基于控制理论的热轧工艺优化设计
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摘要
热轧板带TMCP工艺的制定是一项耗时耗力的研究工作。与此同时,由于热轧过程组织演变的复杂性和实际轧制生产中的各种约束条件,传统的TMCP工艺开发方法只能给出较好而并非最优的工艺制度。因此,开发出以产品力学性能为目标优化热轧工艺的新方法是非常有必要的。它的基本概念为建立钢材热轧过程组织演变与性能预测模型,以热轧生产线的设备能力为约束条件,优化计算工艺参数从而达到预设的力学性能目标。在课题的研究中,作者分别采用物理冶金学理论和人工智能技术对热轧过程的组织演变和化学成份-工艺-力学性能关系进行描述,从规律性和预测精度两方面完成建模工作；并结合单目标和多目标粒子群算法,实现了热轧工艺的优化设计。本论文的主要创新性工作如下：
(1)连续冷却过程中可加性法则有效性的研究
针对四种不同成份的Nb微合金钢,采用热膨胀实验测定了不同冷却速度条件下奥氏体向铁素体的相变动力学。首次将Rios推导的理论方法应用于连’续冷却过程相变建模,利用相变初期数据拟合lnln[1／(1-X)]和1n(|CR|)(CR-冷却速率)获得了很好的线性关系,计算得出了Johnxon-Mehl-Avrami-Kolmogorov (JMAK)方程中的指数n。当结合RIOS方法计算的动力学参数k用于连续冷却相变预测时产生了较大的偏差。而通过假设参数k与温度呈高斯函数关系,采用优化方法计算出的参数k表明了与冷却速率的相关性,用于预测连续冷却相变动力学时也获得了较高的精度。研究表明如果将冷却速率的因素考虑在内,可加性法则基本成立。
(2)基于数值分析的连续冷却过程相变建模
在RIOS方法的基础之上,开发了用于分析连续冷却热膨胀数据的数值方法,从数学的角度解决了连续冷却相变动力学的建模问题。通过预设JMAK方程中的指数n和温度梯度ΔT,利用可加性法则可以计算出相变任意时刻的参数k。通过不同冷速条件下参数k的对比分析,可得参数k与温度的关系及与已相变份数X的相关性；综合应用RIOS方法和基于JMAK方程与可加性法则的建模新方法,建立了TRIP钢和CP钢相变动力学模型,模型预测值与实测值吻合良好,充分验证了建模方法的有效性。
(3)贝叶斯神经网络在热轧组织-性能预测中的应用
基于贝叶斯方法的神经网络在网络训练目标函数中引入代表网络复杂程度的惩罚项,融入“奥克姆剪刀”理论防止网络“过训练”的发生,使网络具有较好的泛化性能。Bhadeshia和Mackey等将贝叶斯神经网络广泛的应用于钢材扭转、焊接、裂纹扩展等领域的建模,均获得了突出的效果。本论文将基于贝叶斯理论框架的神经网络程序化,首次将其应用于热轧生产现场化学成份-工艺-力学性能的关系建模,在网络的稳定性、收敛速度和泛化能力上均优于传统的BP神经网络,为热轧工艺优化设计提供了高精度的模型基础。
(4)热轧工艺优化设计的实现
以连续冷却相变模型为基础,结合单目标粒子群优化方法,实现了针对连续冷却过程的工艺优化设计。通过冷却速度的控制实现钢材内部铁素体、贝氏体、马氏体不同的相组成和铁素体晶粒尺寸。以贝叶斯神经网络模型为基础,结合多目标粒子群算法,实现了针对整个热轧过程的工艺优化设计。该方法能在较短的时间内搜索得到帕累托前沿,解决了在单目标优化中工艺窗口计算困难的问题,且计算精度较高。工业生产数据的验证表明,根据坯料的化学成份和现场的设备约束条件,可以通过工艺参数的优化达到客户提出的力学性能需求,这为柔性生产方式的实现提供了理论指导和技术支持。
The design of TMCP (Thermal Mechanical Controlled Processing) parameters for hot rolled plate/strip is a time-consuming and exhausting research work. At the same time, because of the complexity of microstrual evolution and constraints of equipments in hot rolling process, it is difficult to determine the optimal TMCP parameters in traditional way. Therefore, development of new ways, which is to optimize the hot rolling process with the mechanical properties set up as the target, is of great necessity. The mathematical model for description of microstructure evolution and mechanical properties prediction, and the optimization of hot rolling process under the constraints of equipments to achieve the required mechanical properties constitute the basic concept of optimal design of hot rolling process. In the present paper, the physical-metallurgical theory and the artificial intelligence were applied in the modeling work for the microstructural evolution and the relationship between chemical compositions, process parameters and mechanical properties, accounting for the regularity and prediction precision. The optimal design of hot rolling process was finally realized by the employment of single-and multi-objective particle swarm optimization method. The chief original work of this paper is as follows.
(1) Research work concerning the effectiveness of additivity rule applied to the modeling of phase transformation in the continuous cooling process
The dilatometric test was employed to measure the transformation kinetics of austenite to ferrite in four kinds of Nb bearing steels with different niobium contents. The theoretical method developed by Rios was for the first time applied to the modeling of phase transformation in the continuous cooling process. The relationship between lnln[1/(1-X)] and ln(|CR|) (CR-cooling rate) was plotted using the data at early stage of transformation, which successfully fitted a linear relationship to calculate the exponential values of n in the JMAK equation. The values of k in the JMAK equation obtained with the Rios method, however, have led to big discrepancies when the isothermal equations were used to predict the transformation kinetics during cooling. By assuming a Gaussian dependence of temperature, k was calculated by using an optimization method based on the rule of additivity and exhibited cooling rate correlation. The isothermal transformation model was used to predict the transformation kinetics during cooling, showing good agreements with the measured data. It has been proved that even though the rule of additivity has to be relaxed to take into account the effects of cooling rates, precise conversion between non-isothermal and isothermal kinetics can still be realized.
(2) Modeling of phase transformation during continuous cooling process based on mathematical anlysis
Based on the Rios'method, a new mathematical method designed to analyze the dilation data of phase transformation in the continuous cooling process was developed. The modeling work of phase transformation kinetics was solved mathematically. According to the preset of exponential n and temperature step, the parameter k at any moment during the transformation was calculated based on the inverse application of additivity rule. Relationship between k and temperature and transformed fraction dependence of k could be revealed by the comparison of k under different cooling rate. Combined with the Rios'method, the transformation model for TRIP and CP steels were developed. Good agreements between measured and predicted value of transformation kinetics have validated the effectiveness of the new method.
(3) Application of Bayesian neural network in the microstructure and mechanical properties prediction for the hot rolling process
The punishment item, based on the "Occam's razor" theory, was introduced into the objective function for the training of neural network in order to prevent the occurrence of "over-fitting" and improve the generalization ability. Extraodinary results have been obtained when the Bayesian neural network was applied to the modeling work in the field of hot torsion, welding and fatigue crack growth rate by Bhadeshia and Mackey. In the present work, the Bayesian neural network was programmed and used to model the relationship between chemical composition, process parameters and mechanical properties, wich has exhibited better stability, fast convergence rate and generalization ability when compared with the traditional BP neural network. It could provide model basis with high precision for the optimal design of hot rolling process.
