Identification of geotechnical dynamical systems and function estimation: Modeling and estimation

A method to identify mechanical properties of geotechnical dynamical systems is presented herein. The function estimation problem is defined, and two classes of estimators, Bayes-type and minimax-type, are introduced. Special attention is paid to a minimax-type estimator, called the nonlinear thresholding estimator. This estimator is nearly-minimax over every Besov function space due to the nonlinearity and the sparse representation provided by the wavelet bases. Spatially inhomogeneous functions are highlighted since many signals and functions pertaining to geotechnical dynamical systems are of this class. The necessity of a nonlinear estimator and a sparse representation for the function estimation problem of this class of functions is discussed.; Three data sets of geotechnical dynamical systems are studied. They are (1) microseismic data, (2) vertical seismic array data, and (3) seismic slope displacement experiment data, and the purposes of the corresponding identification problems are (1) to identify the microseismic source functions, (2) to identify the soil degradation behaviors, and (3) to identify the failure mechanisms of the soil slopes, respectively.; According to their nature, the above three identification problems are classified into the following three categories: (1) a time-invariant linear system, (2) a slowly time-varying system, and (3) a rapidly time-varying system. Three different models and estimators are proposed to solve the problems using the function estimation approach, i.e. the three identification problems are first converted into function estimation problems, and a Bayes-type or minimax-type estimator is applied to estimate the target functions.; The results of the microseismic case study indicate that a nonparametric Besov-space model with the nonlinear thresholding estimator outperforms Bayes-type estimators. The thresholding estimator can eliminate high-frequency noise without destroying spatially inhomogeneous features in the microseismic source functions, while no Bayes-type estimator can achieve this.; The results of the vertical-array case study indicate that a time-varying infinite-impulse-response filter model and an enhanced Bayes-type estimator with a random-walk function model are appropriate for non-liquefied cases. The conclusions of the identification agree with the common understanding about soil degradation behaviors and results of previous research. Moreover, non-instantaneously recoverable soil degradation is found for several vertical array data sets.; An approach based on a semi-parametric model and the nonlinear thresholding estimator is proposed to study the liquefaction case in the vertical-array data set and the seismic slope displacement experiments. The identification results are consistent with the results of previous research and experimental observations.