Thermal spalling in heterogeneous rocks under rapid heating poses critical risks to deep mining and geothermal operations.In this study,we develop a coupled thermal-mechanical-damage(TM D)model that explicitly incorpo...Thermal spalling in heterogeneous rocks under rapid heating poses critical risks to deep mining and geothermal operations.In this study,we develop a coupled thermal-mechanical-damage(TM D)model that explicitly incorporates Weibull distributed heterogeneity to a single fracture in rock,and validate it against ceramic quenching and granite acoustic emission experiments.Distance based generalized sensitivity analysis(DGSA)is applied to quantify the influence and interactions of key parameters,revealing the dominant controls on spalling onset,severity,and damage morphology.The results demonstrate that thermal stress dominates crack initiation and propagation,that lateral constraints can significantly delay and suppress spalling,and that material heterogeneity markedly influences peak stress and damage modes within a certain range of thermal expansion coefficient and has multiple effects on thermal spalling.This study provides a theoretical basis for quantitative assessment and parameter optimization of thermal spalling processes in rock masses.展开更多
Tilt-to-length(TTL)coupling noise is a critical issue in space-based gravitational wave detection due to its complex dependence on multiple interacting factors,which complicates the identification of dominant paramete...Tilt-to-length(TTL)coupling noise is a critical issue in space-based gravitational wave detection due to its complex dependence on multiple interacting factors,which complicates the identification of dominant parameters.To address this challenge,we develop a simulation model of the Taiji scientific interferometer,generating noise datasets under multiparameter conditions.Given the uniqueness of the telescope as well as the convergence behavior of the algorithm,the analysis is structured hierarchically:(i)the telescope level and(ii)the optical bench level.A hierarchical framework combining XGBoost and SHapley Additive exPlanations(SHAP)values is employed to model the intricate relationships between parameters and TTL coupling noise,supplemented by sensitivity analysis.Our results identify pointing jitter and telescope radius as the dominant parameters at the telescope level,while the angles of the plane mirrors and beam splitters are most influential at the optical bench level.The parameter space is reduced from 86 dimensions to 14 dimensions without sacrificing model accuracy.This approach offers actionable insights for optimizing the Taiji interferometer design.展开更多
This study aims to establish an integrated sensitivity analysis framework for optimization and design of the dynamic performance of mechanical systems such as tracked vehicles,by combining the direct differentiation m...This study aims to establish an integrated sensitivity analysis framework for optimization and design of the dynamic performance of mechanical systems such as tracked vehicles,by combining the direct differentiation method(DDM)with the linear multibody system transfer matrix method(linear MSTMM).The rigid-flexible coupled multibody system dynamics model of a tracked vehicle is established using the linear MSTMM and validated through the modal test.Building upon the existing DDM-based eigenvalue sensitivity analysis method within the linear MSTMM,the DDM is embedded into it to enable programmable and efficient computation of dynamic response sensitivities for mechanical systems.The proposed approach is used to quantitatively evaluate the sensitivities of both natural vibration characteristics(e.g.,natural frequencies and mode shapes)and transient dynamic responses of the tracked vehicle with respect to system parameters,successfully identifying critical structural parameters.Compared to conventional finite difference methods,the developed methodology eliminates sensitivity to perturbation step sizes.The contributions of this work lie in establishing a unified theoretical foundation and analysis framework for guiding dynamics optimization and design of mechanical systems,and extending the applicability of the linear MSTMM to sensitivity analysis of transient dynamic responses.展开更多