(4) The realization of optimal design of hot rolling process
Combined with the single-objective particle swarm optimization method, the phase transformation model was used to realize the optimal design of continuous cooling process. Different ferrite grain size and combination of ferrite, bainite and martensite phases were obtained according to the control of cooling rate. And based on the Bayesian neural network, the multi-objective particle swarm optimization method was emplyed to build up the optimal design system for the whole hot rolling process. The process window was determined through the calculation of Pareto front with a high precision, which could be difficult for single-objective optimization. The production data has suggested that, the required mechanical properties can be achieved through the optimization of process parameters based on the chemical composition and constraints of equipment. It could provid theoretical guidance and technical support for flexible production mode.
(1)连续冷却过程中可加性法则有效性的研究
针对四种不同成份的Nb微合金钢,采用热膨胀实验测定了不同冷却速度条件下奥氏体向铁素体的相变动力学。首次将Rios推导的理论方法应用于连’续冷却过程相变建模,利用相变初期数据拟合lnln[1／(1-X)]和1n(|CR|)(CR-冷却速率)获得了很好的线性关系,计算得出了Johnxon-Mehl-Avrami-Kolmogorov (JMAK)方程中的指数n。当结合RIOS方法计算的动力学参数k用于连续冷却相变预测时产生了较大的偏差。而通过假设参数k与温度呈高斯函数关系,采用优化方法计算出的参数k表明了与冷却速率的相关性,用于预测连续冷却相变动力学时也获得了较高的精度。研究表明如果将冷却速率的因素考虑在内,可加性法则基本成立。
(2)基于数值分析的连续冷却过程相变建模
在RIOS方法的基础之上,开发了用于分析连续冷却热膨胀数据的数值方法,从数学的角度解决了连续冷却相变动力学的建模问题。通过预设JMAK方程中的指数n和温度梯度ΔT,利用可加性法则可以计算出相变任意时刻的参数k。通过不同冷速条件下参数k的对比分析,可得参数k与温度的关系及与已相变份数X的相关性；综合应用RIOS方法和基于JMAK方程与可加性法则的建模新方法,建立了TRIP钢和CP钢相变动力学模型,模型预测值与实测值吻合良好,充分验证了建模方法的有效性。
(3)贝叶斯神经网络在热轧组织-性能预测中的应用
基于贝叶斯方法的神经网络在网络训练目标函数中引入代表网络复杂程度的惩罚项,融入“奥克姆剪刀”理论防止网络“过训练”的发生,使网络具有较好的泛化性能。Bhadeshia和Mackey等将贝叶斯神经网络广泛的应用于钢材扭转、焊接、裂纹扩展等领域的建模,均获得了突出的效果。本论文将基于贝叶斯理论框架的神经网络程序化,首次将其应用于热轧生产现场化学成份-工艺-力学性能的关系建模,在网络的稳定性、收敛速度和泛化能力上均优于传统的BP神经网络,为热轧工艺优化设计提供了高精度的模型基础。
(4)热轧工艺优化设计的实现
以连续冷却相变模型为基础,结合单目标粒子群优化方法,实现了针对连续冷却过程的工艺优化设计。通过冷却速度的控制实现钢材内部铁素体、贝氏体、马氏体不同的相组成和铁素体晶粒尺寸。以贝叶斯神经网络模型为基础,结合多目标粒子群算法,实现了针对整个热轧过程的工艺优化设计。该方法能在较短的时间内搜索得到帕累托前沿,解决了在单目标优化中工艺窗口计算困难的问题,且计算精度较高。工业生产数据的验证表明,根据坯料的化学成份和现场的设备约束条件,可以通过工艺参数的优化达到客户提出的力学性能需求,这为柔性生产方式的实现提供了理论指导和技术支持。
The design of TMCP (Thermal Mechanical Controlled Processing) parameters for hot rolled plate/strip is a time-consuming and exhausting research work. At the same time, because of the complexity of microstrual evolution and constraints of equipments in hot rolling process, it is difficult to determine the optimal TMCP parameters in traditional way. Therefore, development of new ways, which is to optimize the hot rolling process with the mechanical properties set up as the target, is of great necessity. The mathematical model for description of microstructure evolution and mechanical properties prediction, and the optimization of hot rolling process under the constraints of equipments to achieve the required mechanical properties constitute the basic concept of optimal design of hot rolling process. In the present paper, the physical-metallurgical theory and the artificial intelligence were applied in the modeling work for the microstructural evolution and the relationship between chemical compositions, process parameters and mechanical properties, accounting for the regularity and prediction precision. The optimal design of hot rolling process was finally realized by the employment of single-and multi-objective particle swarm optimization method. The chief original work of this paper is as follows.
(1) Research work concerning the effectiveness of additivity rule applied to the modeling of phase transformation in the continuous cooling process
The dilatometric test was employed to measure the transformation kinetics of austenite to ferrite in four kinds of Nb bearing steels with different niobium contents. The theoretical method developed by Rios was for the first time applied to the modeling of phase transformation in the continuous cooling process. The relationship between lnln[1/(1-X)] and ln(|CR|) (CR-cooling rate) was plotted using the data at early stage of transformation, which successfully fitted a linear relationship to calculate the exponential values of n in the JMAK equation. The values of k in the JMAK equation obtained with the Rios method, however, have led to big discrepancies when the isothermal equations were used to predict the transformation kinetics during cooling. By assuming a Gaussian dependence of temperature, k was calculated by using an optimization method based on the rule of additivity and exhibited cooling rate correlation. The isothermal transformation model was used to predict the transformation kinetics during cooling, showing good agreements with the measured data. It has been proved that even though the rule of additivity has to be relaxed to take into account the effects of cooling rates, precise conversion between non-isothermal and isothermal kinetics can still be realized.
(2) Modeling of phase transformation during continuous cooling process based on mathematical anlysis
Based on the Rios'method, a new mathematical method designed to analyze the dilation data of phase transformation in the continuous cooling process was developed. The modeling work of phase transformation kinetics was solved mathematically. According to the preset of exponential n and temperature step, the parameter k at any moment during the transformation was calculated based on the inverse application of additivity rule. Relationship between k and temperature and transformed fraction dependence of k could be revealed by the comparison of k under different cooling rate. Combined with the Rios'method, the transformation model for TRIP and CP steels were developed. Good agreements between measured and predicted value of transformation kinetics have validated the effectiveness of the new method.
(3) Application of Bayesian neural network in the microstructure and mechanical properties prediction for the hot rolling process
The punishment item, based on the "Occam's razor" theory, was introduced into the objective function for the training of neural network in order to prevent the occurrence of "over-fitting" and improve the generalization ability. Extraodinary results have been obtained when the Bayesian neural network was applied to the modeling work in the field of hot torsion, welding and fatigue crack growth rate by Bhadeshia and Mackey. In the present work, the Bayesian neural network was programmed and used to model the relationship between chemical composition, process parameters and mechanical properties, wich has exhibited better stability, fast convergence rate and generalization ability when compared with the traditional BP neural network. It could provide model basis with high precision for the optimal design of hot rolling process.
(4) The realization of optimal design of hot rolling process
Combined with the single-objective particle swarm optimization method, the phase transformation model was used to realize the optimal design of continuous cooling process. Different ferrite grain size and combination of ferrite, bainite and martensite phases were obtained according to the control of cooling rate. And based on the Bayesian neural network, the multi-objective particle swarm optimization method was emplyed to build up the optimal design system for the whole hot rolling process. The process window was determined through the calculation of Pareto front with a high precision, which could be difficult for single-objective optimization. The production data has suggested that, the required mechanical properties can be achieved through the optimization of process parameters based on the chemical composition and constraints of equipment. It could provid theoretical guidance and technical support for flexible production mode.
