passive and adaptive fault-tolerant control laws. By constructing a new Lyapunov-Krasovskii functional (LKF) and by using Jensen’s inequality with a free-weighting matrix approach, some new delay-dependent synchronization criteria are obtained in terms of linear matrix inequalities (LMIs). By using the Lyapunov stability theory, the existence condition for the adaptive controller that guarantees the robust mean-square synchronization of complex interconnected neural networks in terms of LMIs are derived. Finally, a numerical example is presented to demonstrate the performance of the developed approach.

It has been extensively studied to employ memristors to model the relationship between the electromagnetic field and the membrane potential, especially for the research of modeling and dynamical analyses of electrical activity using HR neurons with memristors. This paper proposes a novel 4D HR model with a threshold flux-controlled memristor (MHR), which describes the electromagnetic induction effect. The proposed 4D HR model retains the original HR properties and can describe the complex dynamics of neurons' electrical activities with fewer parameters than the existing models. Due to the particularity of the no equilibrium point of the MHR model, the hidden dynamics are found in the proposed MHR model. The generalized Hamiltonian function is fully derived for the MHR neuron model using Helmholtz's theorem. The simplest form of the Hamiltonian form is given by assigning special values. The average Hamiltonian energy and its bifurcation are employed to find the connection between energy and firing patterns. The band-limited white noise is also studied, and it is found that it positively influences the electrical activities in the proposed MHR system.

We study long time dynamics of a randomly perturbed non-autonomous coupled system ( x , y ) , whose x coordinate satisfies a semilinear parabolic equation with an additive noise, and y coordinate satisfies a differential equation whose solutions do not converge too rapidly. The noise is either the white noise induced by a Brownian motion W ( t , ω ) or a stationary process ζ δ ( θ t ω ) whose integral is approximating W ( t , ω ) . After addressing certain assumptions for such system, we show that for δ = 0 (resp. δ > 0 ) with respect to the noise W ( t , ω ) (resp. integral of ζ δ ( θ t ω ) ) there exists a invariant manifold which is exponentially attracting any other solution outside it. Also, as δ tends to 0, the invariant manifold and its derivative in y for the case δ > 0 are approaching to those for δ = 0 .

Design/optimization of the tuned mass damper (TMD) system may not always lead toward robust performance if uncertainties exist. In view of this, a stochastic design of multiple TMD (MTMD) systems has been proposed in the present study taking into account various uncertainties. Taylor-expansion is used to perturb the objective function facilitating stochastic design/optimization. An interval-extension is used to observe the effect of uncertainties of different levels. The Lyapunov equation is used in the design of TMD systems by minimizing the dispersion of displacement of the primary system. The present work takes into account a model of generalized MTMD system. Seismic excitation is considered as a random process in the form of both: (a) stationary Kanai–Tajimi (KT) filter and (b) stationary Gaussian white noise directly applied to the base of structure. A numerical investigation is carried out to observe the consequences of uncertainties on the optimum design of MTMD parameters for both the excitation models (with and without incorporating Kanai–Tajimi filter). Efficiency of the MTMD systems (with variation of number of MTMD mass-units) is compared under various levels of uncertainties. Finally, some significant earthquake records are utilized toward more realistic understanding on the performance of stochastic design of TMD/MTMD systems under seismic excitation with various levels of uncertainties.

LoRa (Long Range) is one of the most promising technologies for building the ground Internet of Things and has the advantages of low power consumption and large coverage. Based on an analysis of LoRa's performance in the field of the Internet of Things, the paper investigates LoRa's performance in the low-orbit Internet of Things satellite. First, imitate the simulation coefficients of LEO system (Iridium) to obtain the performance of LoRa under the Rician channel model with Gaussian white noise, and then analyze and compare the LoRa system under different Doppler residual frequency differences, spreading factors and transmit power Under the performance, simulation results show that LoRa modulation can meet the throughput requirements of the system. Therefore, under the simulation conditions of this paper, LoRa modulation can meet the performance requirements of low-orbit satellite Internet of Things scenarios.

