Asymptotic analysis of the random decrement

The Random Decrement (RD) algorithm was introduced in the late sixties by Henry Cole as a method of identification of structures under ambient loadings. Although this method was frequently used during almost half of a century, the theory is still incomplete, and some errors of analysis are frequently made, which can lead to bias in estimations. In fact, the result depends strongly on the specific way the tests are implemented in the algorithm. The practice is with discretized data. Hence, there are two cases for asymptotic analysis: one is when the number of data goes to infinity, and the other is when the discretization step goes to zero. Both of these aspects are studied in this paper. Some specific algorithms are fully studied, and the tools are given to perform the analysis of a large class of RD algorithms.