As a means of quantitative interpretation,forward calculations of the global lithospheric magnetic field in the Spherical Harmonic(SH)domain have been widely used to reveal geophysical,lithological,and geothermal vari...As a means of quantitative interpretation,forward calculations of the global lithospheric magnetic field in the Spherical Harmonic(SH)domain have been widely used to reveal geophysical,lithological,and geothermal variations in the lithosphere.Traditional approaches either do not consider the non-axial dipolar terms of the inducing field and its radial variation or do so by means of complicated formulae.Moreover,existing methods treat the magnetic lithosphere either as an infinitesimally thin layer or as a radially uniform spherical shell of constant thickness.Here,we present alternative forward formulae that account for an arbitrarily high maximum degree of the inducing field and for a magnetic lithosphere of variable thickness.Our simulations based on these formulae suggest that the satellite magnetic anomaly field is sensitive to the non-axial dipolar terms of the inducing field but not to its radial variation.Therefore,in forward and inverse calculations of satellite magnetic anomaly data,the non-axial dipolar terms of the inducing field should not be ignored.Furthermore,our results show that the satellite magnetic anomaly field is sensitive to variability in the lateral thickness of the magnetized shell.In particular,we show that for a given vertically integrated susceptibility distribution,underestimating the thickness of the magnetic layer overestimates the induced magnetic field.This discovery bridges the greatest part of the alleged gap between the susceptibility values measured from rock samples and the susceptibility values required to match the observed magnetic field signal.We expect the formulae and conclusions of this study to be a valuable tool for the quantitative interpretation of the Earth's global lithospheric magnetic field,through an inverse or forward modelling approach.展开更多
Saline aquifers are considered as highly favored reservoirs for CO_(2)sequestration due to their favorable properties.Understanding the impact of saline aquifer properties on the migration and distribution of CO_(2)pl...Saline aquifers are considered as highly favored reservoirs for CO_(2)sequestration due to their favorable properties.Understanding the impact of saline aquifer properties on the migration and distribution of CO_(2)plume is crucial.This study focuses on four key parameters-permeability,porosity,formation pressure,and temperature-to characterize the reservoir and analyse the petrophysical and elastic response of CO_(2).First,we performed reservoir simulations to simulate CO_(2)saturation,using multiple sets of these four parameters to examine their significance on CO_(2)saturation and the plume migration speed.Subsequently,the effect of these parameters on the elastic properties is tested using rock physics theory.We established a relationship of compressional wave velocity(V_(p))and quality factor(Q_(p))with the four key parameters,and conducted a sensitivity analysis to test their sensitivity to V_(p) and Q_(p).Finally,we utilized visco-acoustic wave equation simulated time-lapse seismic data based on the computed V_(p) and Q_(p) models,and analysed the impact of CO_(2) saturation changes on seismic data.As for the above nu-merical simulations and analysis,we conducted sensitivity analysis using both homogeneous and heterogeneous models.Consistent results are found between homogeneous and heterogeneous models.The permeability is the most sensitive parameter to the CO_(2)saturation,while porosity emerges as the primary factor affecting both Q_(p) and V_(p).Both Q_(p) and V_(p) increase with the porosity,which contradicts the observations in gas reservoirs.The seismic simulations highlight significant variations in the seismic response to different parameters.We provided analysis for these observations,which serves as a valuable reference for comprehensive CO_(2)integrity analysis,time-lapse monitoring,injection planning and site selection.展开更多
While steady improvements have been achieved for the track forecasts of typhoons,there has been a lack of improvement for intensity forecasts.One challenge for intensity forecasts is to capture the rapid intensificati...While steady improvements have been achieved for the track forecasts of typhoons,there has been a lack of improvement for intensity forecasts.One challenge for intensity forecasts is to capture the rapid intensification(RI),whose nonlinear characteristics impose great difficulties for numerical models.The ensemble sensitivity analysis(ESA)method is used here to analyze the initial conditions that contribute to typhoon intensity forecasts,especially with RI.Six RI processes from five typhoons(Chaba,Haima,Meranti,Sarika,and Songda)in 2016,are applied with ESA,which also gives a composite initial condition that favors subsequent RI.Results from individual cases have generally similar patterns of ESA,but with different magnitudes,when various cumulus parameterization schemes are applied.To draw the initial conditions with statistical significance,sample-mean azimuthal components of ESA are obtained.Results of the composite sensitivity show that typhoons that experience RI in 24 h favor enhanced primary circulation from low to high levels,intensified secondary circulation with increased radial inflow at lower levels and increased radial outflow at upper levels,a prominent warm core at around 300 hPa,and increased humidity at low levels.As the forecast lead time increases,the patterns of ESA are retained,while the sensitivity magnitudes decay.Given the general and quantitative composite sensitivity along with associated uncertainties for different cumulus parameterization schemes,appropriate sampling of the composite sensitivity in numerical models could be beneficial to capturing the RI and improving the forecasting of typhoon intensity.展开更多
