A comprehensive study of the delay vector variance method for quantification of nonlinearity in dynamical systems.

V Jaksic,D P Mandic,B Basu,K Ryan,V Pakrashi

doi:10.1098/rsos.150493

Abstract

Although vibration monitoring is a popular method to monitor and assess dynamic structures, quantification of linearity or nonlinearity of the dynamic responses remains a challenging problem. We investigate the delay vector variance (DVV) method in this regard in a comprehensive manner to establish the degree to which a change in signal nonlinearity can be related to system nonlinearity and how a change in system parameters affects the nonlinearity in the dynamic response of the system. A wide range of theoretical situations are considered in this regard using a single degree of freedom (SDOF) system to obtain numerical benchmarks. A number of experiments are then carried out using a physical SDOF model in the laboratory. Finally, a composite wind turbine blade is tested for different excitations and the dynamic responses are measured at a number of points to extend the investigation to continuum structures. The dynamic responses were measured using accelerometers, strain gauges and a Laser Doppler vibrometer. This comprehensive study creates a numerical and experimental benchmark for structurally dynamical systems where output-only information is typically available, especially in the context of DVV. The study also allows for comparative analysis between different systems driven by the similar input.

Highlights

Changes in mass, stiffness, natural frequency, etc., are often indicators of structural damage [1]
This paper has investigated the estimation, assessment and interpretation of signal nonlinearities of mechanical dynamical systems from output-only conditions from a theoretical and experimental point of view and has employed the delay vector variance (DVV) method in this regard
Outcome of DVV analysis on response signal is represented by a single number, root mean squared error (RMSE) value, which quantifies deviation of the DVV scatter plot from the bisector line

Summary

Introduction

Stiffness, natural frequency, etc., are often indicators of structural damage [1]. Statistical analyses and benchmarking of time or frequency domain dynamic responses of structures are popular in structural health monitoring (SHM) [4,5,6,7,8]. In signal analysis of dynamical systems, there is often a need to assess and quantify the extent of nonlinearity in the response signal and possibly in the system [9]. In this regard, a theoretically well-established technique for detecting the nature or nonlinearity of time series is the surrogate data method [10], which was originally motivated by statistical hypothesis testing and presents an indirect way of detecting nonlinearity in a signal [11]. Many non-parametric analysis techniques have been developed for the detection of nonlinearity in the signal [16]

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Conclusion