In the study of reliability of systems with multiple failure modes, approximations can be obtained by calculating the probability of failure for each state function. The first-order reliability method and the second-order reliability method are effective, but they may introduce significant errors when dealing with certain nonlinear situations. Simulation methods such as line sampling method and response surface method can solve implicit function problems, but the large amount of calculation results in low efficiency. The curved surface integral method (CSI) has good accuracy in dealing with nonlinear problems. Therefore, a system reliability analysis method (CSIMMS) is proposed on the basis of CSI for solving multiple failure modes system reliability problems with non-overlapping failure domains. The order of magnitude of the failure probability is evaluated based on the reliability index and the degree of nonlinearity, ignoring the influence of low order of magnitude failure modes, and reducing the calculation of the system failure probability. Finally, CSIMMS and other methods are compared by three numerical examples, and the results show the stability and accuracy of the proposed method.
{"title":"A Curved Surface Integral Method for Reliability Analysis of Multiple Failure Modes System with Non-Overlapping Failure Domains","authors":"Zhenzhong Chen, H. Mu, Xiaoke Li","doi":"10.1115/1.4065857","DOIUrl":"https://doi.org/10.1115/1.4065857","url":null,"abstract":"\u0000 In the study of reliability of systems with multiple failure modes, approximations can be obtained by calculating the probability of failure for each state function. The first-order reliability method and the second-order reliability method are effective, but they may introduce significant errors when dealing with certain nonlinear situations. Simulation methods such as line sampling method and response surface method can solve implicit function problems, but the large amount of calculation results in low efficiency. The curved surface integral method (CSI) has good accuracy in dealing with nonlinear problems. Therefore, a system reliability analysis method (CSIMMS) is proposed on the basis of CSI for solving multiple failure modes system reliability problems with non-overlapping failure domains. The order of magnitude of the failure probability is evaluated based on the reliability index and the degree of nonlinearity, ignoring the influence of low order of magnitude failure modes, and reducing the calculation of the system failure probability. Finally, CSIMMS and other methods are compared by three numerical examples, and the results show the stability and accuracy of the proposed method.","PeriodicalId":52254,"journal":{"name":"Journal of Verification, Validation and Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141688344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multi-fidelity (MF) models abound in simulation-based engineering fields. Many MF strategies have been proposed to improve the efficiency in engineering processes, especially in design optimization. When it comes to assessing the performance of MF optimization techniques, existing practice usually relies on test cases involving contrived MF models of seemingly random math functions, due to limited access to real-world MF models. While it is acceptable to use contrived MF models, these models are often manually written up rather than created in a systematic manner. This gives rise to the potential pitfall that the test MF models may be not representative of general scenarios. We propose a framework to generate test MF models systematically and characterize tested MF optimization methods' performances comprehensively. In our framework, the MF models are generated based on given high-fidelity (HF) model and come with two parameters to control their fidelity levels and allow model randomization. In our testing process, MF case problems are systematically formulated using our model creation method. Running the given MF optimization technique on these problems produces what we call “savings curve” that characterizes the method's performance similarly to how ROC curves characterize machine learning classifiers. Our test results also allow plotting “optimality curves” that serve similar functionality to savings curves in certain types of problems. The flexibility of our MF model creation facilitates the development of testing processes for general MF problem scenarios, and our framework can be easily extended to other MF applications than optimization.
