An introduction to complexity measure: Non-linear statistical parameters in measurements: Part 35 in a series of tutorials on instrumentation and measurement

In previous parts of this tutorial series, several data processing techniques have been introduced to benefit members of the Instrumentation and Measurement Society (IMS). These include the Fourier transform [1], the wavelet transform [2], and correlation dimension analysis [3]. The first two techniques have been widely used in various engineering domains, and the underlying principle of those techniques comes from linear system theory. On the other hand, correlation dimension analysis is rooted in non-linear dynamics, and it has been used to interpret signals measured from physical systems where non-linear behaviors exist. With the advance of non-linear dynamics, more and more non-linear statistical parameters have been introduced to characterize physical systems from measured data [4]-[6]. Among these, the complexity measure has been applied to measuring depth of anesthesia for patients [7], detecting human motions [8], identifying image features for compression [9], and assessing machine failures [10]. In this article, we provide an introduction to how the complexity measure is calculated as an indicator for characterizing many of the signals measured during experiments in engineering practice and show its application in the field of bearing degradation measurement.