The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving t...The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving the coupled conduction,convection,and radiation problem,leading to suboptimal efficiency that fails to meet real-time control demands.To overcome this difficulty,comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem.However,the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency.It is necessary to present an efficient method for the equivalence.The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer,and the gray-equivalent radiative characteristics are successfully recovered.It is our intention that the issue of low inverse efficiency,which has been observed when the least-squares method is employed,will be resolved.To enhance the performance of the Levenberg-Marquardt algorithm,a modification is implemented for determining the damping factor.Detailed investigations are also conducted to evaluate its accuracy,stability of convergence,efficiency,and robustness of the algorithm.Subsequently,a comparison is made between the results achieved using each method.展开更多
The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The ...The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The homotopy Levenberg-Marquardt algorithm was proposed to accurately solve nonlinear equations with singular Jacobian matrices,and is constructed by the Saha equation and Guldberg-Waage equation combined with mass conservation,the electric neutrality principle and Dalton’s partial pressure law,to solve the problem of dependence on the initial value in the process of iteration calculation.In this research,the equations at a higher temperature were solved and used as the auxiliary equations,and the homotopy control parameters’sequence of the homotopy equations was selected by equal ratios.For auxiliary equations,the iterative initial value was obtained by assuming that there were only the highestvalence atomic cations and electrons at this temperature,and the plasma equilibrium composition distribution with the required accuracy was ultimately solved under the current conditions employing the Levenberg-Marquardt algorithm.The control parameter sequence was arranged according to the geometric sequence and the homotopy step was gradually shortened to ensure continuity of the homotopy process.Finally,the equilibrium composition and thermodynamic properties of pure N_(2),Mg(30%)-CO_(2)(70%)and Mg(40%)-CO(50%)-N_(2)(10%)mixture plasma at atmospheric pressure were calculated and the calculation process of some specified temperatures was shown and analyzed.The calculation accuracy of equilibrium composition is higher than other findings in the literature.The results for the thermodynamic properties are in good agreement with data reported by the literature.展开更多
A flexible calibration method based on a front-coated flat mirror is proposed for a laser light-sectioning three-dimensional(3D)measurement system. Since the calibration target and its mirror image are spatially separ...A flexible calibration method based on a front-coated flat mirror is proposed for a laser light-sectioning three-dimensional(3D)measurement system. Since the calibration target and its mirror image are spatially separated and can be recorded in an image by a camera,the proposed method requires only a single composite image that contains a non-planar checkerboard pattern,a laser strip projected on the target and their mirror images to complete the calibration of the camera and the laser plane in one step. Levenberg-Marquardt(LM)algorithm is used to optimize the system parameters,and the measurement accuracy and speed are improved to enable online 3D inspection. Static and dynamic online 3D measurements are carried out on a cup and a triple stepped shaft,respectively,to validate the proposed method. The shaft has two steps with the depth of(0.5±0.01)mm and(2±0.01)mm to be measured online when the shaft is rotated and translated at the same time. The measurement results can be output at a frequency of 7 to 11 readings per second with standard deviations of 0.040 mm and 0.051 mm. The experimental results verify the effectiveness and flexibility of the proposed method.展开更多
基金supported by the Na⁃tional Natural Science Foundation of China(No.12172078)the Fundamental Research Funds for the Central Univer⁃sities(No.DUT24MS007).
文摘The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving the coupled conduction,convection,and radiation problem,leading to suboptimal efficiency that fails to meet real-time control demands.To overcome this difficulty,comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem.However,the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency.It is necessary to present an efficient method for the equivalence.The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer,and the gray-equivalent radiative characteristics are successfully recovered.It is our intention that the issue of low inverse efficiency,which has been observed when the least-squares method is employed,will be resolved.To enhance the performance of the Levenberg-Marquardt algorithm,a modification is implemented for determining the damping factor.Detailed investigations are also conducted to evaluate its accuracy,stability of convergence,efficiency,and robustness of the algorithm.Subsequently,a comparison is made between the results achieved using each method.
基金supported by the National Key Research and Development Program of China(No.2017YFA0700300)the Fundamental Research Funds for the Central Universities(No.N2025032)the Liaoning Provincial Natural Science Foundation(No.2020-MS-362)。
文摘The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The homotopy Levenberg-Marquardt algorithm was proposed to accurately solve nonlinear equations with singular Jacobian matrices,and is constructed by the Saha equation and Guldberg-Waage equation combined with mass conservation,the electric neutrality principle and Dalton’s partial pressure law,to solve the problem of dependence on the initial value in the process of iteration calculation.In this research,the equations at a higher temperature were solved and used as the auxiliary equations,and the homotopy control parameters’sequence of the homotopy equations was selected by equal ratios.For auxiliary equations,the iterative initial value was obtained by assuming that there were only the highestvalence atomic cations and electrons at this temperature,and the plasma equilibrium composition distribution with the required accuracy was ultimately solved under the current conditions employing the Levenberg-Marquardt algorithm.The control parameter sequence was arranged according to the geometric sequence and the homotopy step was gradually shortened to ensure continuity of the homotopy process.Finally,the equilibrium composition and thermodynamic properties of pure N_(2),Mg(30%)-CO_(2)(70%)and Mg(40%)-CO(50%)-N_(2)(10%)mixture plasma at atmospheric pressure were calculated and the calculation process of some specified temperatures was shown and analyzed.The calculation accuracy of equilibrium composition is higher than other findings in the literature.The results for the thermodynamic properties are in good agreement with data reported by the literature.
基金supported in part by the National Natural Science Foundation of China (No. 11802132)the Natural Science Foundation of Jiangsu Province(No.BK20180446)。
文摘A flexible calibration method based on a front-coated flat mirror is proposed for a laser light-sectioning three-dimensional(3D)measurement system. Since the calibration target and its mirror image are spatially separated and can be recorded in an image by a camera,the proposed method requires only a single composite image that contains a non-planar checkerboard pattern,a laser strip projected on the target and their mirror images to complete the calibration of the camera and the laser plane in one step. Levenberg-Marquardt(LM)algorithm is used to optimize the system parameters,and the measurement accuracy and speed are improved to enable online 3D inspection. Static and dynamic online 3D measurements are carried out on a cup and a triple stepped shaft,respectively,to validate the proposed method. The shaft has two steps with the depth of(0.5±0.01)mm and(2±0.01)mm to be measured online when the shaft is rotated and translated at the same time. The measurement results can be output at a frequency of 7 to 11 readings per second with standard deviations of 0.040 mm and 0.051 mm. The experimental results verify the effectiveness and flexibility of the proposed method.
