Abstract
For when a structure is both subjected to unknown loads and characterized by unknown parameters and structural parameter identification and load identification algorithms cannot be applied under these circumstances, this article proposes a new algorithm based on the perturbation method for the simultaneous identification of the load and unknown structural parameters using a few response points. The impulse response matrix is expanded with respect to the unknown parameters, and then the load term is combined with the unknown parameter perturbation term to generate the parameter–load term; finally, the load and unknown parameters can be simultaneously identified by iteration. The proposed algorithm is verified by an example of a 10-storey shear frame, and the effect of noise level, the number of response points, and the truncation ratio, which is a parameter introduced to improve the accuracy of the proposed algorithm, are studied. Moreover, the effect of the distribution of response points is discussed for another example of a simply supported beam, and the results show that when the response points are distributed over the full beam, the error is obviously smaller than when the response points are distributed over only part of the beam.
Highlights
Civil engineering structures have been subjected to environmental and human loads during many decades of operation, which may cause damage to the structures, thereby changing the structural parameters
Suppose that an unknown parameter has a small perturbation at its initial value; the discrete impulse response functions are calculated before and after the occurrence of the perturbation, and the difference between the two impulse response functions is treated as the partial derivative of the impulse response function with respect to this unknown parameter
This article proposes a new algorithm for the simultaneous identification of the load and unknown parameters of the structure using only a few response points based on the perturbation method
Summary
Civil engineering structures have been subjected to environmental and human loads during many decades of operation, which may cause damage to the structures, thereby changing the structural parameters. Based on the perturbation theory, this article proposes a new algorithm for simultaneous identification of the load and unknown parameters of the structure using a few response points. Initial values are assumed for unknown parameters, and the convolution equation for solving the structural dynamic response is discretized. The partial derivative matrices of the impulse response matrix with respect to the unknown parameters are obtained by the difference method. Using the orthogonality of the mass matrix, stiffness matrix, and damping matrix with respect to the mode shape matrix, the displacement of the selected response points calculated by the superposition method is discretized according to time sampling points as in equation (3). It should be noted that it is not recommended to use the number of positive and negative elements in rfi to determine the positive and negative properties of the unknown parameter perturbation term because this method does not yield a good result. Suppose that an unknown parameter has a small perturbation at its initial value; the discrete impulse response functions are calculated before and after the occurrence of the perturbation, and the difference between the two impulse response functions is treated as the partial derivative of the impulse response function with respect to this unknown parameter
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