Metamodel-based Uncertainty Propagation And Reduction For Structural Dynamics

Actual engineering problems are affected by many uncertain factors,and the physical parameters involved are usually uncertain and random.Since uncertainty has a non-negligible effect on the design and safety analysis of structures,uncertainty analysis and its treatment have gradually become important issues in science and engineering.At present,the mainstream tool for quantitatively describing uncertainty in engineering design is the probabilistic method,however,the establishment of accurate probabilistic models requires a large amount of response data.Simulation-based structural analysis and design methods have the advantages of intelligence,efficiency,safety,and less environmental constraints,and can realize virtual prediction and achieve supervision of product performance.Especially with the rapid development of computer technology,finite element(FE)modeling and simulation has been widely used in high-tech fields such as automobiles,aerospace,machinery,and weapon systems.Using the FE model to replace the real physical model can realize the full-size and full-detail simulation,providing a large amount of simulation data.However,with the design objects gradually becoming larger and elaborate,the number of FE meshes has increased dramatically,resulting in a substantial increase in the single simulation time for large and complex structures such as automobiles.For these time-consuming FE models,the solution efficiency is low,thus it is impossible to perform reanalysis and optimization design.In order to shorten the design cycle and improve development efficiency,engineering researchers are urgently required to find a new effective method to meet the needs for modern product design and development.Data-driven metamodeling technology has gradually attracted attention under such background.In structural reanalysis and optimization design,using metamodel to replace finite element simulation can significantly reduce the calculation amount and improve efficiency.At present,the research on metamodels has become a frontier and hot spot.Although metamodel technology has accumulated some theoretical results,its advantages in structural dynamics have not been fully discovered.There are still many challenges and difficulties.Different from the single-output of response in other disciplines,the response data featured with multiple-output,functional output and multi-fidelity in structural dynamics makes it difficult to create metamodels.To this end,this thesis explores and studies the key issues of metamodel technology in structural dynamics field.The main contents and conclusions are as follows:(1)Research on metamodeling and uncertainty propagation for the frequency response functionFrequency response function is an important description of structural systems in the frequency domain.In the presence of uncertainty,investigating the performance change under parameter variations is crucial for structural design and analysis.However,due to the high cost,the use of traditional stochastic analysis methods for uncertainty propagation of frequency response function is difficult to achieve.In order to speed up this process,a novel metamodeling method for frequency response function is proposed.Using the idea of "decomposition-training-reconstruction",the high dimensional of the frequency response function is transformed into a vector output of the modal parameters.Then a multi-output Gaussian process(MOGP)is used to quickly predict the modal parameters and subsequently to reconstruct frequency response function.The research results show that,compared with the latest methods in the literature,the proposed method has obvious computational advantages in predicting a single frequency response and its statistical information(mean,standard deviation,confidence interval,etc.)without a degradation of accuracy.The proposed method has good application prospects.(2)Research on metamodeling and uncertainty propagation for structure with clustered eigenvaluesIn the case of a system with clustered eigenvalues,e.g.,a structure exhibiting symmetry or periodicity,a small perturbation to clustered eigenvalues may lead to significant changes in the corresponding eigenvectors.Neglecting the effect of mode interactions may produce large errors for modal metamodels in this case.To meet this challenge,an effective automated mode tracking method(AMTM)is proposed.A general modal metamodel is built to predict both eigenvalues and eigenvectors in the presence of mode interactions.The results show that: 1)The combination of AMTM and metamodels can provide satisfactory results of uncertainty propagation for structures with clustered eigenvalues in a multidimensional parametric space.2)AMTM increases the range of applicability of modal metamodels in(nearly)symmetric periodic structures.3)AMTM can be used to identify the regions of mode veering/crossing in the design space.Such knowledge of these regions can be used in the design of reliable dynamic systems.(3)Research on multi-fidelity metamodel and model updating using metamodelsThe accuracy of metamodeling is largely depended on training data.Traditional metamodeling methods use only training data from single fidelity model.In order to improve the accuracy and efficiency of the metamodeling,a model fusion technique that integrates response data from different fidelity models is carried out,and a new multi-fidelity metamodel is established.In addition,considering the parameter differences between the simulation model and the real structure,a metamodel-based FE model updating method is further proposed to improve the prediction accuracy of the FE model.The research results show that: 1)An efficient and accurate response prediction of metamodel can be obtained with a large number of low-fidelity samples and a small number of high-fidelity samples.2)The method of FE model updating using metamodel has many advantages,including simple calculation,fast iterative convergence,and can be easily combined with advanced optimization algorithms.The proposed method has great potential in engineering practice.(4)Research on adaptive metamodeling in structural reliability designUncertainty inevitably exists in the actual product design,which produces the deviation between the pre-designed value and real value,which affects the product quality.Reliability based design aims to reduce the influence of uncertainty on the product,so that the structural performance is stable,safe and reliable.However,the limit state functions of engineering structures are usually implicit with strong nonlinearity.To address these problems,an adaptive sampling method is proposed and integrated with the reliability method to modify the classical SORA algorithm.The results show that: 1)Compared with other reliability methods,the reliability computation based on the metamodel has higher accuracy with a lower calculation amount.2)The improved optimization algorithm takes full use of the advantages of the original SORA algorithm,has better problem adaptability in reliability analysis and design.The proposed method can provide useful technical reference for engineering designers.