Research On High-fidelity Model Validation Of Aircraft Based On Fuzzy Surrogate

The rapid development of the aerospace industry has put forward higher requirements on the level of aircraft design.Constructing a high-fidelity model,e.g.,finite element model or computational fluid dynamics model,can not only flexibly and conveniently evaluate the performance of the design and verify the pros and cons,but also serves as the basis for optimization design and reliability analysis,thus significantly improving the level of aircraft design.However,since “all models are wrong”,before applying the high-fidelity model,the accuracy and confidence level of the model must first be evaluated,i.e.,model validation.At present,due to the computational complexity of the aircraft high-fidelity models and the small samples of aircraft tests,it is difficult to conduct model validation in aircraft field.This paper systematically researches the validation of high-fidelity models in the aircraft field.Three techniques in model validation,i.e.,surrogate modeling,validation metric,and calibration,are studied and a systematic model validation framework has been formed.Further,the framework is applied to two engineering examples,i.e.,satellite coverage traffic volume model and satellite structure finite element model.In terms of model validation method research:Considering the computational complexity of the high-fidelity models,the surrogate modeling technique based on fuzzy neural network is studied.A new surrogate named disjunctive fuzzy neural network(DJFNN)is proposed,which includes a new network architecture and a novel learning algorithm based on greedy search.DJFNN can achieve a reasonable balance of prediction accuracy,interpretability,and model training calculations,which is especially suitable for surrogate modeling of high-fidelity models of high-dimensional and complex aircraft.Besides,DJFNN has strong scalability,i.e.,it can be combined with other models to produce new surrogate models.The performance of DJFNN has been verified by a numerical example,28 real-world database and satellite engineering examples.Considering the challenge of small samples when calculating validation metric,a new model validation metric considering limited experimental data is studied.The classical area metric is extended to interval form,forming the interval area metric.The interval area metric has considered the epistemic uncertainty caused by the limited experimental data through constructing boundary distribution functions of physical observations,thus,it can avoid overconfident judgments and get more realistic validation results.The validity of the proposed method has been verified by a numerical example and a practical satellite engineering example.Considering the challenge of small samples when conducting model calibration,a Bayesian calibration method based on fuzzy model is studied.First,the T-S type model discrepancy function is proposed,i.e.,modeling the model discrepancy as a 0-order T-S model.Compared with the traditional black-box and data-driven method,the T-S type model discrepancy function has the advantages of: strong ability to exploit expert knowledge,low calculation cost,and easy to interpret.Then,the Bayesian calibration based on T-S type model discrepancy function is proposed.The proposed method first constructs a surrogate of the high-fidelity model using DJFNN,then applies FCM to construct the T-S type model discrepancy function,and finally obtains the posteriors of parameters based on Bayesian inference and Markov Chain Monte Carlo(MCMC)sampling algorithm.The good identifiability property of the proposed method is verified by the analysis of Fisher information matrix.The effectiveness of the method has been verified by a numerical example,Sandia 2014 V&V challenge problem,and a satellite engineering example.In terms of model validation application research:The application of the proposed methods in the satellite coverage ADS-B traffic model is studied.Based on part of the ADS-B messages obtained by Tiantuo-5 satellite,an approximate global distribution of aircraft equipped with ADS-B is constructed and a satellite coverage ADS-B traffic model is established.The proposed validation framework is applied to validate the satellite coverage ADS-B traffic model,which leads to a realistic evaluation of the model and gets a more accurate model parameter.The application of the proposed methods in the Tiantuo-3 satellite structure finite element model is studied.To predict the first-order natural frequency of the Tiantuo-3structure,a finite element model of the Tiantuo-3 structure is constructed.Based on the vibration test data,the interval area metric is used to validate the finite element model of the Tiantuo-3 structure.Then,a static test of the support rod structure is designed.Based on the measured strain data,the Bayesian model calibration based on T-S model is used to calibrate the model parameter thus a more accurate parameter is obtained.