【摘要】：對(duì)重要土木工程結(jié)構(gòu)進(jìn)行健康監(jiān)測(cè)和狀態(tài)評(píng)估,是當(dāng)前世界范圍內(nèi)的熱點(diǎn)課題；而包括參數(shù)識(shí)別與荷載識(shí)別兩類逆問題在內(nèi)的結(jié)構(gòu)動(dòng)力學(xué)系統(tǒng)辨識(shí)技術(shù),是結(jié)構(gòu)健康監(jiān)測(cè)與狀態(tài)評(píng)估理論的核心內(nèi)容。近幾十年來(lái),國(guó)內(nèi)外學(xué)者在這一領(lǐng)域開展了大量研究工作,提出了許多理論與算法,主要分為頻域法、時(shí)域法以及在此基礎(chǔ)上發(fā)展出來(lái)的其他方法。與頻域法相比,時(shí)域法直接利用時(shí)域信號(hào)進(jìn)行辨識(shí),在工程實(shí)際應(yīng)用中更為方便,所以近年來(lái)得到廣泛關(guān)注,取得大量研究成果。然而,受結(jié)構(gòu)復(fù)雜性及環(huán)境干擾等因素的影響和制約,這些成果在實(shí)際應(yīng)用中還存在一些有待解決的問題,如輸出數(shù)據(jù)的不完備性、測(cè)量噪聲和模型誤差等的不確定性以及逆問題的不適定性等,都會(huì)對(duì)辨識(shí)精度產(chǎn)生不利影響。此外,系統(tǒng)辨識(shí)之前需要對(duì)結(jié)構(gòu)進(jìn)行動(dòng)力測(cè)試,但測(cè)試傳感器只能布設(shè)在有限結(jié)構(gòu)位置上,傳感器布置的合理與否會(huì)對(duì)辨識(shí)結(jié)果產(chǎn)生重要影響。 針對(duì)上述問題,本文開展了時(shí)域系統(tǒng)辨識(shí)問題的算法優(yōu)化及傳感器優(yōu)化布置方法的研究。論文的主要工作和取得的成果如下： (1)基于時(shí)域動(dòng)態(tài)荷載識(shí)別方程的不適定分析,從識(shí)別方程的性態(tài)出發(fā),提出了一種新的傳感器優(yōu)化布置準(zhǔn)則——最小不適定性準(zhǔn)則,并基于該準(zhǔn)則提出了兩種傳感器數(shù)目確定條件下的位置優(yōu)化方法：一種是基于結(jié)構(gòu)系統(tǒng)馬爾科夫參數(shù)矩陣條件數(shù)的直接算法,其缺點(diǎn)是當(dāng)可能的傳感器組合數(shù)目較大時(shí),計(jì)算較為耗時(shí)：另一種是基于馬爾科夫參數(shù)矩陣相關(guān)性分析的快速算法,定義了可以描述馬爾科夫參數(shù)矩陣性態(tài)的相關(guān)性矩陣及傳感器布置的優(yōu)化指標(biāo)。數(shù)值模擬結(jié)果表明,由兩種傳感器優(yōu)化布置方法確定的最優(yōu)傳感器布置均可獲得穩(wěn)定性好、計(jì)算精度高的荷載識(shí)別結(jié)果,可用于解決時(shí)域動(dòng)態(tài)荷載識(shí)別的傳感器優(yōu)化布置問題；隨著備選傳感器組合數(shù)目的增加,直接算法的計(jì)算時(shí)長(zhǎng)會(huì)顯著增加,而快速算法幾乎不變,計(jì)算效率明顯占優(yōu)。 (2)基于轉(zhuǎn)換矩陣的概念,將動(dòng)態(tài)荷載識(shí)別的狀態(tài)空間法拓展成了外界激勵(lì)未知條件下的結(jié)構(gòu)時(shí)域響應(yīng)重構(gòu)方法,僅利用部分測(cè)點(diǎn)的動(dòng)態(tài)響應(yīng),通過轉(zhuǎn)換矩陣重構(gòu)出其他未測(cè)試位置處的響應(yīng),可用于解決時(shí)域辨識(shí)中輸出數(shù)據(jù)不完備的問題。此外,還提出了一種傳感器兩步布設(shè)法：第一步,以重構(gòu)方程具有穩(wěn)定解為目標(biāo),基于單邊Jacobi變換法和QR正交三角分解對(duì)全部備選測(cè)點(diǎn)對(duì)應(yīng)的馬爾科夫參數(shù)矩陣進(jìn)行奇異值分解,將非零奇異值對(duì)應(yīng)的傳感器位置作為初始傳感器布置；第二步,采用逐步積累法,以噪聲效應(yīng)放大指標(biāo)最小為目標(biāo),在初始布置的基礎(chǔ)上逐步增加傳感器,直至達(dá)到收斂要求后獲得最終傳感器布置。數(shù)值模擬結(jié)果表明,該方法可根據(jù)工程實(shí)際需要,在保證重構(gòu)方程具有穩(wěn)定解的前提下,靈活確定最終傳感器布置,獲得所需的重構(gòu)精度。 (3)針對(duì)振動(dòng)響應(yīng)靈敏度損傷識(shí)別方法,提出了一種修正Tikhonov正則化方法,可用于解決同時(shí)考慮測(cè)量噪聲和模型誤差干擾的條件下,傳統(tǒng)Tikhonov正則化解不易收斂的問題。首先,對(duì)邊界約束實(shí)施閾值控制,以保證解的物理意義;其次,對(duì)確定正則化參數(shù)的L-曲線方法進(jìn)行修正；再次,對(duì)測(cè)量響應(yīng)進(jìn)行切比雪夫多項(xiàng)式去噪處理,減小噪聲對(duì)識(shí)別結(jié)果的不利影響。數(shù)值模擬結(jié)果表明,當(dāng)同時(shí)考慮噪聲干擾和模型誤差時(shí),修正Tikhonov正則化方法可以使待識(shí)別的結(jié)構(gòu)剛度參數(shù)逐漸收斂到一個(gè)相對(duì)正確的路徑上,其損傷識(shí)別精度明顯優(yōu)于傳統(tǒng)正則化方法。 (4)針對(duì)振動(dòng)響應(yīng)靈敏度損傷識(shí)別方法,提出了一種基于多重優(yōu)化目標(biāo)的傳感器優(yōu)化布置方法。首先,推導(dǎo)了結(jié)構(gòu)剛度差異參數(shù)對(duì)三種典型不確定性因素——模型誤差、測(cè)量噪聲和荷載誤差的靈敏度,進(jìn)而得到不同因素所對(duì)應(yīng)的識(shí)別誤差協(xié)方差矩陣；然后,基于識(shí)別誤差最小準(zhǔn)則,定義了考慮多重不確定性因素的目標(biāo)函數(shù),并采用啟發(fā)式搜索算法,獲得了多重優(yōu)化目標(biāo)問題的Pareto最優(yōu)解。數(shù)值模擬結(jié)果表明,考慮多重不確定性因素的條件下,由該方法確定的最優(yōu)傳感器布置,其損傷識(shí)別的準(zhǔn)確性和可靠性均比較高。
[Abstract]:Health monitoring and state assessment of important civil engineering structures is a hot topic in the world at present. Structural dynamic system identification technology, including parameter identification and load identification inverse problems, is the core content of structural health monitoring and state assessment theory. A great deal of research work has been done in the domain, and many theories and algorithms have been put forward, which are mainly divided into frequency domain method, time domain method and other methods developed on this basis. However, due to the influence and restriction of structural complexity and environmental disturbance, there are still some unsolved problems in practical applications, such as incompleteness of output data, uncertainty of measurement noise and model error, and ill-posedness of inverse problems, which will have adverse effects on identification accuracy. The dynamic test of the structure is necessary before the identification of the system, but the test sensors can only be located in a limited position of the structure. The reasonable arrangement of the sensors will have an important impact on the identification results.
