The classic polynomial chaos method（PCM）, characterized as an intrusive methodology,has been applied to uncertainty propagation（UP） in many dynamic systems. However, the intrusive polynomial chaos method（IPCM） r...The classic polynomial chaos method（PCM）, characterized as an intrusive methodology,has been applied to uncertainty propagation（UP） in many dynamic systems. However, the intrusive polynomial chaos method（IPCM） requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method（NIPCM） that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.展开更多
The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to ...The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.展开更多
Offshore wind substations are subjected to uncertain loads from waves,wind and currents.Sea states are composed of irregular waves which statistics are usually characterized.Irregular loads may induce fatigue failure ...Offshore wind substations are subjected to uncertain loads from waves,wind and currents.Sea states are composed of irregular waves which statistics are usually characterized.Irregular loads may induce fatigue failure of some structural components of the structures.By combining fatigue damage computed through numerical simulations for each sea state endured by the structure,it is possible to assess fatigue failure of the structure over the whole deployment duration.Yet,the influence of the discretization error on the fatigue damage is rarely addressed.It is possible to estimate the discretization error on the quantity of interest computed at the structural detail suspected to fail.However,the relation between this local quantity of interest and the fatigue damage is complex.In this paper,a method that allows propagating error bounds towards fatigue damage is proposed.While increasing computational burden,computing discretization error bounds is a useful output of finite element analysis.It can be utilized to either validate mesh choice or guide remeshing in case where potential error on the fatigue damage is too large.This method is applied to an offshore wind substation developped by Chantiers de l’Atlantique using two discretization error estimators in a single sea state.展开更多
Configuration stability is essential for a space-based Gravitational-Wave(GW)observatory,which can be impacted by orbit insertion uncertainties.Configuration uncertainty propagation is vital for investigating the infl...Configuration stability is essential for a space-based Gravitational-Wave(GW)observatory,which can be impacted by orbit insertion uncertainties.Configuration uncertainty propagation is vital for investigating the influences of uncertainties on configuration stability and can be potentially useful in the navigation and control of GW observatories.Current methods suffer from drawbacks related to high computational burden.To this end,a Radial-Tangential-Ddirectional State Transition Tensor(RT-DSTT)-based configuration uncertainty propagation method is proposed.First,two sensitive directions are found by capturing the dominant secular terms.Considering the orbit insertion errors along the two sensitive directions only,a reduced-order RT-DSTT model is developed for orbital uncertainty propagation.Then,the relationship between the uncertainties in the orbital states and the uncertainties in the configuration stability indexes is mapped using highorder derivatives.The result is a semi-analytical solution that can predict the deviations in the configuration stability indexes given orbit insertion errors.The potential application of the proposed RT-DSTT-based method in calculating the feasible domain is presented.The performance of the proposed method is validated on the Laser Interferometer Space Antenna(LISA)project.Simulations show that the proposed method can provide similar results to the STT-based method but requires only half of the computational time.展开更多
Interval Uncertainty Propagation(IUP)holds significant importance in quantifying uncertainties in structural outputs when confronted with interval input parameters.In the aviation field,the precise determination of pr...Interval Uncertainty Propagation(IUP)holds significant importance in quantifying uncertainties in structural outputs when confronted with interval input parameters.In the aviation field,the precise determination of probability models for input parameters of aeronautical structures entails substantial costs in both time and finances.As an alternative,the use of interval variables to describe input parameter uncertainty becomes a pragmatic approach.The complex task of solving the IUP for aeronautical structures,particularly in scenarios marked by pronounced nonlinearity and multiple outputs,necessitates innovative methodologies.This study introduces an efficient deep learning-driven approach to address the challenges associated with IUP.The proposed approach combines the Deep Neural Network(DNN)with intelligent optimization algorithms for dealing with the IUP in aeronautical structures.An inventive extremal value-oriented weighting technique is presented,assigning varying weights to different training samples within the loss function,thereby enhancing the computational accuracy of the DNN in predicting extremal values of structural outputs.Moreover,an adaptive framework is established to strategically balance the global exploration and local exploitation capabilities of the DNN,resulting in a predictive model that is both robust and accurate.To illustrate the effectiveness of the developed approach,various applications are explored,including a high-dimensional numerical example and two aeronautical structures.The obtained results highlight the high computational accuracy and efficiency achieved by the proposed approach,showcasing its potential for addressing complex IUP challenges in aeronautical engineering.展开更多
This paper reviews the recent advances of practical techniques within different method frameworks for improved uncertainty propagation in orbital dynamics.The uncertainty propagation problem has been explored in many ...This paper reviews the recent advances of practical techniques within different method frameworks for improved uncertainty propagation in orbital dynamics.The uncertainty propagation problem has been explored in many applications in orbital dynamics,such as orbit determination,relative motion,space debris removal,and small body exploration.In recent years,to further improve the accuracy and efficiency of uncertainty propagation,many practical techniques have been presented within different method frameworks.Among these,most techniques are within the frameworks of the continuity equation,the Gaussian mixture model,and the surrogate model.To facilitate the research work for nonlinear uncertainty propagation in orbital dynamics,a classification of the present method frameworks and the practical techniques for improved uncertainty propagation within different method frameworks is given and discussed in this paper.展开更多
