A cumulative entropy method for distribution recognition of model error

• A cumulative entropy method is proposed to recognize the distribution of model error.
• Lévy stable distribution is used to detect the statistical properties of model error.
• Compared with Shannon entropy, the cumulative entropy method is easy to be validated.
• Lévy stable distribution can well depict the distribution of model error.

This paper develops a cumulative entropy method (CEM) to recognize the most suitable distribution for model error. In terms of the CEM, the Lévy stable distribution is employed to capture the statistical properties of model error. The strategies are tested on 250 experiments of axially loaded CFT steel stub columns in conjunction with the four national building codes of Japan (AIJ, 1997), China (DL/T, 1999), the Eurocode 4 (EU4, 2004), and United States (AISC, 2005). The cumulative entropy method is validated as more computationally efficient than the Shannon entropy method. Compared with the Kolmogorov–Smirnov test and root mean square deviation, the CEM provides alternative and powerful model selection criterion to recognize the most suitable distribution for the model error.