基于仿真模型的动态响应优化算法研究
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摘要
本文在国家“863”高技术研究发展计划项目2006AA04Z121、国家自然科学基金项目50775084资助下,对基于仿真模型的动态响应优化展开研究,主要研究内容包括动态响应优化问题并行化处理、基于时间谱元法的动态响应优化、基于MARS的动态响应优化和基于模糊聚类的全局动态响应优化等问题。
首先,研究了仿真优化中SQP算法的并行处理与调度策略,提出了SQP并行优化调度策略的抽象调度模型即等式约束离散变量优化模型,从理论上探讨了并行化处理与调度策略的可行性；通过工作池,应用集中式动态负载平衡技术实现并行任务调度。以F14战斗机简易模型动态响应的控制参数优化为例,验证了本方法的有效性。
其次,研究了基于时间谱元法的系统动态响应优化算法。深入分析了在时间域内离散动态响应,将运动微分方程或方程组转化成代数方程组,精确解出瞬态响应,改善了传统求解动态响应时误差大的缺点,达到谱收敛精度。用高斯-洛巴托-勒让德点法(GLL)和关键点法(KPM)处理时间约束。这样,动态响应优化算法就可以在超曲线或超曲面上找到满足所有时间约束的变化的目标函数。以线性单自由度吸振器设计、线性2自由度弹簧减振器设计和线性5自由度汽车悬挂系统设计为例,引入人工设计变量,详细分析了两种处理约束方法的优缺点,也说明了此方法的正确性。这些内容可为进一步研究动态响应优化提供参考,如在固定端承受振动输入的矩形变截面梁的动态响应优化设计,在不同边界条件下承受垂直平面均布瞬态动载荷作用的弹性梁的动态响应优化设计等。
第三,利用多变量自适应回归样条(MARS)的特点,提出了结合移动极限策略和置信域方法以及数据驱动且适合基于计算昂贵的黑箱仿真模型的动态响应优化算法。MARS是一个自适应的回归过程,采用了将高维问题简化为低维高精度模型的修改回归分块策略。MLS是在设计空间确定子区间的位置和大小,其不仅反映了函数近似质量,而且反映了优化过程的收敛历史。应用MARS的目的是减小了传统响应面的不利因素,特别是对于高维非线性问题。以高维函数和高维工程问题为例进行测试,结果表明了该方法的可行性和有效性,并且和二次响应面(QRS)在计算效率和精度方面进行了比较。还测试了调用仿真器ANSYS的变截面悬臂梁外形形状优化的问题,并与基于SQP的仿真优化进行了比较；测试了线性2自由度弹簧减振器设计问题和5自由度汽车悬挂系统动态响应优化设计问题,结果说明了移动极限策略和MARS响应而结合的优越性。
将MARS、数据驱动、置信域法(TRM)与增广拉格朗日方法相结合起来研究动态响应优化算法。当最优点在数据库中或者有很近的点在数据库中时,将用数据库中的点对应的目标函数和约束函数的值代替最优点的目标函数和约束函数的值,而不需要再进行计算昂贵的仿真分析,如果不存在这样的点,只能通过计算昂贵的仿真分析获得最优点的目标函数和约束函数的值。随着优化的进行,数据库越来越成熟,这样更加有利于建立精确的响应面并且快速找到全局最优点。以一个10维工程问题以及线性2自由度弹簧减振器设计和5自由度汽车悬挂系统动态响应优化设计问题为例进行测试,测试结果与文献中提供的数据进行了比较,证明了此方法的可行性和有效性。
最后,首次将模糊聚类应用于基于仿真模型的全局动态响应优化中,并且取得很好的效果。用近似模型代替密集计算进行分析和仿真,计算速度快。模糊聚类确定采样子区间的位置,最近两次迭代结果决定采样子区域的大小。确定了要采样的子区间后小样本采样,仿真评估目标函数及约束函数,然后构造全局Kriging响应面,再在整个设计域内大样本采样,之后仿真评估全局Kriging响应面,将仿真结果模糊聚类,再确定下一次迭代的子区问,反复迭代直到收敛。在模糊聚类全局动态响应优化中,每一次迭代采用3个聚类中心和它们的几何中心效果较好,这3个中心就是局部最优点或者其附近点,这3个聚类中心的几何中心有更大的概率成为最优点；排序这4个点的函数值,将函数值最小值的点作为本次迭代的最优点。以10个标准全局优化问题和1个线性单自由度吸振器设计问题为例进行测试,并与遗传算法(GA),模拟退火算法(SA),粒子群算法(PSO)和模式追踪算法(MPS)进行比较,证明该方法的精确性和鲁棒性,更重要的是明显减少了昂贵黑箱函数的仿真评估次数。
Supported by the National "863" High-Tech Development Project of China under the grant No.2006AA04Z121 and National Natural Science Fund under the grant No.50775084, the simulation model based dynamic response optimization methods have been studied, which focus on dynamic response optimization problems and parallel processing, time spectral element method based on the dynamic response optimization, MARS based dynamic response optimization techniques and simulation based global dynamic response optimization of fuzzy clustering, and so on.
