Improved Kriging with extremum response surface method for structural dynamic reliability and sensitivity analyses

The safety and reliability of any complex mechanical structures are critical to ensure that they can function properly. Therefore, we need to thoroughly evaluate their reliability by performing dynamic probabilistic analyses, including the reliability and sensitivity analyses, which take the variation in the input variables into consideration. The typical approach is by performing the Monte Carlo (MC) simulation, which requires thousands of runs and could be computationally intractable. An efficient and accurate surrogate model can help reduce the computational burden in these analyses. To further reduce the computational complexity, we model only the extremum values, instead of modeling all the output responses within the time domain of interest. The developed surrogate model is called the improved Kriging (IK) algorithm with extremum response surface method (ERSM), or the IK-ERSM model. Compared to the previously developed QP-ERSM, which uses the quadratic polynomial (QP) model, the improved Kriging can better model the nonlinearity within the system. To build the IK model, we employ the genetic algorithm (GA) method to find the Kriging hyperparameters θ, by solving the maximum likelihood equation (MLE). This model shows a good accuracy, with a testing error of less than 1%. The effectiveness of the developed IK-ERSM model is demonstrated to perform the reliability and sensitivity analyses of the compressor blisk radial deformation. For the direct simulation, we consider the fluid–structure coupling of the system, for a more realistic analysis. The results show that the compressor blisk has a reliability degree of 0.9984 when the allowable value of the compressor blisk radial deformation is 1.60×10⁻³ m. From the sensitivity analysis results, we identify that the angular speed has the highest impact on the output response, followed by the inlet velocity and material density. Through the validation process, we see that the developed IK-ERSM model has a better overall performance than the QP-ERSM and K-ERSM models, in terms of the fitting times and testing errors. With these results, the IK-ERSM is demonstrated to be efficient and accurate in structural dynamic probabilistic analysis. This study provide a useful insight for the dynamic probabilistic design of complex structure and enrich mechanical reliability theory.