Probabilistic distribution of fragments number from explosion of horizontal tank based on maximum entropy principle

The relations between the fragments number from the vessel explosion, the tank shape, the type of the primary scenario and the fracture mechanics were analyzed. The data of the past explosions leading to the fragment projection were collected and researched, and then the number of events for the four explosion categories of the horizontal tank and the corresponding observed probabilities of the fragments number were obtained by statistics on the basis of the more available data. The available information including the average and variance of the fragments number was obtained by analyzing the accident data. The probability density functions for the fragments number from the four categories of explosions were developed by the maximum entropy principle. The results showed that all the intervals of the number of fragments from each type of accident were generally [1, 9], the fragments number 1, 2, 3 and 4 account for larger proportions in any event, and the fragments number and their observed probabilities were different for different accidental events. The theoretical histograms derived by the four models were compared to the accident frequencies. The fragments number followed the discrete exponential distributions within the interval [1, 9].