Hybrid Testing Method For Civil Structures Based On Model Updating

Hybrid testing is a combination of numerical simulation and physical testing, which is increasingly being recognized as a powerful emerging technique that offers the opportunity for evaluation of large scale civil structures subjected to dynamic loading. In recent decades, a great deal of progress has been made in hybrid testing such as numerical integration algorithms, loading control methods, actuator delay compensation and testing error analysis. However, researchers generally might still encounter a number of difficulties when conducting hybrid testing for complex structures like high-rise buildings or large-scale bridges. One of the challenging issues is how to model the numerical substructure, when the whole structure exhibit strong nonlinearity subjected to extreme loading like strong earthquake and it is not economically realistic to physically test all the critical parts of the structure. To improve accuracy of numerical model during the hybrid testing, the hybrid testing method based on model updating with constrainted unscented Kalman filter(CUKF) is presented, which is of great theory significance and practical value in improving the hybrid tesing method and revealing the dynamic behavior of large scale civil structures.Several key issues of hybrid testing method for civil engineering based on model updating are inestigated in this paper. The main research work and concludings are as follows:(1) Online parameter identification method for the bilinear hysteretic model using the least square estimation is researched, which is verified by numerical simulation and experiment under the same loading paths. It is demonstrated that the on-line identification algorithm is in high precision and computational efficiency. Hybrid tesings with model updating for frame-brace structure of two degrees of freedom using MTS system are conducted firstly. The test results indicate that online model updating can decrease model errors and improve the precision of hybrid testing compared with conventional hybrid testing.(2) For constant scalar systems, analytic expression of Kalman filter was deduced under the system process noise available and unavailable, and the effects of parameters of kalman filter on the state estimation convariance are researched. Using state estimation variance as an evaluation standard state estimation, suggests of parameter selection in application of the Kalman filter is given. The rationality of the projection method to solve constraints problem in the state estimation method is verified. An optimal recursion algorithm considering the multiplicative noise based the Kalman filter is derived, the effectiveness of the algorithm is verified by elastic stiffness identification.(3) Hybrid testing method based on model updating with the unscented Kalman filter (UKF) is researched and its effectiveness is first confirmed by an actual test with a steel spring as the experimental substructure compared to conventional testing. A new constrained unscented Kalman filter (CUKF) algorithm is proposed based on the Unscented Kalman Filter (UKF) by adjusting the position of the sample points and weights. Compared to existing CUKF, the approach proposed in this paper features the following two aspects.(i) In prediction step, sigma points (i.e., sample point) violating bound constraints are moved onto the bounds, and the relevant sigma points within the boundary are moved correspondingly to retains the symmetry of the new set of sigma points. The proof is given to prove that the proposed replacement of sigma points results in a first-order accuracy for the unscented transformation of mean value if=0.5.(ii) In correction step, the state updating equation is used to generate transformed sigma points, and those transformed sigma points that violate bound constraints are projected to constraints boundary only when the updated state estimate exceeds the boundary. It can be proved that the reformulated equations give exactly the same result of updated mean and covariance with the standard UKF. The algorithm can consider the effect of the boundary constraints on the state estimation of mean as well as covariance, and has high computing efficiency and can realize real-time model updating. Research of Bouc-Wen model updating shows that: compared with UKF methods, CUKF method can effectively reduce volatility of the parameter identification at the early stage, ensure physical meaning of identification parameters, improve the convergence speed and precision of model updating. Filter Parameter Analysis is conducted and advice of initial parameter selection is given.(4) The hybrid testing method based on model updating with CUKF is presented. The effectiveness and feasibility of hybrid testing method based on model updating with CUKF is verified by a hybrid testing numerical simulation for the two freedom nonlinear system. Using dSPACE-MTS test platform, both increased-time and real-time hybrid testing based on model updating for frame structure incorporating all-steel buckling-restrained braces (BRBs) are finished. The results show that the proposed hybrid testing method has better accuracy compared with conventional hybrid testing and hybrid testing based on model updating with UKF.(5) The hybrid testing with model updating using OpenSees is proposed, and a series of numerical simulations of hybrid testing with model updating for a six story frame with BRBs are conducted. The numeirical and physical substructures are simulated by OpenSees, and online identification of the model parameters is realized by Matlab programming. A new twoNodeLink element is set up by modifying source codes of twoNodeLink element in the original OpenSees program to realized online model updating. The data transmission between OpenSees and Matlab is realized using Socket communication technology. The classical Bouc-Wen and Bouc-Wen considering the strength and stiffness degradation are respectively selected to analyze the influences of model error on accuracy of the hybrid testing with model updating. Simulation results show that parameter identification values are difficult to converge to a steady value due to the model error, which can reduce precision of hybrid test with model updating. Combining model updating with distributed hybrid test is put forward to reduce the negative influence of model error. Try to select more than one key component as testing substructure, then update respectively model of the numerical substructure which has the similar loading path and degree of the nonlinear to case of the corresponding testing substructure. Results show that when the model error is inevitable, the proposed method can effectively reduce the effect of model error on model updating, and the precision of hybrid testing with model updating is improved further.