In view of the above problems, this paper carries out the research on algorithm optimization and sensor optimal placement of time-domain system identification problems.
(1) Based on the ill-posed analysis of the time-domain dynamic load identification equation, a new optimal sensor placement criterion, the minimum ill-posed criterion, is proposed from the properties of the identification equation. Based on this criterion, two optimal methods for locating sensors under certain number of sensors are proposed: one is based on the Markov parameters of the structural system. The disadvantage of the direct algorithm of the conditional number of the number matrix is that it is time-consuming when the number of possible sensor combinations is large. The other is a fast algorithm based on the correlation analysis of the Markov parameter matrix. The correlation matrix which can describe the performance of the Markov parameter matrix and the optimization index of the sensor arrangement are defined. The results show that the optimal sensor placement determined by the two optimal sensor placement methods can obtain good stability and high precision load identification results, which can be used to solve the problem of optimal sensor placement for time domain dynamic load identification. The fast algorithm is almost unchanged, and the computational efficiency is obviously superior.
(2) Based on the concept of transition matrix, the state space method for dynamic load identification is extended to the time domain response reconstruction method under the condition of unknown external excitation. By using only the dynamic response of some measuring points, the response of other unmeasured locations is reconstructed from the transition matrix, which can be used to solve the problem of incomplete output data in time domain identification. In addition, a two-step sensor placement method is proposed. In the first step, the singular value decomposition (SVD) of the Markov parameter matrices corresponding to all candidate points is performed based on unilateral Jacobi transform and QR orthogonal trigonometric decomposition (QR orthogonal trigonometric decomposition) with the goal of stabilizing the reconstructed equation. In the second step, with the objective of minimizing the amplification index of noise effect, the sensor is added gradually on the basis of the initial arrangement until the final arrangement is achieved. The final sensor layout is determined and the required reconfiguration accuracy is obtained.
(3) A modified Tikhonov regularization method is proposed to solve the problem that the traditional Tikhonov regularization method is not easy to converge under the condition that both measurement noise and model error are taken into account. The L-curve method with regularization parameters is modified. Thirdly, the measured response is denoised by Chebyshev polynomial to reduce the adverse effects of noise on the identification results. The numerical simulation results show that the modified Tikhonov regularization method can make the structural stiffness parameters to be identified one by one when both noise interference and model error are considered. It gradually converges to a relatively correct path, and its damage identification accuracy is much better than that of the traditional regularization method.
(4) An optimal sensor placement method based on multi-objective optimization is proposed for the damage identification method of vibration response sensitivity. Firstly, the sensitivity of structural stiffness difference parameters to three typical uncertainties-model error, measurement noise and load error is deduced, and then the identification error corresponding to different factors is obtained. Then, based on the identification error minimization criterion, the objective function considering multiple uncertainties is defined, and the Pareto optimal solution of the multiple optimization objective problem is obtained by using a heuristic search algorithm. The accuracy and reliability of damage identification are relatively high.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2013
【分類號(hào)】：TU317

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本文編號(hào)：2186353