In this paper, we develop a rumor spreading model by introducing white noise into the model. We establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the stochastic model by constructing a suitable stochastic Lyapunov function, which provides us a good description of persistence. Finally, we provide some numerical simulations to illustrate the analytical results.

In this study, for feature extraction of seismic- and nonlinear trend terms of the nonlinear and nonstationary high-rate Global Navigation Satellite System (GNSS) seismic displacements, we present an adaptive complete ensemble empirical mode decomposition (CEEMD) method based on correlation coefficient. We also introduce an improved CEEMD (ICEEMD) based on multiway principal component analysis (MPCA), hereafter, ICEEMD-MPCA, denoising method for boosting the high-rate GNSS seismic displacements with/without nonlinear trend. The results show that the proposed method is suitable for extracting features of nonlinear and nonstationary high-rate GNSS seismic displacements. The ICEEMD-MPCA denoising method is able to obviously eliminate white noise at high frequencies, remove systematic errors, and effectively preserve the earthquake wave signals. The denoising method reflects that high-rate GNSS has millimeter-level accuracy in the vertical component and submillimeter-level accuracy in the horizontal component. To verify the performance characteristics of the feature extraction and denoising method, the focal mechanism inversion for the 2010 El Mayor–Cucapah earthquake is estimated using the high-rate GNSS data (5 Hz) and collocated strong motion data (50 and 200 Hz). The focal mechanism of the earthquake estimated using the denoised high-rate GNSS with/without nonlinear trend are more consistent with the teleseismic estimates than those estimated using the raw high-rate GNSS and strong motion data. For the GNSS observations, the inversion results are more affected by errors in low-frequency, which accumulate over time and display their signatures as trend in coseismic displacements. It can be concluded that with the adaptive CEEMD method and the ICEEMD-MPCA denoising method, high-rate GNSS at near-field stations only or combined with GNSS/strong-motion records can be applied to yield better information regarding the earthquake focal mechanism inversion, the lower bounds of earthquake magnitudes, and earthquake rupture parameters for small to moderate earthquakes.

Recent work has demonstrated a passive radio sounding approach that uses the Sun as a source for echo detection and ranging. As the Sun is a moving source with a position that is known a priori , we evaluate this technique’s capabilities to measure the echo’s phase history, map topography, and perform synthetic aperture radar (SAR) focusing. Here, we present our approach to implementing passive SAR using a compact, temporally incoherent radio-astronomical source as a signal of opportunity. We first evaluate the passive system’s capabilities to obtain an echo from a rough surface by determining the critical signal-to-noise ratio (SNR) for reliably observing the Sun’s echo reflection with our passive instrument. We then demonstrate that our technique can detect the necessary changes in range, phase, and reflectivity of an echo from the Sun. We next present the experimental results of our passive radar testing using the Sun at Dante’s View, Death Valley, to highlight this technique’s ability to perform 2-D imaging. Finally, with synthetic data, we demonstrate that we can use time-domain backprojection to focus a planar white noise signal, perform passive SAR imaging, and improve the measurement’s SNR and azimuth resolution. The results of passive SAR focusing on white noise highlight the potential for the Sun and Jupiter’s radio emissions to perform surface and subsurface imaging for planetary and terrestrial observations.

It is sometimes difficult to model the stochastic differential equations for strongly nonlinear multi-stable vibration energy harvesters, especially for those under additive and multiplicative white noises, because of the existing challenges in quantifying noise intensities, nonlinear stiffness coefficients and damping coefficient. From the perspective of machine learning, a sparse identification method is devised to discover the general governing equation of energy harvester by using observed data on system state time series. With the observed data, the drift term and the diffusion term can be learned and then the stochastic differential equation can be identified. A penta-stable vibration energy harvester is taken as an example to verify the feasibility and effectiveness of the devised sparse identification method, which indicates that the method can be successfully applied to model the governing equation of a multi-stable vibration energy harvesting system under random excitation. Based on the learned data-driven stochastic differential equation for energy harvester, the stochastic dynamics can be further explored by appropriately adjusting the system parameters to improve energy harvesting performance and optimize the miniaturization design.

