Interval-based non-dimensionalization method (IBNM) and its application

In the face of interval sensitive data, aiming at the disadvantages of rationality and adaptability of linear dimensionless method, as well as the complexity of constructing polyline and curve dimensionless method, this paper proposes an Interval-based Non-dimensionalization Method (IBNM). Assuming that the data can be divided into n levels within its domain, IBNM divides n intervals based on these n grades. N + 1 connection points were set by taking the critical points between the intervals as abscissa and the sequence values corresponding to the n grades of the critical points as ordinate. Then, the dimensionless transformation function IBNM is constructed by connecting adjacent connection points according to fuzzy mathematics theory. If the connection mode of IBNM is simple piecewise linear function, then called it polyline IBNM. Accordingly, if the connection mode adopts exponential function, logarithmic function and other curve functions, it is called curve IBNM. IBNM is scientific, reasonable, simple and practical. This paper takes PM2.5 air quality grade prediction as an example and constructs four kinds of air quality grade prediction models. A variety of traditional dimensionless methods, polyline IBNM and curve IBNM were used to process the data, respectively, and were applied to these prediction models. The results show that the effect of polyline IBNM and curve IBNM is better than that of traditional non-dimensionalization methods.