本文選題：不確定性分析 + 資料同化��； 參考：《南京信息工程大學(xué)》2017年碩士論文

【摘要】：在優(yōu)化設(shè)計、優(yōu)化控制和反問題應(yīng)用中,人們常采用模型降階方法來構(gòu)造低自由度下大規(guī)模動力系統(tǒng)的降階模型,從而滿足在保證一定物理精度的同時提高計算效率的要求.特征正交分解法(Proper orthogonal decomposition, POD)由于其恢復(fù)數(shù)值信息的能力而成為最常用的模型降階方法之一.本論文首先針對一個典型的耦合Burgers方程,通過POD方法構(gòu)造其在Galerkin投影下的降階模型(Reduced-order model, ROM),并引入離散經(jīng)驗插值法(Discrete empirical interpolation method, DEIM)來減少降階模型中非線性項的計算復(fù)雜性.數(shù)值求解離散化以及對POD模的部分截斷會給降階模型的數(shù)值解精度帶來不可避免的損失.在提高數(shù)值精度和維持穩(wěn)定性方面增加POD模數(shù)的確會在一定程度上發(fā)揮一定作用,但這會增加計算負擔(dān).因此本論文發(fā)展了一個訂正的POD降階模型,它通過對POD降階模型分別乘以和加上一組依賴時間的不確定性參數(shù)構(gòu)造而成.這樣訂正降階模型就轉(zhuǎn)化為高維隨機空間中的參數(shù)識別問題.反問題的不適定特征使得相關(guān)計算過程具有一定的挑戰(zhàn)性.這種情況下,我們采用了基于多項式逼近的集合卡爾曼濾波(Polynomial chaos-based ensemble Kalman Filter, PC-EnKF)方法來處理以上問題,同時引入稀疏化算法來識別出模式輸入和模式輸出PC展開式中系數(shù)近乎為零的基函數(shù),這對集合卡爾曼濾波(EnKF)所需統(tǒng)計矩的快速計算是有幫助的.利用最終更新過的輸入?yún)?shù),大雷諾數(shù)Re=10000情況下耦合Burger方程的訂正POD降階模型即被建立起來.數(shù)值實驗表明PC-EnKF方法在恢復(fù)求解精度方面是有效的,在訂正動力系統(tǒng)數(shù)值解方面是可行性.PC-EnKF方法可作為一個一般的模型訂正工具,在當(dāng)前研究基礎(chǔ)上有希望推廣應(yīng)用于更高維模型訂正問題中.
[Abstract]:In the optimization design, optimization control and inverse problem application, the model reduction method is often used to construct the reduced order model of the large power system under the low degree of freedom, so as to meet the requirement of improving the computational efficiency while ensuring a certain physical precision. The Proper orthogonal decomposition (POD) is due to its recovery number. The ability of value information is one of the most commonly used model reduction methods. Firstly, this paper constructs a reduced order model (Reduced-order model, ROM) under the Galerkin projection for a typical coupled Burgers equation, and introduces the discrete empirical interpolation (Discrete empirical interpolation method, DEIM) to reduce the reduction of order by POD method. The computational complexity of the nonlinear term in the model. The numerical solution dispersion and the partial truncation of the POD model will bring the inevitable loss to the precision of the numerical solution of the reduced order model. The increase of the POD modulus in the improvement of the numerical accuracy and the maintenance of the stability will certainly play a certain role, but this will increase the calculation burden. This paper develops a revised POD order reduction model, which is constructed by multiplying POD reduced order models respectively and adding a set of uncertain parameters with a set of dependent time. The revised reduced order model is transformed into a parameter identification problem in the high dimensional random space. The discomfort characteristics of the inverse problem make the related computing process a certain challenge. In this case, we use the Polynomial chaos-based ensemble Kalman Filter (PC-EnKF) method based on polynomial approximation to deal with the above problems. At the same time, we introduce a sparsity algorithm to identify the base function with a nearly zero coefficient in the mode input and mode output PC expansion, which is for the collection of Calman filters. The fast calculation of the statistical moments needed for the wave (EnKF) is helpful. Using the final updated input parameters, the revised POD reduced order model of the coupled Burger equation with the large Reynolds number Re=10000 is established. The numerical experiments show that the PC-EnKF method is effective in restoring the accuracy of the solution, and it is feasible in the numerical solution of the revised dynamic system. The sex.PC-EnKF method can be used as a general model correction tool. Based on the current research, it is hoped to be applied to the correction of higher dimensional models.
【學(xué)位授予單位】：南京信息工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O241.8

【參考文獻】

相關(guān)博士學(xué)位論文 前1條

1 杜娟;流體力學(xué)方程基于POD方法的降維數(shù)值解法研究[D];北京交通大學(xué);2011年

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本文編號：1953989