Reconstructing slow-time dynamics from fast-time measurements

2007 ◽  
Vol 366 (1866) ◽  
pp. 729-745 ◽  
Author(s):  
David Chelidze ◽  
Ming Liu
Keyword(s):  
Phase Space ◽  
Potential Field ◽  
Damage Identification ◽  
Feature Space ◽  
Operating Conditions ◽  
Fast Time ◽  
Slow Time ◽  
Time Dynamics ◽  
Feature Vectors ◽  
Nonlinear Potential

This paper considers a dynamical system subjected to damage evolution in variable operating conditions to illustrate the reconstruction of slow-time (damage) dynamics using fast-time (vibration) measurements. Working in the reconstructed fast-time phase space, phase space warping-based feature vectors are constructed for slow-time damage identification. A subspace of the feature space corresponding to the changes in the operating conditions is identified by applying smooth orthogonal decomposition (SOD) to the initial set of feature vectors. Damage trajectory is then reconstructed by applying SOD to the feature subspace not related to the changes in the operating conditions. The theory is validated experimentally using a vibrating beam, with a variable nonlinear potential field, subjected to fatigue damage. It is shown that the changes in the operating condition (or the potential field) can be successfully separated from the changes caused by damage (or fatigue) accumulation and SOD can identify the slow-time damage trajectory.

Local Flow Variation Method for Damage Identification

2005 ◽  
Author(s):  
Ming Liu ◽  
David Chelidze
Keyword(s):  
Phase Space ◽  
Damage Identification ◽  
Computing Time ◽  
Variation Method ◽  
Fast Time ◽  
Slow Time ◽  
Local Flow ◽  
Flow Variation ◽  
Damage Process ◽  
Phase Space Warping

In this paper, a damage identification method called local flow variation is introduced. It is a practical implementation of a phase space warping concept. A hierarchical dynamical system is considered where a slow-time damage process causes drifts in the parameters of fast-time system describing measurable response of a structure. The method is based on the hypothesis that the probability distribution function of the fast-time trajectory in its phase space is a function of damage state. In this method, an ensemble of estimated expectations of trajectory in different locations of the reconstructed phase space is used as a damage feature vector. Using these feature vectors, damage identification is realized by a smooth orthogonal decomposition. An experiment is conducted to validate the method. A two dimensional slow-time damage process is identified from experimental fast-time data. Although damage identification through the local flow variation is not as accurate as trough phase space warping, the required computing time is about two-orders-of-magnitude shorter.

Multidimensional Hidden Slow Variable Tracking in a Hierarchical Dynamical System

2003 ◽  
Author(s):  
David Chelidze
Keyword(s):  
Phase Space ◽  
Linear Models ◽  
Damage Identification ◽  
Systems Approach ◽  
Signal To Noise Ratio ◽  
Slow Variable ◽  
Fast Time ◽  
Time Dynamics ◽  
Affine Projection ◽  
Actual Damage

In this paper, we present a novel method for multidimensional damage identification based on a dynamical systems approach to damage evolution. This approach does not depend on the knowledge of particular damage physics, and is appropriate for systems where damage evolves on much slower time scale then the directly observable dynamics. In an experimental context, the phase space reconstruction and locally linear models are used to quantify small distortions occurring in a dynamical system’s phase space due to damage accumulation. These measurements are then related to the drifts in damage variables. A mathematical model of a harmonically driven cantilever beam in a force field of two battery-powered electromagnets is used to demonstrate validity of the method. It is explicitly demonstrated that an affine projection of the described damage metric accurately tracks the two competing damage processes. For practical damage identification purposes, the tracking data is analyzed using the proper orthogonal decomposition (POD) and optimal tracking (OT) methods. Both methods correctly identify the two dominant damage modes. However, the OT is more impervious to changes in fast-time dynamics and provides a significantly better signal-to-noise ratio. The OT-based damage observer is demonstrated to be within a linear transformation from the actual damage states.

