Contribution of K-Nearest Neighbors in an Adaptive Importance Sampling-Based Structural Reliability Method
摘要
Finding efficient and accurate methods to estimate the probability of failure is one of the most important goals of structural reliability analysis. In the present paper, this has been achieved by means of one of the approaches of machine learning combined with an approach in adaptive importance sampling method. Samples are generated based on a sampling density function, which is continuously updated. Using a specific updating rule of design point, the location of the sampling density function gradually approaches the design point, resulting in better efficiency of importance sampling. On the other hand, by using the K-Nearest Neighbors of machine learning, it is no longer necessary to evaluate limit state function for all generated samples in the process of adaptive importance sampling. In fact, if the predefined conditions of K-Nearest Neighbors are satisfied for a sample, it is possible to predict whether the generated sample is in the safe domain or failure domain without function evaluation. As a result, the probability of failure is estimated accurately and efficiently due to the simultaneous use of adaptive importance sampling and machine learning. The accuracy and efficiency of this method have been shown by using a number of numerical examples. Based on the results of the numerical examples, although the same number of samples might be generated in the proposed method, a smaller proportion of them has to be evaluated directly by replacing in the limit state function. In fact, whether the value of the limit state function is positive or negative, is guessed for the majority of samples. Consequently, the efficiency of the method is promoted due to the reduction of function evaluations.