Kangbao County is located in the northwest of Bashang in Hebei Province,which is a sub-arid area in the middle temperate zone,with a cold and arid climate and frequent disastrous weather.The meteorological data of Kan...Kangbao County is located in the northwest of Bashang in Hebei Province,which is a sub-arid area in the middle temperate zone,with a cold and arid climate and frequent disastrous weather.The meteorological data of Kangbao County Meteorological Station from 1994 to 2023 were selected,and the meteorological elements such as air pressure,temperature,precipitation,wind,relative humidity,sunshine,thunderstorm,hail,gale,rainstorm,fog,and snow cover were counted.The climate background analysis and high-impact weather analysis were carried out in combination with the topographic characteristics,geographical location,and climate characteristics.The results of meteorological sensitivity survey in the park showed that industries such as food,agriculture and new energy are very sensitive to temperature.During the visit to the enterprises in the park,it was found that heavy precipitation,snow,strong winds and hail had a great impact on many industries,and it was recommended to carry out long-term planning and reasonable design of buildings.It should pay close attention to forecasts and early warnings,formulate emergency plans for high-impact weather defense,and actively take preventive measures.展开更多
The impact of different global and local variables in urban development processes requires a systematic study to fully comprehend the underlying complexities in them.The interplay between such variables is crucial for...The impact of different global and local variables in urban development processes requires a systematic study to fully comprehend the underlying complexities in them.The interplay between such variables is crucial for modelling urban growth to closely reflects reality.Despite extensive research,ambiguity remains about how variations in these input variables influence urban densification.In this study,we conduct a global sensitivity analysis(SA)using a multinomial logistic regression(MNL)model to assess the model’s explanatory and predictive power.We examine the influence of global variables,including spatial resolution,neighborhood size,and density classes,under different input combinations at a provincial scale to understand their impact on densification.Additionally,we perform a stepwise regression to identify the significant explanatory variables that are important for understanding densification in the Brussels Metropolitan Area(BMA).Our results indicate that a finer spatial resolution of 50 m and 100 m,smaller neighborhood size of 5×5 and 3×3,and specific density classes—namely 3(non-built-up,low and high built-up)and 4(non-built-up,low,medium and high built-up)—optimally explain and predict urban densification.In line with the same,the stepwise regression reveals that models with a coarser resolution of 300 m lack significant variables,reflecting a lower explanatory power for densification.This approach aids in identifying optimal and significant global variables with higher explanatory power for understanding and predicting urban densification.Furthermore,these findings are reproducible in a global urban context,offering valuable insights for planners,modelers and geographers in managing future urban growth and minimizing modelling.展开更多
Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting ...Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting multi-hazard dynamic responses to super high-rise structures has significant engineering and scientific value. This study performed a parametric global sensitivity analysis (GSA) for multi-hazard dynamic response prediction of super high-rise structures using the multiple-degree-of-freedom shear (MFS) model. Polynomial chaos Kriging (PCK) was introduced to build a surrogate model that allowed GSA to be combined with Sobol’ indices. Monte Carlo simulation (MCS) is also conducted for the comparison to verify the accuracy and efficiency of the PCK method. Parametric sensitivity analysis is performed for a wide range of aleatory uncertainty (intensities of coupled multi-hazard), epistemic uncertainty (bending stiffness, k_(m);shear stiffness, kq;density, ρ;and damping ratio, ξ), probability distribution types, and coefficients of variation. The results indicate that epistemic uncertainty parameters, k_(m), ρ, and ξ dramatically affect the multi-hazard dynamic responses of super high-rise structures;in addition, Sobol’ indices between the normal and lognormal distributions are insignificant, while the variation levels have remarkably influenced the sensitivity indices.展开更多
