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In this paper a novel method is presented to analyze the dynamical reliability of the stochastic power systems with discrete random variability. It is inevitable for the power systems to suffer from external stochastic disturbance. At the same time, the components' failure will bring abrupt changes in their substructures, which can be considered as the internal stochastic disturbance. It is demonstrated that the components' failure performs random jumpy factors switching between a finite number of modes. This salient feature allows us to identify this type of dynamic behavior as the response of the hybrid power systems undergoing Markovian jumps. Utilizing a two-step approximate technique, the considered multi-DOF hybrid system can be reduced to a one-dimensional averaged Itô equation of the form of the system's total energy. The approximate analytical solution of the associated back Kolmogorov equation of the system's energy is derived to predict the dynamical reliability of the original hybrid systems. [ABSTRACT FROM AUTHOR]

The bi-stable piezoelectric energy harvester can produce higher voltage and efficiency than traditional energy harvester. In this manuscript, the reliability of the bi-stable piezoelectric energy harvester excited by Gaussian white noise is investigated. The equivalent uncoupled equation of system is deduced on the basis of the generalized harmonic transformation for the bi-stable piezoelectric energy harvester original coupling system. The averaged stochastic differential equation for system energy of the equivalent uncoupled system is established using the stochastic averaging method. The conditional reliability function and the mean first-passage time are derived through the backward Kolmogorov equation and the generalized Pontryagin equation associated with the averaged stochastic differential equation. The influences of noise intensity, electromechanical coupling coefficient, and time constant ratio on the conditional reliability function and mean first-passage time are discussed. The analytical results are highly consistent with the numerical results that are obtained by the Monte Carlo numerical simulation. [ABSTRACT FROM AUTHOR]

The random‐time‐delay (RTD) occurs inevitably in feedback control, caused by the utilization of a multi‐user network with random demands. This paper is devoted to the stochastic stabilization of multi‐degree‐of‐freedom (MDOF) nonlinear RTD controlled systems. Firstly, a two‐step approximated method is proposed to deal with RTD: by modeling the RTD as a Markov jump process, the RTD control is formulated as the one with discrete jump varying delay; utilizing the randomly periodic characteristic, the Markov jump delay is taken out of the control as a parameter. The stochastic averaging principle is applied to generate a less‐dimensional averaged governing equation of system's energies. Secondly, the dynamical programming principle is applied to the ergodic control problem of the average systems with an undetermined cost function, which is determined by the demand of stabilizing the averaged systems, then the optimal control law is deduced. A largest Lyapunov exponent is introduced to the averaged systems to evaluate the asymptotic stability with probability one. Finally, an example is worked out to demonstrate the application and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Dielectric elastomers are widely used in many fields due to their advantages of high deformability, light weight, biological compatibility, and high efficiency. In this study, the stochastic dynamic response and bifurcation of a dielectric elastomer balloon (DEB) with viscoelasticity are investigated. Firstly, the rheological model is adopted to describe the viscoelasticity of the DEB, and the dynamic model is deduced by using the free energy method. The effect of viscoelasticity on the state of equilibrium with static pressure and voltage is analysed. Then, the stochastic differential equation about the perturbation around the state of equilibrium is derived when the DEB is under random pressure and static voltage. The steady-state probability densities of the perturbation stretch ratio are determined by the generalized cell mapping method. The effects of parameter conditions on the mean value of the perturbation stretch ratio are calculated. Finally, sinusoidal voltage and random pressure are applied to the viscoelastic DEB, and the phenomenon of P-bifurcation is observed. Our results are compared with those obtained from Monte Carlo simulation to verify their accuracy. This work provides a potential theoretical reference for the design and application of DEs. [ABSTRACT FROM AUTHOR]

A fractionally damped vibration energy harvester excited by the wide-band random noise is investigated theoretically in this paper. Firstly, by introducing the generalized harmonic transformation, an equivalent uncoupled system only with respect to the mechanical states is established, while the external circuit and the fractional derivative damping are decoupled into damping and stiffness with amplitude-dependent coefficients, respectively. Then, a stochastic averaging operator technique is carried out to derive the stationary distribution of the mechanical states and furtherly obtain the mean square electric voltage (MSEV) and mean output power (MOP) of the energy harvester theoretically. Finally, the relationships between the fractional derivative and the MSEV and MOP are explored in detail to help improve the performance of the energy harvester. [ABSTRACT FROM AUTHOR]