引文
[1]王国栋,刘相华,李维娟,等.超级Super-SS400钢的工业轧制实验[J].钢铁,2001,36(5)：39-43.
[2]王国栋,刘相华,朱伏先,等.新一代钢铁材料的研究开发现状和发展趋势[J].鞍钢技术,2005,4：1-8.
[3]胡燕慧,杜林秀,高彩茹,等.500MPa级超级钢工业实验[J].钢铁,2004,39(10)：54-58.
[4]刘相华,陆匠心,张丕君,等.400-500MPa级碳素钢先进工业化制造技术[J].中国有色金属学报,2004,14(1)：207-210.
[5]杜林秀,姚圣杰,熊明鲜,王国栋.低碳结钢钢的奥氏体晶粒超细化[J].东北大学学报(自然科学版),2007,28(11)：1575-1578.
[6]张红梅,杜林秀,李维娟,等.400MPa超级钢控轧控冷优化工艺及工业实验[J].钢铁研究,2001,3：27-31.
[7]Kwon O. A technology for the prediction and control of microstructure changes and mechanical properties in steel [J]. ISIJ International,1992,32(2):350-358.
[8]Yada H, Senuma T. Computer modeling fro predicting microstructure and mechanical properties of steels. Bulletin of Japan Institute of Metals,1990,29(6):430-439.
[9]Yoshie A, Fujioka M, et al. Modelling of microstructual evolution and mechanical properties of steel plates produced by Thermo-Mechanical Control Process [J]. ISIJ International,1992,32(3):395-404.
[10]刘振宇.加速冷却对C-Mn钢力学性能的影响[J].钢铁,1994,29(2)：31-34.
[11]刘振宇.C-Mn钢热轧板带组织-性能预测模型的开发及在生产中的应用[D].沈阳：东北大学,1995.
[12]曲锦波HSLA钢板热轧组织性能控制与预测模型[D].沈阳：东北大学,1998.
[13]许云波.基于物理冶金和人工智能的热轧钢材组织性能预测与控制[D].沈阳：东北大学,2003.
[14]朱丽娟.热轧TRIP钢的组织性能预测[D].沈阳：东北大学,2007.
[15]李殿中,张玉妥,刘实,等.材料制备工艺的计算机模拟[J].金属学报,2001,37(5)：449-452.
[16]郑坚,唐广波,程杰锋,等.珠钢CSP热轧组织性能预报软件设计[J].轧钢,2003,20(1)：15-17.
[17]Militzer M, Samarasekera I V, Jin D Q热连轧带钢组织性能预报模型的进展[J].钢铁,1999,34(增刊)：658-669.
[18]Andorfer J, Auzinger D等.使用VAI-Q Strip系统首次实现热轧带钢力学性能的全面控制[J].钢铁,2001,36(1)：42-46.
[19]Loffler H U, Doll R. Commercial application of microstructure modelling in hot strip mills[C]. Recrystallization and Grain Growth Proceedings of the First Joint International Conference.Springer-Verlag,2001. Trowsdale A J, Tunstall J P, Randerson K, et al. Modeling of metal rolling processes[C], British steel plc. London: Church House Conference Centre London, UK,1999:12-21.
[20]Watanabe Y Y, Shimomura S I, Funato K, et al. Integrated model for microstructural evolution and properties of steel plates manufactured in production line [J]. ISIJ International,1992,32(3):405-413.
[21]刘正东,董翰,干勇.热连轧过程中组织性能预报系统的应用[J].钢铁,2003,38(2)：68-71.
[22]王利明,沙孝春,李殿中,等Rollan带钢热轧过程组织演变与性能预测软件的开发[A].新一代钢铁材料国际会议[C].北京：2001.
[23]Saito Y. Modeling of microstructural evolution during thermomechnical processing of structural steels [J]. Materials Science and Engineering A,1997,223:134-145.
[24]Ray P K, Ganguly R I and Panda A K. Optimization of mechanical properties of an HSLA-100 steel through control of heat treatment variables [J]. Materials Science and Engineering A,2003,346:122-131.
[25]Loffler H U, Doll R, Dun W. Microstructure monitor controls product quality-successful implementation at the hot strip mill at Wuhan iron and steel group[C]. China International Steel Congresses,2004,7, shanghai china:6-10.
[26]Mahfouf M, Jamei M, Linkens D A. Optimal design of alloy steels using multiobjective genetic algorithms [J]. Materials and Manufacturing Processes,2005,20(3):553-567.
[27]Biswas S K, Chen S J and Satyanarayana A. Optimal temperature tracking for accelerated cooling processes in hot rolling of steel [J]. Dynamics and Control,1997, 7(4):327-340.
[28]Abdul Samad M, Rao Ravi S. Minimization of energy in the multipass rolling process [J]. Journal of Manufacturing Science and Engineering,2001,123:135-141
[29]Chakraborti N and Kumar A. The optimal schedualing of a reversing strip mill:studies using multipopulation genetic algorithms and differential evolution [J]. Materials and manufacturing processes,2003,18(3):433-445.
[30]Malas J C III et al.. Optimization of microstructure development during hot working using control theory [J]. Metallurgical and Materials Transactions A,1997,28(9): 1921-1930.
[31]Medina E A et al.. Optimization of microstructure development:application to hot metal extrusion [J]. Journal of Materials Engineering and Performance,1996,5(6): 743-752.
[32]刘相华,王国栋,杜林秀,刘振宇.钢材性能柔性化与柔性轧制技术[J].钢铁,2006,41(11)：32-36.
[33]Kempen A T W, Sommer F, Mittemeijer E J. The kinetics of the austenite-ferrite phase transformation of Fe-Mn:differential thermal analysis during cooling [J]. Acta Materialia,2002,50(14):3545-3555
[34]Serajzadeh S. Prediction of temperature distribution and phase transformation on the run-out table in the process of hot strip rolling [J]. Applied Mathematical Modeling, 2003,27(11):861-875.
[35]Ahmadabadi M N, Farjami S. Transformation kinetics of unalloyed and high Mn austempered ductile iron [J]. Materials Science and Technology,2003,19(5):645-649.
[36]Johnson W A, Mehl R F. Reactions in process of nucleation and growth [J]. Transaction AIME,1939,135 (8):416-442.
[37]Avrami M. Kinetics of phase change [J]. Journal of Chemistry Physics.1939,7 (12): 1103-1112.
[38]Cahn J W. Transformation kinetics during continuous cooling [J]. Acta Metallurgica, 1956,4 (6):572-575.
[39]Kamat R G, Hawbolt E B, Brown L C, Brimacombe J K. Principle of additivity and the proeutectoid ferrite transformation [J]. Metallurgical Materials Transactions A,1992, 23 (9):2469-2690.
[40]Umemoto M, Horiuchi K, and Tamura I. Transformation kinetics of bainite during isothermal holding and continuous cooling [J]. Transaction of ISIJ,1982,22(11): 854-861.
[41]Kuban M B, Jayaraman R, Hawbolt E B, and Brimacombe E K. An assessment of the additivity principle in predicting continuous-cooling austenite-to-pearlite transformation kinetics using isothermal transformation data [J]. Metallurgical Transaction A,1986,17A:1493-1503.
