State analysis of nonlinear systems using local canonical variate analysis

Conference · Wed Jan 01 00:00:00 EST 1997

OSTI ID:434849

Hunter, N F

There are many instances in which time series measurements are used to derive an empirical model of a dynamical system. State space reconstruction from time series measurement has applications in many scientific and engineering disciplines including structural engineering, biology, chemistry, climatology, control theory, and physics. Prediction of future time series values from empirical models was attempted as early as 1927 by Yule, who applied linear prediction methods to the sunspot values. More recently, efforts in this area have centered on two related aspects of time series analysis, namely prediction and modeling. In prediction future time series values are estimated from past values, in modeling, fundamental characteristics of the state model underlying the measurements are estimated, such as dimension and eigenvalues. In either approach a measured time series, [{bold y}(t{sub i})], i= 1,... N is assumed to derive from the action of a smooth dynamical system, s(t+{bold {tau}})=a(s(t)), where the bold notation indicates the (potentially ) multivariate nature of the time series. The time series is assumed to derive from the state evolution via a measurement function c. {bold y}(t)=c(s(t)) In general the states s(t), the state evolution function a and the measurement function c are In unknown, and must be inferred from the time series measurements. We approach this problem from the standpoint of time series analysis. We review the principles of state space reconstruction. The specific model formulation used in the local canonical variate analysis algorithm and a detailed description of the state space reconstruction algorithm are included. The application of the algorithm to a single-degree-of- freedom Duffing-like Oscillator and the difficulties involved in reconstruction of an unmeasured degree of freedom in a four degree of freedom nonlinear oscillator are presented. The advantages and current limitations of state space reconstruction are summarized.

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 434849
• Report Number(s): LA-UR-96-2240; CONF-970112-1; ON: DE96014026
• Resource Relation: Conference: 30. annual Hawaii international conference on system sciences, Wailea, HI (United States), 7-10 Jan 1997; Other Information: PBD: [1997]
• Country of Publication: United States
• Language: English

Related Subjects

99 MATHEMATICS
COMPUTERS
INFORMATION SCIENCE
MANAGEMENT
LAW
MISCELLANEOUS
66 PHYSICS
42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES
NONLINEAR PROBLEMS
MULTIVARIATE ANALYSIS
DEGREES OF FREEDOM
DYNAMICS
MATHEMATICAL MODELS
EIGENVALUES
SERIES EXPANSION
OSCILLATION MODES
OSCILLATIONS
MECHANICAL VIBRATIONS
DIFFERENTIAL EQUATIONS
CANONICAL TRANSFORMATIONS