In this paper, an approximate analytical procedure is proposed to derive the stochastic response of nonlinear viscoelastic systems with time-delayed feedback control force and bounded noise excitation. The viscoelastic force and the time-delayed control force depend on the past histories of the state variables, which will result in infinite-dimensional problem in theoretical analysis. To resolve these difficulties, the viscoelastic force and the time-delayed control force are approximated by the current state variable based on the quasi-periodic behavior of the systematic response. Then, by using the stochastic averaging method for strongly nonlinear systems subjected to bounded noise excitation, an averaged equation for the equivalent system is derived. The Fokker–Plank–Kolmogorov (FPK) equation of the associated averaged equation is solved to derive the stochastic response of the equivalent system. Finally, two typical nonlinear viscoelastic oscillators are worked out and the results demonstrated the effectiveness of the proposed procedure. By utilizing the quasi-periodic behavior and stochastic averaging method of the strongly nonlinear system, the time-delayed control force and the viscoelastic terms can be simplified with equivalent damping force and equivalent restoring force and the resonant response under bounded noise excitation can be obtained analytically. The numerical results showed the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, an optimal time-delay control strategy is designed for multi-degree-of-freedom (multi-DOF) strongly nonlinear systems excited by harmonic and wide-band noises. First, by using the generalized harmonic functions, a stochastic averaging method (SAM) is employed for the time-delay controlled strongly nonlinear system under combined harmonic and wide-band noise excitations, by which a set of partially averaged Itô equations are obtained. Then, by solving the dynamical programming equation associated with the partially averaged Itô equations, the optimal control law can be obtained. Finally, by solving the Fokker–Planck–Kolmogorov (FPK) equation, the responses of the optimally time-delay controlled system are predicted. The analytical results are compared with the Monte Carlo simulation to verify the effectiveness and efficiency of the proposed control strategy. [ABSTRACT FROM AUTHOR]

An optimal bounded control strategy for strongly nonlinear vibro-impact systems under stochastic excitations with actuator saturation is proposed. First, the impact effect is incorporated in an equivalent equation by using a nonsmooth transformation. Under the assumption of light damping and weak random perturbation, the system energy is a slowly varying process. By using the stochastic averaging of envelope for strongly nonlinear systems, the partially averaged Itô stochastic differential equation for system energy can be derived. The optimal control problem is transformed from the original optimal control problem for the state variables to an equivalent optimal control problem for the system energy, which decreases the dimensions of the optimal control problem. Then, based on stochastic maximum principle, an adjoint equation for the adjoint variable and the maximum condition of partially averaged control problem are established. For infinite time-interval ergodic control, the adjoint variable is assumed to be a stationary process and the adjoint equation can be further simplified. Finally, the probability density function of the system energy and other statistics of the optimally controlled system are derived by calculating the associated Fokker–Plank–Kolmogorov equation. For comparison, the bang–bang control is also investigated and the control results are compared to show the advantages of the developed control strategy. [ABSTRACT FROM AUTHOR]

The paper treats stationary response of a stochastically excited multi-degree-of-freedom (multi-DOF) vibro-impact system undergoing Markovian jump. The vibro-impact system with sudden abrupt changes in substructures or external excitations is modeled as a continuous-discrete Markovian jump system, which is essentially different from the traditional vibro-impact model. It is demonstrated that the random jump factors switch between a finite number of modes. This salient feature allows us to identify this type of dynamic behaviors as response of hybrid vibro-impact systems undergoing Markovian jump. Utilizing a two-step approximate technique, we can reduce the considered multi-DOF hybrid system to one-dimensional averaged Itô equation of the form of system's total energy. The approximate analytical solution of the associated Fokker–Planck–Kolmogorov (FPK) equation of system's energy is derived to predict the stationary response of original hybrid systems. [ABSTRACT FROM AUTHOR]