{"title":"A Framework for Developing Systematic Testbeds for Multi-Fidelity Optimization Techniques","authors":"Siyu Tao, Chaitra Sharma, Srikanth Devanathan","doi":"10.1115/1.4065719","DOIUrl":"https://doi.org/10.1115/1.4065719","url":null,"abstract":"\u0000 Multi-fidelity (MF) models abound in simulation-based engineering fields. Many MF strategies have been proposed to improve the efficiency in engineering processes, especially in design optimization. When it comes to assessing the performance of MF optimization techniques, existing practice usually relies on test cases involving contrived MF models of seemingly random math functions, due to limited access to real-world MF models. While it is acceptable to use contrived MF models, these models are often manually written up rather than created in a systematic manner. This gives rise to the potential pitfall that the test MF models may be not representative of general scenarios. We propose a framework to generate test MF models systematically and characterize tested MF optimization methods' performances comprehensively. In our framework, the MF models are generated based on given high-fidelity (HF) model and come with two parameters to control their fidelity levels and allow model randomization. In our testing process, MF case problems are systematically formulated using our model creation method. Running the given MF optimization technique on these problems produces what we call “savings curve” that characterizes the method's performance similarly to how ROC curves characterize machine learning classifiers. Our test results also allow plotting “optimality curves” that serve similar functionality to savings curves in certain types of problems. The flexibility of our MF model creation facilitates the development of testing processes for general MF problem scenarios, and our framework can be easily extended to other MF applications than optimization.","PeriodicalId":52254,"journal":{"name":"Journal of Verification, Validation and Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141350887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
RV (Rotate Vector) reducer is an essential mechanical transmission device extensively used in industrial machinery, robotics, aerospace and other fields. The dynamic transmission characteristics and strength of the cycloidal pin gear, turning arm bearing of RV reducer significantly affect the motion accuracy and reliability of the whole equipment. Uncertainties from manufacturing and assembly error, working loads add complexity to these effects. Developing effective methods for uncertainty propagation and reliability analysis for the RV reducer is crucial. In this work, the mail failure modes of RV reducer are studied, and an effective reliability analysis method for RV reducer considering the correlation between multi-failure modes by combining polynomial chaos expansions (PCE) and saddlepoint approximation method (SPA) is proposed. This paper develops an uncertainty propagation strategy for RV reducer based on dynamic simulation and PCE method with high accuracy. On this basis, a surrogated cumulant generating function (CGF) and SPA are combined to analyze the stochastic characteristic for the failure behavior. Based on the probability density function (PDF) and cumulative distribution function (CDF) calculated by SPA, copula function is employed to quantify the correlations between the multi-failure modes. Then, the system reliability with multi-failure modes is estimated by SPA and optimal copula function. The proposed method provides an effective reliability assessment technology with high-accuracy for complex system under unknown physical model and distribution characteristics. The validity of the proposed approach is illustrated RV-320E reducer reliability estimation, offering a basis to improve the performance of complex dynamic system. .
{"title":"Reliability Analysis for RV Reducer by Combining PCE and Saddlepoint Approximation Considering Multi-Failure Modes","authors":"Shunqi Yang, Huipeng Xiao, Pan Lu, Guohua Xu, Hao Li, Xiaoling Zhang","doi":"10.1115/1.4065690","DOIUrl":"https://doi.org/10.1115/1.4065690","url":null,"abstract":"\u0000 RV (Rotate Vector) reducer is an essential mechanical transmission device extensively used in industrial machinery, robotics, aerospace and other fields. The dynamic transmission characteristics and strength of the cycloidal pin gear, turning arm bearing of RV reducer significantly affect the motion accuracy and reliability of the whole equipment. Uncertainties from manufacturing and assembly error, working loads add complexity to these effects. Developing effective methods for uncertainty propagation and reliability analysis for the RV reducer is crucial. In this work, the mail failure modes of RV reducer are studied, and an effective reliability analysis method for RV reducer considering the correlation between multi-failure modes by combining polynomial chaos expansions (PCE) and saddlepoint approximation method (SPA) is proposed. This paper develops an uncertainty propagation strategy for RV reducer based on dynamic simulation and PCE method with high accuracy. On this basis, a surrogated cumulant generating function (CGF) and SPA are combined to analyze the stochastic characteristic for the failure behavior. Based on the probability density function (PDF) and cumulative distribution function (CDF) calculated by SPA, copula function is employed to quantify the correlations between the multi-failure modes. Then, the system reliability with multi-failure modes is estimated by SPA and optimal copula function. The proposed method provides an effective reliability assessment technology with high-accuracy for complex system under unknown physical model and distribution characteristics. The validity of the proposed approach is illustrated RV-320E reducer reliability estimation, offering a basis to improve the performance of complex dynamic system. .","PeriodicalId":52254,"journal":{"name":"Journal of Verification, Validation and Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141382272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study proposes a theoretical model and assessment method for the resilience of High Consequence System (HCS), addressing the risk assessment and decision-making needs in critical system engineering activities. By analyzing various resilience theories in different domains and considering the characteristics of risk decision-making for HCS, a comprehensive theoretical model for the resilience of HCS is developed. This model considers the operational capability under normal environment (consisting of reliability and maintainability) and the safety capability under abnormal environment (consisting of resistance and emergence response ability). A case study is conducted on a spent fuel transportation packaging system, where the sealing performance after sealing ring aging is regarded as the reliability of the system and calculated using reliability methods, and impact resistance after impact is regard as resistance the impact safety of the packaging system is assessed using finite element analysis and surrogate modelling methods. The surrogate model fits the deformation output results of finite elements. Maintainability and emergency response ability are also essential elements of the resilience model for HCS facing exceptional events. The resilience variation of the spent fuel transportation packaging system is computed under the uncertainty of yielding stress of buffer material. The resilience of the packaging system is evaluated for different buffer thicknesses. The system's resilience decreases with higher uncertainty in the yielding stress of the buffer material, while it increases with thicker buffer materials. The improvement of emergency rescue ability will also lead to the improvement of system resilience.
