Fractional order interval optimization method based on perturbation bound and gamma function of a non-equidistant ROGM

Abstract

Purpose

The purpose of this paper is to propose a fractional order optimization method based on perturbation bound and gamma function of a DGM(r,1).

Design/methodology/approach

By analyzing and minimizing perturbation bound, the sub-optimal solution on fractional order interval is obtained through offline solving without iterative calculation. By this method, an optimized fractional order non-equidistant ROGM (OFONEROGM) is applied in fitting and prediction water quality parameters for a surface water pollution monitoring system.

Findings

This method can narrow fractional order interval in this work. In a surface water pollution monitoring system, the fitting and prediction performances of OFONEROGM are demonstrated comparing with integer order non-equidistant ROGM (IONEROGM).

Originality/value

A method of offline solving the sub-optimal solution on fractional order interval is proposed. It can narrow the optimized fractional order range of NEROGM without iterative calculation. A large number of calculations are eliminated. Besides that, optimized fractional order interval is only related to the number of original data, and convenient for practical application. In this work, an OFONEROGM is modeled for predicting water quality trend for preventing water pollution or stealing sewage discharge. It will provide guiding significance in water quality parameter fitting and predicting for water environment management.

Citation

Lian, Y., Feng, W., Li, P., Lei, Q., Ma, H., Sun, H. and Li, B. (2023), "Fractional order interval optimization method based on perturbation bound and gamma function of a non-equidistant ROGM", Grey Systems: Theory and Application, Vol. 13 No. 1, pp. 101-124. https://doi.org/10.1108/GS-02-2022-0019