Sensitivity Analysis And Model Validation For The Multi-output Structure Systems

For the purpose of reducing experimental cost and shortening development cycles,model validation already becomes an important task of computational simulation in aerospace engineering fields.Due to the challenge of model validation theory in structural uncertainty,sensitivity analysis and model validation methods are mainly discussed in this research.Primary contents of the thesis are summarized as follows:(1)Development of two new validation approaches for models with multiple correlated responses.The first one is the validation approach based on mixed moment with four core metrics.For single validation site,local absolute metric based on mixed moment(LA-3M)and local relative metric based on mixed moment(LR-3M)are defined by the expectation of single dimensional variable and covariance matrix of multi-dimensional variables.For multiple validation site,global absolute metric based on mixed moment(GA-3M)and global relative metric based on mixed moment(GR-3M)are proposed by assessment of global agreement according to observations of multiple responses.The second one is the validation approach based on Mahalanobis distance(MD)with two core metrics.On one hand,the MD area metric is defined for validating multi-responses at single validation site,which provides a comparison between the cumulative distribution function(CDF)of MD for the model and the empirical CDF of MD for experimental observations.On the other hand,the MD pooling metric is proposed to validate multi-responses at multiple validation site,which provides a comparison between CDF of the probability integral transformation(PIT)of MD for the model and the empirical CDF of PIT of MD for experimental observations.Considering both random uncertainty and correlations among multiple responses from models and physical observations,challenges of validation and assessment for models with multiple correlated responses are solved by these two validation approaches mentioned before.Compared with existing validation metrics for multi-output models,the mixed moment based validation metric is superior on clear definition,fast runtime and strong applicability in engineering practice,while MD based validation metrics has advantages of simple calculation and low computational cost.(2)Based on the response characteristics of single output model,two new validation methods are established to validate single output models with mixed uncertainty by fixed interval variables and random variables respectively.Both for single output models with mixed uncertainty,the first is a validation metric defined by the difference between the upper and lower bounds of CDFs of model responses and that of experiments,while the second on the contrary,is a validation metric defined by the comparison between the CDF curves of the upper and lower bounds in same conditions.Case analysis results show that,since the CDF and the bounds can effectively extract the stochastic and the interval characteristics respectively,the two new validation metrics mentioned above are both able to measure the difference between experiments and models,which therefore,could effectively deal with the challenges of validation and assessment for single output model with mixed uncertainty of random and interval variables.(3)Based on the comprehensive statistical characteristics of MD and its CDF for multi outputs,two new validation metrics are proposed for multi-output models with mixed uncertainty of random and interval variables respectively.Both for multi-output models with mixed uncertainty,the first is a validation metric defined by the difference between the upper and lower bounds of MD's CDFs of model responses and that of experiments,while the second on the contrary,is a validation metric defined by the comparison between the MD's CDF curves of the upper and lower bounds in same conditions.Case analysis results show that,since the characteristic of multi responses can be synthesized by the MD,as well as the stochastic and interval uncertainty can be captured by the CDF of MD and the upper and lower bounds respectively,the two new validation metrics mentioned above are both able to measure the difference between experiments and models,which therefore,could effectively deal with the challenges of validation and assessment for single output model with mixed uncertainty of random and interval variables.(4)Two sensitivity indices are proposed for multi-output models under random uncertainty.When some input uncertainty is eliminated for multi-output models,the first one is the importance measure defined by the average shift of the MD variance using the idea of the variance-based importance measure analysis,while the second one is the moment-independent importance measure defined by the average change of the CDF of the MD using the idea of moment-independent importance measure analysis proposed by Borgonovo.Both approaches show the average influence of the input uncertainty on the entire output uncertainty.Case analysis results show that the challenges of the input variable importance measure analysis for multi-output models under random uncertainty are solved from different perspectives by these two new sensitivity indices effectively,considering both uncertainty and correlation among multiple outputs.Compared with the existing sensitivity analysis methods for multi outputs under random uncertainty,the new sensitivity indices efficiently provides alternatives for the input variable importance measure analysis and makes guidance for the robust optimization design or model calibration of structure system by the advantage of simple calculation and low computational cost.