约束子结构模型修正方法
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摘要
结构健康监测是土木结构学科一个研究热点,其中模型修正和损伤识别是结构健康监测的重要理论组成部分。本文针对土木工程中,结构形式复杂、测点少或局部损伤不敏感等问题,提出约束子结构模型修正方法,实现利用少量传感器和局部结构动力响应准确修正识别局部子结构或整体结构。
约束子结构模型修正方法包括两步:第一步构造约束子结构的动力响应,这步是方法的核心;第二步利用经典的模型修正方法,根据构造的动力响应或其模态来修正或识别子结构。根据方法对子结构约束程度的不同,分为完全约束子结构(简称约束子结构)和广义约束子结构:前者是在所关注子结构的边界上布置虚拟支座后,从整体结构中被隔离出来的简单、独立结构;后者虽然并不能将子结构分离出整体,但可以有效地提高子结构的灵敏度,使之更容易修正和识别。
约束子结构的基本构造思想是通过局部子结构响应的卷积组合,使其边界的响应为零(实现将边界传感器模拟为虚拟支座);相应地,子结构内部响应的组合即为约束子结构的响应。根据选用的局部子结构响应的类型和特点,提出以下五种约束子结构模型修正法(简称约束子结构方法):
(1)基于局部模态的约束子结构模型修正方法。利用整体结构低阶模态对应子结构位置的局部元素(局部模态)构造约束子结构的柔度矩阵,然后利用该柔度矩阵修正子结构。该方法首先从静力学的角度提出约束子结构的概念。
(2)基于局部脉冲响应的约束子结构模型修正方法。利用整体结构中局部子结构的脉冲响应直接构造约束子结构的脉冲响应,将方法推广到动态,不但摆脱了局部模态要求振型归一化的限制,而且构造的动力响应往往比静力柔度矩阵包含更丰富的信息,提高修正的精度。并通过进一步理论推导(也适用于下面提出的三种约束子结构方法),对激励类型、激励点位置、虚拟支座形式进行了扩展,以及把方法运用范围扩展到允许子结构外部为非线性的情况,使该方法更容易操作和应用在实际工程中。
(3)基于局部频率响应的约束子结构模型修正方法。该方法把约束子结构方法由时域扩展到频域,利用局部子结构的频率响应构造约束子结构的频率响应,避免了时域方法内大型矩阵求逆中存在的病态问题,提高了计算效率。
(4)联合局部虚拟变形的约束子结构模型修正方法。虚拟变形法(Virtual Distortion Method)是一种结构快速重分析方法,与约束子结构方法相结合,同时利用测量的激励和构造的约束子结构响应在时域里识别子结构,不但加快了优化速度,而且提高了修正精度。
(5)基于局部时间序列的约束子结构模型修正方法。前面提出的几种方法都需要利用测量多组响应来构造约束子结构,而且要求结构的初始状态为零。该方法只需利用一组局部子结构响应的时间序列,通过延时排列的办法构造约束子结构的自由响应。方法应用灵活,操作简单,适用性强,可用于在线的子结构监测。
文中分别利用桁架有限元模型对上述五种方法进行仿真验证。并且,在一个悬臂梁子结构的动态试验中,成功地利用局部脉冲响应、频率响应、联合虚拟变形法、时间序列法构造约束子结构;验证了利用约束子结构方法能剔除子结构以外未知因素(包括子结构外部非线性)的影响,准确地识别子结构的损伤。
子结构边界比较复杂时,其边界运动状态不容易测量,因而难以构造约束子结构。针对此局限,提出广义约束子结构模型修正法。它可以有效地提高子结构灵敏度,使之更容易修正识别。广义约束方法有两种:
(1)基于局部主频率的广义约束子结构模型修正方法。在局部激励的作用下,如果子结构能够主要以单阶子结构变形为主的模态振动,那么对应的该阶频率定义为子结构的局部主频率。局部主频率能更多地反映子结构特性,对子结构损伤的灵敏度高,所以利用局部主频率就可以修正和识别子结构。然而子结构一般并不具有这种性质,为使子结构能具有局部主频率,可以采用以下两种方法:
方法一,在子结构边界附加虚拟支座,增加对子结构边界的约束,减弱其外部构件的影响,从而提高子结构的灵敏度。用此方法有效识别了三层空间框架有限元模型底层柱的损伤。
方法二,在子结构内部附加质量,提高子结构本身的权重来提高子结构灵敏度。通过二十跨空间桁架试验验证了该方法,成功地联合局部主频率和整体结构的低阶频率修正了桁架有限元模型,并进一步准确地识别了杆件损伤。
(2)基于局部虚拟支座的联合约束结构模型修正方法。分别在每个子结构的内部施加虚拟支座,构造广义约束子结构(简称约束结构),使不同约束结构都含有对相应子结构灵敏度较高的低阶频率,继而收集所有这样的模态,联合其来修正整体结构。在数值模拟中,只利用三个传感器的排列组合布置,成功地识别了一个三层空间框架中的所有柱和板的损伤。
Structure Health Monitoring (SHM) is a hot research topic in civil engineering, of which model updating and damage identification are the important theoretical component. In civil engineering, the structures mostly are huge and complex, for which it is hard to obtain the complete measurement, and hence are insensitive to local damages. Aiming at solving these problems, Substructure Isolation Methods are proposed in this paper, which can precisely update or identify the local/global structure by very limited sensors.
