To improve the computational accuracy and efficiency of dynamic probabilistic analysis of complex structures, an extremum Kriging method (EKM) with multi-population genetic algorithm (MPGA) is proposed fusing extremum response surface method (ERSM), Kriging model and MPGA. Particularly, the EKM is developed by combining the Kriging model and ERSM to handle dynamic processes of related variables and to reduce computational burden by regarding the extreme value of response process in each dynamic analysis within the time domain. The MPGA is used to replace gradient decent to find the hyperparameter θ in the Kriging model by solving the maximum-likelihood equation. The effectiveness of the proposed method was validated by performing the dynamic probabilistic analysis of an aeroengine high-pressure compressor blisk radial running deformation with fluid-thermal-structural interaction. The analytical results illustrate that the reliability degree of the blisk is 0·9956 under the allowable value u_allow = 1·75 × 10⁻³ m, and gas temperature is the leading factor against output response, followed by rotational speed, inlet velocity, material density and outlet pressure. Moreover, the developed MPGA-EKM is superior to other methods in computational accuracy and efficiency. The efforts of this study provide a useful insight to design complex structures and enrich mechanical reliability theory.

中文翻译：

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使用替代模型和遗传算法的结构动态概率评估

为了提高复杂结构动态概率分析的计算精度和效率，提出了一种将极值响应面法（ERSM），Kriging模型和MPGA相融合的极值克里格法（EKM）和多种群遗传算法（MPGA）。特别地，通过结合克里格模型和ERSM来开发EKM，以处理相关变量的动态过程并通过考虑时域中每个动态分析中响应过程的极值来减少计算负担。MPGA用于代替体面的梯度以找到超参数θ在克里格模型中通过求解最大似然方程。通过对航空发动机高压压气机叶轮径向运行变形进行流-热-结构相互作用的动态概率分析，验证了该方法的有效性。分析结果表明，在允许值u _allow  = 1·75×10 ^-3的条件下，叶轮的可靠度为0·9956。 m，气体温度是影响输出响应的主要因素，其次是转速，入口速度，材料密度和出口压力。而且，开发的MPGA-EKM在计算精度和效率上都优于其他方法。这项研究的成果为设计复杂结构和丰富机械可靠性理论提供了有用的见识。