Automated classification of human lung sound signals using phase space representation of intrinsic mode function

2021 ◽  
Author(s):  
Sibghatullah I. Khan ◽  
Vikram Palodiya ◽  
Lavanya Poluboyina
Keyword(s):  
Phase Space ◽  
Human Lung ◽  
Feature Space ◽  
Normal Lung ◽  
Space Representation ◽  
Support Vector ◽  
Lung Sounds ◽  
Lung Sound ◽  
Phase Space Representation

Abstract Bronchiectasis and chronic obstructive pulmonary disease (COPD) are common human lung diseases. In general, the expert pulmonologistcarries preliminary screening and detection of these lung abnormalities by listening to the adventitious lung sounds. The present paper is an attempt towards the automatic detection of adventitious lung sounds ofBronchiectasis,COPD from normal lung sounds of healthy subjects. For classification of the lung sounds into a normaland adventitious category, we obtain features from phase space representation (PSR). At first, the empirical mode decomposition (EMD) is applied to lung sound signals to obtain intrinsic mode functions (IMFs). The IMFs are then further processed to construct two dimensional (2D) and three dimensional (3D) PSR. The feature space includes the 95% confidence ellipse area and interquartile range (IQR) of Euclidian distances computed from 2D and 3D PSRs, respectively. The process is carried out for the first four IMFs correspondings to normal and adventitious lung sound signals. The computed features depicta significant ability to discriminate the two categories of lung sound signals.To perform classification, we use the least square support vector machine with two kernels, namely, polynomial and radial basis function (RBF).Simulation outcomes on ICBHI 2017 lung sound dataset show the ability of the proposed method in effectively classifying normal and adventitious lung sound signals. LS-SVM is employing RBF kernel provides the highest classification accuracy of 97.67 % over feature space constituted by first, second, and fourth IMF.

scholarly journals A phase-space beam position monitor for synchrotron radiation

2015 ◽  
Vol 22 (4) ◽  
pp. 946-955 ◽  
Author(s):  
Nazanin Samadi ◽  
Bassey Bassey ◽  
Mercedes Martinson ◽  
George Belev ◽  
Les Dallin ◽  
...  
Keyword(s):  
Phase Space ◽  
Synchrotron Radiation ◽  
Incident Angle ◽  
Operating Conditions ◽  
Photon Beam ◽  
Profile Measurement ◽  
Beam Position Monitor ◽  
Position Measurement ◽  
Beam Position ◽  
X Ray

The stability of the photon beam position on synchrotron beamlines is critical for most if not all synchrotron radiation experiments. The position of the beam at the experiment or optical element location is set by the position and angle of the electron beam source as it traverses the magnetic field of the bend-magnet or insertion device. Thus an ideal photon beam monitor would be able to simultaneously measure the photon beam's position and angle, and thus infer the electron beam's position in phase space. X-ray diffraction is commonly used to prepare monochromatic beams on X-ray beamlines usually in the form of a double-crystal monochromator. Diffraction couples the photon wavelength or energy to the incident angle on the lattice planes within the crystal. The beam from such a monochromator will contain a spread of energies due to the vertical divergence of the photon beam from the source. This range of energies can easily cover the absorption edge of a filter element such as iodine at 33.17 keV. A vertical profile measurement of the photon beam footprint with and without the filter can be used to determine the vertical centroid position and angle of the photon beam. In the measurements described here an imaging detector is used to measure these vertical profiles with an iodine filter that horizontally covers part of the monochromatic beam. The goal was to investigate the use of a combined monochromator, filter and detector as a phase-space beam position monitor. The system was tested for sensitivity to position and angle under a number of synchrotron operating conditions, such as normal operations and special operating modes where the photon beam is intentionally altered in position and angle at the source point. The results are comparable with other methods of beam position measurement and indicate that such a system is feasible in situations where part of the synchrotron beam can be used for the phase-space measurement.

A New Model for Long-Term Stochastic Analysis and Prediction—Part I: Theoretical Background

1992 ◽  
Vol 36 (01) ◽  
pp. 1-16
Author(s):  
G. A. Athanassoulis ◽  
P. B. Vranas ◽  
T. H. Soukissian
Keyword(s):  
Time Scale ◽  
Random Function ◽  
Spectral Characteristics ◽  
Time History ◽  
Time Variable ◽  
Sea Surface ◽  
Surface Elevation ◽  
Fast Time ◽  
Slow Time

A new approach for calculating the long-term statistics of sea waves is proposed. A rational long-term stochastic model is introduced which recognizes that the wave climate at a given site in the ocean consists of a random succession of individual sea states, each sea state possessing its own duration and intensity. This model treats the sea-surface elevation as a random function of a "fast" time variable, and the time history of the spectral characteristics of the successive sea states as a random function of a "slow" time variable. By developing an appropriate conceptual framework, it becomes possible to express various probabilistic characteristics of the sea-surface elevation, which are sensible only in the fast-time scale, in terms of the statistics of sea-states duration and intensity, which is meaningful only in the slow-time scale. As an example, we study the random quantity MU(T) = "number of maxima of the sea-surface elevation lying above the level u and occurring during a long-term time period [0,T]." Exploiting the proposed framework, it is shown that, under certain clearly defined assumptions, Mu(T) can be given the structure of a renewal-reward (cumulative) process, whose interarrival times correspond to the duration of successive sea states. Thus, using renewal theory, the complete characterization of the probability structure of MU(T) is obtained. As a consequence, the long-term probability distribution function of the individual wave height is rigorously defined and calculated. The relation of the present results with corresponding ones previously obtained is thoroughly discussed. The proposed model can be extended twofold: either by replacing some of the simplifying assumptions by more realistic ones, or by extending the model for treating the corresponding problems for ship and structures responses.