Substructure Isolation Methods consist of two main steps: the first one is to construct the dynamic response of the isolated substructure, which is the core idea of the method; then, the classical modal updating techniques are applied to update/identify the concerned substructure via the constructed response. According to the extent of isolation, two kinds of isolated substructures are presented: Complete Isolated Substructure (“Isolated Substructure”for short) and Generalized Isolated Substructure. The former refers to an independent simple structure which is isolated from the global structure by adding virtual support on the boundary of the concerned substructure; while the latter facilitates the updating and identification by effectively increasing the sensitivity to the substructure(“substructure sensitivity”for short), although it can’t be isolated from the global structure completely.
The basic idea of the Isolated Substructure construction is the convolution combination of the local substructural response, which makes its boundary response vanish to zero, that is, the boundary sensors are counted as virtual supports. Correspondingly, the combined response inside the substructural is the constructed response of the Isolated Substructure. Five kinds of Substructure Isolation Methods (SIM) for model updating are proposed as following, which lie on the different characteristics of the considered local substructural responses:
(1) Substructure Isolation and model updating based on local mode. In the low-order global structural modes, the elements which are regard to the degree of freedom of the substructure are defined as the local mode. And then the flexibility matrix of the Isolated Substructure is constructed by the local mode. This approach first proposes the concept of the Substructure Isolation from the static mechanics.
(2) Substructure Isolation and model updating based on local impulse response. In the global structure, the local impulse response of the substructure is used to construct the impulse response of the Isolated Substructure directly, which extends the isolation method to dynamic scope. It overcomes the limitation of normalized mode shape which is required in the method based on local mode. Moreover, the constructed dynamic response contains more useful information than static flexibility matrix. In addition, the theory is extended further to make the proposed isolation methods including the following three dynamic isolation methods, performed easier in the real application, such as the extension of the excitation type, of the excitation placement, as well as the extension of the virtual support type. Besides those extensions, the Substructure Isolation Methods is expanded to allow its application even in case that the elements outside substructure are nonlinear.
(3) Substructure Isolation and model updating based on local frequency response. This approach extends the application of Substructure Isolation Methods from time domain to frequency domain, in which the frequency response of the local substructure is used to construct the frequency response of the Isolated Substructure. In this way, it avoids the ill-conditioning problem which often exists in the calculation of large inverse matrix, and moreover increases the computational efficiency.
(4) Substructure Isolation and model updating Combined with local VDM. VDM (Virtual Distortion Method) belongs to fast structural reanalysis method. The Substructure Isolation Methods combined with VDM allows the substructure identification using simultaneously measured excitation and the constructed response of the Isolated Substructure in time domain. And hence it not only speeds up the optimization but also increases the identification accuracy.
(5) Substructure Isolation and model updating based on local time series. The above proposed methods all require several groups of measurements to construct the Isolated Substructure, and in addition demand the zero initial structural state. This method only needs one group of measured time series of local substructural. The free vibration response of the Isolated Substructure is constructed by a delayed arrangement of the measured time series. The performance of the method is more flexible, easier, practical, and can be used for online local substructural monitoring.
