Non-parametric system identification from non-linear stochastic response

• Published in: Probabilistic engineering mechanics Vol. 16; no. 3; pp. 233 - 243
• Main Authors: Rüdinger, Finn, Krenk, Steen
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-07-2001; Elsevier Science
• Subjects: Damping; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Measurement and testing methods; Measurement methods and techniques in continuum mechanics of solids; Physics; Solid mechanics; Stochastic response; Structural and continuum mechanics; System identification; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Stochastic response; Damping; System identification; Level crossing; Probabilistic approach; Random excitation; Non parametric estimation; Numerical method; Stationary response; Non linear system; Vibration damping; White noise; Stationary noise; Measurement method; Random vibration
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/S0266-8920(01)00005-4

An estimation method is proposed for identification of non-linear stiffness and damping of single-degree-of-freedom systems under stationary white noise excitation. Non-parametric estimates of the stiffness and damping along with an estimate of the white noise intensity are obtained by suitable processing of records of the stochastic response. The stiffness estimation is based on a local iterative procedure, which compares the elastic energy at mean-level crossings with the kinetic energy at the extremes. The damping estimation is based on a generic expression for the probability density of the energy at mean-level crossings, which yields the damping relative to white noise intensity. Finally, an estimate of the noise intensity is extracted by estimating the absolute damping from the autocovariance functions of a set of modified phase plane variables at different energy levels. The method is demonstrated using records obtained by numerical simulation.