[42]Lusk M and Jou H-J. On the rule of additivity in phase transformation kinetics [J]. Metallurgical Transaction A.1997,28(2):287-291.
[43]Ye J S, Chang H B, Hsu T Y. On the application of additivity rule in pearlitic transformation in low alloy steels [J]. Metallurgical and Materials Transactions A, 2003,34 (6):1259-1264.
[44]Zhu Y T, Lowe T C. Application of, and precautions for the use of, the rule of additivity in phase transformation [J]. Metallurgical and Materials Transactions B, 2000,31 (4):675-682.
[45]Pont D, Bergheau J M, Rochette M and Fortunier R. Proc.2nd Int. Symp. on'Inverse Problems in Engineering Mechanics', Paris, France, November 1994, Balkema, Rotterdam,151-156.
[46]Malinov S, Guo Z, Sha W and Wilson A. Differential scanning calorimetry study and computer modeling of β→α phase transformation in a Ti-6A1-4V alloy [J]. Metallurgical and Materials Transaction A,2001,32(4):879-887.
[47]Rios P R. Relationship between non-isothermal transformation curves and isothermal and non-isothermal kinetics [J]. Acta Materialia,2005,53(18):4893-4901.
[48]Liu Z Y, Wang G D and Gao W. Prediction of the mechanical properties of hot-rolled C-Mn steels using artificial neural networks [J]. Journal of Materials Processing Technology,1996,57(3-4):332-336.
[49]刘振宇,王昭东,王国栋,等.应用神经网络预测热轧C-Mn钢力学性能[J].钢铁研究学报,1995,7(4)：61-66.
[50]王殿辉,刘振宇,等.利用神经网络预测热轧板带力学性能[J].钢铁,1995,30(1)：28-31.
[51]井玉安,胡晓东,等.人工神经网络在热轧宽厚板力学性能预测中的应用[J].钢铁,2002,37(9)：26-30.
[52]左秀荣,薛向欣,姜茂发,等.利用人工神经网络研究合金元素对SCM822H钢性能的影响[J].钢铁研究学报,2002,14(1)：51-54.
[53]郑晖,王昭东,等.利用人工神经网络模型预测SS400热轧板带力学性能[J].钢铁,37(7)：37-40.
[54]刘贵立,张国英,曾梅光.用人工神经网络模型研究微量元素对钢力学性能的影响[J].钢铁研究,2000,1：48-50.
[55]Haque M E, Sudhakar K V. ANN back-propagation prediction model for fracture toughness in microalloy steel. International Journal of Fatigue.2002,24(9): 1003-1010.
[56]谭文,刘振宇,等.热轧中厚板冲击功的神经网络预报模型[J].钢铁,42(2)：51-55．
[57]Mackay D J C. A Practical bayesian framework for backpropagation networks [J]. Neural Computation A,1992,4(3):448-472.
[58]Mackay D J C. Bayesian interpolation [J]. Neural Computation A,1992,4(3):415-447.
[59]Narayan V, Abad R, Lopez B, Bhadeshia H K D H and Mackay D J C. Estimation of hot torsion stress strain curves in iron alloys using a neural network analysis [J]. ISIJ International,1999,39(10):999-1005.
[60]Cool T, Bhadeshia H K D H and Mackay D J C. The yield and ultimate tensile strength of steel welds [J]. Materials Science and Engineering A.1997,223(1-2):186-200.
[61]Lalam S H, Bhadeshia H K D H and Mackay D J C. Estimation of mechanical properties of ferritic steel welds Part 1:Yield and tensile strength. Science and Technology of Welding and Joining [J].2000,5(3):135-147.
[62]Metzbower E A, DeLoach J J, Lalam S H and Bhadeshia H K D H. Neural network analysis of strength and ductility of welding alloys for high strength low alloy shipbuilding steels [J]. Science and Technology of Welding and Joining.2001,6(2): 116-124.
[63]FUJII H, Mackay D J C and Bhadeshia H K D H. Bayesian neural network analysis of fatigue crack growth rate in nickel base superalloys [J]. ISIJ International.1996, 36(11):1373-1382.
[64]Capdevila C, Caballero F G and Garcia de andres C. Neural network model for isothermal pearlite transformation. Part Ⅰ:Interlamellar spacing [J]. ISIJ International, 2005,45(2):229-237.
[65]Vasudevan M, Bhaduri A K, Raj B, Prasad Rao K. Delta ferrite prediction in stainless steel welds using neural network analysis and comparison with other prediction methods [J]. Journal of Materials Processing Technology,2003,142(1):20-28.
[66]Herrera F, Lozano M, Verdegay J L. Tackling real-coded genetic algorithms:operators and tools for behavioural analysis. Artificial Intelligence Review,1998,12(4): 265-319.
[67]薛家庆.最优化原理与方法[M].冶金工业出版社,2001.
[68]Yuan X Q, Liu Z Y, Jiao S H, Ma L Q and Wang G D. The onset temperature of γ to α-phase transformation in hot deformed and non-deformed Nb micro-alloyed steels [J]. ISIJ international,2006,46(4):579-585.
[69]Pham T T, Hawbolt E B and Brimacombe J K. Predicting the onset of transformation under noncontinuous cooling conditions:Part Ⅰ. Theory [J]. Metallurgical and Materials Transaction A.1995,26(8):1987-1992.
[70]Pham T T, Hawbolt E B andBrimacombe J K. Predicting the onset of transformation under noncontinuous cooling conditions:Part Ⅱ.Application to the austenite pearlite transformation [J]. Metallurgical and Materials Transaction A.1995,26(8):1993-2000.
[71]Onink M et al. The lattice parameter of austenite and ferrite in iron-carbon alloys as function of carbon concentration and temperature [J]. Scripta Metallurgical Materials, 1993,29(8):1011-1016.
[72]Bhadeshia H K D H et al. Stress induced transformation to bainite in Fe-Cr-Mo-C pressure vessel steel [J]. Materials Science and Technology,1991,7(8):686-698.
[73]Teti T, Felde I. A non-linear extension of the additivity rule [J]. Computational Materials Science.1999,15(4):466-482.
[74]Enomoto M and Yang J B. Simulation of nucleation of proeutectoid ferrite at austenite grain boundary during continuous cooling [J]. Metallurgical Transaction A,2008, 39(5):994-1002.
[75]Enomoto M and Aaronson H I. Nucleation kinetics of proeutectoid ferrite at austenite grain boundary in Fe-C-X alloys [J]. Metallurgical Transaction A.1986,17(8): 1385-1397.
[76]Enomoto M, Lange W F Ⅲ and Aaronson H I. The kinetics of ferrite nucleation at austenite grain edges in Fe-C and Fe-C-X alloys. [J]. Metallurgical Transaction A.1986, 17(8):1399-1407.
[77]Lange W F Ⅲ, Enomoto M and Aaronson H I. The kinetics of ferrite nucleation at austenite grain boundary in Fe-C alloys [J]. Metallurgical Transaction A.1988,19(3): 427-440.
[78]Abe T, Aaronson H I and Shiflet G J. Growth kinetics and morphology of grain boundary ferrite allotriomorphs in an Fe-C-V alloy [J]. Metallurgical Transaction A. 1985,16(4):521-527.
[79]Inagakl H. Nucleation of the proeutectoid ferrite and its role in the formation of the transformation texture in a low carbon steel [J]. Zeitschrift fuer Metallkde.1987,78(2): 87-96.
