Inference of dominant modes for linear stochastic processes

For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer (estimate) their dominant modes from observations in real time. The modes can be real or complex. For a real mode (monotone decay), the goal is to infer its damping rate and mode shape. For a complex mode (oscillatory decay), the goal is to infer its frequency, damping rate and (complex) mode shape. Their amplitudes and correlations are encoded in a mode covariance matrix that is also to be inferred. The work is motivated and illustrated by the problem of detection of oscillations in power flow in AC electrical networks. Suggestions of some other applications are given.

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Optimization of the power flow of photovoltaic generators in electrical networks by MPPT algorithm and parallel active filters

Energy Reports ◽

10.1016/j.egyr.2021.07.103 ◽

2021 ◽

Vol 7 ◽

pp. 491-505

Author(s):

Kitmo ◽

Répélé Djidimbélé ◽

Dieudonné Kaoga Kidmo ◽

Guy Bertrand Tchaya ◽

Noël Djongyang

Keyword(s):

Power Flow ◽

Active Filters ◽

Electrical Networks ◽

Photovoltaic Generators

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Structure Vibration Shape Optimization Based on Power Flow Response Analysis

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.490-491.712 ◽

2014 ◽

Vol 490-491 ◽

pp. 712-718

Author(s):

Xue Bao Xia ◽

Yang Xiang ◽

Shao Wei Wu

Keyword(s):

Shape Optimization ◽

Mode Shape ◽

Power Flow ◽

Flow Analysis ◽

Optimization Method ◽

Weight Coefficient ◽

Surface Shape ◽

Response Analysis ◽

Flow Response ◽

Vibration Power Flow

Power flow analysis is a method to describe the dynamic behavior of structures by taking not only the amplitude of exciting force and velocity response into account, but also the phase between the two qualities. Shape optimization is an effective method to reduce vibration level. By choosing the vibration power flow as design objective, a shape optimization method of structure is presented. The structure surface is restructured with a series of mode shape superposition. By using genetic algorithm, the weight coefficient of each mode shape is optimized to get the best surface shape with minimum power flow response. Some examples are demonstrated to verify the efficiency and accuracy of the method.

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Analysis of Instabilities in Railway Vehicles Employing Operational Modal Analysis

2015 Joint Rail Conference ◽

10.1115/jrc2015-5697 ◽

2015 ◽

Author(s):

Lara Erviti Calvo ◽

Gorka Agirre Castellanos ◽

Germán Gimenez

Keyword(s):

Numerical Model ◽

Modal Analysis ◽

Mode Shape ◽

Operational Modal Analysis ◽

Mode Shapes ◽

Correct Identification ◽

Unstable Condition ◽

Static Tests ◽

Railway Vehicles ◽

Damping Rate

The application of Operational Modal Analysis (OMA) in the railway sector opens a broad field of opportunities. The validation of the numerical model employed in the design phase is usually performed employing data obtained in static tests. The drawback is that some suspension parameters, such as dampers, only have an influence in the dynamic behavior and not in the static behavior. Because of that, the use of the mode shapes identified from track measurements in combination with the static tests leads to a more accurate validation of the numerical model. Apart from that, most passenger comfort and dynamic problems are associated to slightly damped modes. A correct identification of the modal parameters can be used as a continuous design improvement tool to improve the comfort and dynamic characteristics of future designs. Another valuable application of OMA techniques is the identification of the mode shapes corresponding to instabilities, due to the safety impact that they have. In railway vehicles, instabilities are associated to mode shapes that present a damping rate which decreases with the increase of the running speed. Above a certain speed value, the excitation coming from track cannot be damped by the vehicle and it reaches an unstable condition. This unstable condition leads to high acceleration levels experienced by the passengers and high interaction forces between the wheel and the rail that may lead to safety hazards. The speed above which the vehicle is unstable is known as critical speed, and has to be greater than the maximum speed of the vehicle with a reasonable safety margin. The use of OMA techniques allows identifying the mode shape that causes the instability. This paper presents the application of OMA techniques to measurements performed on a passenger vehicle, in which the speed was increased until the vehicle was unstable. The mode shape that caused the instability was identified as well as its corresponding natural frequency and damping rate.

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Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems

Mathematics ◽

10.3390/math8060915 ◽

2020 ◽

Vol 8 (6) ◽

pp. 915

Author(s):

Robert Vrabel

Keyword(s):

Linear Systems ◽

Linear Time ◽

Upper Bounds ◽

Time Varying ◽

Asymptotically Stable ◽

Lower And Upper Bounds ◽

Linear Time Invariant ◽

Vector Norm ◽

Linear Time Invariant Systems ◽

Stable Linear

Based on the eigenvalue idea and the time-varying weighted vector norm in the state space R n we construct here the lower and upper bounds of the solutions of uniformly asymptotically stable linear systems. We generalize the known results for the linear time-invariant systems to the linear time-varying ones.