Digital currency price prediction is vital to both sellers and purchasers. Over these years, decomposition and integration models have been applied more and more to realize the goal of precise prediction, however, many of them tend to neglect the reconstruction of features or the residual series. Altogether, one of the biggest drawbacks of the decomposition and integration framework is the method applied requires manual parameter setting whether it is for decomposition or integration. Still, for the results, they are merely satisfied with the point prediction which brings high uncertainty. In this paper, an optimized feature reconstruction decomposition and two-step nonlinear integration method is proposed which gives consideration to feature reconstruction, nonlinear integration, optimization and interval prediction. The original data series is decomposed through improved variational mode decomposition based approximate entropy feature reconstruction system. Then, improved particle swarm optimization-gated recurrent unit (iPSO-GRU) is utilized in the first and second nonlinear integration part separately. Meanwhile, the residual series is given attention, if it is not a white noise series, the residual will be the input of iPSO-GRU whose result will be added back to the second integration result to form the point prediction result. Based on the point prediction result, interval prediction estimate will be generated as well via maximum likelihood function. This study chooses three kinds of digital currency as cases and the results show that the MAPE values of point prediction are all below 3.5%, and CP values of interval prediction are all 1 with suitable MWP. In addition, compared with other benchmark models, the proposed model shows better performance.

This paper studied a stochastic epidemic model of the spread of the novel coronavirus (COVID-19). Severe factors impacting the disease transmission are presented by white noise and compensated Poisson noise with possibly infinite characteristic measure. Large time estimates are established based on Kunita’s inequality rather than Burkholder-Davis-Gundy inequality for continuous diffusions. The effect of stochasticity is taken into account in the formulation of sufficient conditions for the extinction of COVID-19 and its persistence. Our results prove that environmental fluctuations can be privileged in controlling the pandemic behavior. Based on real parameter values, numerical results are presented to illustrate obtained results concerning the extinction and the persistence in mean of the disease. [ABSTRACT FROM AUTHOR] Copyright of Stochastic Analysis & Applications is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We consider a system of two coupled stochastic lattice equations driven by additive white noise processes, where the strength of the coupling is given by a parameter κ≥0. We show that these equatio...

Time delay, where it depends on the current state and on the past situation, is often occurred in biological activities, for example, the process by which microorganism consume nutrients into their available biomass is not instantaneous. This investigation inspects the dynamic behavior of stochastic turbidostat model coupled with distributed delay and degenerate diffusion, including sufficient conditions of the extinction and the existence of a unique stationary distribution. What’s more, the existence and uniqueness of globally positive equilibrium of the exploited model are studied. The findings manifest that the turbidostat system is ergodic only when the intensity of white noise is very small. Finally, some numerical examples are proposed to indicate the validity of the theoretical results.

This study investigated the impact of white noise on the HIV/AIDS model with a cytotoxic T lymphocyte (CTL) immune response. The model introduced the interactions between the virus and two kinds of target cells, CD4+ T cells and macrophages. It was theoretically proved that the solution of the stochastic model is positive and global, as well as the existence of an ergodic stationary distribution. The sufficient conditions were established for viral eradication. By comparing these new results to those of a deterministic model, it is determined that white noise can promote the extinction of the virus. Theoretical results have been verified by numerical simulation of several examples.

This paper proposes a new procedure to build factor models for high-dimensional unit-root time series by postulating that a $p$-dimensional unit-root process is a nonsingular linear transformation of a set of unit-root processes, a set of stationary common factors, which are dynamically dependent, and some idiosyncratic white noise components. For the stationary components, we assume that the factor process captures the temporal-dependence and the idiosyncratic white noise series explains, jointly with the factors, the cross-sectional dependence. The estimation of nonsingular linear loading spaces is carried out in two steps. First, we use an eigenanalysis of a nonnegative definite matrix of the data to separate the unit-root processes from the stationary ones and a modified method to specify the number of unit roots. We then employ another eigenanalysis and a projected principal component analysis to identify the stationary common factors and the white noise series. We propose a new procedure to specify the number of white noise series and, hence, the number of stationary common factors, establish asymptotic properties of the proposed method for both fixed and diverging $p$ as the sample size $n$ increases, and use simulation and a real example to demonstrate the performance of the proposed method in finite samples. We also compare our method with some commonly used ones in the literature regarding the forecast ability of the extracted factors and find that the proposed method performs well in out-of-sample forecasting of a 508-dimensional PM$_{2.5}$ series in Taiwan., Comment: 45 pages, 11 figures. arXiv admin note: text overlap with arXiv:1808.07932

