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Strategy for the selection of input ground motion for inelastic structural response analysis based on naïve Bayesian classifier

Abstract:

An application of the naïve Bayesian classifier for selecting strong motion data in terms of the deformation probably induced on a given structural system is presented. The main differences between the proposed method and the “standard” procedure based on the inference of a polynomial relationship between a single intensity measure and the engineering demand parameter are: the discrete description of the engineering demand parameter; the use of an array of intensity measures; the combination of the information issued from the training phase via a Bayesian formulation. Six non-linear structural systems with initial fundamental frequency of 1, 2 and 5 Hz and with different strength reduction factors are modelled. Their behaviour is described using the Takeda hysteretic model and the engineering demand parameter is expressed as the relative drift. A database of 6,373 strong motion records is built from worldwide catalogues and is described by a set of “classical” intensity measures; it constitutes the “training dataset” used to feed the Bayesian classifier. The structural system response is reduced to a description of three possible classes: elastic, if the induced drift is lower than the yield displacement; plastic, if the drift ranges between the yield and the ultimate drift values; fragile if the drift reaches the ultimate drift. The goal is to evaluate the conditional probability of observing a given status of the system as a function of the intensity measure array. To validate the presented methodology and evaluate its prediction capability, a blind test on a second dataset, completely disjointed from the training one, composed of 7,000 waveforms recorded in Japan, is performed. The Japanese data are classed using the probability distribution functions derived on the first data set. It is shown that, by combining several intensity measures through the likelihood product, a stable result is obtained whereby most of the data ($$>$$>75 %) are well classed. The degree of correlation between the intensity measure and the engineering demand parameter controls the reliability of the probability curves associated to each intensity measure.