[80]Umemoto M, Guo Z H and Tamura I. Effect of cooling rate on grain size of ferrite in a carbon steel [J]. Materials Science and Technology,1987,3(4):249-255.
[81]YE J S and HSU T Y. Modification of the additivity hypothesis with experiment [J]. ISIJ International.2004,44(4):777-779.
[82]HSU T Y. Additivity hypothesis and effects of stress on phase transformations in steel [J]. Current Opinion in Solid State and Materials Science,2005,9(6):256-268.
[83]Sarkar S and Militzer M. Microstructure evolution model for hot strip rolling of a Nb-microalloyed complex-phase steel [J]. Materials Science and Technology,2008, in press.
[84]Liu D S et al. A microstructure evolution model for hot rolling of a Mo-TRIP steel [J]. Metallurgical and materials transactions A.2007,38(4):894-909.
[85]Zhao J Z, Mesplont C and De Cooman B C. Kinetics of phase transformations in steels: A new method for analyzing dilatometric results [J]. ISIJ International,2001,41(5): 492-497.
[86]Gomez M, Medina S F and Caruana G. Modelling of phase transformation kinetics by correction of dilatometry results for a ferrite Nb-microalloyed steel [J]. ISIJ International,2003,43(8):1228-1237.
[87]Militzer M, Hawbolt E B and Meadowcroft T R. Microstructural model for hot rolling of high-strength low-alloy steels [J]. Metallurgical and Materials Transactions A,2000, 31 (4):1247-1259.
[88]Militzer M, Pandi R and Hawbolt E B. Ferrite nucleation and growth during continuous cooling [J]. Metallurgical and Materials Transactions A,1996,27 (6):1547-1556.
[89]Suehiro M, Sato K, Tsukano Y, Yada H, Senuma T and Matsumura Y. Computational modeling of microstructural change and strength of low carbon steel in hot strip rolling [J]. Transactions of ISIJ,1987,27(6):439-445.
[90]Ali A and Bhadeshia H K D H. Nucleation of widmanstatten ferrite [J]. Materials Science and Technology,1990,6(8):781-784.
[91]Fazeli F and Militzer M. Solid-Solid Phase Transformations in Inorganic Materials 2005, eds. J.M. Howe, E.D. Laughlin, J.K. Lee, D. J. Srolovitz, and U. Dahmen, TMS, Warrendale, PA,2005,835-841.
[92]阎平凡.人工神经网络与模拟进化计算[M].北京：清华大学出版社,2000.
[93]魏东,张明廉.基于贝叶斯方法的神经网路非线性模型辨识[J].计算机工程与应用,2005,11：5-11.
[94]Chua C G and Goh A T C. A hybrid Bayesian back-propagation neural network approach to multivariate modeling [J]. International Journal for numerical and analytical methods in geomechanics.2003,27:651-667.
[95]Penny W D, Roberts S J. Bayesian neural networks for classification:how useful is the evidence framework [J].Neural Networks,1999,12:877-892.
[96]Thodberg H H. A review of bayesian neural networks with an application to near infrared spectroscopy [J]. IEEE Transactions on Neural Networks,1996,7(1):56-72.
[97]Martin T H, Mohammad B M. Training feedforward networks with the marquardt algorithm [J]. IEEE Transactions on Neural Networks,1994,5(6):989-993.
[98]Foresee F D, Hagan M T. Gauss-Newton approximation to Bayesian learning [C]// Proceedings of International Conference on Neural Networks (ICNN'97). New York: IEEE,1997:1930-1935.
[99]Kennedy J, Eberhart R C. Particle Swarm Optimization [C]. IEEE International Conference on Neural Networks, New York, NY, USA:IEEE,1995:1942-1948.
[100]Eberhart R, Kennedy J. New optimizer using particle swarm theory[C]. Proceedings of the International Symposium on Micromechatronics and Human Science, Piscataway, NJ, USA:IEEE,1995:39-43.
[101]陈得宝,赵春霞.阶梯型粒子群算法及在函数优化中的应用[J].系统仿真学报,2007,19(24)：5659-5662.
[102]丁敬国,胡贤磊,焦景民,等.变异PSO算法协同神经元网络在轧制力预报中的应用[J].钢铁研究学报,2007,19(12)：56-59.
[103]Eberhart C, Shi Y. Particle swarm optimization:developments, applications and resources[C]. In:Proc. Congress on Evolutionary Computation 2001, Piscataway, NJ: IEEE Press,2001:81-86.
[104]周先东,杨大地,马翠.求解运输问题的GAPSO算法[J].计算机仿真,2008,2：286-289.
[105]孙波,陈卫东,席裕庚.基于粒子群优化算法的移动机器人全局最优路径规划[J].控制与决策,2005,20(9)：1052-1055.
[106]Shi Y., Eberhart R C, Parameter Selection in Particle Swarm Optimization [Z]. Evolutionary Programming Ⅶ Proc. Ep98. New York:Springer-Verlag,1998, 591-600.
[107]Kennedy J. The Particle Swarm:Social Adaption of Knowledge [M]. Proc. Int.1. Conf. on Evolutionary Computation. Indianapolis, Piscataway, NJ:IEEE Service Center, 1997,303-308.
[108]潘江峰,钟约先,袁朝龙.板料拉深成形工艺参数的多目标遗传算法优化[J].清华大学学报(自然科学版),2007,47(8)：1267-1269.
[109]王建宇,周春光,郭东伟,等.基于Rank的进化算法解决多目标TSP问题[J].计算机工程与科学,2008,30(2)：75-77.
[110]Datta Shubhabrata, Pettersson Frank et.al. Designing high strength multi-phase steel for improved strength-ductility balance using neural networks and multi-objective genetic algorithms [J]. ISIJ International,2007,47(8):1195-1203.
[111]Chakraborti N, Siva Kumar B et. al. Optimizing surface profile during hot rolling:A genetic algorithms based multi-objective optimization [J]. Computational Materials Science,2006,37(1-2):159-165.
[112]Wang D D, Tieu A K and D'Alessio Giovanni. Computational intelligence-based process optimization for tandem cold rolling [J]. Materials and Manufacturing Processes,2005,20(3):479-496.
[113]Xie H B, Jiang Z Y et al. On-line optimization of coiling temperature control on run-out table [J]. Key Engineering Materials,2007,344:701-706.
[114]Pettersson F, Chakraborti N, Sinqh S B. Neural network analysis of steel plate processing augmented by multi-objective genetic algorithms[J]. Steel Research International,2007,78(12):890-898.
[115]Srinivas N and Deb K. Multi-Objective function optimization using non-dominated sorting genetic algorithms [J], Evolutionary Computation,2(3):221-248.
[116]Mahfouf M, Chen M-Y, and Linkens D A. Adaptive Weighted Particle Swarm Optimization for Multi-objective Optimal Design of Alloy Steels [J]. Lecture Notes in Computational Science,2004,3242:762-771.
[117]Deb K, Agrawal S, Pratap A, and Meyarivan T. A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization:NSGA-II [J]. Lecture Notes in Computational Science,2000,1917:1-11.
[118]Li X-D. A Non-dominated sorting particle swarm optimizer for multiobjective optimization [J]. Lecture Notes in Computer Science,2003,2723:37-48.
[119]Deb K and Goel T. Controlled Elitist Non-dominated sorting genetic algorithms for better convergence [J]. Lecture Notes in Computer Science,2001,1993:67-81.