This paper presents an extensive experimental investigation to identify the influence of signal parameters on a piezoelectric harvester’s performance. A macro-fibre composite energy harvester was studied as an advanced, flexible, high-performance energy material. Gaussian white noise, and single-frequency and multi-frequency excitation were used to investigate nonlinearity and multiple-frequency interactions. Using single low and high frequencies, we identified the nonlinearity of the harvester’s vibration. Multi-frequency excitation with a series of low-to-high-frequency harmonics mimicked the practical vibration signal. Under such multi-frequency excitation, the harvester’s nonlinear behaviour was studied. Finally, the interaction effects among multiple frequencies were identified. The results show that under pure resonant excitation, high-level vibration led to high-level mechanical strain, which caused nonlinear vibration behaviour. Moreover, it was shown that the different harmonics excited the various structure bending modes, which caused the nonlinearity of multi-frequency excitation. The first four harmonics of the real-time signal were important. The experimental results emphasise the resonant nonlinearity and interactions of multi-frequency excitation effects.

We study global-in-time dynamics of the stochastic nonlinear wave equations (SNLW) with an additive space-time white noise forcing, posed on the two-dimensional torus. Our goal in this paper is two-fold. (i) By introducing a hybrid argument, combining the $I$-method in the stochastic setting with a Gronwall-type argument, we first prove global well-posedness of the (renormalized) cubic SNLW in the defocusing case. Our argument yields a double exponential growth bound on the Sobolev norm of a solution. (ii) We then study the stochastic damped nonlinear wave equations (SdNLW) in the defocusing case. In particular, by applying Bourgain's invariant measure argument, we prove almost sure global well-posedness of the (renormalized) defocusing SdNLW with respect to the Gibbs measure and invariance of the Gibbs measure., 33 pages. To appear in Internat. Math. Res. Not. Minor typos corrected

Ramanujan sums (RS) have been found to be very successful in signal processing recently. However, as far as we know, the RS have not been applied to image analysis. In this paper, we propose two novel algorithms for image analysis, including moment invariants and pattern recognition. Our algorithms are invariant to the translation, rotation and scaling of the 2D shapes. The RS are robust to Gaussian white noise and occlusion as well. Our algorithms compare favourably to the dual-tree complex wavelet (DTCWT) moments and the Zernike’s moments in terms of correct classification rates for three well-known shape datasets.

In this letter, we study the Ramanujan Sums (RS) transform by means of matrix multiplication. The RS are orthogonal in nature and therefore offer excellent energy conservation capability. The 1-D and 2-D forward RS transforms are easy to calculate, but their inverse transforms are not defined in the literature for non-even function . We solved this problem by using matrix multiplication in this letter.

In this work we show how it is possible to derive a new set of nudging equations, a tool still used in many data assimilation problems, starting from statistical physics considerations and availing ourselves of stochastic parameterizations that take into account unresolved interactions. The fluctuations used are thought of as Gaussian white noise with zero mean. The derivation is based on the conditioned Langevin dynamics technique. Exploiting the relation between the Fokker–Planck and the Langevin equations, the nudging equations are derived for a maximally observed system that converges towards the observations in finite time. The new nudging term found is the analog of the so called quantum potential of the Bohmian mechanics. In order to make the new nudging equations feasible for practical computations, two approximations are developed and used as bases from which extending this tool to non-perfectly observed systems. By means of a physical framework, in the zero noise limit, all the physical nudging parameters are fixed by the model under study and there is no need to tune other free ad-hoc variables. The limit of zero noise shows that also for the classical nudging equations it is necessary to use dynamical information to correct the typical relaxation term. A comparison of these approximations with a 3DVar scheme, that use a conjugate gradient minimization, is then shown in a series of four twin experiments that exploit low order chaotic models.