{"title":"Machine Learning-Based Resilience Modeling and Assessment of High Consequence Systems Under Uncertainty","authors":"Liu Cong, Fengjun Wang, Chaoyang Xie","doi":"10.1115/1.4065466","DOIUrl":"https://doi.org/10.1115/1.4065466","url":null,"abstract":"\u0000 This study proposes a theoretical model and assessment method for the resilience of High Consequence System (HCS), addressing the risk assessment and decision-making needs in critical system engineering activities. By analyzing various resilience theories in different domains and considering the characteristics of risk decision-making for HCS, a comprehensive theoretical model for the resilience of HCS is developed. This model considers the operational capability under normal environment (consisting of reliability and maintainability) and the safety capability under abnormal environment (consisting of resistance and emergence response ability). A case study is conducted on a spent fuel transportation packaging system, where the sealing performance after sealing ring aging is regarded as the reliability of the system and calculated using reliability methods, and impact resistance after impact is regard as resistance the impact safety of the packaging system is assessed using finite element analysis and surrogate modelling methods. The surrogate model fits the deformation output results of finite elements. Maintainability and emergency response ability are also essential elements of the resilience model for HCS facing exceptional events. The resilience variation of the spent fuel transportation packaging system is computed under the uncertainty of yielding stress of buffer material. The resilience of the packaging system is evaluated for different buffer thicknesses. The system's resilience decreases with higher uncertainty in the yielding stress of the buffer material, while it increases with thicker buffer materials. The improvement of emergency rescue ability will also lead to the improvement of system resilience.","PeriodicalId":52254,"journal":{"name":"Journal of Verification, Validation and Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141006679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Davis Equation Of State (EOS) is commonly used to model thermodynamic relationships for High Explosive reactants. Typically, the parameters in the EOS are calibrated, with uncertainty, using a Bayesian framework and Markov Chain Monte Carlo (MCMC) methods. However, MCMC methods are computationally expensive, especially for complex models with many parameters. This paper provides a comparison between MCMC and less computationally expensive variational methods (Variational Bayesian and Hessian Variational Bayesian) for computing the posterior distribution and approximating the posterior covariance matrix based on heterogeneous experimental data. All three methods recover similar posterior distributions and posterior covariance matrices. This study demonstrates that for this EOS parameter calibration application, the assumptions made in the two Variational methods significantly reduce the computational cost but do not substantially change the results compared to MCMC.