A robust analytical model of Eccentric Braced Frames (EBFs), as a well-known seismic resistance system, helps to comprehensive earthquake-induced risk assessment of buildings in different performance levels. Recently,...A robust analytical model of Eccentric Braced Frames (EBFs), as a well-known seismic resistance system, helps to comprehensive earthquake-induced risk assessment of buildings in different performance levels. Recently, the modeling parameters have been introduced to simulate the hysteretic behavior of shear links in EBFs with specific Coefficient of Variation associated with each parameter to consider the uncertainties. The main purpose of this paper is to assess the effect of these uncertainties in the seismic response of EBFs by combining different sources of aleatory and epistemic uncertainties while making a balance between the required computational effort and the accuracy of the responses. This assessment is carried out in multiple performance levels using Endurance Time (ET) method as an efficient Nonlinear Time History Analysis. To demonstrate the method, a 4-story EBF that considers behavioral parameters has been considered. First, a sensitivity analysis using One-Variable-At-a-Time procedure and the ET method has been utilized to sort the parameters with regard to their importance in seismic responses in two intensity levels. A sampling-based reliability method is first used to propagate the modeling uncertainties into the fragility curves of the structure. Radial Basis Function Networks are then utilized to estimate the structural responses, which makes it feasible to propagate the uncertainties with an affordable computational effort. The Design of Experiments technique is implemented to acquire the training data, reducing the required data. The results show that the mathematical relationships defined by Artificial Neural Networks and using the ET method can estimate the median Intensity Measures and shifts in dispersions with acceptable accuracy.展开更多
Experimentally measured neutron activation cross sections are presented for the^(65)Cu(n,α)^(62m)Cu,^(41)K(n,α)^(38)Cl,and^(65)Cu(n,2n)^(64)Cu reactions with detailed uncertainty propagation.The neutron cross sectio...Experimentally measured neutron activation cross sections are presented for the^(65)Cu(n,α)^(62m)Cu,^(41)K(n,α)^(38)Cl,and^(65)Cu(n,2n)^(64)Cu reactions with detailed uncertainty propagation.The neutron cross sections were measured at an incident energy of 14.92±0.02 MeV,and the neutrons were based on the t(d,n)αfusion reaction.The^(27)Al(n,α)^(24)Na reaction was used as a reference reaction for the normalization of the neutron flux.The pre-calibrated lead-shielded HPGe detector was used to detect the residues'γ-ray spectra.The data from the measured cross sections are compared to the previously measured cross sections from the EXFOR database,theoretically calculated cross sections using the TALYS and EMPIRE codes,and evaluated nuclear data.展开更多
The usage of state transition tensors(STTs)was proved as an effective method for orbital uncertainty propagation.However,orbital maneuvers and their uncertainties are not considered in current STT-based methods.Uncert...The usage of state transition tensors(STTs)was proved as an effective method for orbital uncertainty propagation.However,orbital maneuvers and their uncertainties are not considered in current STT-based methods.Uncertainty propagation of spacecraft trajectory with maneuvers plays an important role in spaceflight missions,e.g.,the rendezvous phasing mission.Under the effects of impulsive maneuvers,the nominal trajectory of a spacecraft will be divided into several segments.If the uncertainty is piecewise propagated using the STTs one after another,large approximation errors will be introduced.To overcome this challenge,a set of modified STTs is derived,which connects the segmented trajectories together and allows for directly propagating uncertainty from the initial time to the final time.These modified STTs are then applied to analytically propagate the statistical moments of navigation and impulsive maneuver uncertainties.The probability density function is obtained by combining STTs with the Gaussian mixture model.The proposed uncertainty propagator is shown to be efficient and affords good agreement with Monte Carlo simulations.It also has no dimensionality problem for high-dimensional uncertainty propagation.展开更多
Long-term configuration stability is essential for an interferometric detection constellation(IDC),which is closely related to initial uncertainty.Therefore,it is vital to evaluate the uncertainty and characterize the...Long-term configuration stability is essential for an interferometric detection constellation(IDC),which is closely related to initial uncertainty.Therefore,it is vital to evaluate the uncertainty and characterize the configuration stability.In this study,an analytical method was developed for the configuration uncertainty propagation of a geocentric triangular IDC.The angular momentum and the argument latitude were found to be significantly affected by the initial uncertainty and were selected as the core variables.By averaging the perturbation in one revolution,an analytical solution was proposed for propagating the core orbital elements in one revolution.Subsequently,the analytical solution of the orbit elements during the mission period is obtained by multiplying the solutions in iterative revolutions.The relationship between the selected orbital elements and the configuration stability parameters was established using an analytical solution.The effects of the initial uncertainty in different directions on the configuration and stable domains were studied.Simulations show that the developed method is highly efficient and accurate in predicting the configuration stability.The relative error with respect to the Monte Carlo simulations was less than 3%with a time consumption of 0.1%.The proposed method can potentially be useful for constellation design and stability analysis.展开更多
This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, wh...This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, which combines the advantages of the response surface method and the traditional stochastic collocation method, only sets integral points at the guide lines of the response surface. The statistics, in an engineering problem with many uncertain parameters, are then transformed into a linear combination of simple functions' statistics. Furthermore, the issue of determining a simple method to solve the weight-factor sets is discussed in detail. The weight-factor sets of two commonly used probabilistic distribution types are given in table form. Studies on the computational accuracy and efforts show that a good balance in computer capacity is achieved at present. It should be noted that it's a non-gradient and non-intrusive algorithm with strong portability. For the sake of validating the procedure, three numerical examples concerning a mathematical function with analytical expression, structural design of a straight wing, and flutter analysis of a composite wing are used to show the effectiveness of the guided stochastic collocation method.展开更多