We study the two-dimensional stochastic nonlinear heat equation (SNLH) and stochastic damped nonlinear wave equation (SdNLW) with an exponential nonlinearity $\lambda\beta e^{\beta u }$, forced by an additive space-time white noise. We prove local and global well-posedness of these equations, depending on the sign of $\lambda$ and the size of $\beta^2 > 0$, and invariance of the associated Gibbs measures. See the abstract of the paper for a more precise abstract. (Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here.), Comment: 70 pages. To appear in Comm. Math. Phys. Minor typos corrected

The topic of direction-of-arrival (DOA) estimation has attracted extensive attention in wireless communications, radars, sonars, etc. Compared to the traditional scalar sensor, electromagnetic vector sensor (EMVS) is attractive since it provides two-dimensional (2D) DOA estimation and additional polarization information of the incoming signals. However, existing algorithms are only suitable for Gaussian white noise scenario. In this paper, we investigate into DOA estimation using EMVS array with spatially colored noise, and a parallel factor (PARAFAC) estimator is proposed. Unlike the conventional direct PARAFAC algorithm, the covariance tensor-based PARAFAC model is considered. For fast PARAFAC decomposition purpose, the fourth-order covariance PARAFAC tensor is rearranged into a third-order PARAFAC tensor, so that the existing COMFAC algorithm is available and thus the factor matrices are estimated. Thereafter, the elevation angle estimation is accomplished via least squares (LS) technique, and the azimuth angles are estimated via vector cross-product. Besides, the polarization status of the source signal can be estimated via LS approach, which may be helpful to identify weak signals. Our estimator is flexible since it can be easily extended to nonuniform array and spatially colored noise scenario. Moreover, it offers better estimation performance than the traditional PARAFAC algorithm in the presence of colored noise. Detailed analyses concerning identifiability, complexity as well as Cramer–Rao bound (CRB) are provided. To show the effectiveness of the proposed estimator, numerical simulations have been designed.

The article presents an innovative approach to the description of the aircraft range parameter in discrete time when simulating the process of its repositioning in space. A method of describing the dynamics of changes in signal delay in discrete time when the aircraft is changing its spatial position is proposed. Such a model adequately describes the change in signal delay in discrete time. The direction of estimation for the adequacy of radio signal delay change simulation in algorithms of optimum filtration is defined in accordance with the aerodynamic properties of the aircraft. Simulation of the signal delay dynamic change is carried out (it is completely described by the dynamics of change in the distance to the aircraft). The transformation stages of simulation data for the initial model in continuous time with realization of the standard Gaussian random numbers are justified. Information on the simulation data transformation taking into account the correlation matrix of discrete white noise is provided. A method of calculating the transition matrix through the Laplace transform is proposed. The scientific-applied direction of research is determined – it lies in the development of a method for the legitimate representation for the mathematical model of aircraft’s changing range in discrete time within one-dimensional space: the longitudinal and the transverse dimensions. This approach takes into account the continuous description for a system of stochastic differential equations. A comprehensive algorithm for modeling the values of discrete white noise on modern computer equipment and calculating the dynamics of the aircraft range parameter changes is proposed. This algorithm allows to correctly form the a priori information about the change of the vector parameters of the aircraft spatial position at discrete moments of time. As a result, it was shown that the use of the obtained information in the optimal filtering algorithms minimizes the error when determining distance to the aircraft and, accordingly, allows to increase the accuracy and adequacy of the signal delay simulation in discrete time. The results of this research can be used in modernization of the existing models and development of promising on-board radar stations, integrated rangefinders, systems of radio technical reconnaissance and electronic warfare systems, as well as in technical implementation of aircraft flight simulation systems.