Accurate quantification of carbon and water fluxes dynamics in arid and semi-arid ecosystems is a critical scientific challenge for regional carbon neutrality assessments and sustainable water resource management.In t...Accurate quantification of carbon and water fluxes dynamics in arid and semi-arid ecosystems is a critical scientific challenge for regional carbon neutrality assessments and sustainable water resource management.In this study,we developed a multi-flux global sensitivity discriminant index(D_(sen))by integrating the Biome-BGCMuSo model with eddy covariance flux observations.This index was combined with a Bayesian optimization algorithm to conduct parameter optimization.The results demonstrated that:(1)Sensitivity analysis identified 13 highly sensitive parameters affecting carbon and water fluxes.Among these,the canopy light extinction coefficient(k)and the fraction of leaf N in Rubisco(FLNR)exhibited significantly higher sensitivity to carbon fluxes(GPP,NEE,Reco;D_(sen)>10%)compared to water flux(ET).This highlights the strong dependence of carbon cycle simulations on vegetation physiological parameters.(2)The Bayesian optimization framework efficiently converged 30 parameter spaces within 50 iterations,markedly improving carbon fluxes simulation accuracy.The Kling-Gupta efficiency(KGE)values for Gross Primary Production(GPP),Net Ecosystem Exchange(NEE),and Total Respiration(Reco)increased by 44.94%,69.23%and 123%,respectively.The optimization prioritized highly sensitive parameters,underscoring the necessity of parameter sensitivity stratification.(3)The optimized model effectively reproduced carbon sink characteristics in mountain meadows during the growing season(cumulative NEE=-375 g C/m^(2)).It revealed synergistic carbon-water fluxes interactions governed by coupled photosynthesis-stomatal pathways and identified substrate supply limitations on heterotrophic respiration.This study proposes a novel multi-flux sensitivity index and an efficient optimization framework,elucidating the coupling mechanisms between vegetation physiological regulation(k,FLNR)and environmental stressors(VPD,SWD)in carbonwater cycles.The methodology offers a practical approach for arid ecosystem model optimization and provides theoretical insights for grassland management through canopy structure regulation and water-use efficiency enhancement.展开更多
This paper presents a sensitivity analysis method for analyzing the key factors affecting the stability problem of the transonic compressors.The adjoint method is integrated into the meridional stability model,a linea...This paper presents a sensitivity analysis method for analyzing the key factors affecting the stability problem of the transonic compressors.The adjoint method is integrated into the meridional stability model,a linear stability prediction model utilized to analyze the flow stability problem of the compressor,and the sensitivity analysis method is further developed for the flow stability problem of the compressor.The study selects the NASA Rot or 37,a transonic compressor,as the research object to verify the proposed method and explore the sensitive factors leading to the stall inception.The results of sensitivity analysis to both the flow parameters and the external source terms reveal that the stall inception is sensitive to the base flow field at the rotor tip and the stability margin of the compressor can be enhanced by improving the flow field at this region.Physical explanations are presented and discussed to correlate the three-dimensional flow field to the results obtained via the employed analysis method,which shows that flow structures and characteristics near the end-wall region,especially the tip leakage flow or the tip leakage vortex and its interaction with the shock wave,contribute to the stall inception.展开更多
This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-...This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.展开更多
Roll coating is a vital industrial process used in printing,packaging,and polymer film production,where maintaining a uniform coating is critical for product quality and efficiency.This work models non-isothermal Carr...Roll coating is a vital industrial process used in printing,packaging,and polymer film production,where maintaining a uniform coating is critical for product quality and efficiency.This work models non-isothermal Carreau fluid flow between a rotating roll and a stationary wall under fixed boundary constraints to evaluate how non-Newtonian and thermal effects influence coating performance.The governing equations are transformed into non-dimensional form and simplified using lubrication approximation theory.Approximate analytical solutions are obtained via the perturbation technique,while numerical results are computed using both the finite difference method and the BVPMidrich technique.Furthermore,Response surface methodology(RSM)is employed for optimization and sensitivity analysis.Analytical and numerical results show strong agreement(<1%deviation).The model predicts coating thickness 0.55≤λ≤0.64,power input 1.05≤P_(w)≤1.99,and separation force 0.91≤S_(f)≤1.82 for 0.1≤We≤0.9 and 0.01≤F≤0.09.Increasing We enhances the coating thickness and power input but reduces velocity and separation force.The findings provide physical insight into elastic and viscous effects in roll coating,providing insight for optimizing coating uniformity,minimizing wear,improving industrial coating processes,and extending substrate lifespan.展开更多
