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In vibration design, we need to estimate the damping ratio to calculate the dynamic response of a structure. In particular, an estimation of its probability distribution is important to carry out so-called probabilistic design. For this paper, we developed an estimation method using the Bayesian approach to generate the probability distribution of the damping ratio from a vibration test with a small sample size. The Bayesian approach has special significance to engineering design, where available test data is invariably limited, for the approach can systematically incorporate subjective judgments based on experience or indirect information with observed data. We supposed that the probability distribution of the damping ratio has a normal distribution. Therefore, we applied the Bayesian approach to estimate unknown parameters of the distribution. In addition, we compared this method with a method of moments classified as a classical estimation and investigated the influence of sample size by conducting an evaluation test. With the results of our analysis, we came to the following conclusions. First, he true standard deviation of the damping ratio is less than 0.4, and the prior distribution of the standard deviation ranges between 0 and 0.5. (1) The estimated probability distributions determined by the Bayesian approach and the classical approach almost fully agree across more than 40 specimens. (2) The Bayesian approach provides good agreement, less than 10 percent error, with a true standard deviation for approximately 10 specimens. Even though the prior distribution of standard deviation ranges between 0 and 1.0, almost the same accuracy is obtained for approximately 10 specimens.

Estimation Method for Determining Probability Distribution of the Damping Ratio of a Structure based on the Bayesian Approach