The problem of mathematical simulation of motion of dynamic systems characteristics and their coincidence with real experimental data which correspond to these characteristics is investigated in this paper. Mathematic...The problem of mathematical simulation of motion of dynamic systems characteristics and their coincidence with real experimental data which correspond to these characteristics is investigated in this paper. Mathematical description of process will be named as adequate mathematical description if the results of mathematical simulation by the help of this description coincide with experiment with inaccuracy of initial data. The synthesis of such description is very important at mathematical modeling and forecast of motion of real physical phenomena. The specified problem is still poorly investigated and hardly adapted to formalization. The requirements to the adequate mathematical description of dynamic system are considered for the case when mathematical description of dynamic systems is represented by linear system of the ordinary differential equations. In this paper the mathematical model of process is given a priori with inexact parameters and then the models of external loads are being determined for which the results of simulation coincide with experiment. The methods of obtaining of the steady models of external loads are suggested. The example of the adequate description construction of the main mechanical line dynamics of rolling mill is given.展开更多
Solubility of quinine in supercritical carbon dioxide(SCCO_2) was experimentally measured in the pressure range of 8 to 24 MPa, at three constant temperatures: 308.15 K, 318.15 K and 328.15 K. Measurement was carried ...Solubility of quinine in supercritical carbon dioxide(SCCO_2) was experimentally measured in the pressure range of 8 to 24 MPa, at three constant temperatures: 308.15 K, 318.15 K and 328.15 K. Measurement was carried out in a semi-dynamic system. Experimental data were correlated by iso-fugacity model(based on cubic equations of state, CEOS), Modified Mendez–Santiago–Teja(MST) and Modified Bartle semi-empirical models. Two cubic equations of state: Peng–Robinson(PR) and Dashtizadeh–Pazuki–Ghotbi–Taghikhani(DPTG) were adopted for calculation of equilibrium parameters in CEOS modeling. Interaction coefficients(k_(ij)& l_(ij)) of van der Waals(vdW) mixing rules were considered as the correlation parameters in CEOS-based modeling and their contribution to the accuracy of model was investigated. Average Absolute Relative Deviation(AARD) between correlated and experimental data was calculated and compared as the index of validity and accuracy for different modeling systems. In this basis it was realized that the semi-empirical equations especially Modified MST can accurately support the theoretical studies on phase equilibrium behavior of quinine–SCCO_2 media. Among the cubic equations of state DPGT within two-parametric vd W mixing rules provided the best data fitting and PR within one-parametric vd W mixing rules demonstrated the highest deviation respecting to the experimental data. Overall, in each individual modeling system the best fitting was observed on the data points attained at 318 K, which could be perhaps due to the moderate thermodynamic state of supercritical phase.展开更多
文摘The problem of mathematical simulation of motion of dynamic systems characteristics and their coincidence with real experimental data which correspond to these characteristics is investigated in this paper. Mathematical description of process will be named as adequate mathematical description if the results of mathematical simulation by the help of this description coincide with experiment with inaccuracy of initial data. The synthesis of such description is very important at mathematical modeling and forecast of motion of real physical phenomena. The specified problem is still poorly investigated and hardly adapted to formalization. The requirements to the adequate mathematical description of dynamic system are considered for the case when mathematical description of dynamic systems is represented by linear system of the ordinary differential equations. In this paper the mathematical model of process is given a priori with inexact parameters and then the models of external loads are being determined for which the results of simulation coincide with experiment. The methods of obtaining of the steady models of external loads are suggested. The example of the adequate description construction of the main mechanical line dynamics of rolling mill is given.
基金Supported by the National Natural Science Foundation of China(20976103)
文摘Solubility of quinine in supercritical carbon dioxide(SCCO_2) was experimentally measured in the pressure range of 8 to 24 MPa, at three constant temperatures: 308.15 K, 318.15 K and 328.15 K. Measurement was carried out in a semi-dynamic system. Experimental data were correlated by iso-fugacity model(based on cubic equations of state, CEOS), Modified Mendez–Santiago–Teja(MST) and Modified Bartle semi-empirical models. Two cubic equations of state: Peng–Robinson(PR) and Dashtizadeh–Pazuki–Ghotbi–Taghikhani(DPTG) were adopted for calculation of equilibrium parameters in CEOS modeling. Interaction coefficients(k_(ij)& l_(ij)) of van der Waals(vdW) mixing rules were considered as the correlation parameters in CEOS-based modeling and their contribution to the accuracy of model was investigated. Average Absolute Relative Deviation(AARD) between correlated and experimental data was calculated and compared as the index of validity and accuracy for different modeling systems. In this basis it was realized that the semi-empirical equations especially Modified MST can accurately support the theoretical studies on phase equilibrium behavior of quinine–SCCO_2 media. Among the cubic equations of state DPGT within two-parametric vd W mixing rules provided the best data fitting and PR within one-parametric vd W mixing rules demonstrated the highest deviation respecting to the experimental data. Overall, in each individual modeling system the best fitting was observed on the data points attained at 318 K, which could be perhaps due to the moderate thermodynamic state of supercritical phase.