The Truss finite element model is used in this paper respectively to numerically verify the above proposed Isolation Methods. Moreover, a dynamic experiment of a cantilever beam is performed, in which the Isolated Substructure is constructed successfully based on local impulse response, local frequency response, local VDM, and local time series. The experiment validates that the Substructure Isolation Methods can remove the influence of the unknown factors outside the substructure (including the nonlinearity), and thus denitrify the local substructural damage effectively and precisely.
For the substructure with complex boundary, it is hard measure all the boundary states, which are required in construction of the above Isolated Substructure. Aiming at improving the drawbacks, a Generalized Substructure Isolation Method for model updating is proposed which can obviously enhance the substructure sensitivity, and hence facilitate the substructure updating and identification. Two kinds of Generalized Substructure Isolation Method are as following:
(1) Generalized Substructure Isolation and model updating based on Local Primary Frequency. Apply the local excitation on concerned substructure, if the substructure can vibrate mainly at one single model which consist mostly of the substructural distortion, then the corresponding frequency are defined as the substructural Local Primary Frequency, which can reflect more characteristics of the substructure and are more sensitive to the substructural damage. Thus, Local Primary Frequency is enough to be used for substructural updating and identification. However, generally substructures don’t own this character. Two approaches are developed and adopted to make the concerned substructure have its Local Primary Frequency:
Approach I: Virtual supports are applied on the substructural boundary, such that it can raise the constraint on the boundary, and reduce the influence from the elements outside the substructure. In this way, the substructure sensitivity is enhanced. The bottom columns of a three-story space frame structure are testified that damage is identified effectively by this method.
Approach II: Mass are added to the substructure interior, which increases the weighting of the substructure itself and thus enhances its sensitivity. A twenty-span space truss experiment is used to validate the effectiveness of this method, in which the finite element model of the truss is updated successfully by combining the Local Primary Frequency and the low-order mode of the global structure. Using the updated model, the local element damage is further identified accurately.
(2) United Isolated Structure for model updating based on Local Virtual Support. Virtual supports are added respectively inside each substructure to construct the respective Generalized Isolated Substructure (“Isolated Structure”for short). It aims at making each Isolated Structure own the low-order frequencies which are high sensitive to the corresponding substructure. Then all these frequencies are collected and united to update the global structure. A numerical example of a three-story space frame proves that this method can identify damages of all the columns and plates successfully using only three sensors.
约束子结构模型修正方法包括两步:第一步构造约束子结构的动力响应,这步是方法的核心;第二步利用经典的模型修正方法,根据构造的动力响应或其模态来修正或识别子结构。根据方法对子结构约束程度的不同,分为完全约束子结构(简称约束子结构)和广义约束子结构:前者是在所关注子结构的边界上布置虚拟支座后,从整体结构中被隔离出来的简单、独立结构;后者虽然并不能将子结构分离出整体,但可以有效地提高子结构的灵敏度,使之更容易修正和识别。
约束子结构的基本构造思想是通过局部子结构响应的卷积组合,使其边界的响应为零(实现将边界传感器模拟为虚拟支座);相应地,子结构内部响应的组合即为约束子结构的响应。根据选用的局部子结构响应的类型和特点,提出以下五种约束子结构模型修正法(简称约束子结构方法):
(1)基于局部模态的约束子结构模型修正方法。利用整体结构低阶模态对应子结构位置的局部元素(局部模态)构造约束子结构的柔度矩阵,然后利用该柔度矩阵修正子结构。该方法首先从静力学的角度提出约束子结构的概念。