In recent years,incidents of simultaneous exceedance of PM_(2.5)and O_(3) concentrations,termed PM_(2.5)and O_(3) co-pollution events,have frequently occurred in China.This study conducted atmospheric circulation anal...In recent years,incidents of simultaneous exceedance of PM_(2.5)and O_(3) concentrations,termed PM_(2.5)and O_(3) co-pollution events,have frequently occurred in China.This study conducted atmospheric circulation analysis on two typical co-pollution events in Beijing,occurring from July 22 to July 28,2019,and from April 25 to May 2,2020.These events were categorized into pre-trough southerly airflow type(Type 1)and post-trough northwest flow type(Type 2).Subsequently,sensitivity analyses using the GRAPES-CUACE adjoint model were performed to quantify the contributions of precursor emissions from Beijing and surrounding areas to PM_(2.5)and O_(3) concentrations in Beijing for two types of co-pollution.The results indicated that the spatiotemporal distribution of sensitive source region varied among different circulation types.Primary PM_(2.5)(PPM_(2.5))emissions from Hebei contributed the most to the 24-hour average PM_(2.5)(24-h PM_(2.5))peak concentration(41.6%-45.4%),followed by Beijing emissions(31%-35.7%).The maximum daily 8-hour average ozone peak concentration was primarily influenced by the emissions from Hebei and Beijing,with contribution ratios respectively of 32.8%-44.8% and 29%-42.1%.Additionally,NO_(x)emissions were the main contributors in Type 1,while both NO_(x)and VOCs emissions contributed similarly in Type 2.The iterative emission reduction experiments for two types of co-pollution indicated that Type 1 required emission reductions in NO_(x)(52.4%-71.8%)and VOCs(14.1%-33.8%)only.In contrast,Type 2 required combined emission reductions in NO_(x)(37.0%-65.1%),VOCs(30.7%-56.2%),and PPM_(2.5)(31%-46.9%).This study provided a reference for controlling co-pollution events and improving air quality in Beijing.展开更多
The water hammer problem is an important issue in the dynamics of liquid propulsion system.This paper aims to use the Lattice Boltzmann Method(LBM)with entropy limiter to study the water hammer problems in propellant ...The water hammer problem is an important issue in the dynamics of liquid propulsion system.This paper aims to use the Lattice Boltzmann Method(LBM)with entropy limiter to study the water hammer problems in propellant feedlines.The dynamic characteristics of valve-closing water hammer and filling water hammer are investigated by this method,and the sensitivity of filling water hammer is analyzed with a single factor sensitivity analysis with 8 factors and 9 levels and a multi-factor sensitivity analysis with L_(27)(3^(13))orthogonal experiment based on range method.It is found that the solving result of LBM with entropy limiter is basically in good agreement with finite volume method,and using the entropy limiter can eliminate numerical oscillations when solving valve-closing water hammer problems and solve the numerical"blow up"when solving filling water hammer problems.It can be seen that the dynamic characteristics of valve-closing water hammer are relatively simple,while there are many factors that affect the filling water hammer and the degree of these effects varies.The effects on the maximum water hammer pressure are relatively uniform,but those on the water hammer response time vary greatly through the skewness analysis.展开更多
In this study,the multi-scale(meso and macro)modelling was used to predict the electric response of the material.Porosity was introduced through a sugar-templating process to enhance compressibility and sensitivity.Me...In this study,the multi-scale(meso and macro)modelling was used to predict the electric response of the material.Porosity was introduced through a sugar-templating process to enhance compressibility and sensitivity.Mean-field homogenization was employed to predict the electrical conductivity of the nanocomposites,which was validated experimentally through I–V characterisation,confirming stable Ohmic behavior.The homogenised material parameters were incorporated into COMSOLMultiphysics to simulate diaphragmdeflection and capacitance variation under applied pressure.Experimental