The frictional resistance coefficient of ventilation of a roadway in a coal mine is a very important technical parameter in the design and renovation of mine ventilation. Calculations based on empirical formulae and field tests to calculate the resistance coefficient have limitations. An inversion method to calculate the mine ventilation resistance coefficient by using a few representative data of air flows and node pressures is proposed in this study. The mathematical model of the inversion method is developed based on the principle of least squares. The measured pressure and the calculated pressure deviation along with the measured flow and the calculated flow deviation are considered while defining the objective function, which also includes the node pressure, the air flow, and the ventilation resistance coefficient range constraints. The ventilation resistance coefficient inversion problem was converted to a nonlinear optimisation problem through the development of the model. A genetic algorithm (GA) was adopted to solve the ventilation resistance coefficient inversion problem. The GA was improved to enhance the global and the local search abilities of the algorithm for the ventilation resistance coefficient inversion problem.

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A two-year-long data set of air temperature from four different altitudes above Petuniabukta, central Spitsbergen, was analysed in order to assess the near-surface temperature lapse rates and the relative frequency of air temperature inversion occurrence. From August 2013 to July 2015, air temperatures at adjacent altitudes in Petuniabukta were strongly correlated. The near-surface lapse rates in all three layers differed significantly both from the average lapse rate in the international standard atmosphere (0.65°C 100 m-1) and the lapse rate calculated by linear regression. A pronounced annual cycle was detected in the lowermost air layer (from 23 to 136 m a.s.l.) with a variable near-surface lapse rate in the winter months, while an annual cycle was not apparent in the air layers above 136 m a.s.l. The lowermost layer was also characterized by a notable daily cycle in near-surface lapse rate in spring and autumn. Air temperature inversions occurred in up to 80% of the study period in the air layer below 136 m a.s.l., with the relative frequency being much lower in the other two air layers. The air temperature inversions lasted as long as 139 hours. A case study revealed that one of the strongest air temperature inversions was connected to an area of lower pressure gradients at the 850-hPa pressure level.

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Słowa kluczowe
numerical inversion of the Laplace transform
mathematical modelling
axial gas dispersion coefficient
Maple®

In this paper, a new simple method for determination of flow parameters, axial dispersion coefficients DL and Péclet numbers Pe was presented. This method is based on an accurate measurement model considering pulse tracer response. Our method makes it possible to test the character of gas flow motion and precisely measure flow parameters for different pressures and temperatures. The idea of combining the transfer function, numerical inversion of the Laplace transform and optimisation method gives many benefits like a simple and effective way of finding solution of inverse problem and model coefficients. The calculated values of flow parameters (DL and/or Pe) suggest that in the considered case the gas flow is neither plug flow nor perfect mixing under operation condition. The obtained outcomes agree with the gas flow theory. Calculations were performed using the CAS program type, Maple®.

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