Inferring operating rules for reservoir operations using fuzzy regression and ANFIS

The methods of ordinary least-squares regression (OLSR), fuzzy regression (FR), and adaptive network-based fuzzy inference system (ANFIS) are compared in inferring operating rules for a reservoir operations optimization problem. Dynamic programming (DP) is used as an example optimization tool to provide the input-output data set to be used by OLSR, FR, and ANFIS models. The coefficients of an FR model are found by solving a linear programming (LP) problem. The objective function of the LP is to minimize the total fuzziness of the FR model, which is related to the width of fuzzy coefficients in the regression model. Before applying FR to the reservoir operations problem, two FR formulations and interval regression (IR) are first examined in a simple tutorial example. ANFIS is also used to derive the reservoir operating rules as fuzzy IF-THEN rules. The OLSR, FR, and ANFIS based rules are then simulated and compared based on their performance in simulation. The methods are applied to a long-term planning problem as well as to a medium-term implicit stochastic optimization model. The results indicate that FR is useful to derive operating rules for a long-term planning model, where imperfect and partial information is available. ANFIS is beneficial in medium-term implicit stochastic optimization as it is able to extract important features of the system from the generated input-output set and represent those features as general operating rules.