基于模态观测的结构健康监测的传感器优化布置方法研究
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摘要
传感器优化布置是设计结构健康监测系统的关键问题之一,它对数据采集的有效性有着至关重要的影响。考虑到实际工程场地条件和经济条件等因素,只能在结构有限的位置上布置相对较少的传感器,因此监测传感器的布设应该满足以下两个目标:第一,最大程度地反映结构系统的信息,第二,对结构状态退化足够敏感。本文针对目前土木工程结构健康监测中传感器优化布置存在的若干问题,包括模态可观测性与损伤可识别性的不一致、性能矩阵与优化准则的适应性、反问题的不适定性、选取合适的模态数目、结构反应的敏感性与系统鲁棒性的矛盾、具有扭转自由度的结构传感器优化布置等进行了系统的研究,研究主要包括以下几个方面内容:
一、提出了基于模态可观测性与损伤可识别性相协调的Fisher信息矩阵,并研究了其与优化准则的适应性。首先由结构运动方程出发,考虑损伤导致的结构响应的变化,以近似解析的方式推导出结构响应及振型与损伤灵敏度之间的关系。根据Fisher信息熵原理,建立了同时包含模态振型信息和损伤灵敏度信息的Fisher信息矩阵,并分析了基于振型和基于损伤灵敏度的Fisher信息矩阵与新的Fisher信息矩阵表达式之间的关系。通过三维网架数值算例,探讨了三种Fisher信息矩阵与几种常见的评价准则(条件数最小、范数最大、矩阵的迹最大准则等)之间的适应性问题。
二、建立了结构反应敏感性与系统鲁棒性相协调的优化准则,并发展了一种启发式的搜索算法。传感器优化布置从属于反问题范畴,它的不适定性表现为系数矩阵的病态程度,即条件数的大小。在以往的传感器优化布置研究中,由于矩阵的病态性而造成的不适定性现象并未得到足够重视。如果仅考虑Fisher信息熵最大(本质上反应的是对系统反应的敏感性最强),那么系统识别的控制方程的条件数可能会同时出现较大(即病态性较强)的情况。为了克服以上矛盾,本文建立了使Fisher信息矩阵最大化与系数矩阵条件数最小化相协调的目标函数,并且以Fisher信息矩阵的范数为启发函数,同时以系数矩阵的条件数为代价函数,发展了启发式的传感器测点优化算法。通过数值模拟,比较了本文方法与有效独立法及损伤灵敏度法的传感器测点优化结果以及基于有限模态测试数据的结构损伤识别能力。进一步设计、实施了海底悬跨管线的模型试验,验证了本文方法在实际工程中的可行性。
三、建议了损伤灵敏度中模态数目选取方法及两条评价准则。以结构各自由度的模态信息为条件,计算出结构的Fisher信息矩阵,根据矩阵范数的定义,把Fisher信息矩阵2-范数在前i阶次和前i+1阶次上的变化率作为衡量模态数目影响的指标,通过其变化率曲线来判断模态数目的选取。根据传感器优化前后信息特征和结构损伤识别一致的评价准则,在节点具有两个自由度(二维桁架)、三个自由度(空间网壳)和六个自由度(海底管道)的结构上验证了该方法的有效性和适用性。
四、考虑结构转角信息对传感器优化布置和结构损伤识别的影响,提出了一种考虑扭转自由度的传感器优化布置方法。首先利用IRS缩减法由结构平动反应重构结构转角信息,从而设计一种新的结构反应的性能矩阵,然后结合本文提出的模态数目确定方法,建立了考虑扭转自由度的传感器优化布置方法。海洋平台立管数值算例验证了该法的有效性,而且结构转角信息无重构、Guyan缩减法重构结构转角信息以及IRS缩减法重构结构转角信息对传感器优化布置及损伤识别的影响并不相同,同时Guyan缩减法和IRS缩减法重构结构转角信息的相对误差也存在差异。悬索拱桥的数值算例表明基于IRS缩减法重构结构转角信息的传感器优化布置方法优于经验式方法。
Optimal sensor placement is one of key problems of designing stuctural health monitoring system,because it has an essential effect on the availability of the data collection. Due to field conditions and cost considerations,a given number of sensors are limitted.The goal is to use a minimum number of sensors,placed at the right locations,so that both presence and extent of damage of the structure system can be identified effectively.The author has systematically studied several problems of optimal sensor placement in structural health monitoring,such as the inconsistency between modal observability and damage identifiability,the adaptability of performance matrix and optimization criterion,ill-posed characteristic of system inverse problem,reasonable selection of mode numbers,the contradiction between sensitivity of structural response and system robustness,optimal sensor placement for structures with torsional degrees of freedom.The detail research contents of paper are as follows:
Firstly,a Fisher information matrix(FIM) based on coordination of modal observability and damage identifiability is put forward,and the adaptability of the matrix and optimization criterion is investigated.Considering the structural response changes that result from damage, the relationship between the structural response and damage was deduced from the structural motion equation by a quasi-analytical mode.According to the information entropy,an object function was set up including the information of mode independence and damage sensitivity. Then,the difference between three FIMs is examined by a quasi-analytical mode.In addition, the relation of these matrixes is derived.Numerical example of three-dimensional scaffold is applied to explore the adaptability between the three FIMs and several evaluation criterions.
