本文關(guān)鍵詞：基于一階優(yōu)化算法和響應(yīng)面算法的有限元模型修正方法研究　出處：《長安大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 一階優(yōu)化 響應(yīng)面法 ANSYS 靈敏度分析 有限元模型修正 MINITAB

【摘要】：盡管在過去20多年間有限元修正的技術(shù)得到了廣泛的研究和應(yīng)用,但是到目前為止,由于人們認(rèn)識水平、測量技術(shù)與實際條件的原因,使得在有限元模型修正過程中出現(xiàn)一些問題,例如收斂速度慢、修正參數(shù)過多、計算量大等�；诖�,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遠(yuǎn)意義。本文就橋梁結(jié)構(gòu)有限元模型修正方法進行了研究,主要工作有:(1)基于一數(shù)值梁,運用ANSYS自帶的一階優(yōu)化算法,進行了有限元模型修正的過程。采用剛度折減的方式模擬已有損傷的梁結(jié)構(gòu)作為實際梁,通過此“實際梁”得到的模態(tài)頻率與無損情況的梁結(jié)構(gòu)計算得到的模態(tài)頻率逼近,得到優(yōu)化結(jié)果,包括修正參數(shù)值、目標(biāo)函數(shù)收斂曲線。在修正參數(shù)選取過程中,運用ANSYS自帶的靈敏度分析模塊得到對目標(biāo)函數(shù)影響顯著的修正參數(shù),避免由于靠經(jīng)驗選取導(dǎo)致修正參數(shù)過多而帶來的計算量大的問題。為了證實一階優(yōu)化算法在應(yīng)用上的可靠性,選取了美國佛羅里達(dá)大學(xué)一框架梁UCF,之所以選取此梁,是因為這個橋梁試驗?zāi)Ｐ偷臏y試結(jié)果已經(jīng)得到了學(xué)者的廣泛認(rèn)可。以UCF梁的試驗?zāi)Ｐ蜑榛A(chǔ),建立相應(yīng)的有限元模型,并通過修正參數(shù)選取、靈敏度分析、模型修正等過程的實現(xiàn),證明了一階優(yōu)化算法的可靠性和有效性。(2)為了探索收斂速度快、計算量小的有限元模型修正方法,選取結(jié)合了數(shù)學(xué)方法與統(tǒng)計學(xué)方法的響應(yīng)面法。同樣選取了與一階優(yōu)化算法相同的數(shù)值梁和UCF梁進行了模型修正的過程。借用ANSYS計算得到響應(yīng)特征值完成因子設(shè)計表,經(jīng)過分析設(shè)計表得到pareto圖從而確定修正參數(shù),與一階優(yōu)化算法得到的結(jié)果一致,驗證了響應(yīng)面方法的可靠性。采用MINITAB軟件建立響應(yīng)面模型,運用最優(yōu)化理論對得到的響應(yīng)面模型進行迭代優(yōu)化。(3)在數(shù)值梁和UCF梁的基礎(chǔ)上,將一階優(yōu)化算法與響應(yīng)面法計算得到的結(jié)果進行比較,在修正參數(shù)的確定上,兩種方法得到的結(jié)果是一致的;在目標(biāo)函數(shù)的收斂圖上可以看出,基于響應(yīng)面法的有限元模型修正收斂速度更快效率更高,基于一階優(yōu)化算法的修正,目標(biāo)函數(shù)也得到了收斂只是相比響應(yīng)面法不夠快。綜上所述,兩種方法在有限元模型修正方面的實用性是可靠的,均可以用于工程實際應(yīng)用;響應(yīng)面法在收斂速度和效率上更有優(yōu)勢,能夠有效的減少計算量并縮短收斂時間,可以用于復(fù)雜的大型工程結(jié)構(gòu)。
[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.
【學(xué)位授予單位】：長安大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：U441

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