Let $$\xi $$ be a Gaussian white noise on $${\mathbb {R}}^d$$ ( $$d=1,2,3$$ ). Let $$(\xi _\varepsilon )_{\varepsilon >0}$$ be continuous Gaussian processes such that $$\xi _\varepsilon \rightarrow \xi $$ as $$\varepsilon \rightarrow 0$$ , defined by convolving $$\xi $$ against a mollifier. We consider the asymptotics of the parabolic Anderson model (PAM) with noise $$\xi _{\varepsilon (t)}$$ for large time $$t\gg 1$$ , and the Dirichlet eigenvalues of the Anderson Hamiltonian (AH) with potential $$\xi _{\varepsilon (t)}$$ on large boxes $$(-t,t)^d$$ , where the parameter $$\varepsilon (t)$$ vanishes as $$t\rightarrow \infty $$ . We prove that the asymptotics in question exhibit a phase transition in the rate at which $$\varepsilon (t)$$ vanishes, which distinguishes between the behavior observed in the AH/PAM with continuous Gaussian noise and white noise. By comparing our main theorems with previous results on the AH/PAM with white noise, our results show that some asymptotics of the latter can be accessed with solely elementary methods, and we obtain quantitative estimates on the difference between the AH/PAM with white noise and its continuous-noise approximations as $$t\rightarrow \infty $$ .

Aiming at the output saturation problem of the classical tristable stochastic resonance (CTSR) system, stochastic resonance of an unsaturated piecewise tristable system driven by a periodic forcing and Gaussian white noise is investigated. The dimensionality of the six-type function is reduced to four-type and quadratic function. The potential function and mean first passage time (MFPT) is analyzed, and then the spectral amplification (SA) formula of the system is derived. The fourth-order Runge–Kutta method is utilized to carry out the numerical simulation. Finally, the proposed system is introduced into fault detection. In this work, the potential feld structure of the proposed system is discussed. The MFPT and SA derived and the influence of the parameters on the proposed system is discussed. The influence of output saturation on weak signal detection performance under strong noise is compared. Both theoretical analysis and numerical simulation show that the unsaturated piecewise system has much better anti-noise performance and frequency spectrum amplification factor. Bearing fault diagnosis results show that the fault frequency can be more accurately identified by the unsaturated piecewise tristable system and the characteristic signal’s energy can be enhanced more. The theoretical basis and reference value of the system are provided for further application in practical engineering testing.

Subjected to stochastic seismic and/or strong wind loads, the self-centering structures may undergo remarkable random oscillations which may deteriorate the operating performance or even induce complete failure. This paper aims to investigate the first-passage failure of self-centering systems under random excitation. A single-degree-of-freedom self-centering system subjected to Gaussian white noise excitation is considered. The model of hysteretic restoring force is chosen as flag-shape type. With application of the generalized harmonic balance technique, the hysteretic restoring force is approximated as the combination of amplitude dependent equivalent damping and equivalent stiffness, and the motion of equation is then recast. The averaged Ito equation with respect to amplitude is deduced by merit of the principle of stochastic averaging. The backward Kolmogorov (BK) equation associated with the averaged Ito equation is deduced, and numerically solved to obtain the conditional reliability function and the conditional probability density function. The significant parameters of system are examined in detail. In addition, the data obtained with Monte Carlo simulation are applied to validate the theoretical solutions.

Automatic speaker recognition (ASR) is a challenging task when the duration of the test speech is very short i.e., a few seconds. Source features extracted from short speech utterances are shown to be effective for such cases. This paper proposes a system based on LP residual for text independent speaker recognition. Discrete wavelet transform (DWT) and stationary wavelet transform (SWT) are experimented to parameterize the LP residual. DWT works well in case of denoising and compression. SWT works well in reconstructing the noised signal at higher levels of decomposition than DWT. SWT/DWT coefficients of LP residual are used for implementing an i-vector/P-LDA based speaker recognition system. Effectiveness of the system is evaluated by using 10 s–10 s task of NIST speaker recognition evaluation (SRE) 2010 database. To evaluate robustness in degraded environments, the speech files are mixed with white noise from NOISEX-92 database. Speaker recognition using SWT level-3 results in an equal error rate (EER) of 40 and decision cost function (DCF) of 0.3956 for voice part of the signal in 10 s training—10 s testing data set. It has been shown that the proposed method gives robust speaker recognition performance in terms of DCF.

In this paper, we study the Wong-Zakai approximations and long term behavior of the stochastic FitzHugh-Nagumo system driven by a white noise. We first prove the existence and uniqueness of tempere...