Influences of Randomly Uncertain Factors on Dynamic Coefficients of an Interlocking Labyrinth Seal-Rotor System

Many randomly uncertain factors inevitably arise when gas flows through a labyrinth seal, and the orbit of the rotor center will not rotate along a steady trajectory, as previously studied. Here, random uncertainty is considered in an interlocking labyrinth seal-rotor system to investigate the fluctuations of dynamic coefficients. The bounded noise excitation is introduced into the momentum equation of the gas flow, and as a result, the orbit of the rotor center is expressed as the combination of an elliptic trajectory with the bounded noise perturbation. Simulation results of the coefficients under randomly uncertain perturbations with various strengths are comparatively investigated with the traditional predictions under ideal conditions, from which the influences of random uncertain factors on dynamic coefficients are analyzed in terms of the rotor speed, pressure difference, and inlet whirl velocity. It is shown that the deviation levels of the dynamic coefficients are directly related to the random perturbations and routinely increase with such perturbation strengths, and the coefficients themselves may exhibit distinct variation patterns against the rotor speed, pressure difference, and inlet whirl velocity.

Design of ℓ1 New Suboptimal Fractional Delays Controller for Discrete Non-Minimum Phase System under Unknown-but-Bounded Disturbance

ℓ1-regularization methodologies have appeared recently in many pattern recognition and image processing tasks frequently connected to ℓ1-optimization in the control theory. We consider the problem of optimal stabilizing controller synthesis for a discrete non-minimum phase dynamic plant described by a linear difference equation with an additive unknown-but-bounded noise. Under considering the “worst” case of noise, the solving of these optimization problem has a combinatorial complexity. The choosing of an appropriate sufficiently high sampling rate allows to achieve an arbitrarily small level of suboptimality using a noncombinatorial algorithm. In this paper, we suggest to use fractional delays to achieve a small level of suboptimality without increasing the sampling rate so much. We propose an approximation of the fractional lag with a combination of rounding and a first-order fractional lag filter. The suggested approximation of the fractional delay is illustrated via a simulation example with a non-minimum phase second-order plant. The proposed methodology appears to be suitable to be used in various pattern recognition approaches.

Double Accelerated Convergence ZNN with Noise-Suppression for Handling Dynamic Matrix Inversion

Matrix inversion is commonly encountered in the field of mathematics. Therefore, many methods, including zeroing neural network (ZNN), are proposed to solve matrix inversion. Despite conventional fixed-parameter ZNN (FPZNN), which can successfully address the matrix inversion problem, it may focus on either convergence speed or robustness. So, to surmount this problem, a double accelerated convergence ZNN (DAZNN) with noise-suppression and arbitrary time convergence is proposed to settle the dynamic matrix inversion problem (DMIP). The double accelerated convergence of the DAZNN model is accomplished by specially designing exponential decay variable parameters and an exponential-type sign-bi-power activation function (AF). Additionally, two theory analyses verify the DAZNN model’s arbitrary time convergence and its robustness against additive bounded noise. A matrix inversion example is utilized to illustrate that the DAZNN model has better properties when it is devoted to handling DMIP, relative to conventional FPZNNs employing other six AFs. Lastly, a dynamic positioning example that employs the evolution formula of DAZNN model verifies its availability.

Low rank matrix recovery with adversarial sparse noise

Many problems in data science can be treated as recovering a low-rank matrix from a small number of random linear measurements, possibly corrupted with adversarial noise and dense noise. Recently, a bunch of theories on variants of models have been developed for different noises, but with fewer theories on the adversarial noise. In this paper, we study low-rank matrix recovery problem from linear measurements perturbed by $\ell_1$-bounded noise and sparse noise that can arbitrarily change an adversarially chosen $\omega$-fraction of the measurement vector. For Gaussian measurements with nearly optimal number of measurements, we show that the nuclear-norm constrained least absolute deviation (LAD) can successfully estimate the ground-truth matrix for any $\omega<0.239$. Similar robust recovery results are also established for an iterative hard thresholding algorithm applied to the rank-constrained LAD considering geometrically decaying step-sizes, and the unconstrained LAD based on matrix factorization as well as its subgradient descent solver.

A varying-gain ZNN model with fixed-time convergence and noise-tolerant performance for time-varying linear equation and inequality systems

<div>In this paper, a varying-gain zeroing (or Zhang) neural network (VG-ZNN) is proposed to obtain the online solution of the time-varying linear equation and inequality system. Distinguished from the fixed-value design parameter in</div><div>the original zeroing (or Zhang) neural network (ZNN) models, the design parameter of the VG-ZNN model is a nonlinear function that changes with time. The VG-ZNN model composed of the new time-varying design parameter we proposed can achieve fixed-time convergence and tolerate time-varying bounded noise and time-varying derivable noise. The theoretical detailed analysis of the convergence and robustness of the VG-ZNN model are given.</div>

A varying-gain ZNN model with fixed-time convergence and noise-tolerant performance for time-varying linear equation and inequality systems

<div>In this paper, a varying-gain zeroing (or Zhang) neural network (VG-ZNN) is proposed to obtain the online solution of the time-varying linear equation and inequality system. Distinguished from the fixed-value design parameter in</div><div>the original zeroing (or Zhang) neural network (ZNN) models, the design parameter of the VG-ZNN model is a nonlinear function that changes with time. The VG-ZNN model composed of the new time-varying design parameter we proposed can achieve fixed-time convergence and tolerate time-varying bounded noise and time-varying derivable noise. The theoretical detailed analysis of the convergence and robustness of the VG-ZNN model are given.</div>

On Systems of Active Particles Perturbed by Symmetric Bounded Noises: A Multiscale Kinetic Approach

We consider an ensemble of active particles, i.e., of agents endowed by internal variables u(t). Namely, we assume that the nonlinear dynamics of u is perturbed by realistic bounded symmetric stochastic perturbations acting nonlinearly or linearly. In the absence of birth, death and interactions of the agents (BDIA) the system evolution is ruled by a multidimensional Hypo-Elliptical Fokker–Plank Equation (HEFPE). In presence of nonlocal BDIA, the resulting family of models is thus a Partial Integro-differential Equation with hypo-elliptical terms. In the numerical simulations we focus on a simple case where the unperturbed dynamics of the agents is of logistic type and the bounded perturbations are of the Doering–Cai–Lin noise or the Arctan bounded noise. We then find the evolution and the steady state of the HEFPE. The steady state density is, in some cases, multimodal due to noise-induced transitions. Then we assume the steady state density as the initial condition for the full system evolution. Namely we modeled the vital dynamics of the agents as logistic nonlocal, as it depends on the whole size of the population. Our simulations suggest that both the steady states density and the total population size strongly depends on the type of bounded noise. Phenomena as transitions to bimodality and to asymmetry also occur.

Stochastic Response of Nonlinear Viscoelastic Systems with Time-Delayed Feedback Control Force and Bounded Noise Excitation

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.