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The stochastic pseudo-excitation method (SPEM) is applied to improve the efficiency of the random vibration analysis of an uncertain train–bridge interaction (TBI) system. This method is combined with the first-order reliability method to handle the reliability analysis of the system. It is characterized by the introduction of a random variable of the amplitude coefficient based on the principle of the PEM, establishing stochastic excitation at each selected frequency point. Unlike the traditional PEM, the calculation results by the SPEM can consider the random characteristics of external loads and also reflect the effect of uncertain parameters. Two comparisons were conducted to verify the accuracy and efficiency of the proposed method for the dynamic analysis of an uncertain TBI system. First, the results calculated using the SPEM were compared with those calculated using the PEM, indicating that the SPEM can calculate the dynamic responses of the TBI system without uncertainties. Second, the stochastic responses of the uncertain TBI system obtained by the SPEM were compared with those obtained by the MCM, which exhibited good agreement and verified the efficiency of the proposed method. Third, the system response of the simplified TBI model was analyzed to determine the parametric sensitivity. Finally, the reliability of the TBI model was studied based on the selected sensitive parameters. These results indicated that the uncertain mass of the train played an essential role in the random vibration of the system. In addition, the safety index of the structure became more accurate with increasing number of samples, and the probabilistic distribution of the dynamic responses of the uncertain TBI system followed a Gaussian distribution extremely well, further verifying the appropriateness of the selected amplitude coefficient in the SPEM. [ABSTRACT FROM AUTHOR]

Based on the theory of pseudo excitation method, a so-called stochastic pseudo excitation method is proposed to acquire the sampling results of stochastic dynamic response of uncertain bridge structure directly, which cannot be achieved by the classical pseudo excitation method. In order to reduce the computational cost of the dynamic finite element analysis of the samples to gain the probability density function of structural responses, the response surface method was adopted to handle the sampling results. The stochastic pseudo excitation method combing response surface method is verified by comparing with Monte Carlo method in good agreement. As an example, the stochastic response of a super-high slender bridge tower subjected to the Davenport fluctuating wind excitations is evaluated taking into account the uncertainties of material properties and wind speed. Numerical results show that the effect of uncertainties of structure or excitations plays a constant role in the stochastic response at the different levels of external excitations. [ABSTRACT FROM AUTHOR]

A hybrid method combining the stochastic pseudo excitation method (SPEM) and the response surface method (RSM) was presented to handle the effect of both random characteristics of power spectral density of excitation and uncertain parameters. Based on basic principle of pseudo excitation method (PEM), an optimized algorithm was proposed to be SPEM. The effects of the uncertainties of structure and excitations could be considered through SPEM, thus directly acquiring the whole sampling results of random vibration of uncertain structural system. To reduce the cost of computing the total number of required finite element analysis simulations, RSM was adopted to hold calculated sampling results to gain the probability density function (PDF) of random vibration. The proposed method can consider both the effects of random characteristics of power spectrum of random excitations and the uncertainties of target system. Neverthless, Since the proposed method is based on the pseudo excitation method, the SPEM-RSM can handle the stochastic vibration analysis of determine and uncertain structure. In order to verify the accuracy and efficiency of proposed method, taking a single degree of freedom linear uncertain oscillator and a pier construction as two verification cases, the PDF of responses computed by the hybrid method was verified by Monte Carlo method (MCM), and the efficiency of the proposed method was presented. Then, stochastic responses of the railway continuous bridge subjected to earthquake were calculated, several uncertainties are involved in the computation. In addition, sensitivity analysis was solved for uncertain parameters. • A named as stochastic pseudo excitation method (SPEM) is proposed. • A hybrid method combing the SPEM and the response surface method (RSM) was presented. • The hybrid method handle the stochastic vibration of linear structure with various excitation. • The structural uncertainties can increase predictive uncertainty and discreteness for the stochastic response in this case study. • The most significant uncertain parameter in sensitivity of all the random variable is damping ratio. [ABSTRACT FROM AUTHOR]