Mine Ventilation Network Calibration Based on Slack Variables and Sequential Quadratic Programming

In mine ventilation network calibration, sparse and inconsistent airflow measurements often lead to infeasibility in traditional optimization models. To overcome this challenge, this paper proposes a nonlinear programming calibration model incorporating slack variables. The model treats aerodynamic resistance corrections, airflow adjustments, unknown airflows, and resistance lower-bound slack variables as decision variables. The objective function is formulated to minimize the weighted sum of squares of resistance corrections, while penalty terms account for airflow adjustments and slack variables. Constraints integrate Kirchhoff’s laws with relaxed inequality constraints for resistance lower bounds. A calibration tool integrated via the ObjectARX interface was developed using C++, utilizing the Sequential Quadratic Programming (SQP) algorithm for the solution. The method was validated via a case study of a network comprising 39 branches and 16 measured airflows, optimized under five distinct initial conditions. Results demonstrate that the inclusion of slack variables mathematically guarantees the existence of feasible solutions. With a resistance correction weight of 10−2 and a penalty coefficient of 105, the model applies only minimal necessary corrections to handle overly tight constraints or data conflicts. The SQP algorithm exhibits superior global convergence, consistently iterating to optimal solutions that satisfy network balance laws regardless of initial values. This approach effectively resolves the infeasibility and data conflict issues inherent in traditional methods, demonstrating significant robustness and practical engineering utility.