An improved fourth-order moment reliability method for strongly skewed distributions
- PDF / 759,479 Bytes
- 13 Pages / 595.276 x 790.866 pts Page_size
- 72 Downloads / 182 Views
RESEARCH PAPER
An improved fourth-order moment reliability method for strongly skewed distributions Long-Wen Zhang 1 Received: 4 June 2019 / Revised: 25 October 2019 / Accepted: 11 February 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract High-order statistical moment method uses only moments of random variable for reliability analysis and can widely address the problem of unknown probability distribution. However, for practical cases with strongly skewed distributions, the existing fourth-moment methods may produce large errors or result in instability in the analysis process. Thus, an improved expression of the fourth-order moment reliability index based on the fourth-moment standardization function for strongly skewed distributions is developed. First, the coefficients of the fourth-moment standardization function are modified for strongly skewed distributions by fitting the coefficients of the third-order polynomial transformation, and an improved fourth-moment standardization function is developed. Then, the accuracy of the improved model is demonstrated by analyzing the relative errors between the estimated moments and their target values. Furthermore, the complete reliability index formula is derived according to the monotonic expression of the third-order polynomial transformation. Finally, numerical examples show the improved accuracy achieved by the proposed method. It can be concluded that, compared to the original methods, the proposed method is more accurate and stable for reliability analysis in which the distribution is strongly skewed. Keywords Reliability index . Fourth-order moment method . Statistical moments . Strongly skewed distribution . Fourth-moment standardization function
1 Introduction A fundamental problem encountered in structural reliability theory is the computation of failure probability described as a multifold probability integral. Various approximate reliability methods have been proposed to overcome the difficulty in computing this probability (Madsen et al. 1986). Of interest here is the high-order statistical moment method (Zhao and Ono 2000, 2001; Zhao and Lu 2007; Lu et al. 2017), which is one of the important approaches for structural reliability analysis. In this method, no shortcomings are associated with the design points, and neither iteration nor the computation of derivatives is required, thus making it convenient for application to structural reliability analysis (Zhao and Ono 2000, Responsible Editor: Palaniappan Ramu * Long-Wen Zhang [email protected] 1
College of Water Resources & Civil Engineering, Hunan Agricultural University, 1 Nongda Road, Changsha 410128, China
2001; Rajan et al. 2016; Xu and Lu 2017). In the moment method, the probabilistic characteristics of random variables are expressed using only statistical moments. This is particular advantageous when probability distributions are not available. Because the first four moments (i.e., mean, standard deviation, skewness, and kurtosis) with clear physical definitions
Data Loading...