Experimentally measured neutron activation cross sections are presented for the ^(65)Cu(n,0)^(62m)Cu,^(41) K(n,a)^(38C)l,and ^(65)Cu(n.2n)^(64)Cu reactions with detailed uncertainty propagation.The neutron cross secio...Experimentally measured neutron activation cross sections are presented for the ^(65)Cu(n,0)^(62m)Cu,^(41) K(n,a)^(38C)l,and ^(65)Cu(n.2n)^(64)Cu reactions with detailed uncertainty propagation.The neutron cross secions were measured at an incident energy of 14.92±0.02 MeV,and the neutrons were based on the(d,n)a fusion reaction.The ^(27) Al(n,a)^(24)Na reaction was used as a reference reaction for the normalization of the neutron flux.The pre-calib-rated lead-shielded HPGe detector was used to detect the residues'γ-ray spetra.The data from the measured cross sections are compared to the previously measured cross sections from the EXFOR database,theoretically calculated cross sections using the TALYS and EMPIRE codes,and evaluated nuclear data.展开更多
The cross section values of the^(71)Ga(n,γ)^(72)Ga reaction are measured,which are 9.14±0.81 mb and 5.74±0.50 mb at 2.15 and 3.19 MeV,respectively.The detailed uncertainty propagation and covariance analysi...The cross section values of the^(71)Ga(n,γ)^(72)Ga reaction are measured,which are 9.14±0.81 mb and 5.74±0.50 mb at 2.15 and 3.19 MeV,respectively.The detailed uncertainty propagation and covariance analysis are also given.The^(7)Li(p,n)^(7)Be reaction was used to generate the neutrons,and the neutron flux was normalized using the^(115)In(n,n′)^(115)In^(m)monitor reaction.The measured cross section data are compared with the data available in the EXFOR database,the data obtained using nuclear reaction model codes EMPIRE-3.2 and TALYS-1.95,and also the evaluated nuclear data from ENDF/B-VIII.0 and JEFF-3.1/A.The comparison shows that our result at 3.19 MeV is in good agreement with those of EMPIRE-3.2 and JEFF-3.1/A.Since there are no other measurements available at3.19 MeV,our data could not be compared with literature data at 3.19 MeV,but they are consistent with the cross section values available at 2.98±0.26 and 3.0±0.1 MeV.Our result at 2.15 MeV is slightly higher than the literature value available in EXFOR,evaluated value,and theoretically predicted result.展开更多
Model calibration is the procedure that adjusts the unknown parameters in order to fit the model to experimental data and improve predictive capability.However,it is difficult to implement the procedure because of the...Model calibration is the procedure that adjusts the unknown parameters in order to fit the model to experimental data and improve predictive capability.However,it is difficult to implement the procedure because of the aleatory uncertainty.In this paper,a new method of model calibration based on uncertainty propagation is investigated.The calibration process is described as an optimization problem.A two-stage nested uncertainty propagation method is proposed to resolve this problem.Monte Carlo Simulation method is applied for the inner loop to propagate the aleatory uncertainty.Optimization method is applied for the outer loop to propagate the epistemic uncertainty.The optimization objective function is the consistency between the result of the inner loop and the experimental data.Thus,different consistency measurement methods for unary output and multivariate outputs are proposed as the optimization objective function.Finally,the thermal challenge problem is given to validate the reasonableness and effectiveness of the proposed method.展开更多
An ocean-acoustic joint model is developed for research of acoustic propagation uncertainty in internal wave environments.The internal waves are numerically produced by tidal forcing over a continental slope using an ...An ocean-acoustic joint model is developed for research of acoustic propagation uncertainty in internal wave environments.The internal waves are numerically produced by tidal forcing over a continental slope using an ocean model.Three parameters(i.e.,internal wave,source depth,and water depth)contribute to the dynamic waveguide environments,and result in stochastic sound fields.The sensitivity of the transmission loss(TL)to environment parameters,statistical characteristics of the TL variation,and the associated physical mechanisms are investigated by the Sobol sensitivity analysis method,the Monte Carlo sampling,and the coupled normal mode theory,respectively.The results show that the TL is most sensitive to the source depth in the near field,resulted from the initial amplitudes of higher-order modes;while in middle and far fields,the internal waves are responsible for more than 80%of the total acoustic propagation contribution.In addition,the standard deviation of the TL in the near field and the shallow layer is smaller than those in the middle and far fields and the deep layer.展开更多
This paper proposes a non-intrusive uncertainty analysis method for artillery dynamics involving hybrid uncertainty using polynomial chaos expansion(PCE).The uncertainty parameters with sufficient information are rega...This paper proposes a non-intrusive uncertainty analysis method for artillery dynamics involving hybrid uncertainty using polynomial chaos expansion(PCE).The uncertainty parameters with sufficient information are regarded as stochastic variables,whereas the interval variables are used to treat the uncertainty parameters with limited stochastic knowledge.In this method,the PCE model is constructed through the Galerkin projection method,in which the sparse grid strategy is used to generate the integral points and the corresponding integral weights.Through the sampling in PCE,the original dynamic systems with hybrid stochastic and interval parameters can be transformed into deterministic dynamic systems,without changing their expressions.The yielded PCE model is utilized as a computationally efficient,surrogate model,and the supremum and infimum of the dynamic responses over all time iteration steps can be easily approximated through Monte Carlo simulation and percentile difference.A numerical example and an artillery exterior ballistic dynamics model are used to illustrate the feasibility and efficiency of this approach.The numerical results indicate that the dynamic response bounds obtained by the PCE approach almost match the results of the direct Monte Carlo simulation,but the computational efficiency of the PCE approach is much higher than direct Monte Carlo simulation.Moreover,the proposed method also exhibits fine precision even in high-dimensional uncertainty analysis problems.展开更多
