A modified grid search-based optimization for possibly repetitive global extremum with an application to edge intelligence in IIoT towards time-domain signals

Nowadays, fast, reliable and accurate optimization methods are extensively used to realize edge intelligence in industrial applications of internet of things in order to better processing of big data collected by different environmental sensors on the ground and under the sea. Sometimes, the collected data is a one-dimensional signal with periodic/semi-periodic pattern (in terms of time, distance, etc.) which shows important features of the sensed data. However, finding the general extremum (global maximum or minimum) may not be easy in some measurements of such observed signals. The global points are critical to be found very accurately because of their importance to find optimal velocity, effective distance (or optimum range), the moment of optimality, and so on (related to physical measurements that need to be optimized). In this study, an analysis to find global optimal points of generic trigonometric functions with relatively complicated periodic patterns is carried out based on a modified form of grid search (GS) technique while there is a possibility of repetitive global points. As it is shown, some marine signals behave in such a way that can make the optimization process more complicated with losing optimal points while using the basic GS method. The basic method cannot find all repetitive maximum/minimum points in some signals. There is therefore a challenge in the use of the basic method in practice, because some global optimum points may be classified as local optimum points. We used some trigonometric functions to model the signals, and apply the modified GS method to them to find all repetitive points. Our results confirm that the modified solution can find all the repetitive points of the functions under a normally determined accuracy (not very high). Thus, we have proposed this new version of grid search to safely find all global points without a high accuracy parameter setting for sensitive data. This is indeed toward less complexity of the optimization algorithm.