{"title":"Posterior Covariance Matrix Approximations","authors":"Abigail Schmid, Stephen Andrews","doi":"10.1115/1.4065378","DOIUrl":"https://doi.org/10.1115/1.4065378","url":null,"abstract":"\u0000 The Davis Equation Of State (EOS) is commonly used to model thermodynamic relationships for High Explosive reactants. Typically, the parameters in the EOS are calibrated, with uncertainty, using a Bayesian framework and Markov Chain Monte Carlo (MCMC) methods. However, MCMC methods are computationally expensive, especially for complex models with many parameters. This paper provides a comparison between MCMC and less computationally expensive variational methods (Variational Bayesian and Hessian Variational Bayesian) for computing the posterior distribution and approximating the posterior covariance matrix based on heterogeneous experimental data. All three methods recover similar posterior distributions and posterior covariance matrices. This study demonstrates that for this EOS parameter calibration application, the assumptions made in the two Variational methods significantly reduce the computational cost but do not substantially change the results compared to MCMC.","PeriodicalId":52254,"journal":{"name":"Journal of Verification, Validation and Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140669692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thomas H. Hannah, V. Martin, Stephen Ellis, Reuben H. Kraft
The purpose of this work is to develop and verify a method for quantitatively analyzing data collected from Kolsky bar experiments and to confirm its validity by comparing it to a finite element (FE) model. This study also aims to demonstrate the need for higher sample rate capture in miniature Kolsky bars, 3.16mm diameter used in this work, by comparing results from two different data acquisition setups on identically sized experimental setups. We identified that the sample capture rate needed to accurately depict experimental results on small scale systems is at least 400 kHz, which is far greater than what is typically assumed for lager bar systems. Finally, a statistical method for evaluating results is presented an expanded upon which removes the dependence on the knowledge and experience of the experimentalist to interpret the data. Using this analysis technique on the two different systems examined in this study, we find upwards of 3.5 times better loading condition reproducibility and up to a 20 MPa reduction in the standard deviation of the sample stress profile, confirming the need for higher quality frequency capture rates.
{"title":"Influence of Sampling Rate on Reproducibility and Accuracy of Miniature Kolsky Bar Experiments","authors":"Thomas H. Hannah, V. Martin, Stephen Ellis, Reuben H. Kraft","doi":"10.1115/1.4065207","DOIUrl":"https://doi.org/10.1115/1.4065207","url":null,"abstract":"\u0000 The purpose of this work is to develop and verify a method for quantitatively analyzing data collected from Kolsky bar experiments and to confirm its validity by comparing it to a finite element (FE) model. This study also aims to demonstrate the need for higher sample rate capture in miniature Kolsky bars, 3.16mm diameter used in this work, by comparing results from two different data acquisition setups on identically sized experimental setups. We identified that the sample capture rate needed to accurately depict experimental results on small scale systems is at least 400 kHz, which is far greater than what is typically assumed for lager bar systems. Finally, a statistical method for evaluating results is presented an expanded upon which removes the dependence on the knowledge and experience of the experimentalist to interpret the data. Using this analysis technique on the two different systems examined in this study, we find upwards of 3.5 times better loading condition reproducibility and up to a 20 MPa reduction in the standard deviation of the sample stress profile, confirming the need for higher quality frequency capture rates.","PeriodicalId":52254,"journal":{"name":"Journal of Verification, Validation and Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140372656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thomas H. Hannah, V. Martin, Stephen Ellis, Reuben H. Kraft
Typical Kolsky bars are 10-20mm in diameter with lengths of each main bar being on the scale of meters. To push 104+ strain rates, smaller systems are needed. As the diameter and mass decreases the precision in the alignment must increase to maintain the same relative tolerance, and the potential impacts of gravity and friction change. Finite Element models are typically generated assuming a perfect experiment with exact alignment and no gravity. Additionally, these simulations tend to take advantage of the radial symmetry of an ideal experiment which removes any potential for modeling non-symmetric effects, but has the benefit of reducing computational load. In this work we discuss results from these fast-running symmetry models to establish a baseline and demonstrate their first-order use case. We then take advantage of high-performance computing techniques to generate half symmetry simulations using Abaqu to model gravity and misalignment. The imperfection is initially modeled using a static general step followed by a dynamic explicit step to simulate the impact events. This multi-step simulation structure can properly investigate the impact of these real-world, non-axis symmetric effects. These simulations explore the impacts of these experimental realities and are described in detail to allow other researchers to implement a similar FE modeling structure to aid in experimentation and diagnostic efforts. It is shown that of the two sizes evaluated, the smaller 3.16mm system is more sensitive than the larger 12.7mm system to such imperfections