Secondly,a novel criterion with the sensitivity of structural response and system robustness coordinated and a heuristic search algorithm are developed.In nature,optimal sensor placement for structural damage detection is an inverse problem,which the ill-posed characteristic is manifested as condition number of the identification equation(CNIE).The results of the sensor optimization are dependent upon not only FIM but also CNIE.However, the large CNIE due to the degree-of-freedom(DOF) deletion,which leads to the ill-poseness of the inverse problem,are commonly ignored in previous literatures.The main object of this paper is to develop a novel criterion for sensor optimization that can remedy the ill-poseness due to DOF deletion and simultaneously maintain FIM as maximum as possible.Thus,the optimization criterion of simultaneously maximizing FIM and minimizing CNIE is proposed. And a heuristic search algorithm is developed to delete DOFs until to the given number of the sensors.The proposed approach is numerically studied by Two-dimensional truss structure. The results of sensor placement and structural damage detection are compared with effective independence algorithm and damage sensitivity method.The usefulness and feasibility of the algorithm is illustrated through the dynamic test for free spanning submarine pipeline.
Thirdly,a method of selecting suitable number of modes for damage sensitivity is put forward,and the two corresponding evaluating criterions are established.The rate of change of 2- norm of the FIM between the first i modes and the first i+1 modes is taken as the index of selecting the number of modes,which is described by the rate of change curve chart. According to the two evaluating criterions of the consistency of information feature and the results of damage detection before and after optimal sensor placement,the effectiveness and universality of the method are verified by three numerical examples:two-dimensional truss with two DOFs on node,three-dimensional shell with three DOFs on node,three-dimensional submarine pipleline with six DOFs on node.
Fourthly,considering the effect of structural rotational response on optimum sensor placement and structural damage detection,a method of optimium sensor locations for structures with torsional DOFs is studied.Utlizing the improved reduced system(IRS) method,the rotational response is calculated by the translational response.Then,a new FIM is designed.Finally,combined with the method of selecting mode number,the modified optimum sensor placement method is developed.The riser of offshore platform numerical example shows that the modified method is effective and the influence and relative error of reconstruction of rotational response by the methods of Guyan and IRS are both different.The numerical example of suspension arch bridge shows that the modified optimum sensor placement method based on IRS method is superior to empirical method.
一、提出了基于模态可观测性与损伤可识别性相协调的Fisher信息矩阵,并研究了其与优化准则的适应性。首先由结构运动方程出发,考虑损伤导致的结构响应的变化,以近似解析的方式推导出结构响应及振型与损伤灵敏度之间的关系。根据Fisher信息熵原理,建立了同时包含模态振型信息和损伤灵敏度信息的Fisher信息矩阵,并分析了基于振型和基于损伤灵敏度的Fisher信息矩阵与新的Fisher信息矩阵表达式之间的关系。通过三维网架数值算例,探讨了三种Fisher信息矩阵与几种常见的评价准则(条件数最小、范数最大、矩阵的迹最大准则等)之间的适应性问题。
二、建立了结构反应敏感性与系统鲁棒性相协调的优化准则,并发展了一种启发式的搜索算法。传感器优化布置从属于反问题范畴,它的不适定性表现为系数矩阵的病态程度,即条件数的大小。在以往的传感器优化布置研究中,由于矩阵的病态性而造成的不适定性现象并未得到足够重视。如果仅考虑Fisher信息熵最大(本质上反应的是对系统反应的敏感性最强),那么系统识别的控制方程的条件数可能会同时出现较大(即病态性较强)的情况。为了克服以上矛盾,本文建立了使Fisher信息矩阵最大化与系数矩阵条件数最小化相协调的目标函数,并且以Fisher信息矩阵的范数为启发函数,同时以系数矩阵的条件数为代价函数,发展了启发式的传感器测点优化算法。通过数值模拟,比较了本文方法与有效独立法及损伤灵敏度法的传感器测点优化结果以及基于有限模态测试数据的结构损伤识别能力。进一步设计、实施了海底悬跨管线的模型试验,验证了本文方法在实际工程中的可行性。
三、建议了损伤灵敏度中模态数目选取方法及两条评价准则。以结构各自由度的模态信息为条件,计算出结构的Fisher信息矩阵,根据矩阵范数的定义,把Fisher信息矩阵2-范数在前i阶次和前i+1阶次上的变化率作为衡量模态数目影响的指标,通过其变化率曲线来判断模态数目的选取。根据传感器优化前后信息特征和结构损伤识别一致的评价准则,在节点具有两个自由度(二维桁架)、三个自由度(空间网壳)和六个自由度(海底管道)的结构上验证了该方法的有效性和适用性。
四、考虑结构转角信息对传感器优化布置和结构损伤识别的影响,提出了一种考虑扭转自由度的传感器优化布置方法。首先利用IRS缩减法由结构平动反应重构结构转角信息,从而设计一种新的结构反应的性能矩阵,然后结合本文提出的模态数目确定方法,建立了考虑扭转自由度的传感器优化布置方法。海洋平台立管数值算例验证了该法的有效性,而且结构转角信息无重构、Guyan缩减法重构结构转角信息以及IRS缩减法重构结构转角信息对传感器优化布置及损伤识别的影响并不相同,同时Guyan缩减法和IRS缩减法重构结构转角信息的相对误差也存在差异。悬索拱桥的数值算例表明基于IRS缩减法重构结构转角信息的传感器优化布置方法优于经验式方法。