Based on the Monte Carlo approach and conventional error analysis theory,taking the heaviest doubly magic nucleus 208Pb as an example,we first evaluate the propagated uncertainties of universal potential parameters fo...Based on the Monte Carlo approach and conventional error analysis theory,taking the heaviest doubly magic nucleus 208Pb as an example,we first evaluate the propagated uncertainties of universal potential parameters for three typical types of single-particle energy in the phenomenological Woods–Saxon mean field.Accepting the Woods–Saxon modeling with uncorrelated model parameters,we found that the standard deviations of singleparticle energy obtained through the Monte Carlo simulation and the error propagation rules are in good agreement.It seems that the energy uncertainty of the single-particle levels regularly evoluate with certain quantum numbers to a large extent for the given parameter uncertainties.Further,the correlation properties of the single-particle levels within the domain of input parameter uncertainties are statistically analyzed,for example,with the aid of Pearson’s correlation coefficients.It was found that a positive,negative,or unrelated relationship may appear between two selected single-particle levels,which will be extremely helpful for evaluating the theoretical uncertainty related to the single-particle levels(e.g.,K isomer)in nuclear structural calculations.展开更多
As the core of spatial planning in China,delineation of the production-living-ecological space(PLES)refers to dividing the overall land use into three functional spaces.Spatial units are optimally configured as the mo...As the core of spatial planning in China,delineation of the production-living-ecological space(PLES)refers to dividing the overall land use into three functional spaces.Spatial units are optimally configured as the most suitable functional type,while beset by various uncertainties.Weight uncertainties,being affected by subjective preferences,are highly arbitrary and seriously affect PLES.Taking Xuzhou as the study area,this paper studies the perturbation mechanism and response measure of weight uncertainties on PLES.First,weight samples are obtained through quasi-random sampling to serve as sources of uncertainties for input into the optimized delineation of PLES.Next,the Monte Carlo simulation is applied to simulate the spatial probability distribution of PLES.The global sensitivity analysis method is then adopted to identify the main sources that cause uncertainties in the delineation of PLES.Subsequently,the flexible space(FS)of PLES at a certain level of significance is formulated by comparing the distribution probabilities of spatial units for different functional spaces,acting as a countermeasure for the perturbation.The results show that weight uncertainties bring disturbances to the PLES by affecting the multi-criteria evaluation(MCE)of PLES delineation.The PLES is affected by the weight uncertainties of the factors alone or through interactions with other weights.FS is the spatial response measure of PLES when uncertainties occurred at a certain level of significance.The study introduces the perspective of uncertainty for PLES,which contributes toward improving the scientificity and reliability of PLES.展开更多
An on-the-fly,self-localization system is developed for mobile robot which is operative in a 3D environment with elaborative 3D landmarks.The robot estimates its pose recursively through a MAP estimator that incorpora...An on-the-fly,self-localization system is developed for mobile robot which is operative in a 3D environment with elaborative 3D landmarks.The robot estimates its pose recursively through a MAP estimator that incorporates the information collected from odometry and unidirectional camera.We build the nonlinear models for these two sensors and maintain that the uncertainty manipulation of robot motion and inaccurate sensor measurements should be embedded and tracked throughout our system.We describe the uncertainty framework in a probabilistic geometry viewpoint and use unscented transform to propagate the uncertainty,which undergoes the given nonlinear functions.Considering the processing power of our robot,image features are extracted in the vicinity of corresponding projected features.In addition,data associations are evaluated by statistical distance.Finally,a series of systematic experiments are conducted to prove the reliable and accurate performance of our system.展开更多
It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions.In order to seek a more robust natural laminar flow contro...It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions.In order to seek a more robust natural laminar flow control effect,it is necessary to develop an effective optimization design method.Meanwhile,attention must be given to the impact of crossflow(CF)instability brought on by the sweep angle.This paper constructs a robust optimization design framework based on discrete adjoint methods and non-intrusive polynomial chaos.Transition prediction is implemented by coupled Reynolds-Averaged Navier-Stokes(RANS)and simplified e^(N)method,which can consider both Tollmien-Schlichting(TS)wave and crossflow vortex instability.We have performed gradient enhancement processing on the general Polynomial Chaos Expansion(PCE),which is advantageous to reduce the computational cost of single uncertainty propagation.This processing takes advantage of the gradient information obtained by solving the coupled adjoint equations considering transition.The statistical moment gradient solution used for the robust optimization design also uses the derivatives of coupled adjoint equations.The framework is applied to the robust design of a 25°swept wing with infinite span in transonic flow.The uncertainty quantification and sensitivity analysis on the baseline wing shows that the uncertainty quantification method in this paper has high accuracy,and qualitatively reveals the factors that dominate in different flow field regions.By the robust optimization design,the mean and standard deviation of the drag coefficient can be reduced by 29%and 45%,respectively,and compared with the deterministic optimization design results,there is less possibility of forming shock waves under flight condition uncertainties.Robust optimization results illustrate the trade-off between the transition delay and the wave drag reduction.展开更多
基金supported by the National Natural Science Foundation of China (No. 51105034)the Doctoral Thesis Build Project of Beijing 2012 (China)
文摘The classic polynomial chaos method（PCM）, characterized as an intrusive methodology,has been applied to uncertainty propagation（UP） in many dynamic systems. However, the intrusive polynomial chaos method（IPCM） requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method（NIPCM） that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.