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Stability Criteria for Nonclassically Damped Systems With Nonlinear Uncertainties

Journal of Applied Mechanics ◽

10.1115/1.1778719 ◽

2004 ◽

Vol 71 (5) ◽

pp. 632-636 ◽

Cited By ~ 1

Author(s):

D. Q. Cao ◽

Y. M. Ge ◽

Y. R. Yang

Keyword(s):

Output Feedback Control ◽

Degree Of Freedom ◽

Asymptotically Stable ◽

Nonlinear Perturbations ◽

Stability Criteria ◽

Lyapunov Approach ◽

Nonlinear Uncertainties ◽

The Stability ◽

Damped Systems ◽

Stable Linear

The asymptotic stability of nonclassically damped systems with nonlinear uncertainties is addressed using the Lyapunov approach. Bounds on nonlinear perturbations that maintain the stability of an asymptotically stable, linear multi-degree-of-freedom system with nonclassical damping are derived. The explicit nature of the construction permits us to directly express the algebraic criteria in terms of plant parameters. The results are then applied to the symmetric output feedback control of multi-degree-of-freedom systems with nonlinear uncertainties. Numerical examples are given to demonstrate the new stability criteria and to compare them with the previous results in the literature.

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Bifurcation in Mean Phase Portraits for Stochastic Dynamical Systems with Multiplicative Gaussian Noise

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420502168 ◽

2020 ◽

Vol 30 (11) ◽

pp. 2050216

Author(s):

Hui Wang ◽

Athanasios Tsiairis ◽

Jinqiao Duan

Keyword(s):

Dynamical Systems ◽

Gaussian Noise ◽

Stochastic Systems ◽

Planck Equation ◽

Phase Portraits ◽

Stochastic Bifurcation ◽

Stochastic Dynamical Systems ◽

Solution Processes ◽

Bifurcation Phenomena ◽

Stability Type

We investigate the bifurcation phenomena for stochastic systems with multiplicative Gaussian noise, by examining qualitative changes in mean phase portraits. Starting from the Fokker–Planck equation for the probability density function of solution processes, we compute the mean orbits and mean equilibrium states. A change in the number or stability type, when a parameter varies, indicates a stochastic bifurcation. Specifically, we study stochastic bifurcation for three prototypical dynamical systems (i.e. saddle-node, transcritical, and pitchfork systems) under multiplicative Gaussian noise, and have found some interesting phenomena in contrast to the corresponding deterministic counterparts.

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Optimal Fuzzy Control of Nonlinear Dynamical Systems Using Evolutionary Algorithms

10.47890/jadct/2020/seahosseini/10123452 ◽

2020 ◽

Vol 1 (1) ◽

Author(s):

Mohammad Dashti Javan ◽

Seyed Ehsan Aghakouchaki Hosseini ◽

Mohammad Bagher Menhaj

Keyword(s):

Dynamical Systems ◽

Evolutionary Algorithms ◽

Fuzzy Controller ◽

Nonlinear Dynamical Systems ◽

Distribution Networks ◽

Electrical Networks ◽

Dynamic Voltage Restorer ◽

Nonlinear Dynamical ◽

Voltage Restorer ◽

Dynamic Voltage

Goal of this research is to produce a controlling voltage for Pulse Width Modulation (PWM) generator so that its Total Harmonic Distortion (THD) characteristic is reduced and Dynamic Voltage Restorer (DVR) compensates function of the system against error as well as turbulence in such a way that the end user has no trouble with supplied voltage. In this study, a DVR system has been utilized which is capable of counteracting adverse effects of changing voltage against sensitive loads. Continuous and stable supply of energy is the most important goal in serviceability of electrical networks. Turbulence in distribution networks causes disturbances in level and quality of the voltage. To eliminate destructive effects of these disturbances especially over sensitive users, one could use compensator devices. So, a PSO-Fuzzy controller has been employed to optimize SAG characteristics of voltage of the sensitive load. Simulation results obtained in this study, considering the complicated and nonlinear nature of DVR system, demonstrates efficiency of proposed PSO-Fuzzy controller in improving behavior of the dynamic voltage restorer introduced to the network for the purpose of eliminating destructive effects of imminent disturbances over sensitive users. Keywords:Fuzzy Controller; Evolutionary Algorithms; Nonlinear Dynamical Systems;

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Flutter of Low Pressure Turbine Blades With Cyclic Symmetric Modes: A Preliminary Design Method

Journal of Turbomachinery ◽

10.1115/1.1650380 ◽

2004 ◽

Vol 126 (2) ◽

pp. 306-309 ◽

Cited By ~ 11

Author(s):

Robert Kielb ◽

Jack Barter ◽

Olga Chernycheva ◽

Torsten Fransson

Keyword(s):

Mode Shape ◽

Design Method ◽

Turbine Blades ◽

Current Method ◽

Low Pressure ◽

Mode Shapes ◽

Preliminary Design ◽

Complex Mode ◽

Low Pressure Turbine ◽

Reduced Frequency

A current preliminary design method for flutter of low pressure turbine blades and vanes only requires knowledge of the reduced frequency and mode shape (real). However, many low pressure turbine (LPT) blade designs include a tip shroud that mechanically connects the blades together in a structure exhibiting cyclic symmetry. A proper vibration analysis produces a frequency and complex mode shape that represents two real modes phase shifted by 90 deg. This paper describes an extension to the current design method to consider these complex mode shapes. As in the current method, baseline unsteady aerodynamic analyses must be performed for the three fundamental motions, two translations and a rotation. Unlike the current method work matrices must be saved for a range of reduced frequencies and interblade phase angles. These work matrices are used to generate the total work for the complex mode shape. Since it still only requires knowledge of the reduced frequency and mode shape (complex), this new method is still very quick and easy to use. Theory and an example application are presented.

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