Abstract
To obtain the optimal probability distribution models of geotechnical parameters, the goodness of fit of the normal information diffusion (NID) distribution and Weibull distribution were investigated and compared for actual engineering samples and Monte Carlo (MC) simulated samples. Two datasets from actual engineering parameters (the strength of a rock mass and the average wind speed) were used to test the fitting abilities of these two distributions. The results show that the parameters of the NID distribution are easily estimated, the Kolmogorov-Smirnov (K-S) test results of the NID distribution are smaller than those of the Weibull distribution, and the NID distribution curves can perfectly reflect the stochastic volatility of geotechnical parameters with small sample sizes. The sample size effects on the fitting accuracy of the NID distribution and Weibull distribution were also investigated in this paper. Eight simulated samples with different sample sizes, namely, 15, 20, 30, 50, 100, 200, 500, and 1000, were produced by using the MC method based on two known Weibull distributions. The results show that with an increase in the sample size, the K-S test results of the NID distribution gradually decrease and tend to converge, while the chi-square test results of the NID distribution remain low and are always lower than those of the Weibull distribution. The cumulative probability values of the NID distribution are larger than those of the Weibull distribution and are always equal to 1.0000. Finally, the comparison of the fitting accuracy between the NID distribution and normalized Weibull distribution was also analyzed.
Highlights
Due to the natural attributes of rock materials, the complexity of the geological environment and the randomness of external loading, uncertainty is inevitable in geotechnical engineering [1,2,3]
Considering that the sample sizes obtained in actual geotechnical engineering are generally small, to study the effect of the sample size on the fitting accuracy with the normal information diffusion (NID) distribution and Weibull distribution, eight simulated samples of different sizes were produced by using the Monte Carlo (MC) method in this paper
1) The probability density function (PDF) of two sets of geotechnical samples were fitted with the NID distribution and Weibull distribution
Summary
Due to the natural attributes of rock materials, the complexity of the geological environment and the randomness of external loading (such as impact loads, seismic response, vibratory action, etc.), uncertainty is inevitable in geotechnical engineering [1,2,3]. In the reliability analysis of geotechnical engineering under quasi-static loads or vibrations loads, the inference of optimal probability density function (PDF) or cumulative distribution function (CDF) of a geotechnical parameter is one of the most essential tasks; this is the first step in a reliability analysis and plays a central role in ensuring the precision and accuracy of the geotechnical reliability analysis [15, 16]. INFERENCE OF THE OPTIMAL PROBABILITY DISTRIBUTION MODEL FOR GEOTECHNICAL PARAMETERS BY USING WEIBULL AND NID DISTRIBUTIONS. NID theory was introduced to fit the optimal PDFs or CDFs of geotechnical parameters. The results show that NID distribution can make full use of the sample information to deduce the PDFs of the geotechnical parameters and that its fit is more accurate than that of the Weibull distribution
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