{"title":"Impact of Imperfect Kolsky Bar Experiments Across Different Scales Assessed Using Finite Elements","authors":"Thomas H. Hannah, V. Martin, Stephen Ellis, Reuben H. Kraft","doi":"10.1115/1.4065206","DOIUrl":"https://doi.org/10.1115/1.4065206","url":null,"abstract":"\u0000 Typical Kolsky bars are 10-20mm in diameter with lengths of each main bar being on the scale of meters. To push 104+ strain rates, smaller systems are needed. As the diameter and mass decreases the precision in the alignment must increase to maintain the same relative tolerance, and the potential impacts of gravity and friction change. Finite Element models are typically generated assuming a perfect experiment with exact alignment and no gravity. Additionally, these simulations tend to take advantage of the radial symmetry of an ideal experiment which removes any potential for modeling non-symmetric effects, but has the benefit of reducing computational load. In this work we discuss results from these fast-running symmetry models to establish a baseline and demonstrate their first-order use case. We then take advantage of high-performance computing techniques to generate half symmetry simulations using Abaqu to model gravity and misalignment. The imperfection is initially modeled using a static general step followed by a dynamic explicit step to simulate the impact events. This multi-step simulation structure can properly investigate the impact of these real-world, non-axis symmetric effects. These simulations explore the impacts of these experimental realities and are described in detail to allow other researchers to implement a similar FE modeling structure to aid in experimentation and diagnostic efforts. It is shown that of the two sizes evaluated, the smaller 3.16mm system is more sensitive than the larger 12.7mm system to such imperfections","PeriodicalId":52254,"journal":{"name":"Journal of Verification, Validation and Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140372142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the realm of reliability analysis methods, the First-Order Reliability Method (FORM) exhibits excellent computational accuracy and efficiency in linear problems. However, it fails to deliver satisfactory performance in nonlinear ones. Therefore, this paper proposes an Approximate Integral Method (AIM) to calculate the failure probability of nonlinear problems. Firstly, based on the Most Probable Point (MPP) of failure and the reliability index β obtained from the FORM, the Limit State Function (LSF) can be equivalent to an Approximate Parabola (AP) which divides the hypersphere space into feasible and failure domains. Secondly, through the ratio of the approximate region occupied by a parabolic curve to the entire hypersphere region, the failure probability can be calculated by integration. To avoid the computational complexity in the parabolic approximate area due to high dimensionality, this paper employs a hyper-rectangle, constructed from chord lengths corresponding to different curvatures, as a substitute for the parabolic approximate area. Additionally, a function is utilized to adjust this substitution, ensuring accuracy in the calculation. Finally, compared with the calculated result of the Monte Carlo simulation (MCS) and the FORM, the feasibility of this method can be demonstrated through five numerical examples.
在可靠性分析方法领域，一阶可靠性方法（FORM）在线性问题中表现出卓越的计算精度和效率。然而，它在非线性问题中却无法提供令人满意的性能。因此，本文提出了一种近似积分法（AIM）来计算非线性问题的失效概率。首先，根据 FORM 得出的失效最可能点（MPP）和可靠性指数 β，可将极限状态函数（LSF）等价为近似抛物线（AP），将超球空间划分为可行域和失效域。其次，通过抛物线所占近似区域与整个超球区域的比率，可以通过积分计算出失效概率。为避免抛物线近似区域因维度过高而带来的计算复杂性，本文采用由不同曲率对应的弦长构建的超矩形来替代抛物线近似区域。此外，还利用一个函数来调整这种替代，以确保计算的准确性。最后，通过与蒙特卡罗模拟（MCS）和 FORM 的计算结果进行比较，通过五个数值示例证明了该方法的可行性。
{"title":"Approximate Integral Method for Nonlinear Reliability Analysis","authors":"Zhenzhong Chen, Guiming Qiu, Xiaoke Li, Rui Jin","doi":"10.1115/1.4065183","DOIUrl":"https://doi.org/10.1115/1.4065183","url":null,"abstract":"In the realm of reliability analysis methods, the First-Order Reliability Method (FORM) exhibits excellent computational accuracy and efficiency in linear problems. However, it fails to deliver satisfactory performance in nonlinear ones. Therefore, this paper proposes an Approximate Integral Method (AIM) to calculate the failure probability of nonlinear problems. Firstly, based on the Most Probable Point (MPP) of failure and the reliability index β obtained from the FORM, the Limit State Function (LSF) can be equivalent to an Approximate Parabola (AP) which divides the hypersphere space into feasible and failure domains. Secondly, through the ratio of the approximate region occupied by a parabolic curve to the entire hypersphere region, the failure probability