[120]张利彪,周春光,马铭,孙彩堂.基于极大极小距离密度的多目标微分进化算法[J].计算机研究与发展,2007,44(1)：177-184.
[2]王国栋,刘相华,朱伏先,等.新一代钢铁材料的研究开发现状和发展趋势[J].鞍钢技术,2005,4：1-8.
[3]胡燕慧,杜林秀,高彩茹,等.500MPa级超级钢工业实验[J].钢铁,2004,39(10)：54-58.
[4]刘相华,陆匠心,张丕君,等.400-500MPa级碳素钢先进工业化制造技术[J].中国有色金属学报,2004,14(1)：207-210.
[5]杜林秀,姚圣杰,熊明鲜,王国栋.低碳结钢钢的奥氏体晶粒超细化[J].东北大学学报(自然科学版),2007,28(11)：1575-1578.
[6]张红梅,杜林秀,李维娟,等.400MPa超级钢控轧控冷优化工艺及工业实验[J].钢铁研究,2001,3：27-31.
[7]Kwon O. A technology for the prediction and control of microstructure changes and mechanical properties in steel [J]. ISIJ International,1992,32(2):350-358.
[8]Yada H, Senuma T. Computer modeling fro predicting microstructure and mechanical properties of steels. Bulletin of Japan Institute of Metals,1990,29(6):430-439.
[9]Yoshie A, Fujioka M, et al. Modelling of microstructual evolution and mechanical properties of steel plates produced by Thermo-Mechanical Control Process [J]. ISIJ International,1992,32(3):395-404.
[10]刘振宇.加速冷却对C-Mn钢力学性能的影响[J].钢铁,1994,29(2)：31-34.
[11]刘振宇.C-Mn钢热轧板带组织-性能预测模型的开发及在生产中的应用[D].沈阳：东北大学,1995.
[12]曲锦波HSLA钢板热轧组织性能控制与预测模型[D].沈阳：东北大学,1998.
[13]许云波.基于物理冶金和人工智能的热轧钢材组织性能预测与控制[D].沈阳：东北大学,2003.
[14]朱丽娟.热轧TRIP钢的组织性能预测[D].沈阳：东北大学,2007.
[15]李殿中,张玉妥,刘实,等.材料制备工艺的计算机模拟[J].金属学报,2001,37(5)：449-452.
[16]郑坚,唐广波,程杰锋,等.珠钢CSP热轧组织性能预报软件设计[J].轧钢,2003,20(1)：15-17.
[17]Militzer M, Samarasekera I V, Jin D Q热连轧带钢组织性能预报模型的进展[J].钢铁,1999,34(增刊)：658-669.
[18]Andorfer J, Auzinger D等.使用VAI-Q Strip系统首次实现热轧带钢力学性能的全面控制[J].钢铁,2001,36(1)：42-46.
[19]Loffler H U, Doll R. Commercial application of microstructure modelling in hot strip mills[C]. Recrystallization and Grain Growth Proceedings of the First Joint International Conference.Springer-Verlag,2001. Trowsdale A J, Tunstall J P, Randerson K, et al. Modeling of metal rolling processes[C], British steel plc. London: Church House Conference Centre London, UK,1999:12-21.
[20]Watanabe Y Y, Shimomura S I, Funato K, et al. Integrated model for microstructural evolution and properties of steel plates manufactured in production line [J]. ISIJ International,1992,32(3):405-413.
[21]刘正东,董翰,干勇.热连轧过程中组织性能预报系统的应用[J].钢铁,2003,38(2)：68-71.
[22]王利明,沙孝春,李殿中,等Rollan带钢热轧过程组织演变与性能预测软件的开发[A].新一代钢铁材料国际会议[C].北京：2001.
[23]Saito Y. Modeling of microstructural evolution during thermomechnical processing of structural steels [J]. Materials Science and Engineering A,1997,223:134-145.
[24]Ray P K, Ganguly R I and Panda A K. Optimization of mechanical properties of an HSLA-100 steel through control of heat treatment variables [J]. Materials Science and Engineering A,2003,346:122-131.
[25]Loffler H U, Doll R, Dun W. Microstructure monitor controls product quality-successful implementation at the hot strip mill at Wuhan iron and steel group[C]. China International Steel Congresses,2004,7, shanghai china:6-10.
[26]Mahfouf M, Jamei M, Linkens D A. Optimal design of alloy steels using multiobjective genetic algorithms [J]. Materials and Manufacturing Processes,2005,20(3):553-567.
[27]Biswas S K, Chen S J and Satyanarayana A. Optimal temperature tracking for accelerated cooling processes in hot rolling of steel [J]. Dynamics and Control,1997, 7(4):327-340.
[28]Abdul Samad M, Rao Ravi S. Minimization of energy in the multipass rolling process [J]. Journal of Manufacturing Science and Engineering,2001,123:135-141
[29]Chakraborti N and Kumar A. The optimal schedualing of a reversing strip mill:studies using multipopulation genetic algorithms and differential evolution [J]. Materials and manufacturing processes,2003,18(3):433-445.
[30]Malas J C III et al.. Optimization of microstructure development during hot working using control theory [J]. Metallurgical and Materials Transactions A,1997,28(9): 1921-1930.
[31]Medina E A et al.. Optimization of microstructure development:application to hot metal extrusion [J]. Journal of Materials Engineering and Performance,1996,5(6): 743-752.
[32]刘相华,王国栋,杜林秀,刘振宇.钢材性能柔性化与柔性轧制技术[J].钢铁,2006,41(11)：32-36.
[33]Kempen A T W, Sommer F, Mittemeijer E J. The kinetics of the austenite-ferrite phase transformation of Fe-Mn:differential thermal analysis during cooling [J]. Acta Materialia,2002,50(14):3545-3555
[34]Serajzadeh S. Prediction of temperature distribution and phase transformation on the run-out table in the process of hot strip rolling [J]. Applied Mathematical Modeling, 2003,27(11):861-875.
[35]Ahmadabadi M N, Farjami S. Transformation kinetics of unalloyed and high Mn austempered ductile iron [J]. Materials Science and Technology,2003,19(5):645-649.
[36]Johnson W A, Mehl R F. Reactions in process of nucleation and growth [J]. Transaction AIME,1939,135 (8):416-442.
[37]Avrami M. Kinetics of phase change [J]. Journal of Chemistry Physics.1939,7 (12): 1103-1112.
[38]Cahn J W. Transformation kinetics during continuous cooling [J]. Acta Metallurgica, 1956,4 (6):572-575.
[39]Kamat R G, Hawbolt E B, Brown L C, Brimacombe J K. Principle of additivity and the proeutectoid ferrite transformation [J]. Metallurgical Materials Transactions A,1992, 23 (9):2469-2690.
[40]Umemoto M, Horiuchi K, and Tamura I. Transformation kinetics of bainite during isothermal holding and continuous cooling [J]. Transaction of ISIJ,1982,22(11): 854-861.
[41]Kuban M B, Jayaraman R, Hawbolt E B, and Brimacombe E K. An assessment of the additivity principle in predicting continuous-cooling austenite-to-pearlite transformation kinetics using isothermal transformation data [J]. Metallurgical Transaction A,1986,17A:1493-1503.
[42]Lusk M and Jou H-J. On the rule of additivity in phase transformation kinetics [J]. Metallurgical Transaction A.1997,28(2):287-291.