基金supported by the major advanced research project of Civil Aerospace from State Administration of Science,Technology and Industry of China.
文摘The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.
文摘Offshore wind substations are subjected to uncertain loads from waves,wind and currents.Sea states are composed of irregular waves which statistics are usually characterized.Irregular loads may induce fatigue failure of some structural components of the structures.By combining fatigue damage computed through numerical simulations for each sea state endured by the structure,it is possible to assess fatigue failure of the structure over the whole deployment duration.Yet,the influence of the discretization error on the fatigue damage is rarely addressed.It is possible to estimate the discretization error on the quantity of interest computed at the structural detail suspected to fail.However,the relation between this local quantity of interest and the fatigue damage is complex.In this paper,a method that allows propagating error bounds towards fatigue damage is proposed.While increasing computational burden,computing discretization error bounds is a useful output of finite element analysis.It can be utilized to either validate mesh choice or guide remeshing in case where potential error on the fatigue damage is too large.This method is applied to an offshore wind substation developped by Chantiers de l’Atlantique using two discretization error estimators in a single sea state.
基金supported by the National Key R&D Program of China(No.2020YFC2201200).
文摘Configuration stability is essential for a space-based Gravitational-Wave(GW)observatory,which can be impacted by orbit insertion uncertainties.Configuration uncertainty propagation is vital for investigating the influences of uncertainties on configuration stability and can be potentially useful in the navigation and control of GW observatories.Current methods suffer from drawbacks related to high computational burden.To this end,a Radial-Tangential-Ddirectional State Transition Tensor(RT-DSTT)-based configuration uncertainty propagation method is proposed.First,two sensitive directions are found by capturing the dominant secular terms.Considering the orbit insertion errors along the two sensitive directions only,a reduced-order RT-DSTT model is developed for orbital uncertainty propagation.Then,the relationship between the uncertainties in the orbital states and the uncertainties in the configuration stability indexes is mapped using highorder derivatives.The result is a semi-analytical solution that can predict the deviations in the configuration stability indexes given orbit insertion errors.The potential application of the proposed RT-DSTT-based method in calculating the feasible domain is presented.The performance of the proposed method is validated on the Laser Interferometer Space Antenna(LISA)project.Simulations show that the proposed method can provide similar results to the STT-based method but requires only half of the computational time.
基金supported by the National Natural Science Foundation of China(Nos. 52205252 and 72331002)the Natural Science Foundation of Sichuan Province, China(No.2023NSFSC0876)the support of the Alexander von Humboldt Foundation of Germany
文摘Interval Uncertainty Propagation(IUP)holds significant importance in quantifying uncertainties in structural outputs when confronted with interval input parameters.In the aviation field,the precise determination of probability models for input parameters of aeronautical structures entails substantial costs in both time and finances.As an alternative,the use of interval variables to describe input parameter uncertainty becomes a pragmatic approach.The complex task of solving the IUP for aeronautical structures,particularly in scenarios marked by pronounced nonlinearity and multiple outputs,necessitates innovative methodologies.This study introduces an efficient deep learning-driven approach to address the challenges associated with IUP.The proposed approach combines the Deep Neural Network(DNN)with intelligent optimization algorithms for dealing with the IUP in aeronautical structures.An inventive extremal value-oriented weighting technique is presented,assigning varying weights to different training samples within the loss function,thereby enhancing the computational accuracy of the DNN in predicting extremal values of structural outputs.Moreover,an adaptive framework is established to strategically balance the global exploration and local exploitation capabilities of the DNN,resulting in a predictive model that is both robust and accurate.To illustrate the effectiveness of the developed approach,various applications are explored,including a high-dimensional numerical example and two aeronautical structures.The obtained results highlight the high computational accuracy and efficiency achieved by the proposed approach,showcasing its potential for addressing complex IUP challenges in aeronautical engineering.
基金supported by the Scientific Research Foundation of Changzhou College of Information Technology(Grant No.SGA070300020395)the Natural Science Research Projects in Colleges and Universities of Jiangsu Province(Grant No.25KJD590001)the National Natural Science Foundation of China(Grant No.11672126)。
文摘This paper reviews the recent advances of practical techniques within different method frameworks for improved uncertainty propagation in orbital dynamics.The uncertainty propagation problem has been explored in many applications in orbital dynamics,such as orbit determination,relative motion,space debris removal,and small body exploration.In recent years,to further improve the accuracy and efficiency of uncertainty propagation,many practical techniques have been presented within different method frameworks.Among these,most techniques are within the frameworks of the continuity equation,the Gaussian mixture model,and the surrogate model.To facilitate the research work for nonlinear uncertainty propagation in orbital dynamics,a classification of the present method frameworks and the practical techniques for improved uncertainty propagation within different method frameworks is given and discussed in this paper.
