Model Updating Based On Substructure Isolation Methods

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.