Parameter Estimation in a Nonlinear Vibrating System Using an Observer for an Extended System

1999 ◽  
Author(s):  
Anindya Chatterjee ◽  
Joseph P. Cusumano
Keyword(s):  
Parameter Estimation ◽  
Time Scale ◽  
Asymptotic Methods ◽  
System Response ◽  
Parameter Estimates ◽  
Fast Time ◽  
State Variables ◽  
Slow Time ◽  
Unknown Parameters ◽  
Lipschitz Continuous

Abstract We present a new observer-based method for parameter estimation for nonlinear oscillatory mechanical systems where the unknown parameters appear linearly (they may each be multiplied by bounded and Lipschitz continuous but otherwise arbitrary, possibly nonlinear, functions of the oscillatory state variables and time). The oscillations in the system may be periodic, quasiperiodic or chaotic. The method is also applicable to systems where the parameters appear nonlinearly, provided a good initial estimate of the parameter is available. The observer requires measurements of displacements. It estimates velocities on a fast time scale, and the unknown parameters on a slow time scale. The fast and slow time scales are governed by a single small parameter ϵ. Using asymptotic methods including the method of averaging, it is shown that the observer’s estimates of the unknown parameters converge like e−ϵt where t is time, provided the system response is such that the coefficient-functions of the unknown parameters are not close to being linearly dependent. It is also shown that the method is robust in that small errors in the model cause small errors in the parameter estimates. A numerical example is provided to demonstrate the effectiveness of the method.

Comparative effects of vasodilator drugs on flow distribution and venous return

1985 ◽  
Vol 63 (11) ◽  
pp. 1345-1355 ◽  
Author(s):  
R. I. Ogilvie
Keyword(s):  
Blood Flow ◽  
Blood Volume ◽  
Time Constant ◽  
Venous Return ◽  
Flow Distribution ◽  
Fast Time ◽  
Central Blood Volume ◽  
Slow Time ◽  
Arterial Resistance ◽  
Slow Time Constant

Systemic vascular effects of hydralazine, prazosin, captopril, and nifedipine were studied in 115 anesthetized dogs. Blood flow [Formula: see text] and right atrial pressure (Pra) were independently controlled by a right heart bypass. Transient changes in central blood volume after an acute reduction in Pra at a constant [Formula: see text] showed that blood was draining from two vascular compartments with different time constants, one fast and the other slow. At three dose levels producing comparable reductions in systemic arterial pressure (30–40% at the highest dose), these drugs had different effects on flow distribution and venous return. Hydralazine and prazosin had parallel and balanced effects on arterial resistance of the two vascular compartments, and flow distribution was unaltered. Captopril preferentially reduced arterial resistance of the compartment with a slow time constant for venous return (−26 ± 6%, −30 ± 6%, −50 ± 5% at 0.02, 0.10, and 0.50 mg∙kg−1∙h−1, respectively; [Formula: see text]) without altering arterial resistance of the fast time-constant compartment. Blood flow to the slow time-constant compartment was increased 43 ± 14% at the highest dose, and central blood volume was reduced 108 ± 15 mL. In contrast, nifedipine had a balanced effect on arterial resistance with the lowest dose (0.025 mg/kg) but caused a preferential reduction in arterial resistance of the fast time-constant compartment at higher doses (−38 ± 4% and −55 ± 2% at 0.05 and 0.10 mg/kg, respectively). Blood flow to the slow time-constant compartment was reduced 36 ± 5% at the highest dose of nifedipine, and central blood volume was increased 66 ± 12 mL. Total systemic venous compliance was unaltered or slightly reduced by each of the four drugs. These results add further evidence to the hypothesis that peripheral blood flow distribution is a major determinant of venous return to the heart.

