Structural Damage Identification Based On Unscented Kalman Filter

Recently structural health monitoring system has played an important role in keeping civil engineering structure safe and protecting them from disaster or accident, but as one of the key factors of structural health monitoring system, damage identification method is limiting the development of structure health monitoring system applied in real structures. So it is of much theory and engineering value to study damage identification method applied in large scale civil engineering structures.Among many damage identification methods, Extended Kalman Filter(EKF) is widely focused as a signal processing of time series which can be used to detect structural damages, because this method has good robustness and can obtain the linear minimum variance estimation in iterated form by building a filter machine in time domain. However, some disadvantages, such as huge cost in calculating Jacobi matrix, high-order errors in linear expansion and the ill-posed characteristic of inverse problems, still exist and affect the damage identification results greatly.For overcoming the disadvantage of EKF, Unscented Kalman Filter(UKF)applied in damage identification is studied. By applying UT transform into Kalman filter, the high order term of the nonlinear system can be contained, and the computational cost of Jacobi matrix is avoided. Then, Unscented Kalman Filter applied in damage identification is proposed through improving the ill posednessof inverse problems and developing the calculation precision of system predicting equations, and prove its application by numerical example and real scale experiment. The content in detail is contained:(1) When UKF is applied in damage identification application, the structural displacement and velocity initial values are usually contained in state vector, but when the structure is complex, and the length of the state vector will be longer, the calculation cost will be too much. So here present a UKF state vector definition method based on modal coordinate transform and modal truncation, so the state vector contain modal coordinate initial values and damage parameters, after the modifying measurement, length of state vector can be reduced, and on the basis of state definition derivation of the UKF iterated equation is obtained.(2) Present UKF algorithm combined with L1-norm regularization. For solving the inverse problem of damage identification, due to the dynamic theory, calculation will be effected by the strong ill-posed characteristic. In UKF iterated process, the ill-posed problem may lead to the iterated algorithm will divergence because the state covariance matrix may not keep positive definite. In this essay considering the inverse problem solving method of the regularization method, and due to sparseness characteristic of the structure damage parameters, apply the L1 regularization method into UKF frame, and prove the application of the proposed algorithm by using numerical example of simply supported beam.(3) Present UKF algorithm combined with Gaussian process response surface. In UKF theory framework, the function between damage parameters and structural modal parameters need be built, the usually used sensitivity method ignore the high order terms, when the nonlinearity of the structure is strong or the damage level is high, the calculation accuracy could not be kept. So the high accuracy Gaussian process response surface is applied in UKF, and prove the identification accuracy and reliability of the proposed algorithm by using numerical example of simply supported beam and 2-D truss.(4) Build different form of beam structure experiment, using the free vibration signal of structure to prove the application of the proposed algorithm. The identification result prove that the modified UKF algorithm proposed in this essay can reduce the effect of the noise in signal, so that the damage level and location can be identified, and the identification error can be also kept low at the undamaged element, the robustness of it could be ideal.