In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and ...In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and co-state variables, and piecewise constant function is used to approximate control variables. Generally, the optimal conditions for the problem are solved iteratively until the control variable reaches error tolerance. In order to calculate all the variables individually and parallelly, we introduce a gradient recovery based two-grid method. First, we solve the small scaled optimal control problem on coarse grids. Next, we use the gradient recovery technique to recover the gradients of state and co-state variables. Finally, using the recovered variables, we solve the large scaled optimal control problem for all variables independently. Moreover, we estimate priori error for the proposed scheme, and use an example to validate the theoretical results.展开更多
Based on a method combined artificial neural network (ANN) with particle swarm optimization (PSO) algorithm, the thermo-mechanical fatigue reliability of plastic ball grid array (PBGA) solder joints was studied. The s...Based on a method combined artificial neural network (ANN) with particle swarm optimization (PSO) algorithm, the thermo-mechanical fatigue reliability of plastic ball grid array (PBGA) solder joints was studied. The simulation experiments of accelerated thermal cycling test were performed by ANSYS software. Based on orthogonal array experiments, a back-propagation artificial neural network (BPNN) was used to establish the nonlinear multivariate relationship between thermo-mechanical fatigue reliability and control factors. Then, PSO was applied to obtaining the optimal levels of control factors by using the output of BPNN as the affinity measure. The results show that the control factors, such as print circuit board (PCB) size, PCB thickness, substrate size, substrate thickness, PCB coefficient of thermal expansion (CTE), substrate CTE, silicon die CTE, and solder joint CTE, have a great influence on thermo-mechanical fatigue reliability of PBGA solder joints. The ratio of signal to noise of ANN-PSO method is 51.77 dB and its error is 33.3% less than that of Taguchi method. Moreover, the running time of ANN-PSO method is only 2% of that of the BPNN. These conclusions are verified by the confirmative experiments.展开更多
Hierarchical evolutionary algorithms based on genetic algorithms (GAs) and Nash strategy of game theory are proposed to accelerate the optimization process and implemented in transonic aerodynamic shape optimization p...Hierarchical evolutionary algorithms based on genetic algorithms (GAs) and Nash strategy of game theory are proposed to accelerate the optimization process and implemented in transonic aerodynamic shape optimization problems Inspired from the natural evolution history that different periods with certain environments have different criteria for the evaluations of individuals’ fitness, a hierarchical fidelity model is introduced to reach high optimization efficiency The shape of an NACA0012 based airfoil is optimized in maximizing the lift coefficient under a given transonic flow condition Optimized results are presented and compared with the single model results and traditional GA展开更多
特高压紧凑型输电技术对于压缩输电线路走廊宽度、提高输电线路自然输送功率、降低单位输送容量的工程造价具有重要价值。作为紧凑型技术的重要方法,导线排列方式的优化有利于进一步提高线路输送容量,改善输电线路周围的电磁环境。提出...特高压紧凑型输电技术对于压缩输电线路走廊宽度、提高输电线路自然输送功率、降低单位输送容量的工程造价具有重要价值。作为紧凑型技术的重要方法,导线排列方式的优化有利于进一步提高线路输送容量,改善输电线路周围的电磁环境。提出了一种1 000 k V紧凑型输电线路的导线排列方式优化方法,该方法以提高自然功率和单位截面积自然功率为目标,并考虑工程实际约束,建立多目标不等式约束的非线性优化模型,通过模型求解得到导线优化的初始方案。在初始方案的基础上,采用粒子群优化方法对初始方案的子导线排列进行了非对称优化,对比分析了优化前后导线的电磁环境因素以及线路的电气参数,并利用有限元分析方法对优化排列后的导线表面电场强度进行了仿真验证。展开更多
文摘In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and co-state variables, and piecewise constant function is used to approximate control variables. Generally, the optimal conditions for the problem are solved iteratively until the control variable reaches error tolerance. In order to calculate all the variables individually and parallelly, we introduce a gradient recovery based two-grid method. First, we solve the small scaled optimal control problem on coarse grids. Next, we use the gradient recovery technique to recover the gradients of state and co-state variables. Finally, using the recovered variables, we solve the large scaled optimal control problem for all variables independently. Moreover, we estimate priori error for the proposed scheme, and use an example to validate the theoretical results.
基金Project(60371046) supported by the National Natural Science Foundation of ChinaProject(9140C0301060C03001) supported by the National Defense Science and Technology Foundation of Key Laboratory, China
文摘Based on a method combined artificial neural network (ANN) with particle swarm optimization (PSO) algorithm, the thermo-mechanical fatigue reliability of plastic ball grid array (PBGA) solder joints was studied. The simulation experiments of accelerated thermal cycling test were performed by ANSYS software. Based on orthogonal array experiments, a back-propagation artificial neural network (BPNN) was used to establish the nonlinear multivariate relationship between thermo-mechanical fatigue reliability and control factors. Then, PSO was applied to obtaining the optimal levels of control factors by using the output of BPNN as the affinity measure. The results show that the control factors, such as print circuit board (PCB) size, PCB thickness, substrate size, substrate thickness, PCB coefficient of thermal expansion (CTE), substrate CTE, silicon die CTE, and solder joint CTE, have a great influence on thermo-mechanical fatigue reliability of PBGA solder joints. The ratio of signal to noise of ANN-PSO method is 51.77 dB and its error is 33.3% less than that of Taguchi method. Moreover, the running time of ANN-PSO method is only 2% of that of the BPNN. These conclusions are verified by the confirmative experiments.
基金Start-up foundation item of the Educational Department of China for returnees
文摘Hierarchical evolutionary algorithms based on genetic algorithms (GAs) and Nash strategy of game theory are proposed to accelerate the optimization process and implemented in transonic aerodynamic shape optimization problems Inspired from the natural evolution history that different periods with certain environments have different criteria for the evaluations of individuals’ fitness, a hierarchical fidelity model is introduced to reach high optimization efficiency The shape of an NACA0012 based airfoil is optimized in maximizing the lift coefficient under a given transonic flow condition Optimized results are presented and compared with the single model results and traditional GA
文摘特高压紧凑型输电技术对于压缩输电线路走廊宽度、提高输电线路自然输送功率、降低单位输送容量的工程造价具有重要价值。作为紧凑型技术的重要方法,导线排列方式的优化有利于进一步提高线路输送容量,改善输电线路周围的电磁环境。提出了一种1 000 k V紧凑型输电线路的导线排列方式优化方法,该方法以提高自然功率和单位截面积自然功率为目标,并考虑工程实际约束,建立多目标不等式约束的非线性优化模型,通过模型求解得到导线优化的初始方案。在初始方案的基础上,采用粒子群优化方法对初始方案的子导线排列进行了非对称优化,对比分析了优化前后导线的电磁环境因素以及线路的电气参数,并利用有限元分析方法对优化排列后的导线表面电场强度进行了仿真验证。
