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The modeling of cracks and identification of dam behavior changes are difficult issues in dam health monitoring research. In this paper, a time-varying identification model for crack monitoring data is built using support vector regression (SVR) and the Bayesian evidence framework (BEF). First, the SVR method is adopted for better modeling of the nonlinear relationship between the crack opening displacement (COD) and its influencing factors. Second, the BEF approach is applied to determine the optimal SVR modeling parameters, including the penalty coefficient, the loss coefficient, and the width coefficient of the radial kernel function, under the principle that the prediction errors between the monitored and the model forecasted values are as small as possible. Then, considering the predicted COD, the historical maximum COD, and the time-dependent component, forewarning criteria are proposed for identifying the time-varying behavior of cracks and the degree of abnormality of dam health. Finally, an example of modeling and forewarning analysis is presented using two monitoring subsequences from a real structural crack in the Chencun concrete arch-gravity dam. The findings indicate that the proposed time-varying model can provide predicted results that are more accurately nonlinearity fitted and is suitable for use in evaluating the behavior of cracks in dams.