文摘A robust analytical model of Eccentric Braced Frames (EBFs), as a well-known seismic resistance system, helps to comprehensive earthquake-induced risk assessment of buildings in different performance levels. Recently, the modeling parameters have been introduced to simulate the hysteretic behavior of shear links in EBFs with specific Coefficient of Variation associated with each parameter to consider the uncertainties. The main purpose of this paper is to assess the effect of these uncertainties in the seismic response of EBFs by combining different sources of aleatory and epistemic uncertainties while making a balance between the required computational effort and the accuracy of the responses. This assessment is carried out in multiple performance levels using Endurance Time (ET) method as an efficient Nonlinear Time History Analysis. To demonstrate the method, a 4-story EBF that considers behavioral parameters has been considered. First, a sensitivity analysis using One-Variable-At-a-Time procedure and the ET method has been utilized to sort the parameters with regard to their importance in seismic responses in two intensity levels. A sampling-based reliability method is first used to propagate the modeling uncertainties into the fragility curves of the structure. Radial Basis Function Networks are then utilized to estimate the structural responses, which makes it feasible to propagate the uncertainties with an affordable computational effort. The Design of Experiments technique is implemented to acquire the training data, reducing the required data. The results show that the mathematical relationships defined by Artificial Neural Networks and using the ET method can estimate the median Intensity Measures and shifts in dispersions with acceptable accuracy.
基金UGC-DAE Consortium for scientific research (UGC-DAE-CSR-KC/CRS/19/NP03/0913)SERB-DST, Government of India (CRG/2019/000360)Institutions of Eminence (IoE) BHU (Grant No. 6031)
文摘Experimentally measured neutron activation cross sections are presented for the^(65)Cu(n,α)^(62m)Cu,^(41)K(n,α)^(38)Cl,and^(65)Cu(n,2n)^(64)Cu reactions with detailed uncertainty propagation.The neutron cross sections were measured at an incident energy of 14.92±0.02 MeV,and the neutrons were based on the t(d,n)αfusion reaction.The^(27)Al(n,α)^(24)Na reaction was used as a reference reaction for the normalization of the neutron flux.The pre-calibrated lead-shielded HPGe detector was used to detect the residues'γ-ray spectra.The data from the measured cross sections are compared to the previously measured cross sections from the EXFOR database,theoretically calculated cross sections using the TALYS and EMPIRE codes,and evaluated nuclear data.
基金the National Natural Science Foundation of China(Nos.11222215 and 11572345)the National Basic Research Program of China(973 Program,No.2013CB733100)the Program for New Century Excellent Talents in University(No.NCET-13-0159).
文摘The usage of state transition tensors(STTs)was proved as an effective method for orbital uncertainty propagation.However,orbital maneuvers and their uncertainties are not considered in current STT-based methods.Uncertainty propagation of spacecraft trajectory with maneuvers plays an important role in spaceflight missions,e.g.,the rendezvous phasing mission.Under the effects of impulsive maneuvers,the nominal trajectory of a spacecraft will be divided into several segments.If the uncertainty is piecewise propagated using the STTs one after another,large approximation errors will be introduced.To overcome this challenge,a set of modified STTs is derived,which connects the segmented trajectories together and allows for directly propagating uncertainty from the initial time to the final time.These modified STTs are then applied to analytically propagate the statistical moments of navigation and impulsive maneuver uncertainties.The probability density function is obtained by combining STTs with the Gaussian mixture model.The proposed uncertainty propagator is shown to be efficient and affords good agreement with Monte Carlo simulations.It also has no dimensionality problem for high-dimensional uncertainty propagation.
基金This work was sponsored by the National Key R&D Program of China(No.2020YFC2201200)Beijing Institute of Technology Research Fund Program for Innovative Talents(No.2022CX01008)Beijing Institute of Technology Research Fund Program for Young Scholars(No.XSQD-202101012).
文摘Long-term configuration stability is essential for an interferometric detection constellation(IDC),which is closely related to initial uncertainty.Therefore,it is vital to evaluate the uncertainty and characterize the configuration stability.In this study,an analytical method was developed for the configuration uncertainty propagation of a geocentric triangular IDC.The angular momentum and the argument latitude were found to be significantly affected by the initial uncertainty and were selected as the core variables.By averaging the perturbation in one revolution,an analytical solution was proposed for propagating the core orbital elements in one revolution.Subsequently,the analytical solution of the orbit elements during the mission period is obtained by multiplying the solutions in iterative revolutions.The relationship between the selected orbital elements and the configuration stability parameters was established using an analytical solution.The effects of the initial uncertainty in different directions on the configuration and stable domains were studied.Simulations show that the developed method is highly efficient and accurate in predicting the configuration stability.The relative error with respect to the Monte Carlo simulations was less than 3%with a time consumption of 0.1%.The proposed method can potentially be useful for constellation design and stability analysis.
基金supported by the Defense Industrial Technology Development Program(Grant Nos.A2120110001 and B2120110011)the National Natural Science Foundation of China(Grant No.A020317)
文摘This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, which combines the advantages of the response surface method and the traditional stochastic collocation method, only sets integral points at the guide lines of the response surface. The statistics, in an engineering problem with many uncertain parameters, are then transformed into a linear combination of simple functions' statistics. Furthermore, the issue of determining a simple method to solve the weight-factor sets is discussed in detail. The weight-factor sets of two commonly used probabilistic distribution types are given in table form. Studies on the computational accuracy and efforts show that a good balance in computer capacity is achieved at present. It should be noted that it's a non-gradient and non-intrusive algorithm with strong portability. For the sake of validating the procedure, three numerical examples concerning a mathematical function with analytical expression, structural design of a straight wing, and flutter analysis of a composite wing are used to show the effectiveness of the guided stochastic collocation method.