Summary: A feedback control strategy is designed to asymptotically stabilize a multi‐degree‐of‐freedom (DOF) nonlinear stochastic systems undergoing Markovian jumps. First, a class of hybrid nonlinear stochastic systems with Markovian jumps is reduced to a one‐dimensional averaged Itô stochastic differential equation for controlled total energy. Second, the optimal control law is deduced by applying the dynamical programming principle to the ergodic control problem of the averaged systems with an undetermined cost function. Third, the cost function is determined by the demand of stabilizing the averaged systems. A Lyapunov exponent is introduced to analyze approximately the asymptotic stability with probability one of the originally controlled systems. To illustrate the application of the present method, an example of stochastically excited two coupled nonlinear oscillators with Markovian jumps is worked out in detail. [ABSTRACT FROM AUTHOR]

This paper presents a modulus stretch-based circular Synthetic Aperture Radar (SAR) imaging method. This method improves the traditional backprojection algorithm for circular SAR imaging, and introduces the modulus stretch transformation function in the imaging process. By performing a modulus stretch transformation on the intermediate results, the target contour in the final imaging result is thinner and clearer. A thinner and clearer contour can help to increase the recognizability of the target and provide a basis for subsequent target recognition. The proposed method is demonstrated on the line target imaging simulations and Gothca dataset. [ABSTRACT FROM AUTHOR]

In the present paper, the statistical responses of two-special prey–predator type ecosystem models excited by combined Gaussian and Poisson white noise are investigated by generalizing the stochastic averaging method. First, we unify the deterministic models for the two cases where preys are abundant and the predator population is large, respectively. Then, under some natural assumptions of small perturbations and system parameters, the stochastic models are introduced. The stochastic averaging method is generalized to compute the statistical responses described by stationary probability density functions (PDFs) and moments for population densities in the ecosystems using a perturbation technique. Based on these statistical responses, the effects of ecosystem parameters and the noise parameters on the stationary PDFs and moments are discussed. Additionally, we also calculate the Gaussian approximate solution to illustrate the effectiveness of the perturbation results. The results show that the larger the mean arrival rate, the smaller the difference between the perturbation solution and Gaussian approximation solution. In addition, direct Monte Carlo simulation is performed to validate the above results. [ABSTRACT FROM AUTHOR]

The contour thinning algorithm is an imaging algorithm for circular synthetic aperture radar (SAR) that can obtain clear target contours and has been successfully used for circular SAR (CSAR) target recognition. However, the contour thinning imaging algorithm loses some details when thinning the contour, which needs to be improved. This paper presents an improved contour thinning imaging algorithm based on residual compensation. In this algorithm, the residual image is obtained by subtracting the contour thinning image from the traditional backprojection image. Then, the compensation information is extracted from the residual image by repeatedly using the gravitation-based speckle reduction algorithm. Finally, the extracted compensation image is superimposed on the contour thinning image to obtain a compensated contour thinning image. The proposed algorithm is demonstrated on the Gotcha dataset. The convolutional neural network (CNN) is used to recognize the target image. The experimental results show that the image after compensation has a higher target recognition accuracy than the image before compensation. [ABSTRACT FROM AUTHOR]

Target recognition is an important area in Synthetic Aperture Radar (SAR) research. Wide-angle Synthetic Aperture Radar (WSAR) has obvious advantages in target imaging resolution. This paper presents a vehicle target recognition algorithm for wide-angle SAR, which is based on joint feature set matching (JFSM). In this algorithm, firstly, the modulus stretch step is added in the imaging process of wide-angle SAR to obtain the thinned image of vehicle contour. Secondly, the gravitational-based speckle reduction algorithm is used to obtain a clearer contour image. Thirdly, the image is rotated to obtain a standard orientation image. Subsequently, the image and projection feature sets are extracted. Finally, the JFSM algorithm, which combines the image and projection sets, is used to identify the vehicle model. Experiments show that the recognition accuracy of the proposed algorithm is up to 85%. The proposed algorithm is demonstrated on the Gotcha WSAR dataset. [ABSTRACT FROM AUTHOR]