Electric-Parameter-Based Inversion of Dynamometer Card Using Hybrid Modeling for Beam Pumping System

Algorithm 1

Improved free search algorithm.

Input: The initial population size , max algebra , search step length , the parameters and ;

Output: The optimal parameter and ;

Step 1: Initialization

1.1 Normalize the input parameters and with the range of ;

1.2 The initial pheromone is obtained with the initial value, which is released at the same time;

1.3 The initial search results are obtained.

Step 2: Searching process

2.1 Calculate the sensitivity parameter with (36) and (37);

2.2 Confirm the new search point of the next search round using the sensitivity parameter;

2.3 Record the RMSE value of the error between the predicted value and the actual value as the fitness

function. Fitness function is defined as follows;

2.4 The new search results can be obtained by (33) and (34);

2.5 Preserve the best individuals;

2.6 Adjust the search radius according to (35).

Step 3: Termination condition judgement

When the termination condition is satisfied, output the optimal parameter and .