Structural Damage Identification And Experimental Study Based On Extended Ellipsoidal Outer-bounding Set-membership Filter

Factors such as the adverse environment,overload,corrosion or other unexpected factors can lead to structural damage during the long-term service of the engineering structure.In order to avoid major safety accidents caused by damage accumulation,structural health monitoring and safety assessment should be carried out.Therefore,as the core technology of health monitoring system,it is a great significance to carry out the research on structural damage identification methods to ensure the safe operation of structures.At present,based on the time-history response of the structure,the Kalman filter is used to estimate the optimal damage parameters of the structure,which is a commonly used damage identification method.It can obtain the damage optimal estimation(or suboptimal estimation)in the sense of minimum variance.However,Kalman filter generally assume that the noise is random noise(such as the Gaussian noise)which satisfies a certain probability distribution.The actual observed noise often fails to meet the assumed probability distribution strictly,or lack sufficient information to determine the probability distribution,the effect of damage identification will be reduced significantly.Therefore,the unknown but bounded non-probabilistic noise model(the UBB noise)is more suitable for practical engineering applications.For the UBB noise,Extended ellipsoidal outer-bounding set-membership filter(EEOB-SMF)is an effective interval-type state estimation algorithm.Based on the extension and improvement of Extended ellipsoidal outer-bounding set-membership filter,the problem of structural damage identification is studied in this paper.The specific research contents are as follows:(1)The state of the structure and the damage parameters are regarded as the state vectors of the system together.The uncertain factors such as process noise and measurement disturbance are treated as the UBB noise by using the idea of set member and the linearization error of the nonlinear function is incorporated into the process noise ellipsoid.The EEOB-SMF damage identification algorithm is proposed.The damage identification of the structure is realized by numerical simulation examples and experimental research.Then through the multiple degrees of freedom shear model and the forced vibration signal inversion of the beam structure,the effect of the EEOBSMF damage identification algorithm under different working conditions and the influence of uncertainty on the algorithm are analyzed emphatically.Through the free vibration signal inversion of plate girder bridge with spatial characteristics,the influence of spatial-division and the distribution of measuring points on the identification effect is discussed in detail.Finally,the EEOB-SMF algorithm is applied to the experiments of frame structures with different degrees of freedom,different damage positions and degrees of damage.The experimental results show that the algorithm can estimate the motion state of the structure under different damage conditions.Accurately identify the damage location and damage degree of the structure.(2)When the extended set member filtering algorithm is used for damage identification,the noise ellipsoid with linearization error is usually presupposed.When the uncertainty range of the noise ellipsoid is set incorrectly,the stability and recognition accuracy of the algorithm will be affected.In order to solve the problem of linear error delimitation in nonlinear system damage identification,an improved extended ellipsoidal outer-bounding set-membership filter damage identification algorithm for the UBB noise is proposed in this paper.Firstly,the element stiffness reduction factor is introduced into the state vector of the system and the extended state vector of the system is composed of modal coordinates and their time derivatives.All kinds of uncertainty factors are processed into the UBB noise.Secondly,the equation of the structural modal parameters with respect to the damage parameters is formulated by introducing the response surface equation.And the linearization error bounds are estimated automatically by using the non-gradient optimization method.Finally,the estimation of the feasible set of structural damage parameters is realized through the process of time updating and observation updating of the set-membership filter.The analysis of numerical examples of spring particle model and simply supported beam model show that the proposed identification algorithm can obtain the compact boundary of linearization error without reducing the stability of the algorithm.Thus the self-adaptability of the algorithm is improved effectively and it is more conducive to practical application.