On choice and effect of weight matrix for response sensitivity-based damage identification with measurement and model errors

This paper aims to present a thorough view on the choice and effect of the weight matrix for response sensitivity-based damage identification with measurement and/or model errors. The derivation of the optimal weight matrix is mainly twofold. On the one hand, when only measurement errors are involved, the optimal weight matrix is found to be inverse proportional to the measurement error covariance by minimizing the expectation of squares error of the whole identification results. On the other hand, if model errors are additionally considered, the optimal weight matrix then depends not only on the measurement error covariance, but also on the model error covariance. Further analysis reveals that the optimal weight matrix can also make the 'relative error'-square-root of expectation of squares error in every individual damage parameter minimized. Then, the effect of the proposed optimal weight matrix with measurement and/or model errors is studied on two typical examples-a plane frame and a simply-supported plate. Results show that when hybrid types of measurement data-accelerations, displacements and/or eigenfrequencies are used or when the response data is sensitive to model errors, the optimal weight matrix should be invoked to get reasonably good identification results and the improvements brought by the optimal weight matrix are substantial. The whole work shall be instructive for damage identification when different types of measurements are available and when model errors are non-negligible.