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Top1. Introduction
A nonlinear problem in any area is generally difficult to address than a linear problem, and the complication increases with an increase in system nonlinearity. Although it is usually not difficult to ascertain if a system is linear or nonlinear, simply knowing that the system is nonlinear is not enough. It is prudent to know how much nonlinear the system is, i.e., to measure the nonlinearity of a problem. Such quantitative information about the problem reveals the root of the difficulty inherent in dealing with the problem, especially when comparing different processes.
The calculation of the nonlinearity of the system is as follows. For simplicity, a nonlinear function is approximated based on an equivalent linear function, as shown in Figure 1. Let 
be a nonlinear function bounded in a domain with limits 
and 
, and a linear function 
. The nonlinearity in the function corresponding to the straight line is calculated as the difference of 
from 
and is g
. Simply calculating the difference may make a zero-average of the difference between them (Emancipator & Kroll, 1993). So, the difference is squared, averaged, square rooted (Root Mean Squared), and then minimal values of the difference are calculated. But this technique fails if the nonlinearity in the system is high enough. Hence an appropriate measure is needed to define nonlinearity levels in a system.
Figure 1.
Sample of quantitative measure of nonlinearity
Considering the above-said method as a basis, for an overall system, the researchers developed various methods to measure nonlinearity. Nonlinear functions are generally linearised using Taylor series expansion. Beale's pioneering work (Beale, 1960) was the measurement of nonlinearity in terms of the deviation of nonlinear function from the linear function developed using Taylor series expansion. D. M. Bates et al. introduced a method to measure nonlinearity using relative curvatures (Bates & Watts, 1980), and J. Dunik et al. (2016) carried out a detailed survey on nonlinearity using D. M. Bates method. Li et al. (2019) constructed a combined nonlinear function using the time evolution and measurement functions in a filtering problem. M. Mallick et al., (2019) and X. R. Li et al., (2011) further continued the research on MoN. Their work represents a measure of the mean square distance between the given nonlinear system and a subset of all linear systems in a functional space.
Similar methods for measurement of nonlinearity are proposed in (Bucci et al., 2001; Li, 2012) for different applications. Usual methods for measuring nonlinearity can be broadly classified as follows. 1. A general measurement of nonlinearity function by its divergence from the linear function. 2. A specific measure of nonlinearity by using the bend in the nonlinear function at some reference point (Liu & Li, 2015).