Firstly, a parallel processing and scheduling strategy of SQP algorithm in simulation optimization are studied. We propose the abstract scheduling model in parallel optimization problem:a discrete variable optimization model with equality constraints. The thorough theoretical feasibility of parallel algorithm is deeply discussed. The parallel task dispatch is implemented by the centralized dynamic load balancing technology and the work pond. The efficiency of SQP optimization of parallel technique is proved by an example of the dynamic response optimization of control parameters of a simple F14 aircraft model.
Secondly, the optimization design of systems for dynamic response based on temporal spectral element is studied. This paper makes further exploration of how to discrete-time dynamic response, to convert the movement differential equations into algebraic equations, to obtain exact solutions of transient response, and processes the constraints related to the time using GLL points method and key-point method. The optimization example of spring shock absorber of linear 1-DOF, the spring shock absorber of linear 2-DOF and automotive suspension system of 5-DOF are given, the introduction of artificial design variable, a detailed analysis of the advantages and disadvantages for two methods to deal with constraints of, but also shows the correctness of this method. These can provide a reference to be further optimized dynamic response, such as the dynamic optimization design of the rectangular variable cross-section beam bearing vibration at the fixed end, the dynamic response optimization design of the elastic beam bearing uniform transient load of vertical plane at the different boundary conditions and so on.
Thirdly, MARS based dynamic response optimization is studies, which combines the global response surface (GRS) based multivariate adaptive regression splines (MARS) with Move-Limit strategy (MLS) and combines augmented Lagrangian method, trust region method and data driven by using characteristics of MARS. MARS is an adaptive regression process, which fits in with the multidimensional problems. And it adopts a modified recursive partitioning strategy to simplify high-dimensional problems into smaller yet highly accurate models. MLS for moving and resizing the search sub-regions is employed in the space of design variables. The quality of the approximation functions and the convergence history of the optimization process are reflected in MLS. The disadvantages of the conventional response surface method (RSM) have been avoided, specifically, highly nonlinear high-dimensional problems. The method is applied to a high-dimensional test function and an engineering problem and ANSYS based tapered beam shape optimization problem, and compared with quadratic response surface (QRS) models in terms of computational efficiency and accuracy. And calculating examples of the linear 2-DOF spring shock absorber suspension design and 5-DOF vehicle dynamic response optimization problems are given to illustrate its feasibility and convergence.
A data driven based optimization approach combines augmented Lagrangian method, MARS with effective data processing. In the approach, an expensive simulation run is required if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations have been performed. Combining the local response surface of MARS and augmented Lagrangian method improve sequential approximation optimization and reduce simulation times by effective data processing, yet maintain a low computational cost. The approach is applied to a ten dimensional engineering problem, the linear 2-DOF spring shock absorber suspension design and 5-DOF vehicle dynamic response optimization problems to demonstrate its feasibility and convergence and the data provided in literature are compared.
Finally, fuzzy clustering applied in simulation based dynamic response of global optimization, which gets better result. The approximate model substitutes for the computation-intensive analysis and simulation, which result in fast calculation. The sampling locations determined by fuzzy clustering and the subregion size determined by the iterative results of the latest two events. Simulation and Evaluation of the objective function and constrained functions were implemented after the sampling subregion determined. Then, Kriging response surface was structured and fuzzy clustering was implemented, which were not repeated until the convergence. In the fuzzy clustering based global optimization, three clustering center are used in each iteration, which showed a better effect. Three clustering center may include the optimum points or its nearby points. The geometric center is obtained from the cluster centers, and Sort Descending is implemented which minimum value is the subregion center. The proposed algorithm is tested using 10 benchmark global optimization problems and linear single degree of freedom vibration absorber, and the GA, SA, PSO and MPS algorithms are compared to prove its accuracy, robustness. The number of simulation of Expensive black box functions significantly is significantly reduced.