[43]Ye J S, Chang H B, Hsu T Y. On the application of additivity rule in pearlitic transformation in low alloy steels [J]. Metallurgical and Materials Transactions A, 2003,34 (6):1259-1264.
[44]Zhu Y T, Lowe T C. Application of, and precautions for the use of, the rule of additivity in phase transformation [J]. Metallurgical and Materials Transactions B, 2000,31 (4):675-682.
[45]Pont D, Bergheau J M, Rochette M and Fortunier R. Proc.2nd Int. Symp. on'Inverse Problems in Engineering Mechanics', Paris, France, November 1994, Balkema, Rotterdam,151-156.
[46]Malinov S, Guo Z, Sha W and Wilson A. Differential scanning calorimetry study and computer modeling of β→α phase transformation in a Ti-6A1-4V alloy [J]. Metallurgical and Materials Transaction A,2001,32(4):879-887.
[47]Rios P R. Relationship between non-isothermal transformation curves and isothermal and non-isothermal kinetics [J]. Acta Materialia,2005,53(18):4893-4901.
[48]Liu Z Y, Wang G D and Gao W. Prediction of the mechanical properties of hot-rolled C-Mn steels using artificial neural networks [J]. Journal of Materials Processing Technology,1996,57(3-4):332-336.
[49]刘振宇,王昭东,王国栋,等.应用神经网络预测热轧C-Mn钢力学性能[J].钢铁研究学报,1995,7(4)：61-66.
[50]王殿辉,刘振宇,等.利用神经网络预测热轧板带力学性能[J].钢铁,1995,30(1)：28-31.
[51]井玉安,胡晓东,等.人工神经网络在热轧宽厚板力学性能预测中的应用[J].钢铁,2002,37(9)：26-30.
[52]左秀荣,薛向欣,姜茂发,等.利用人工神经网络研究合金元素对SCM822H钢性能的影响[J].钢铁研究学报,2002,14(1)：51-54.
[53]郑晖,王昭东,等.利用人工神经网络模型预测SS400热轧板带力学性能[J].钢铁,37(7)：37-40.
[54]刘贵立,张国英,曾梅光.用人工神经网络模型研究微量元素对钢力学性能的影响[J].钢铁研究,2000,1：48-50.
[55]Haque M E, Sudhakar K V. ANN back-propagation prediction model for fracture toughness in microalloy steel. International Journal of Fatigue.2002,24(9): 1003-1010.
[56]谭文,刘振宇,等.热轧中厚板冲击功的神经网络预报模型[J].钢铁,42(2)：51-55．
[57]Mackay D J C. A Practical bayesian framework for backpropagation networks [J]. Neural Computation A,1992,4(3):448-472.
[58]Mackay D J C. Bayesian interpolation [J]. Neural Computation A,1992,4(3):415-447.
[59]Narayan V, Abad R, Lopez B, Bhadeshia H K D H and Mackay D J C. Estimation of hot torsion stress strain curves in iron alloys using a neural network analysis [J]. ISIJ International,1999,39(10):999-1005.
[60]Cool T, Bhadeshia H K D H and Mackay D J C. The yield and ultimate tensile strength of steel welds [J]. Materials Science and Engineering A.1997,223(1-2):186-200.
[61]Lalam S H, Bhadeshia H K D H and Mackay D J C. Estimation of mechanical properties of ferritic steel welds Part 1:Yield and tensile strength. Science and Technology of Welding and Joining [J].2000,5(3):135-147.
[62]Metzbower E A, DeLoach J J, Lalam S H and Bhadeshia H K D H. Neural network analysis of strength and ductility of welding alloys for high strength low alloy shipbuilding steels [J]. Science and Technology of Welding and Joining.2001,6(2): 116-124.
[63]FUJII H, Mackay D J C and Bhadeshia H K D H. Bayesian neural network analysis of fatigue crack growth rate in nickel base superalloys [J]. ISIJ International.1996, 36(11):1373-1382.
[64]Capdevila C, Caballero F G and Garcia de andres C. Neural network model for isothermal pearlite transformation. Part Ⅰ:Interlamellar spacing [J]. ISIJ International, 2005,45(2):229-237.
[65]Vasudevan M, Bhaduri A K, Raj B, Prasad Rao K. Delta ferrite prediction in stainless steel welds using neural network analysis and comparison with other prediction methods [J]. Journal of Materials Processing Technology,2003,142(1):20-28.
[66]Herrera F, Lozano M, Verdegay J L. Tackling real-coded genetic algorithms:operators and tools for behavioural analysis. Artificial Intelligence Review,1998,12(4): 265-319.
[67]薛家庆.最优化原理与方法[M].冶金工业出版社,2001.
[68]Yuan X Q, Liu Z Y, Jiao S H, Ma L Q and Wang G D. The onset temperature of γ to α-phase transformation in hot deformed and non-deformed Nb micro-alloyed steels [J]. ISIJ international,2006,46(4):579-585.
[69]Pham T T, Hawbolt E B and Brimacombe J K. Predicting the onset of transformation under noncontinuous cooling conditions:Part Ⅰ. Theory [J]. Metallurgical and Materials Transaction A.1995,26(8):1987-1992.
[70]Pham T T, Hawbolt E B andBrimacombe J K. Predicting the onset of transformation under noncontinuous cooling conditions:Part Ⅱ.Application to the austenite pearlite transformation [J]. Metallurgical and Materials Transaction A.1995,26(8):1993-2000.
[71]Onink M et al. The lattice parameter of austenite and ferrite in iron-carbon alloys as function of carbon concentration and temperature [J]. Scripta Metallurgical Materials, 1993,29(8):1011-1016.
[72]Bhadeshia H K D H et al. Stress induced transformation to bainite in Fe-Cr-Mo-C pressure vessel steel [J]. Materials Science and Technology,1991,7(8):686-698.
[73]Teti T, Felde I. A non-linear extension of the additivity rule [J]. Computational Materials Science.1999,15(4):466-482.
[74]Enomoto M and Yang J B. Simulation of nucleation of proeutectoid ferrite at austenite grain boundary during continuous cooling [J]. Metallurgical Transaction A,2008, 39(5):994-1002.
[75]Enomoto M and Aaronson H I. Nucleation kinetics of proeutectoid ferrite at austenite grain boundary in Fe-C-X alloys [J]. Metallurgical Transaction A.1986,17(8): 1385-1397.
[76]Enomoto M, Lange W F Ⅲ and Aaronson H I. The kinetics of ferrite nucleation at austenite grain edges in Fe-C and Fe-C-X alloys. [J]. Metallurgical Transaction A.1986, 17(8):1399-1407.
[77]Lange W F Ⅲ, Enomoto M and Aaronson H I. The kinetics of ferrite nucleation at austenite grain boundary in Fe-C alloys [J]. Metallurgical Transaction A.1988,19(3): 427-440.
[78]Abe T, Aaronson H I and Shiflet G J. Growth kinetics and morphology of grain boundary ferrite allotriomorphs in an Fe-C-V alloy [J]. Metallurgical Transaction A. 1985,16(4):521-527.
[79]Inagakl H. Nucleation of the proeutectoid ferrite and its role in the formation of the transformation texture in a low carbon steel [J]. Zeitschrift fuer Metallkde.1987,78(2): 87-96.
[80]Umemoto M, Guo Z H and Tamura I. Effect of cooling rate on grain size of ferrite in a carbon steel [J]. Materials Science and Technology,1987,3(4):249-255.
