A new representation method for probability distributions of multimodal and irregular data based on uniform mixture model
Randomness is a major characteristic of observed data from practical engineering. Sometimes the probability distributions of observed data may exhibit bimodal, multimodal or even irregular features. Under these circumstances, the adequacy of typical unimodal distributions may be questioned. To solve this issue, a new representation method for probability distributions of multimodal and irregular data is presented in this study. Firstly, an uniform mixture model (UMM) is developed by a weighted combination of multiple uniform distribution components. Then, the UMM is applied to approximate probability distributions of multimodal and irregular data, and the weighting coefficients of UMM can be easily derived from the frequency histogram of observed data. Finally, the fatigue crack growth data of 2024-T351 aluminum alloy are used to verify the validity of the proposed method. The results indicate that the proposed method is accurate and flexible enough to characterize the probability distributions of various kinds of multimodal and irregular data. The average relative errors of the proposed method are very small, and the approximation accuracy can be improved by reducing the interval width.
KeywordsMultimodal and irregular data Uniform mixture model Randomness Fatigue crack Reliability
This research was supported by the National Natural Science Foundation of China under Contract No. 51665029.
- Hernández-Bastida, A., & Fernández-Sánchez, M. P. (2018). How adding new information modifies the estimation of the mean and the variance in PERT: A maximum entropy distribution approach. Annals of Operations Research, 3, 1–18.Google Scholar
- Huang, X. Z., & Zhang, Y. M. (2014). A probability estimation method for reliability analysis using mapped Gegenbauer polynomials. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 228(1), 72–82.Google Scholar
- Litmanovich, E. A., & Ivleva, E. M. (2010). The problem of bimodal distributions in dynamic light scattering: Theory and experiment. Polymer Science, 52(6), 671–678.Google Scholar