Quadratic programming model for calibration of mine ventilation network under limited measured air quantities

A calibration model for mine ventilation network based on optimization theory was established to address the issue of manual repeated adjustment of air resistance and low consistency between simulated and measured results when using ventilation network calculation method to calibrate mine ventilation network. This model studied is a quadratic programming that takes the corrected value of the initial airway resistance as the decision variable, minimizes the correction of the initial airway resistance as the objective function, takes the air pressure balance equations of the basic meshes as the equality constraint condition, and takes the lower limit value of the airway resistance as the inequality constraint condition. The existence of the model solution was analyzed based on the KKT (Karush-Kuhn-Tucker) conditions in optimization theory, and a computer program has been developed and applied in a calculation example containing 35 branches. The results show that the “adding-edge method” could dynamically find the basic meshes, ensuring that the constraint equation system is linearly independent when solving this model using the active set method. The developed software can be used for the calibration of a mine ventilation network with only a limited measured air quantities. The optimal solution of the ventilation network in the example was obtained after 49 iterations, a significant improvement over the times of trial and error, which could reach 3.4×1010 for the worst-case scenario. The model that only considers equality constraints may obtain minimal or even negative unintentional air resistance values and the model considering the lower limit value of resistance can confine the resistance within a reasonable range, avoiding the correction of negative air resistance values for seven branches in the example. Using the corrected air resistance for mine ventilation network calculation, the calculated air quantities and fan pressures are exactly the same as the measured values, eliminating the tedious manual adjustment of air resistance in network calculation method.