Abstract：The ill-conditioned least squares problems often appear in structural damage recognition using noisy data to cause calculation results being fully distorted. Here, to significantly improve calculation accuracy, a feedback ridge estimate (FRE) technique was proposed to obtain accurate and stable damage recognition results. The proposed method has three steps. Firstly, the first ridge estimate (RE) calculation was done for linear equation set in structural damage evaluation to obtain the rough solution to damage parameters. Secondly, a new diagonal matrix was designed to be used in the second RE calculation according to the rough solution to damage parameters. Thirdly, the second RE calculation was done with FRE technique for linear equation set in structural damage evaluation to obtain damage parameters’ high-precision solution. A beam structure was taken as a numerical example to explore the effectiveness of the proposed method under 10% noise level. The calculation results were compared with those using the ordinary RE method and the singular value truncation (SVT) one. The results showed that the proposed FRE method can significantly improve calculation accuracy; even under 10% noise level, it can be used to obtain calculation results with very high precision.
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