results showed a linear and stable capacitance response at the force magnitude of 0–7 N.The Graphene nanoplatelets(GnP)–Polydimethylsiloxane(PDMS)sensor demonstrated superior sensitivity(0.0032 pF/N)compared to the CNT–PDMS sensor(0.0019 pF/N),attributed to improved filler dispersion and higher effective surface area of GnP.Finite element simulations were further conducted to evaluate stress distribution in a GnP–PDMS-based capacitive sensor integrated into a shoe insole for gait analysis.The results correlated well with experimental capacitance changes,validating the sensor’s mechanical reliability and pressure sensitivity.This comparative study establishes the GnP–PDMS composite as a more effective candidate for low-cost,biocompatible,and high-performance flexible pressure sensors in wearable biomedical and gait monitoring applications.展开更多
Correction to:Nuclear Science and Techniques(2025)36:111 https://doi.org/10.1007/s41365-025-01681-9.In the sentence beginning‘The weights of the parameters used for the…’in this article,the text‘RCSs’should have ...Correction to:Nuclear Science and Techniques(2025)36:111 https://doi.org/10.1007/s41365-025-01681-9.In the sentence beginning‘The weights of the parameters used for the…’in this article,the text‘RCSs’should have read‘SCRs’.In Table 7 of this article,the column header ρ_fuel was incorrect and should have read CPv_fuel.For completeness and transparency,the old incorrect version and the corrected version of Table 7 are displayed below.展开更多
The Toraja Highlands,encompassing Tana Toraja and North Toraja,form the strategic upper reaches of the Saddang Watershed in South Sulawesi,where steep terrain,active land-cover change,and high ecological sensitivity c...The Toraja Highlands,encompassing Tana Toraja and North Toraja,form the strategic upper reaches of the Saddang Watershed in South Sulawesi,where steep terrain,active land-cover change,and high ecological sensitivity converge.This study addresses the need for an objective and validated ecological sensitivity map to support sustainable mountain watershed management.We construct an ecological sensitivity index based on principal component analysis using four key indicators:land cover,vegetation density(NDVI),slope,and rainfall,and evaluate its reliability through multi-source validation.Inputs integrate national elevation models,Landsat 8 imagery,and satellite-derived rainfall.Rainfall represents a multi-year climatology for 2015–2024,whereas land cover and NDVI reflect recent surface conditions derived from a cloud-free 2024 composite.The resulting sensitivity zonation indicates that 41.10%of Tana Toraja and 67.11%of North Toraja fall into the very high sensitivity class,concentrated on steep slopes and intensively converted landscapes.Eventbased spatial cross-validation against independent landslide records yields overall accuracies of 67.65%and 66.67%,while field verification produces Kappa values of 0.847 and 0.871.Stakeholder appraisal further corroborates the mapped patterns.Together,these convergent lines of evidence identify priority areas for reforestation,soil conservation,slope stabilization,and sustainable watershed management.The transparent and reproducible workflow supports evidence-based risk reduction and resilience building in the upper reaches of the Saddang Watershed.展开更多
This paper puts forward a rigorous approach for a sensitivity analysis of stochastic user equilibrium with the elastic demand （SUEED） model. First, proof is given for the existence of derivatives of output variables...This paper puts forward a rigorous approach for a sensitivity analysis of stochastic user equilibrium with the elastic demand （SUEED） model. First, proof is given for the existence of derivatives of output variables with respect to the perturbation parameters for the SUEED model. Then by taking advantage of the gradient-based method for sensitivity analysis of a general nonlinear program, detailed formulae are developed for calculating the derivatives of designed variables with respect to perturbation parameters at the equilibrium state of the SUEED model. This method is not only applicable for a sensitivity analysis of the logit-type SUEED problem, but also for the probit-type SUEED problem. The application of the proposed method in a numerical example shows that the proposed method can be used to approximate the equilibrium link flow solutions for both logit-type SUEED and probit-type SUEED problems when small perturbations are introduced in the input parameters.展开更多
基金funded by the National Natural Science Foundation of China(Nos.52574100,52574001,and 52311530070)the Major National Science and Technology Project for Deep Earth of China(No.2024ZD1003805)+1 种基金the Fundamental Research Funds for the Central Universities of China(No.FRF-IDRY-20-003,Interdisciplinary Research Project for Young Teachers of USTB)DE gratefully acknowledges support from the G.Albert Shoemaker endowment.
