Characterization and quantification of dynamic measurements is an ongoing area of research in the metrological community as new calibration methods are being developed to address dynamic measurement applications. The development undertaken to date largely assumes that nominally linear transducers can be used with linear assumptions in deconvolution of the input from the response and in system identification. To quantify the errors that arise from these assumptions, in this article, the effects of weak nonlinearities in transducers that are assumed to operate linearly during dynamic excitations are studied. Specifically, a set of first-order and second-order systems, which can model many transducers with weak nonlinearities, are used to numerically quantify the systemic errors due to the linear assumptions underlying the deconvolution.

 

We use numerical methods to integrate nonlinear differential equations and generate the nonlinear response to a gaussian impulse excitation. Using the differential equation and ignoring the nonlinear terms, we generate an inferred input representative of a deconvolution constrained by linear assumptions. The errors that arise are characterized by metrics that evaluate the maximum error between the inferred input and the actual input, the error at the peak inferred input, and the integral of the error. We demonstrate how these error metrics evolve over a large parameter space of weakly nonlinear systems that model many nominally linear transducers. If upper bounds to the nonlinear coefﬁcients and the input amplitudes for a transducer are known, then an upper bound to the error metrics can be approximated. This may be useful in quantifying the uncertainty due to this linear assumption. Furthermore, we provide an interpolating function for estimating error in deconvolution valid within a factor of two in the parameter space that is presented here.

 

For practical considerations we consider the errors from using linear system identification when applying this methodology to a transducer. An example of quantification of the errors due to linear assumptions in system identification is demonstrated using a time-series sparse regression system identification strategy. It is shown that the errors generated from linear system identification of a nonlinear transducer can counteract the systemic errors that arise in the linear deconvolution when the linear system identification was performed in similar loading conditions.

 

In general, the methodology and results presented here can be useful for understanding the effect of nonlinearity in single degree of freedom transient dynamics deconvolution and specifically in specifying certain metrics of errors in transducers with known weak nonlinearity.

 

 

 


Error Quantification in Dynamic Applications of Weakly Nonlinear Transducers

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

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