基金the UGC-DAE Consortium for scientific research(UGC-DAE-CSR-KC/CRS/19/NP03/0913)SERB-DST+1 种基金Government of India(CRG/2019/000360)Institutions of Eminence(IoE)BHU(Grant No.6031)。
文摘Experimentally measured neutron activation cross sections are presented for the ^(65)Cu(n,0)^(62m)Cu,^(41) K(n,a)^(38C)l,and ^(65)Cu(n.2n)^(64)Cu reactions with detailed uncertainty propagation.The neutron cross secions were measured at an incident energy of 14.92±0.02 MeV,and the neutrons were based on the(d,n)a fusion reaction.The ^(27) Al(n,a)^(24)Na reaction was used as a reference reaction for the normalization of the neutron flux.The pre-calib-rated lead-shielded HPGe detector was used to detect the residues'γ-ray spetra.The data from the measured cross sections are compared to the previously measured cross sections from the EXFOR database,theoretically calculated cross sections using the TALYS and EMPIRE codes,and evaluated nuclear data.
基金Under the financial assistance of the B.R.N.S.,DAE,Mumbai(Sanction No.2012/36/17-BRNS Dated 14.08.2012),this research was carried out as part of a collaborative research project between the Department of Physics,Mizoram University and BARC,Mumbaithe grants received from the Institutions of Eminence(IoE)BHU(6031-B)UGC-DAE Consortium for Scientific Research(CRS/2021-22/02/474)
文摘The cross section values of the^(71)Ga(n,γ)^(72)Ga reaction are measured,which are 9.14±0.81 mb and 5.74±0.50 mb at 2.15 and 3.19 MeV,respectively.The detailed uncertainty propagation and covariance analysis are also given.The^(7)Li(p,n)^(7)Be reaction was used to generate the neutrons,and the neutron flux was normalized using the^(115)In(n,n′)^(115)In^(m)monitor reaction.The measured cross section data are compared with the data available in the EXFOR database,the data obtained using nuclear reaction model codes EMPIRE-3.2 and TALYS-1.95,and also the evaluated nuclear data from ENDF/B-VIII.0 and JEFF-3.1/A.The comparison shows that our result at 3.19 MeV is in good agreement with those of EMPIRE-3.2 and JEFF-3.1/A.Since there are no other measurements available at3.19 MeV,our data could not be compared with literature data at 3.19 MeV,but they are consistent with the cross section values available at 2.98±0.26 and 3.0±0.1 MeV.Our result at 2.15 MeV is slightly higher than the literature value available in EXFOR,evaluated value,and theoretically predicted result.
基金This work is supported by the National Natural Science Foundation of China(Grant No.61403097)the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.2015035).
文摘Model calibration is the procedure that adjusts the unknown parameters in order to fit the model to experimental data and improve predictive capability.However,it is difficult to implement the procedure because of the aleatory uncertainty.In this paper,a new method of model calibration based on uncertainty propagation is investigated.The calibration process is described as an optimization problem.A two-stage nested uncertainty propagation method is proposed to resolve this problem.Monte Carlo Simulation method is applied for the inner loop to propagate the aleatory uncertainty.Optimization method is applied for the outer loop to propagate the epistemic uncertainty.The optimization objective function is the consistency between the result of the inner loop and the experimental data.Thus,different consistency measurement methods for unary output and multivariate outputs are proposed as the optimization objective function.Finally,the thermal challenge problem is given to validate the reasonableness and effectiveness of the proposed method.
基金the National Key Research and Development Program of China(Grant No.2020YFA0607900)the National Natural Science Foundation of China(Grant Nos.42176019 and 11874061)the Youth Innovation Promotion Association CAS(Grant No.2021023).
文摘An ocean-acoustic joint model is developed for research of acoustic propagation uncertainty in internal wave environments.The internal waves are numerically produced by tidal forcing over a continental slope using an ocean model.Three parameters(i.e.,internal wave,source depth,and water depth)contribute to the dynamic waveguide environments,and result in stochastic sound fields.The sensitivity of the transmission loss(TL)to environment parameters,statistical characteristics of the TL variation,and the associated physical mechanisms are investigated by the Sobol sensitivity analysis method,the Monte Carlo sampling,and the coupled normal mode theory,respectively.The results show that the TL is most sensitive to the source depth in the near field,resulted from the initial amplitudes of higher-order modes;while in middle and far fields,the internal waves are responsible for more than 80%of the total acoustic propagation contribution.In addition,the standard deviation of the TL in the near field and the shallow layer is smaller than those in the middle and far fields and the deep layer.
基金financially supported by the National Natural Science Foun-dation of China[Grant Nos.301070603,11572158]。
文摘This paper proposes a non-intrusive uncertainty analysis method for artillery dynamics involving hybrid uncertainty using polynomial chaos expansion(PCE).The uncertainty parameters with sufficient information are regarded as stochastic variables,whereas the interval variables are used to treat the uncertainty parameters with limited stochastic knowledge.In this method,the PCE model is constructed through the Galerkin projection method,in which the sparse grid strategy is used to generate the integral points and the corresponding integral weights.Through the sampling in PCE,the original dynamic systems with hybrid stochastic and interval parameters can be transformed into deterministic dynamic systems,without changing their expressions.The yielded PCE model is utilized as a computationally efficient,surrogate model,and the supremum and infimum of the dynamic responses over all time iteration steps can be easily approximated through Monte Carlo simulation and percentile difference.A numerical example and an artillery exterior ballistic dynamics model are used to illustrate the feasibility and efficiency of this approach.The numerical results indicate that the dynamic response bounds obtained by the PCE approach almost match the results of the direct Monte Carlo simulation,but the computational efficiency of the PCE approach is much higher than direct Monte Carlo simulation.Moreover,the proposed method also exhibits fine precision even in high-dimensional uncertainty analysis problems.
