Structural Damage Identification Based On Improved Karman Filter And Cointegration Method

The long-span bridge is an important infrastructure of the city,and the safe operation of bridge is directly related to the life and property safety of the people.How to monitor the operation status of the long-span bridge through efficient and reliable modern technology is a content of creating a smart city.In recent years,many domestic bridges have gradually installed Structural Health Monitoring(SHM)system,which uses effective damage identification methods to analyze the monitoring data and obtain bridge damage information,which can ensure the safety of long-span bridge structures and construction of smart bridge.Structural damage identification methods based on vibration characteristics have received extensive attention in recent years and have achieved rapid development.However,most of the current methods can only be used for laboratory models,and rarely used for actual structures.The main reason is that the environmental conditions in the laboratory can be controlled,however the actual structure is easily affected by external environmental factors.For example,it is common for a bridge that temperature causes 5%bridge frequency change.The changes in structural dynamic characteristics caused by damage may be completely overwhelmed in changes caused by environmental factors,which result in that the actual damage of the structure cannot be effectively identified,and the structural health monitoring cannot be carried out smoothly.Therefore,it is of great significance to remove those structural changes(damage features)caused by external influences from actual structural damage,which is the core and key difficulty in the field of structural health monitoring and damage identification.In addition,for structural damage identification,the number of measurement locations is always limited due to technical and economic reasons.The ability to detect damage from very few measurements is very important in structural health monitoring.To overcome the above difficulties in SHM,the vibration data of the structure is taken as the research object,and the extended Kalman filter damage identification method with sparsity constraints is proposed,and improved cointegration method used for removing environmental factor is carried out.The specific research contents of this paper are as follows:(1)In actual engineering structures,damage usually occurs in a few locations,therefore the distribution of damage is sparse.In this paper,the sparse characteristic of damage is introduced into the EKF algorithm as a lp regularization constraint,which forms the EKF-lp damage detection approach.To obtain a recursive solution in proposed EKF-lp method,a pseudo-measurement equation is used to embed the lp-norm constraint into the recursive EKF.In addition,to select an appropriate p value in the EKF-lp method,a novel L-surface approach is proposed.The results of numerical examples and experimental examples show that,by considering the sparse characteristics of the damage,the proposed method can accurately identify the damage even if the measurement information is very little;meanwhile,the damage identification is not sensitive to the measurement noise.(2)In order to obtain a suitable p-value in the EKF-lp method,a large number of solution norms and residual norms of different p-values need to be obtained.This process requires a large amount of calculation,which make it difficult to online identity structural damage.Meanwhile,if the non-linearity of the pseudo-measurement equation is large,the error of the linearization process is large in the EKF-lp method.To overcome the above shortcomings,two improved methods of applying sparse constraints are proposed,which are called UKF-lp method and EKF-Atan method.In the proposed UKF-lp method,sparsity constraint is introduced by UKF instead of EKF,and UT transformation is used to reduce the linearization error.In the proposed EKF-Atan method,arctangengt function is used as the penalty function.The EKF-Atan method does not need to choose the p value,but the same sparse solution can be obtained as EKF-lp.Through shear structure experiment and cantilever beam experiment examples,the effectiveness of the two methods is proved.(3)When traditional cointegration method is used for damage identification,it needs to establish the cointegration equation with undamaged data of all changing environments.However,obtaining these data is very difficult,especially in the early monitoring stage.Moreover,the traditional cointegration method is difficult to identify damage online because of an offline phase.To overcome the shortcomings of traditional cointegration,this paper proposes an online damage identification algorithm that combines cointegration and Kalman filter.In this proposed method,the cointegration coefficients are used to form the state vector,and the cointegration equation is used as the observation equation under the KF framework.The cointegration coefficients are estimated online by the KF algorithm,and damage can be identified through the changes of the cointegration coefficients.In addition,to avoid the problem of inaccurate identification of time-varying parameters caused by traditional KF's excessive dependence on old observations,an adaptive fading factor is introduced into KF to increase the weight of new observations.Finally,a numerical example of a truss bridge and Tianjin Yonghe Bridge field data are used to verify the effectiveness of the proposed method.(4)Because the traditional cointegration method is a linear algorithm,it is only useful when monitored variables meet a good linear relationship.In order to overcome this shortcoming of cointegration,an improved method that combines cointegration and kernel canonical correlation analysis is proposed.First,a nonlinear transformation of monitored variables from the low-dimensional space to a high-dimensional space was performed by kernel canonical correlation analysis,therefore the nonlinear monitored variables in low-dimensional space was changed to the linear kernel canonical variables in high-dimensional space.Then,because the cointegration method can remove the common trend among variables,the cointegration was applied to remove the environmental influences in kernel canonical variables,and damage can be identified by the change of cointegration residual.Through an experiment of a wooden bridge and the measured data of Z24 bridge,the effectiveness of the proposed method is verified.