can be calculated by integration. To avoid the computational complexity in the parabolic approximate area due to high dimensionality, this paper employs a hyper-rectangle, constructed from chord lengths corresponding to different curvatures, as a substitute for the parabolic approximate area. Additionally, a function is utilized to adjust this substitution, ensuring accuracy in the calculation. Finally, compared with the calculated result of the Monte Carlo simulation (MCS) and the FORM, the feasibility of this method can be demonstrated through five numerical examples.","PeriodicalId":52254,"journal":{"name":"Journal of Verification, Validation and Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140379416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The inherent randomness of fluid dynamics problems or human cognitive limitations results in non-negligible uncertainties in CFD modeling and simulation, leading to doubts about the credibility of CFD results. Therefore, scientific and rigorous quantification of these uncertainties is crucial for assessing the reliability of CFD predictions and informed engineering decisions. Although mature uncertainty propagation methods have been developed for individual output quantities, the challenges lie in the multi-dimensional correlated flow field variables. This article proposes an advanced uncertainty propagation modeling approach based on proper orthogonal decomposition and artificial neural networks. By projecting the multi-dimensional correlated responses onto an orthogonal basis function space, the dimensionality of output is significantly reduced, simplifying the subsequent model training process. An artificial neural network that maps the uncertain parameters of the CFD model to the coefficients of the basis functions is established. Due to the bidirectional representation of flow field variables and basis function coefficients through proper orthogonal decomposition, combined with artificial neural network modeling, rapid prediction of flow field variables under any model parameters is achieved. To effectively identify the most influential model parameters, we employ a multi-output global sensitivity analysis method based on covariance decomposition. Through two exemplary cases of NACA0012 airfoil and M6 wing, we demonstrate the accuracy and efficacy of our proposed approach in predicting multi-dimensional flow field variables under varying model coefficients. Large-scale random sampling is conducted to quantify the uncertainties and identify the key factors that significantly impact the overall flow field.
{"title":"Uncertainty Quantification for Multi-Dimensional Correlated Flow Field Responses","authors":"Wei Zhao, Luogeng Lv, Jiao Zhao, Wei Xiao, Jiangtao Chen, Xiaojun Wu","doi":"10.1115/1.4065070","DOIUrl":"https://doi.org/10.1115/1.4065070","url":null,"abstract":"\u0000 The inherent randomness of fluid dynamics problems or human cognitive limitations results in non-negligible uncertainties in CFD modeling and simulation, leading to doubts about the credibility of CFD results. Therefore, scientific and rigorous quantification of these uncertainties is crucial for assessing the reliability of CFD predictions and informed engineering decisions. Although mature uncertainty propagation methods have been developed for individual output quantities, the challenges lie in the multi-dimensional correlated flow field variables. This article proposes an advanced uncertainty propagation modeling approach based on proper orthogonal decomposition and artificial neural networks. By projecting the multi-dimensional correlated responses onto an orthogonal basis function space, the dimensionality of output is significantly reduced, simplifying the subsequent model training process. An artificial neural network that maps the uncertain parameters of the CFD model to the coefficients of the basis functions is established. Due to the bidirectional representation of flow field variables and basis function coefficients through proper orthogonal decomposition, combined with artificial neural network modeling, rapid prediction of flow field variables under any model parameters is achieved. To effectively identify the most influential model parameters, we employ a multi-output global sensitivity analysis method based on covariance decomposition. Through two exemplary cases of NACA0012 airfoil and M6 wing, we demonstrate the accuracy and efficacy of our proposed approach in predicting multi-dimensional flow field variables under varying model coefficients. Large-scale random sampling is conducted to quantify the uncertainties and identify the key factors that significantly impact the overall flow field.","PeriodicalId":52254,"journal":{"name":"Journal of Verification, Validation and Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140246376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reviewer's Recognition","authors":"","doi":"10.1115/1.4064715","DOIUrl":"https://doi.org/10.1115/1.4064715","url":null,"abstract":"","PeriodicalId":52254,"journal":{"name":"Journal of Verification, Validation and Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140406197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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