[81]YE J S and HSU T Y. Modification of the additivity hypothesis with experiment [J]. ISIJ International.2004,44(4):777-779.
[82]HSU T Y. Additivity hypothesis and effects of stress on phase transformations in steel [J]. Current Opinion in Solid State and Materials Science,2005,9(6):256-268.
[83]Sarkar S and Militzer M. Microstructure evolution model for hot strip rolling of a Nb-microalloyed complex-phase steel [J]. Materials Science and Technology,2008, in press.
[84]Liu D S et al. A microstructure evolution model for hot rolling of a Mo-TRIP steel [J]. Metallurgical and materials transactions A.2007,38(4):894-909.
[85]Zhao J Z, Mesplont C and De Cooman B C. Kinetics of phase transformations in steels: A new method for analyzing dilatometric results [J]. ISIJ International,2001,41(5): 492-497.
[86]Gomez M, Medina S F and Caruana G. Modelling of phase transformation kinetics by correction of dilatometry results for a ferrite Nb-microalloyed steel [J]. ISIJ International,2003,43(8):1228-1237.
[87]Militzer M, Hawbolt E B and Meadowcroft T R. Microstructural model for hot rolling of high-strength low-alloy steels [J]. Metallurgical and Materials Transactions A,2000, 31 (4):1247-1259.
[88]Militzer M, Pandi R and Hawbolt E B. Ferrite nucleation and growth during continuous cooling [J]. Metallurgical and Materials Transactions A,1996,27 (6):1547-1556.
[89]Suehiro M, Sato K, Tsukano Y, Yada H, Senuma T and Matsumura Y. Computational modeling of microstructural change and strength of low carbon steel in hot strip rolling [J]. Transactions of ISIJ,1987,27(6):439-445.
[90]Ali A and Bhadeshia H K D H. Nucleation of widmanstatten ferrite [J]. Materials Science and Technology,1990,6(8):781-784.
[91]Fazeli F and Militzer M. Solid-Solid Phase Transformations in Inorganic Materials 2005, eds. J.M. Howe, E.D. Laughlin, J.K. Lee, D. J. Srolovitz, and U. Dahmen, TMS, Warrendale, PA,2005,835-841.
[92]阎平凡.人工神经网络与模拟进化计算[M].北京：清华大学出版社,2000.
[93]魏东,张明廉.基于贝叶斯方法的神经网路非线性模型辨识[J].计算机工程与应用,2005,11：5-11.
[94]Chua C G and Goh A T C. A hybrid Bayesian back-propagation neural network approach to multivariate modeling [J]. International Journal for numerical and analytical methods in geomechanics.2003,27:651-667.
[95]Penny W D, Roberts S J. Bayesian neural networks for classification:how useful is the evidence framework [J].Neural Networks,1999,12:877-892.
[96]Thodberg H H. A review of bayesian neural networks with an application to near infrared spectroscopy [J]. IEEE Transactions on Neural Networks,1996,7(1):56-72.
[97]Martin T H, Mohammad B M. Training feedforward networks with the marquardt algorithm [J]. IEEE Transactions on Neural Networks,1994,5(6):989-993.
[98]Foresee F D, Hagan M T. Gauss-Newton approximation to Bayesian learning [C]// Proceedings of International Conference on Neural Networks (ICNN'97). New York: IEEE,1997:1930-1935.
[99]Kennedy J, Eberhart R C. Particle Swarm Optimization [C]. IEEE International Conference on Neural Networks, New York, NY, USA:IEEE,1995:1942-1948.
[100]Eberhart R, Kennedy J. New optimizer using particle swarm theory[C]. Proceedings of the International Symposium on Micromechatronics and Human Science, Piscataway, NJ, USA:IEEE,1995:39-43.
[101]陈得宝,赵春霞.阶梯型粒子群算法及在函数优化中的应用[J].系统仿真学报,2007,19(24)：5659-5662.
[102]丁敬国,胡贤磊,焦景民,等.变异PSO算法协同神经元网络在轧制力预报中的应用[J].钢铁研究学报,2007,19(12)：56-59.
[103]Eberhart C, Shi Y. Particle swarm optimization:developments, applications and resources[C]. In:Proc. Congress on Evolutionary Computation 2001, Piscataway, NJ: IEEE Press,2001:81-86.
[104]周先东,杨大地,马翠.求解运输问题的GAPSO算法[J].计算机仿真,2008,2：286-289.
[105]孙波,陈卫东,席裕庚.基于粒子群优化算法的移动机器人全局最优路径规划[J].控制与决策,2005,20(9)：1052-1055.
[106]Shi Y., Eberhart R C, Parameter Selection in Particle Swarm Optimization [Z]. Evolutionary Programming Ⅶ Proc. Ep98. New York:Springer-Verlag,1998, 591-600.
[107]Kennedy J. The Particle Swarm:Social Adaption of Knowledge [M]. Proc. Int.1. Conf. on Evolutionary Computation. Indianapolis, Piscataway, NJ:IEEE Service Center, 1997,303-308.
[108]潘江峰,钟约先,袁朝龙.板料拉深成形工艺参数的多目标遗传算法优化[J].清华大学学报(自然科学版),2007,47(8)：1267-1269.
[109]王建宇,周春光,郭东伟,等.基于Rank的进化算法解决多目标TSP问题[J].计算机工程与科学,2008,30(2)：75-77.
[110]Datta Shubhabrata, Pettersson Frank et.al. Designing high strength multi-phase steel for improved strength-ductility balance using neural networks and multi-objective genetic algorithms [J]. ISIJ International,2007,47(8):1195-1203.
[111]Chakraborti N, Siva Kumar B et. al. Optimizing surface profile during hot rolling:A genetic algorithms based multi-objective optimization [J]. Computational Materials Science,2006,37(1-2):159-165.
[112]Wang D D, Tieu A K and D'Alessio Giovanni. Computational intelligence-based process optimization for tandem cold rolling [J]. Materials and Manufacturing Processes,2005,20(3):479-496.
[113]Xie H B, Jiang Z Y et al. On-line optimization of coiling temperature control on run-out table [J]. Key Engineering Materials,2007,344:701-706.
[114]Pettersson F, Chakraborti N, Sinqh S B. Neural network analysis of steel plate processing augmented by multi-objective genetic algorithms[J]. Steel Research International,2007,78(12):890-898.
[115]Srinivas N and Deb K. Multi-Objective function optimization using non-dominated sorting genetic algorithms [J], Evolutionary Computation,2(3):221-248.
[116]Mahfouf M, Chen M-Y, and Linkens D A. Adaptive Weighted Particle Swarm Optimization for Multi-objective Optimal Design of Alloy Steels [J]. Lecture Notes in Computational Science,2004,3242:762-771.
[117]Deb K, Agrawal S, Pratap A, and Meyarivan T. A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization:NSGA-II [J]. Lecture Notes in Computational Science,2000,1917:1-11.
[118]Li X-D. A Non-dominated sorting particle swarm optimizer for multiobjective optimization [J]. Lecture Notes in Computer Science,2003,2723:37-48.
[119]Deb K and Goel T. Controlled Elitist Non-dominated sorting genetic algorithms for better convergence [J]. Lecture Notes in Computer Science,2001,1993:67-81.
[120]张利彪,周春光,马铭,孙彩堂.基于极大极小距离密度的多目标微分进化算法[J].计算机研究与发展,2007,44(1)：177-184.