结构时域辨识方法及传感器优化布置问题研究

发布时间：2018-08-16 15:08

【摘要】：对重要土木工程结构进行健康监测和状态评估,是当前世界范围内的热点课题；而包括参数识别与荷载识别两类逆问题在内的结构动力学系统辨识技术,是结构健康监测与状态评估理论的核心内容。近几十年来,国内外学者在这一领域开展了大量研究工作,提出了许多理论与算法,主要分为频域法、时域法以及在此基础上发展出来的其他方法。与频域法相比,时域法直接利用时域信号进行辨识,在工程实际应用中更为方便,所以近年来得到广泛关注,取得大量研究成果。然而,受结构复杂性及环境干扰等因素的影响和制约,这些成果在实际应用中还存在一些有待解决的问题,如输出数据的不完备性、测量噪声和模型误差等的不确定性以及逆问题的不适定性等,都会对辨识精度产生不利影响。此外,系统辨识之前需要对结构进行动力测试,但测试传感器只能布设在有限结构位置上,传感器布置的合理与否会对辨识结果产生重要影响。针对上述问题,本文开展了时域系统辨识问题的算法优化及传感器优化布置方法的研究。论文的主要工作和取得的成果如下： (1)基于时域动态荷载识别方程的不适定分析,从识别方程的性态出发,提出了一种新的传感器优化布置准则——最小不适定性准则,并基于该准则提出了两种传感器数目确定条件下的位置优化方法：一种是基于结构系统马尔科夫参数矩阵条件数的直接算法,其缺点是当可能的传感器组合数目较大时,计算较为耗时：另一种是基于马尔科夫参数矩阵相关性分析的快速算法,定义了可以描述马尔科夫参数矩阵性态的相关性矩阵及传感器布置的优化指标。数值模拟结果表明,由两种传感器优化布置方法确定的最优传感器布置均可获得稳定性好、计算精度高的荷载识别结果,可用于解决时域动态荷载识别的传感器优化布置问题；随着备选传感器组合数目的增加,直接算法的计算时长会显著增加,而快速算法几乎不变,计算效率明显占优。 (2)基于转换矩阵的概念,将动态荷载识别的状态空间法拓展成了外界激励未知条件下的结构时域响应重构方法,仅利用部分测点的动态响应,通过转换矩阵重构出其他未测试位置处的响应,可用于解决时域辨识中输出数据不完备的问题。此外,还提出了一种传感器两步布设法：第一步,以重构方程具有稳定解为目标,基于单边Jacobi变换法和QR正交三角分解对全部备选测点对应的马尔科夫参数矩阵进行奇异值分解,将非零奇异值对应的传感器位置作为初始传感器布置；第二步,采用逐步积累法,以噪声效应放大指标最小为目标,在初始布置的基础上逐步增加传感器,直至达到收敛要求后获得最终传感器布置。数值模拟结果表明,该方法可根据工程实际需要,在保证重构方程具有稳定解的前提下,灵活确定最终传感器布置,获得所需的重构精度。 (3)针对振动响应灵敏度损伤识别方法,提出了一种修正Tikhonov正则化方法,可用于解决同时考虑测量噪声和模型误差干扰的条件下,传统Tikhonov正则化解不易收敛的问题。首先,对边界约束实施阈值控制,以保证解的物理意义;其次,对确定正则化参数的L-曲线方法进行修正；再次,对测量响应进行切比雪夫多项式去噪处理,减小噪声对识别结果的不利影响。数值模拟结果表明,当同时考虑噪声干扰和模型误差时,修正Tikhonov正则化方法可以使待识别的结构刚度参数逐渐收敛到一个相对正确的路径上,其损伤识别精度明显优于传统正则化方法。 (4)针对振动响应灵敏度损伤识别方法,提出了一种基于多重优化目标的传感器优化布置方法。首先,推导了结构刚度差异参数对三种典型不确定性因素——模型误差、测量噪声和荷载误差的灵敏度,进而得到不同因素所对应的识别误差协方差矩阵；然后,基于识别误差最小准则,定义了考虑多重不确定性因素的目标函数,并采用启发式搜索算法,获得了多重优化目标问题的Pareto最优解。数值模拟结果表明,考虑多重不确定性因素的条件下,由该方法确定的最优传感器布置,其损伤识别的准确性和可靠性均比较高。
[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.
【学位授予单位】：北京交通大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TU317

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