{'fraction_non_alphanumeric': 0.021722265321955005, 'fraction_numerical': 0.0031031807602792862, 'mean_word_length': 5.231884057971015, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Probability distribution of derailment factor using identical probability distribution evolution method

To better understand the randomness of the derailment factor of the high-speed trains, its probability distribution function (PDF) and extreme value PDF are studied using the identical probability distribution evolution method (IPDEM). The standard deviation and mean of wheel-rail contact forces are obtained by pseudo-excitation method (PEM) and time history simulations. Then, based on the mean and standard deviation, the PDF and extreme value PDF of the derailment factor are obtained by IPDEM. The PDF and extreme value PDF of the derailment factor are validated by Monte Carlo method (MCM) simulations. Using a 6-car Pioneer EMU train passing over a 3-span 32-m long simply supported bridge as a case study, the applicability of the PDF and extreme value PDF of the derailment factor under varying train speeds, different track irregularities and different bridge deflection/span ratios are discussed. Finally, experimental data obtained from a field test are also used to verify the accuracy of the theoretical approaches. The results show that the PDF and extreme value PDF of the derailment factor proposed in this paper can provide a foundation for statistical evaluations.