Variable Perturbation Method Research Articles

Differentially private distributed logistic regression with the objective function perturbation

Distributed learning is a very effective divide-and-conquer strategy for dealing with big data. As distributed learning algorithms become more and more mature, network security issues including the risk of privacy disclosure of personal sensitive data, have attracted high attention and vigilance. Differentially private is an important method that maximizes the accuracy of a data query while minimizing the chance of identifying its records when querying from the given data. The known differentially private distributed learning algorithms are based on variable perturbation, but the variable perturbation method may be non-convergence and the experimental results usually have large deviations. Therefore, in this paper, we consider differentially private distributed learning algorithm based on objective function perturbation. We first propose a new distributed logistic regression algorithm based on objective function perturbation (DLR-OFP). We prove that the proposed DLR-OFP satisfies differentially private, and obtain its fast convergence rate by introducing a new acceleration factor for the gradient descent method. The numerical experiments based on benchmark data show that the proposed DLR-OFP algorithm has fast convergence rate and better privacy protection ability.

On Coupled Delayed Van der Pol-Duffing Oscillators

We investigate the dynamics of a delay differential coupled Duffing-Van der Pol oscillator equation. Using the Lindstedt's method, we derive the in-phase mode solutions and then obtain the slow flow equations governing the stability of the in-phase mode by employing the two variable perturbation method. We solve the slow flow equations using series expansion and obtain conditions for Hopf bifurcation and studied stability of the in-phase mode. Finally, we studied stability and bifurcations of the origin. Our interest in this system is due to the fact that it is related to the coupled laser oscillators.

Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics

An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time.

Prediction of combined static and cyclic load-induced settlement of shallow strip footing on granular soil using artificial neural network

ABSTRACT The present study focuses on the development of an Artificial Neural Network (ANN) model equation to estimate the settlement of a shallow strip footing resting on granular soils due to combination of static and cyclic load. The model is developed using 324 number of datasets obtained from finite element analysis carried out with the help of Opensees. The input parameters are relative density (Dr %) of soil, depth of embedment (Df / B) of footing, intensity of static load depending on the factor of safety (FS), intensity of cyclic load (qd(max) / qu (%)) and frequency (f) of applied cyclic load to estimate non-dimensional settlement, s/su (%) of footing as output. Importance of input parameters are studied using Pearson’s correlation and Spearman’s rank correlation as well as sensitivity analysis based on Variable Perturbation method and Weight methods. The effect of input parameters on output is studied by using Neural Interpretation Diagram (NID).

Using Variable Perturbation Method to Study the Stability of Torsional Self-Excited Vibration in Main Drive System of Rolling Mill

The self-excited vibration of blooming mill is a kind of torsional vibration, which occurs only when the rolling machine slips under appropriate conditions. Once in place, this may cause the larger peak pressure of each component in the main drive system; reduce the service life of the components, cause components′ damage directly. A large number of studies have shown that, at present there are not effective methods for diagnosis, monitoring of slipping and take proper measures in time to stop slipping so as to avoid the occurrence of malignant accidents. In this paper, author set out from another angle, take the main drive system of rolling mill as an example, to study stability of self-excited vibration. The conditions of the stable vibration are gained. By combining with the actual working conditions of blooming mill, author has put forward some effective measures to meet the stable conditions in order to make the blooming mill work in the stable state. Practice research has proved that the effective measures can contribute to reduce structural damage directly caused by the torsional vibration when “slipping” phenomenon occurred and to extend the service life of the components. DOI: http://dx.doi.org/10.11591/telkomnika.v11i6.2699

Study the Stability of Bending-Torsional Coupled Vibration of a Rotor System with a Crack and Variable Perturbation Method

The differential equations of bending-torsional coupled vibration have been established with a switching crack for a Jeffcott rotor system with a transverse crack as the research object. Variable perturbation method has been used to study the stability of bending-torsional coupled vibration of a rotor system with a crack. The theoretical result shows that, when it is close to the natural frequency of 2 times, 3/2 times and 1 times, unstable vibrations exist and conditions of stable vibration. According to the above order, unstable region becomes narrow. While in 1/4 times, 1/6 times, the system is stable. The conclusions provide valuable theoretical basis for a crack rotor system in the real working conditions when corresponding measures need taking.