基金the National Natural Science Foundation of China(No.11975209)the Physics Research and Development Program of Zhengzhou University(No.32410017)the Project of Youth Backbone Teachers of Colleges and Universities of Henan Province(No.2017GGJS008)。
文摘Based on the Monte Carlo approach and conventional error analysis theory,taking the heaviest doubly magic nucleus 208Pb as an example,we first evaluate the propagated uncertainties of universal potential parameters for three typical types of single-particle energy in the phenomenological Woods–Saxon mean field.Accepting the Woods–Saxon modeling with uncorrelated model parameters,we found that the standard deviations of singleparticle energy obtained through the Monte Carlo simulation and the error propagation rules are in good agreement.It seems that the energy uncertainty of the single-particle levels regularly evoluate with certain quantum numbers to a large extent for the given parameter uncertainties.Further,the correlation properties of the single-particle levels within the domain of input parameter uncertainties are statistically analyzed,for example,with the aid of Pearson’s correlation coefficients.It was found that a positive,negative,or unrelated relationship may appear between two selected single-particle levels,which will be extremely helpful for evaluating the theoretical uncertainty related to the single-particle levels(e.g.,K isomer)in nuclear structural calculations.
基金Under the auspices of National Natural Science Foundation of China(No.42171248,42371273)。
文摘As the core of spatial planning in China,delineation of the production-living-ecological space(PLES)refers to dividing the overall land use into three functional spaces.Spatial units are optimally configured as the most suitable functional type,while beset by various uncertainties.Weight uncertainties,being affected by subjective preferences,are highly arbitrary and seriously affect PLES.Taking Xuzhou as the study area,this paper studies the perturbation mechanism and response measure of weight uncertainties on PLES.First,weight samples are obtained through quasi-random sampling to serve as sources of uncertainties for input into the optimized delineation of PLES.Next,the Monte Carlo simulation is applied to simulate the spatial probability distribution of PLES.The global sensitivity analysis method is then adopted to identify the main sources that cause uncertainties in the delineation of PLES.Subsequently,the flexible space(FS)of PLES at a certain level of significance is formulated by comparing the distribution probabilities of spatial units for different functional spaces,acting as a countermeasure for the perturbation.The results show that weight uncertainties bring disturbances to the PLES by affecting the multi-criteria evaluation(MCE)of PLES delineation.The PLES is affected by the weight uncertainties of the factors alone or through interactions with other weights.FS is the spatial response measure of PLES when uncertainties occurred at a certain level of significance.The study introduces the perspective of uncertainty for PLES,which contributes toward improving the scientificity and reliability of PLES.
基金Supported by National Natural Science Foundation of China(60605023,60775048)Specialized Research Fund for the Doctoral Program of Higher Education(20060141006)
文摘An on-the-fly,self-localization system is developed for mobile robot which is operative in a 3D environment with elaborative 3D landmarks.The robot estimates its pose recursively through a MAP estimator that incorporates the information collected from odometry and unidirectional camera.We build the nonlinear models for these two sensors and maintain that the uncertainty manipulation of robot motion and inaccurate sensor measurements should be embedded and tracked throughout our system.We describe the uncertainty framework in a probabilistic geometry viewpoint and use unscented transform to propagate the uncertainty,which undergoes the given nonlinear functions.Considering the processing power of our robot,image features are extracted in the vicinity of corresponding projected features.In addition,data associations are evaluated by statistical distance.Finally,a series of systematic experiments are conducted to prove the reliable and accurate performance of our system.
文摘It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions.In order to seek a more robust natural laminar flow control effect,it is necessary to develop an effective optimization design method.Meanwhile,attention must be given to the impact of crossflow(CF)instability brought on by the sweep angle.This paper constructs a robust optimization design framework based on discrete adjoint methods and non-intrusive polynomial chaos.Transition prediction is implemented by coupled Reynolds-Averaged Navier-Stokes(RANS)and simplified e^(N)method,which can consider both Tollmien-Schlichting(TS)wave and crossflow vortex instability.We have performed gradient enhancement processing on the general Polynomial Chaos Expansion(PCE),which is advantageous to reduce the computational cost of single uncertainty propagation.This processing takes advantage of the gradient information obtained by solving the coupled adjoint equations considering transition.The statistical moment gradient solution used for the robust optimization design also uses the derivatives of coupled adjoint equations.The framework is applied to the robust design of a 25°swept wing with infinite span in transonic flow.The uncertainty quantification and sensitivity analysis on the baseline wing shows that the uncertainty quantification method in this paper has high accuracy,and qualitatively reveals the factors that dominate in different flow field regions.By the robust optimization design,the mean and standard deviation of the drag coefficient can be reduced by 29%and 45%,respectively,and compared with the deterministic optimization design results,there is less possibility of forming shock waves under flight condition uncertainties.Robust optimization results illustrate the trade-off between the transition delay and the wave drag reduction.