(2)基于局部脉冲响应的约束子结构模型修正方法。利用整体结构中局部子结构的脉冲响应直接构造约束子结构的脉冲响应,将方法推广到动态,不但摆脱了局部模态要求振型归一化的限制,而且构造的动力响应往往比静力柔度矩阵包含更丰富的信息,提高修正的精度。并通过进一步理论推导(也适用于下面提出的三种约束子结构方法),对激励类型、激励点位置、虚拟支座形式进行了扩展,以及把方法运用范围扩展到允许子结构外部为非线性的情况,使该方法更容易操作和应用在实际工程中。
(3)基于局部频率响应的约束子结构模型修正方法。该方法把约束子结构方法由时域扩展到频域,利用局部子结构的频率响应构造约束子结构的频率响应,避免了时域方法内大型矩阵求逆中存在的病态问题,提高了计算效率。
(4)联合局部虚拟变形的约束子结构模型修正方法。虚拟变形法(Virtual Distortion Method)是一种结构快速重分析方法,与约束子结构方法相结合,同时利用测量的激励和构造的约束子结构响应在时域里识别子结构,不但加快了优化速度,而且提高了修正精度。
(5)基于局部时间序列的约束子结构模型修正方法。前面提出的几种方法都需要利用测量多组响应来构造约束子结构,而且要求结构的初始状态为零。该方法只需利用一组局部子结构响应的时间序列,通过延时排列的办法构造约束子结构的自由响应。方法应用灵活,操作简单,适用性强,可用于在线的子结构监测。
文中分别利用桁架有限元模型对上述五种方法进行仿真验证。并且,在一个悬臂梁子结构的动态试验中,成功地利用局部脉冲响应、频率响应、联合虚拟变形法、时间序列法构造约束子结构;验证了利用约束子结构方法能剔除子结构以外未知因素(包括子结构外部非线性)的影响,准确地识别子结构的损伤。
子结构边界比较复杂时,其边界运动状态不容易测量,因而难以构造约束子结构。针对此局限,提出广义约束子结构模型修正法。它可以有效地提高子结构灵敏度,使之更容易修正识别。广义约束方法有两种:
(1)基于局部主频率的广义约束子结构模型修正方法。在局部激励的作用下,如果子结构能够主要以单阶子结构变形为主的模态振动,那么对应的该阶频率定义为子结构的局部主频率。局部主频率能更多地反映子结构特性,对子结构损伤的灵敏度高,所以利用局部主频率就可以修正和识别子结构。然而子结构一般并不具有这种性质,为使子结构能具有局部主频率,可以采用以下两种方法:
方法一,在子结构边界附加虚拟支座,增加对子结构边界的约束,减弱其外部构件的影响,从而提高子结构的灵敏度。用此方法有效识别了三层空间框架有限元模型底层柱的损伤。
方法二,在子结构内部附加质量,提高子结构本身的权重来提高子结构灵敏度。通过二十跨空间桁架试验验证了该方法,成功地联合局部主频率和整体结构的低阶频率修正了桁架有限元模型,并进一步准确地识别了杆件损伤。
(2)基于局部虚拟支座的联合约束结构模型修正方法。分别在每个子结构的内部施加虚拟支座,构造广义约束子结构(简称约束结构),使不同约束结构都含有对相应子结构灵敏度较高的低阶频率,继而收集所有这样的模态,联合其来修正整体结构。在数值模拟中,只利用三个传感器的排列组合布置,成功地识别了一个三层空间框架中的所有柱和板的损伤。
Structure Health Monitoring (SHM) is a hot research topic in civil engineering, of which model updating and damage identification are the important theoretical component. In civil engineering, the structures mostly are huge and complex, for which it is hard to obtain the complete measurement, and hence are insensitive to local damages. Aiming at solving these problems, Substructure Isolation Methods are proposed in this paper, which can precisely update or identify the local/global structure by very limited sensors.
Substructure Isolation Methods consist of two main steps: the first one is to construct the dynamic response of the isolated substructure, which is the core idea of the method; then, the classical modal updating techniques are applied to update/identify the concerned substructure via the constructed response. According to the extent of isolation, two kinds of isolated substructures are presented: Complete Isolated Substructure (“Isolated Substructure”for short) and Generalized Isolated Substructure. The former refers to an independent simple structure which is isolated from the global structure by adding virtual support on the boundary of the concerned substructure; while the latter facilitates the updating and identification by effectively increasing the sensitivity to the substructure(“substructure sensitivity”for short), although it can’t be isolated from the global structure completely.
The basic idea of the Isolated Substructure construction is the convolution combination of the local substructural response, which makes its boundary response vanish to zero, that is, the boundary sensors are counted as virtual supports. Correspondingly, the combined response inside the substructural is the constructed response of the Isolated Substructure. Five kinds of Substructure Isolation Methods (SIM) for model updating are proposed as following, which lie on the different characteristics of the considered local substructural responses:
(1) Substructure Isolation and model updating based on local mode. In the low-order global structural modes, the elements which are regard to the degree of freedom of the substructure are defined as the local mode. And then the flexibility matrix of the Isolated Substructure is constructed by the local mode. This approach first proposes the concept of the Substructure Isolation from the static mechanics.