Unravelling the Turing bifurcation using spatially varying diffusion coefficients

. The Turing bifurcation is the basic bifurcation generating spatial pattern, and lies at the heart of almost all mathematical models for patterning in biology and chemistry. In this paper the authors determine the structure of this bifurcation for two coupled reaction diffusion equations on a two-dimensional square spatial domain when the diffusion coefficients have a small explicit variation in space across the domain. In the case of homogeneous diffusivities, the Turing bifurcation is highly degenerate. Using a two variable perturbation method, the authors show that the small explicit spatial inhomogeneity splits the bifurcation into two separate primary and two separate secondary bifurcations, with all solution branches distinct. This splitting of the bifurcation is more effective than that given by making the domain slightly rectangular, and shows clearly the structure of the Turing bifurcation and the way in which the! var ious solution branches collapse together as the spatial variation is reduced. The authors determine the stability of the solution branches, which indicates that several new phenomena are introduced by the spatial variation, including stable subcritical striped patterns, and the possibility that stable stripes lose stability supercritically to give stable spotted patterns..

Robust Output Tracking for Mismatched Uncertain Systems – A Hybrid Approach

This paper is concerned with the robust output tracking for linear systems with mismatched and time-varying uncertainties. By using Stable Combined Variable Perturbation Method (SCVPM) and hybrid control strategy a new robust controller is presented in the paper. It is shown that die controller guarantees the global stability of the closed loop system and sufficiently small tracking errors.

Robust output tracking for nonlinear uncertain systems

The problem of robust output tracking for nonlinear systems in the presence of uncertainties is further studied by extending the results of Behtash (1990) to systems with mismatched uncertainties. A new design method which is called the Stable Combined Variable Perturbation Method (SCVPM) is proposed and a robust controller is presented using high-gain feedback. Our results are compatible with those of Behtash (1990) in a sense that the new controller will degenerate to the one of Behtash (1990) if the so-called generalized matching condition is satisfied. Simulation results verified the effectiveness of the newly proposed method and controller.

Mean wave propagation in a slab of one-dimensional discrete random medium

A study has been made of the propagation of time harmonic waves through a one-dimensional medium of discrete scatterers randomly positioned over a finite interval L. The random medium is modeled by a Poisson impulse process with density λ. The invariant imbedding procedure is employed to obtain a set of initial value stochastic differential equations for the field inside the medium and the reflection coefficient of the layer. By using the Markov properties of the Poisson impulse process. exact integro-differential equations of the Kolmogorov-Feller type are derived for the probability density function of the reflection coefficient and the field. When the concentration of the scatterers is low, a two variable perturbation method in small λ is used to obtain an approximate solution for the mean field. It is shown that this solution, which varies exponentially with respect to λL, agrees exactly with the mean field obtained by Feldy's approximate method.

A variable perturbation method for nuclear spin-lattice relaxation measurements

A variable perturbation method for nuclear spin-lattice relaxation measurements

An asymptotic solution of an initial value problem for a non-linear viscoelastic rod

Stress wave propagation in a one-dimensional materai, described by the non-linear constitutive law ∂σ ∂t − E ∂ε ∂t + k[σ − E'g3 + βε 2] = 0 , is analyzed by a two-time variable perturbation method. Secular terms are “cast out” by employing special orthogonality conditions. The resulting expansion reveals a “mode coupling”, due to the non-linearity, and displays the significance of the three parameters present in the constitutive law. Numerical values for the parameters are assumed and the resulting displacements computed.