Excitation symmetry analysis method (ESAM) for calculation of higher order non-linearities

Abstract

A nonlinear system with third order nonlinearity is fully characterized using Symmetry Analysis applied to the excitation, as it is done in second order nonlinear systems using the pulse inverted method. Symmetry Analysis is performed using irreductible representations and the character table of C 3 rotation point group, which leads to the construction of three eigen-excitations allowing extraction of the third order nonlinearity parameter without the perturbation of fundamental and second order terms. Validation of this concept is based on Excitation Symmetry Analysis Method (ESAM) which was tested on simulated noisy signals and compared with classical spectral analysis.

Nonlinear Time Reversal Tomography of Structural Defects

“…The maximum for parameter N 1 is obtained for transducers T 8 and T 9 ( Figure 7) which are affected by the most reflective part of the crack (Figure 6). Parameters N 2 and N 3 reach maximum for transducer T 8 . This variation should be explained by the crack characteristics along the propagation paths on these trajectories.…”

“…Medium with tiny cracks generally shows an enhanced 3 rd order nonlinearity which could be extracted with the ESAM signal processing approach (Excitation Symmetry Analysis Method) using optimized excitations [8]. ESAM uses nonlinear signature coming from the direct acoustic response as a pre-processing tool for the extraction of nonlinear signature.…”

“…This framework, known as Symmetry Analysis (SA) is based on continuous Lie groups [7] and discrete symmetries. It is used in the ESAM approach [8], and constitutes the bases of a systemic approach aimed at using absolute invariants like Time Reversal (TR), reciprocity between emitters and receivers, and other, nonlinear properties so as to optimize coded excitations (e.g. pulseinversion or chirp-coded processes, etc).…”

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“…Superposition of nonlinear waves in Memristor [37] was studied in Ref. [39], and in Ref. [41] application to crack detection using the time reversed memristor wave was proposed.…”

“…In a memory based ultrasonic transducer, which is called the memosducer, memristor based TR-NEWS (Time Reversal based Nonlinear Elastic Wave Spectroscopy), similar cancellation of nonlinear waves by time reversed nonlinear waves was observed [39][40][41]. There are confusions in the definition of memristance M(φ,Q) = dφ/dQ whereφ = ∫Udt, and which is identified as dφ/dQ = (dφ/dt)/(dQ/dt) = dU/dI [48].…”