首先,研究了仿真优化中SQP算法的并行处理与调度策略,提出了SQP并行优化调度策略的抽象调度模型即等式约束离散变量优化模型,从理论上探讨了并行化处理与调度策略的可行性；通过工作池,应用集中式动态负载平衡技术实现并行任务调度。以F14战斗机简易模型动态响应的控制参数优化为例,验证了本方法的有效性。
其次,研究了基于时间谱元法的系统动态响应优化算法。深入分析了在时间域内离散动态响应,将运动微分方程或方程组转化成代数方程组,精确解出瞬态响应,改善了传统求解动态响应时误差大的缺点,达到谱收敛精度。用高斯-洛巴托-勒让德点法(GLL)和关键点法(KPM)处理时间约束。这样,动态响应优化算法就可以在超曲线或超曲面上找到满足所有时间约束的变化的目标函数。以线性单自由度吸振器设计、线性2自由度弹簧减振器设计和线性5自由度汽车悬挂系统设计为例,引入人工设计变量,详细分析了两种处理约束方法的优缺点,也说明了此方法的正确性。这些内容可为进一步研究动态响应优化提供参考,如在固定端承受振动输入的矩形变截面梁的动态响应优化设计,在不同边界条件下承受垂直平面均布瞬态动载荷作用的弹性梁的动态响应优化设计等。
第三,利用多变量自适应回归样条(MARS)的特点,提出了结合移动极限策略和置信域方法以及数据驱动且适合基于计算昂贵的黑箱仿真模型的动态响应优化算法。MARS是一个自适应的回归过程,采用了将高维问题简化为低维高精度模型的修改回归分块策略。MLS是在设计空间确定子区间的位置和大小,其不仅反映了函数近似质量,而且反映了优化过程的收敛历史。应用MARS的目的是减小了传统响应面的不利因素,特别是对于高维非线性问题。以高维函数和高维工程问题为例进行测试,结果表明了该方法的可行性和有效性,并且和二次响应面(QRS)在计算效率和精度方面进行了比较。还测试了调用仿真器ANSYS的变截面悬臂梁外形形状优化的问题,并与基于SQP的仿真优化进行了比较；测试了线性2自由度弹簧减振器设计问题和5自由度汽车悬挂系统动态响应优化设计问题,结果说明了移动极限策略和MARS响应而结合的优越性。
将MARS、数据驱动、置信域法(TRM)与增广拉格朗日方法相结合起来研究动态响应优化算法。当最优点在数据库中或者有很近的点在数据库中时,将用数据库中的点对应的目标函数和约束函数的值代替最优点的目标函数和约束函数的值,而不需要再进行计算昂贵的仿真分析,如果不存在这样的点,只能通过计算昂贵的仿真分析获得最优点的目标函数和约束函数的值。随着优化的进行,数据库越来越成熟,这样更加有利于建立精确的响应面并且快速找到全局最优点。以一个10维工程问题以及线性2自由度弹簧减振器设计和5自由度汽车悬挂系统动态响应优化设计问题为例进行测试,测试结果与文献中提供的数据进行了比较,证明了此方法的可行性和有效性。
最后,首次将模糊聚类应用于基于仿真模型的全局动态响应优化中,并且取得很好的效果。用近似模型代替密集计算进行分析和仿真,计算速度快。模糊聚类确定采样子区间的位置,最近两次迭代结果决定采样子区域的大小。确定了要采样的子区间后小样本采样,仿真评估目标函数及约束函数,然后构造全局Kriging响应面,再在整个设计域内大样本采样,之后仿真评估全局Kriging响应面,将仿真结果模糊聚类,再确定下一次迭代的子区问,反复迭代直到收敛。在模糊聚类全局动态响应优化中,每一次迭代采用3个聚类中心和它们的几何中心效果较好,这3个中心就是局部最优点或者其附近点,这3个聚类中心的几何中心有更大的概率成为最优点；排序这4个点的函数值,将函数值最小值的点作为本次迭代的最优点。以10个标准全局优化问题和1个线性单自由度吸振器设计问题为例进行测试,并与遗传算法(GA),模拟退火算法(SA),粒子群算法(PSO)和模式追踪算法(MPS)进行比较,证明该方法的精确性和鲁棒性,更重要的是明显减少了昂贵黑箱函数的仿真评估次数。
Supported by the National "863" High-Tech Development Project of China under the grant No.2006AA04Z121 and National Natural Science Fund under the grant No.50775084, the simulation model based dynamic response optimization methods have been studied, which focus on dynamic response optimization problems and parallel processing, time spectral element method based on the dynamic response optimization, MARS based dynamic response optimization techniques and simulation based global dynamic response optimization of fuzzy clustering, and so on.
