Study On The Application Of Surrogate Models For The Analysis Of Vibration Characteristics Of Mistuned Bladed Disks

Bladed disks are one of the vital components of aircraft engines.Long-term exposure to a vibrational working condition may cause high cycle fatigue.And ’mistuning’,which means small but inevitable difference among the sectors,occurs due to machining errors,dispersion of materials,etc.Mistuning makes the structure not periodically symmetric any more,causing vibration localization,which may magnify the amplitude of several blades and lead to crack before the designed lifetime.Therefore,it is important to analyze the vibrational behavior of mistuned bladed disks.In this paper,the application of surrogate models on predicting the forced response and amplification factor of a bladed disk is studied.The influence of sampling methods,training set sizes and model selection on the prediction accuracy is studied.And the influence of engine order,mistuning magnitude and damping ratio is also studied.The following conclusions can be drawn via massive Monte Carlo simulations based on a lumped parameter model where proportional mistuning is applied to the 24 sectors:(1)A training set with 1000 samples may provide the most satisfying accuracy while’overfitting’ may occur when more samples put in use;(2)Surrogate models based on low-discrepancy sequence(Sobol sequence here)server as the most accurate models;and no significant difference on the accuracy appears between surrogate models based on Latin hypercube sampling and simple random sampling;(3)Gauss process regression(GPR)models provide the highest accuracy,followed by second-order polynomial chaos expansion(PCE)models.And second-order polynomial regression(PR)models are the most inaccurate;(4)When the conditions of engine order,mistuning magnitude and damping ratio change,the mean value and 50% quantile can be accurately obtained by GPR models.However,the predicted standard deviation and 99% quantile are a little less than the real observations.Specifically,the ratio of predicted 99% quantile to the real value is about 95%,which can serve as a correction factor.Finally,a new algorithm based on truncated natural characteristics and optimization method due to the fact that prediction accuracy of GPR models gets lower when damping ratio is less.The validity is guaranteed via numerical experiments and the key problem is pointed out that the matrix is ill-conditioned and therefore leads to a oscillating result.