Optimal sensor placement is one of key problems of designing stuctural health monitoring system,because it has an essential effect on the availability of the data collection. Due to field conditions and cost considerations,a given number of sensors are limitted.The goal is to use a minimum number of sensors,placed at the right locations,so that both presence and extent of damage of the structure system can be identified effectively.The author has systematically studied several problems of optimal sensor placement in structural health monitoring,such as the inconsistency between modal observability and damage identifiability,the adaptability of performance matrix and optimization criterion,ill-posed characteristic of system inverse problem,reasonable selection of mode numbers,the contradiction between sensitivity of structural response and system robustness,optimal sensor placement for structures with torsional degrees of freedom.The detail research contents of paper are as follows:
Firstly,a Fisher information matrix(FIM) based on coordination of modal observability and damage identifiability is put forward,and the adaptability of the matrix and optimization criterion is investigated.Considering the structural response changes that result from damage, the relationship between the structural response and damage was deduced from the structural motion equation by a quasi-analytical mode.According to the information entropy,an object function was set up including the information of mode independence and damage sensitivity. Then,the difference between three FIMs is examined by a quasi-analytical mode.In addition, the relation of these matrixes is derived.Numerical example of three-dimensional scaffold is applied to explore the adaptability between the three FIMs and several evaluation criterions.
Secondly,a novel criterion with the sensitivity of structural response and system robustness coordinated and a heuristic search algorithm are developed.In nature,optimal sensor placement for structural damage detection is an inverse problem,which the ill-posed characteristic is manifested as condition number of the identification equation(CNIE).The results of the sensor optimization are dependent upon not only FIM but also CNIE.However, the large CNIE due to the degree-of-freedom(DOF) deletion,which leads to the ill-poseness of the inverse problem,are commonly ignored in previous literatures.The main object of this paper is to develop a novel criterion for sensor optimization that can remedy the ill-poseness due to DOF deletion and simultaneously maintain FIM as maximum as possible.Thus,the optimization criterion of simultaneously maximizing FIM and minimizing CNIE is proposed. And a heuristic search algorithm is developed to delete DOFs until to the given number of the sensors.The proposed approach is numerically studied by Two-dimensional truss structure. The results of sensor placement and structural damage detection are compared with effective independence algorithm and damage sensitivity method.The usefulness and feasibility of the algorithm is illustrated through the dynamic test for free spanning submarine pipeline.
Thirdly,a method of selecting suitable number of modes for damage sensitivity is put forward,and the two corresponding evaluating criterions are established.The rate of change of 2- norm of the FIM between the first i modes and the first i+1 modes is taken as the index of selecting the number of modes,which is described by the rate of change curve chart. According to the two evaluating criterions of the consistency of information feature and the results of damage detection before and after optimal sensor placement,the effectiveness and universality of the method are verified by three numerical examples:two-dimensional truss with two DOFs on node,three-dimensional shell with three DOFs on node,three-dimensional submarine pipleline with six DOFs on node.
Fourthly,considering the effect of structural rotational response on optimum sensor placement and structural damage detection,a method of optimium sensor locations for structures with torsional DOFs is studied.Utlizing the improved reduced system(IRS) method,the rotational response is calculated by the translational response.Then,a new FIM is designed.Finally,combined with the method of selecting mode number,the modified optimum sensor placement method is developed.The riser of offshore platform numerical example shows that the modified method is effective and the influence and relative error of reconstruction of rotational response by the methods of Guyan and IRS are both different.The numerical example of suspension arch bridge shows that the modified optimum sensor placement method based on IRS method is superior to empirical method.
引文
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