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- Title
Generalized Approach to Optimal Polylinearization for Smart Sensors and Internet of Things Devices.
- Authors
Marinov, Marin B.; Dimitrov, Slav
- Abstract
This study introduces an innovative numerical approach for polylinear approximation (polylinearization) of non-self-intersecting compact sensor characteristics (transfer functions) specified either pointwise or analytically. The goal is to partition the sensor characteristic optimally, i.e., to select the vertices of the approximating polyline (approximant) along with their positions, on the sensor characteristics so that the distance (i.e., the separation) between the approximant and the characteristic is rendered below a certain problem-specific tolerance. To achieve this goal, two alternative nonlinear optimization problems are solved, which differ in the adopted quantitative measure of the separation between the transfer function and the approximant. In the first problem, which relates to absolutely integrable sensor characteristics (their energy is not necessarily finite, but they can be represented in terms of convergent Fourier series), the polylinearization is constructed by the numerical minimization of the L 1 -metric (a distance-based separation measure), concerning the number of polyline vertices and their locations. In the second problem, which covers the quadratically integrable sensor characteristics (whose energy is finite, but they do not necessarily admit a representation in terms of convergent Fourier series), the polylinearization is constructed by numerically minimizing the L 2 -metric (area- or energy-based separation measure) for the same set of optimization variables—the locations and the number of polyline vertices.
- Subjects
INTERNET of things; INTELLIGENT sensors; FOURIER series; TRANSFER functions; SMART structures; NONLINEAR equations; PROBLEM solving
- Publication
Computation, 2024, Vol 12, Issue 4, p63
- ISSN
2079-3197
- Publication type
Article
- DOI
10.3390/computation12040063