(2) Substructure Isolation and model updating based on local impulse response. In the global structure, the local impulse response of the substructure is used to construct the impulse response of the Isolated Substructure directly, which extends the isolation method to dynamic scope. It overcomes the limitation of normalized mode shape which is required in the method based on local mode. Moreover, the constructed dynamic response contains more useful information than static flexibility matrix. In addition, the theory is extended further to make the proposed isolation methods including the following three dynamic isolation methods, performed easier in the real application, such as the extension of the excitation type, of the excitation placement, as well as the extension of the virtual support type. Besides those extensions, the Substructure Isolation Methods is expanded to allow its application even in case that the elements outside substructure are nonlinear.
(3) Substructure Isolation and model updating based on local frequency response. This approach extends the application of Substructure Isolation Methods from time domain to frequency domain, in which the frequency response of the local substructure is used to construct the frequency response of the Isolated Substructure. In this way, it avoids the ill-conditioning problem which often exists in the calculation of large inverse matrix, and moreover increases the computational efficiency.
(4) Substructure Isolation and model updating Combined with local VDM. VDM (Virtual Distortion Method) belongs to fast structural reanalysis method. The Substructure Isolation Methods combined with VDM allows the substructure identification using simultaneously measured excitation and the constructed response of the Isolated Substructure in time domain. And hence it not only speeds up the optimization but also increases the identification accuracy.
(5) Substructure Isolation and model updating based on local time series. The above proposed methods all require several groups of measurements to construct the Isolated Substructure, and in addition demand the zero initial structural state. This method only needs one group of measured time series of local substructural. The free vibration response of the Isolated Substructure is constructed by a delayed arrangement of the measured time series. The performance of the method is more flexible, easier, practical, and can be used for online local substructural monitoring.
The Truss finite element model is used in this paper respectively to numerically verify the above proposed Isolation Methods. Moreover, a dynamic experiment of a cantilever beam is performed, in which the Isolated Substructure is constructed successfully based on local impulse response, local frequency response, local VDM, and local time series. The experiment validates that the Substructure Isolation Methods can remove the influence of the unknown factors outside the substructure (including the nonlinearity), and thus denitrify the local substructural damage effectively and precisely.
For the substructure with complex boundary, it is hard measure all the boundary states, which are required in construction of the above Isolated Substructure. Aiming at improving the drawbacks, a Generalized Substructure Isolation Method for model updating is proposed which can obviously enhance the substructure sensitivity, and hence facilitate the substructure updating and identification. Two kinds of Generalized Substructure Isolation Method are as following:
(1) Generalized Substructure Isolation and model updating based on Local Primary Frequency. Apply the local excitation on concerned substructure, if the substructure can vibrate mainly at one single model which consist mostly of the substructural distortion, then the corresponding frequency are defined as the substructural Local Primary Frequency, which can reflect more characteristics of the substructure and are more sensitive to the substructural damage. Thus, Local Primary Frequency is enough to be used for substructural updating and identification. However, generally substructures don’t own this character. Two approaches are developed and adopted to make the concerned substructure have its Local Primary Frequency:
Approach I: Virtual supports are applied on the substructural boundary, such that it can raise the constraint on the boundary, and reduce the influence from the elements outside the substructure. In this way, the substructure sensitivity is enhanced. The bottom columns of a three-story space frame structure are testified that damage is identified effectively by this method.
Approach II: Mass are added to the substructure interior, which increases the weighting of the substructure itself and thus enhances its sensitivity. A twenty-span space truss experiment is used to validate the effectiveness of this method, in which the finite element model of the truss is updated successfully by combining the Local Primary Frequency and the low-order mode of the global structure. Using the updated model, the local element damage is further identified accurately.
(2) United Isolated Structure for model updating based on Local Virtual Support. Virtual supports are added respectively inside each substructure to construct the respective Generalized Isolated Substructure (“Isolated Structure”for short). It aims at making each Isolated Structure own the low-order frequencies which are high sensitive to the corresponding substructure. Then all these frequencies are collected and united to update the global structure. A numerical example of a three-story space frame proves that this method can identify damages of all the columns and plates successfully using only three sensors.
引文
1欧进萍.重大工程结构的累积损伤与安全度评定.走向21世纪的中国力学—中国科协第9次青年科学家论坛报告文集.北京:清华大学出版社, 1996: 179~189
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