Degradation assessment of ball bearings utilizing curvilinear component analysis

2018 ◽  
Vol 233 (3) ◽  
pp. 714-730 ◽  
Author(s):  
Prashant Tiwari ◽  
SH Upadhyay
Keyword(s):  
Feature Space ◽  
Component Analysis ◽  
Performance Degradation ◽  
Quantization Error ◽  
Mapping Technique ◽  
Nonlinear Mapping ◽  
Ball Bearings ◽  
Self Organizing Map ◽  
Feature Vectors ◽  
Self Organizing

The performance degradation assessment of ball bearings is of great importance to increase the efficiency and the reliability of rotating mechanical systems. The large dimensionality of feature space introduces a lot of noise and buries the potential information about faults hidden in the feature data. This paper proposes a novel health assessment method facilitated with two compatible methods, namely curvilinear component analysis and self-organizing map network. The novelty lies in the implementation of a vector quantization approach for the sub-manifolds in the feature space and to extract the fault signatures through nonlinear mapping technique. Curvilinear component analysis is a nonlinear mapping tool that can effectively represent the average manifold of the highly folded information and further preserves the local topology of the data. To answer the complications and to accomplish reliability and accuracy in bearing performance degradation assessment, the work is carried out with following steps; first, ensemble empirical mode decomposition is used to decompose the vibration signals into useful intrinsic mode functions; second, two fault features i.e. singular values and energy entropies are extracted from the envelopes of the intrinsic mode function signals; third, the extracted feature vectors under healthy conditions, further reduced with curvilinear component analysis are used to train the self-organizing map model; finally, the reduced test feature vectors are supplied to the trained self-organizing map and the confidence value is obtained. The effectiveness of the proposed technique is validated on three run-to-failure test signals with the different type of defects. The results indicate that the proposed technique detects the weak degradation earlier than the widely used indicators such as root mean square, kurtosis, self-organizing map-based minimum quantization error, and minimum quantization error-based on the principal component analysis.

scholarly journals Composite Stackelberg Strategy for Singularly Perturbed Bilinear Quadratic Systems

2015 ◽  
Vol 3 (2) ◽  
pp. 154-163
Author(s):  
Ning Bin ◽  
Chengke Zhang ◽  
Huainian Zhu ◽  
Zan Mo
Keyword(s):  
Singularly Perturbed ◽  
Stackelberg Equilibrium ◽  
Order System ◽  
Fast Time ◽  
Slow Time ◽  
Stackelberg Strategy ◽  
Fast Time Scale ◽  
Equilibrium Strategies ◽  
Numerical Result ◽  
Coupled Algebraic Riccati Equations

AbstractBased on singularly perturbed bilinear quadratic problems, this paper proposes to decompose the full-order system into two subsystems of a slow-time and fast-time scale. Utilizing the fixed point iterative algorithm to solve cross-coupled algebraic Riccati equations, equilibrium strategies of the two subsystems can be obtained, and further the composite strategy of the original full-order system. It was proved that such a composite strategy formed ano(ε) (near) Stackelberg equilibrium, and a numerical result of the algorithm was presented in the end.

Analysis of venous flow transients for estimation of vascular resistance, compliance, and blood flow distribution

1987 ◽  
Vol 65 (9) ◽  
pp. 1884-1890 ◽  
Author(s):  
Richard I. Ogilvie ◽  
Danuta Zborowska-Sluis
Keyword(s):  
Time Constant ◽  
Venous Return ◽  
Fast Time ◽  
Slow Time ◽  
Venous Outflow ◽  
Venous Flow ◽  
Time Constants ◽  
Slow Time Constant ◽  
Over Time ◽  
Flow Transients

We analysed venous flow transients using a long venous circuit and right heart bypass in 17 dogs after a rapid decrease in atrial pressure. A biphase curve was obtained which we decomposed into a two-compartmental model, one with a fast time constant for venous return (0.069 min) and 52% of total circulating flow [Formula: see text], and one with a slower time constant (0.456 min) and 48% of [Formula: see text]. Subsequently, separate drainage from splanchnic and peripheral beds (with the renal venous return in the peripheral bed drainage) allowed comparison of time constants and venous outflow in these beds. The sum of the venous outflow volumes over time during separate drainage was indistinguishable from the single biphasic venous outflow volume curve over time observed with a long circuit and single reservoir. The fast time constant of the biphasic curve was not different from that determined by separate drainage from the peripheral circulation. The slow time constant of the single biphasic curve of 0.456 min was hybrid of two time constants, 0.216 min in the splanchnic bed and 0.862 min in the peripheral bed. Separate drainage from peripheral and splanchnic vascular beds demonstrated that the peripheral bed constituted 70% of venous outflow in the fast time constant compartment using Caldini's technique, whereas the splanchnic bed constituted 63% of venous outflow in the slow time constant compartment. It is concluded that, although Caldini's technique demonstrates biphasic venous flow transients, neither the fast nor the slow time constant compartments resolved from this analysis represent a particular anatomical region or vascular bed.

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