Firstly, a parallel processing and scheduling strategy of SQP algorithm in simulation optimization are studied. We propose the abstract scheduling model in parallel optimization problem:a discrete variable optimization model with equality constraints. The thorough theoretical feasibility of parallel algorithm is deeply discussed. The parallel task dispatch is implemented by the centralized dynamic load balancing technology and the work pond. The efficiency of SQP optimization of parallel technique is proved by an example of the dynamic response optimization of control parameters of a simple F14 aircraft model.
Secondly, the optimization design of systems for dynamic response based on temporal spectral element is studied. This paper makes further exploration of how to discrete-time dynamic response, to convert the movement differential equations into algebraic equations, to obtain exact solutions of transient response, and processes the constraints related to the time using GLL points method and key-point method. The optimization example of spring shock absorber of linear 1-DOF, the spring shock absorber of linear 2-DOF and automotive suspension system of 5-DOF are given, the introduction of artificial design variable, a detailed analysis of the advantages and disadvantages for two methods to deal with constraints of, but also shows the correctness of this method. These can provide a reference to be further optimized dynamic response, such as the dynamic optimization design of the rectangular variable cross-section beam bearing vibration at the fixed end, the dynamic response optimization design of the elastic beam bearing uniform transient load of vertical plane at the different boundary conditions and so on.
Thirdly, MARS based dynamic response optimization is studies, which combines the global response surface (GRS) based multivariate adaptive regression splines (MARS) with Move-Limit strategy (MLS) and combines augmented Lagrangian method, trust region method and data driven by using characteristics of MARS. MARS is an adaptive regression process, which fits in with the multidimensional problems. And it adopts a modified recursive partitioning strategy to simplify high-dimensional problems into smaller yet highly accurate models. MLS for moving and resizing the search sub-regions is employed in the space of design variables. The quality of the approximation functions and the convergence history of the optimization process are reflected in MLS. The disadvantages of the conventional response surface method (RSM) have been avoided, specifically, highly nonlinear high-dimensional problems. The method is applied to a high-dimensional test function and an engineering problem and ANSYS based tapered beam shape optimization problem, and compared with quadratic response surface (QRS) models in terms of computational efficiency and accuracy. And calculating examples of the linear 2-DOF spring shock absorber suspension design and 5-DOF vehicle dynamic response optimization problems are given to illustrate its feasibility and convergence.
A data driven based optimization approach combines augmented Lagrangian method, MARS with effective data processing. In the approach, an expensive simulation run is required if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations have been performed. Combining the local response surface of MARS and augmented Lagrangian method improve sequential approximation optimization and reduce simulation times by effective data processing, yet maintain a low computational cost. The approach is applied to a ten dimensional engineering problem, the linear 2-DOF spring shock absorber suspension design and 5-DOF vehicle dynamic response optimization problems to demonstrate its feasibility and convergence and the data provided in literature are compared.
Finally, fuzzy clustering applied in simulation based dynamic response of global optimization, which gets better result. The approximate model substitutes for the computation-intensive analysis and simulation, which result in fast calculation. The sampling locations determined by fuzzy clustering and the subregion size determined by the iterative results of the latest two events. Simulation and Evaluation of the objective function and constrained functions were implemented after the sampling subregion determined. Then, Kriging response surface was structured and fuzzy clustering was implemented, which were not repeated until the convergence. In the fuzzy clustering based global optimization, three clustering center are used in each iteration, which showed a better effect. Three clustering center may include the optimum points or its nearby points. The geometric center is obtained from the cluster centers, and Sort Descending is implemented which minimum value is the subregion center. The proposed algorithm is tested using 10 benchmark global optimization problems and linear single degree of freedom vibration absorber, and the GA, SA, PSO and MPS algorithms are compared to prove its accuracy, robustness. The number of simulation of Expensive black box functions significantly is significantly reduced.
引文
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