基于一阶优化算法和响应面算法的有限元模型修正方法研究

发布时间：2018-01-08 20:29

本文关键词：基于一阶优化算法和响应面算法的有限元模型修正方法研究　出处：《长安大学》2015年硕士论文　论文类型：学位论文

【摘要】：尽管在过去20多年间有限元修正的技术得到了广泛的研究和应用,但是到目前为止,由于人们认识水平、测量技术与实际条件的原因,使得在有限元模型修正过程中出现一些问题,例如收敛速度慢、修正参数过多、计算量大等。基于此,探索研究更加可靠有效的有限元模型修正的方法仍然具有深远意义。本文就桥梁结构有限元模型修正方法进行了研究,主要工作有:(1)基于一数值梁,运用ANSYS自带的一阶优化算法,进行了有限元模型修正的过程。采用刚度折减的方式模拟已有损伤的梁结构作为实际梁,通过此“实际梁”得到的模态频率与无损情况的梁结构计算得到的模态频率逼近,得到优化结果,包括修正参数值、目标函数收敛曲线。在修正参数选取过程中,运用ANSYS自带的灵敏度分析模块得到对目标函数影响显著的修正参数,避免由于靠经验选取导致修正参数过多而带来的计算量大的问题。为了证实一阶优化算法在应用上的可靠性,选取了美国佛罗里达大学一框架梁UCF,之所以选取此梁,是因为这个桥梁试验模型的测试结果已经得到了学者的广泛认可。以UCF梁的试验模型为基础,建立相应的有限元模型,并通过修正参数选取、灵敏度分析、模型修正等过程的实现,证明了一阶优化算法的可靠性和有效性。(2)为了探索收敛速度快、计算量小的有限元模型修正方法,选取结合了数学方法与统计学方法的响应面法。同样选取了与一阶优化算法相同的数值梁和UCF梁进行了模型修正的过程。借用ANSYS计算得到响应特征值完成因子设计表,经过分析设计表得到pareto图从而确定修正参数,与一阶优化算法得到的结果一致,验证了响应面方法的可靠性。采用MINITAB软件建立响应面模型,运用最优化理论对得到的响应面模型进行迭代优化。(3)在数值梁和UCF梁的基础上,将一阶优化算法与响应面法计算得到的结果进行比较,在修正参数的确定上,两种方法得到的结果是一致的;在目标函数的收敛图上可以看出,基于响应面法的有限元模型修正收敛速度更快效率更高,基于一阶优化算法的修正,目标函数也得到了收敛只是相比响应面法不够快。综上所述,两种方法在有限元模型修正方面的实用性是可靠的,均可以用于工程实际应用;响应面法在收敛速度和效率上更有优势,能够有效的减少计算量并缩短收敛时间,可以用于复杂的大型工程结构。
[Abstract]:Although the technology of finite element correction has been widely studied and applied in the past 20 years, up to now, because of the level of people's understanding, the reason of measuring technology and actual condition. It causes some problems in the process of finite element model modification, such as slow convergence rate, too many correction parameters, large amount of calculation and so on. It is still of great significance to explore a more reliable and effective finite element model correction method. In this paper, the finite element model modification method for bridge structure is studied. The main work is: 1) based on a numerical beam. The process of finite element model modification is carried out by using ANSYS's own first-order optimization algorithm. The method of stiffness reduction is used to simulate the existing damaged beam structure as the actual beam. The modal frequency obtained from the "actual beam" is approximated to the modal frequency obtained by the calculation of the non-destructive beam structure, and the optimization results are obtained, including the modified parameter values. Objective function convergence curve. In the process of selecting the correction parameters, the sensitivity analysis module of ANSYS is used to get the correction parameters which have a significant impact on the objective function. In order to verify the reliability of the first-order optimization algorithm, a frame beam UCF is selected. This beam is chosen because the test results of the bridge test model have been widely accepted by scholars. Based on the experimental model of UCF beam, the corresponding finite element model is established. It is proved that the reliability and validity of the first-order optimization algorithm is fast in order to explore the convergence speed through the implementation of the process of parameter selection, sensitivity analysis, model modification and so on. The finite element model correction method with little computation. The response surface method (RSM), which combines mathematical method with statistical method, is selected. Numerical beam and UCF beam, which are the same as first-order optimization algorithm, are also selected to modify the model. The response characteristics are obtained by using ANSYS calculation. Value completion factor design table. The pareto diagram is obtained by analyzing the design table to determine the modified parameters, which is consistent with the results obtained by the first-order optimization algorithm. The reliability of the response surface method is verified. The response surface model is established by using MINITAB software. On the basis of numerical beam and UCF beam, the first order optimization algorithm is compared with the result obtained by response surface method. In the determination of the modified parameters, the results obtained by the two methods are consistent. From the convergence diagram of the objective function, it can be seen that the finite element model based on response surface method is faster and more efficient, and based on the first order optimization algorithm. The convergence of objective function is not fast enough compared with the response surface method. In conclusion, the two methods are reliable in the finite element model modification and can be used in engineering practice. Response surface method (RSM) has more advantages in convergence speed and efficiency. It can effectively reduce the computational cost and shorten the convergence time. It can be used in complex large engineering structures.
【学位授予单位】：长安大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U441

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