文摘Thermal spalling in heterogeneous rocks under rapid heating poses critical risks to deep mining and geothermal operations.In this study,we develop a coupled thermal-mechanical-damage(TM D)model that explicitly incorporates Weibull distributed heterogeneity to a single fracture in rock,and validate it against ceramic quenching and granite acoustic emission experiments.Distance based generalized sensitivity analysis(DGSA)is applied to quantify the influence and interactions of key parameters,revealing the dominant controls on spalling onset,severity,and damage morphology.The results demonstrate that thermal stress dominates crack initiation and propagation,that lateral constraints can significantly delay and suppress spalling,and that material heterogeneity markedly influences peak stress and damage modes within a certain range of thermal expansion coefficient and has multiple effects on thermal spalling.This study provides a theoretical basis for quantitative assessment and parameter optimization of thermal spalling processes in rock masses.
基金Project supported by the National Key Research and Development Program of China(Grant No.2020YFC2200100)the CAS's Strategic Pioneer Program on Space Science(Grant No.XDA1502110201)。
文摘Tilt-to-length(TTL)coupling noise is a critical issue in space-based gravitational wave detection due to its complex dependence on multiple interacting factors,which complicates the identification of dominant parameters.To address this challenge,we develop a simulation model of the Taiji scientific interferometer,generating noise datasets under multiparameter conditions.Given the uniqueness of the telescope as well as the convergence behavior of the algorithm,the analysis is structured hierarchically:(i)the telescope level and(ii)the optical bench level.A hierarchical framework combining XGBoost and SHapley Additive exPlanations(SHAP)values is employed to model the intricate relationships between parameters and TTL coupling noise,supplemented by sensitivity analysis.Our results identify pointing jitter and telescope radius as the dominant parameters at the telescope level,while the angles of the plane mirrors and beam splitters are most influential at the optical bench level.The parameter space is reduced from 86 dimensions to 14 dimensions without sacrificing model accuracy.This approach offers actionable insights for optimizing the Taiji interferometer design.
基金supported by the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20241443)the Jiangsu Funding Program for Excellent Postdoctoral Talent(Grant No.2024ZB072)the National Natural Science Foundation of China(Grant No.92266201).
文摘This study aims to establish an integrated sensitivity analysis framework for optimization and design of the dynamic performance of mechanical systems such as tracked vehicles,by combining the direct differentiation method(DDM)with the linear multibody system transfer matrix method(linear MSTMM).The rigid-flexible coupled multibody system dynamics model of a tracked vehicle is established using the linear MSTMM and validated through the modal test.Building upon the existing DDM-based eigenvalue sensitivity analysis method within the linear MSTMM,the DDM is embedded into it to enable programmable and efficient computation of dynamic response sensitivities for mechanical systems.The proposed approach is used to quantitatively evaluate the sensitivities of both natural vibration characteristics(e.g.,natural frequencies and mode shapes)and transient dynamic responses of the tracked vehicle with respect to system parameters,successfully identifying critical structural parameters.Compared to conventional finite difference methods,the developed methodology eliminates sensitivity to perturbation step sizes.The contributions of this work lie in establishing a unified theoretical foundation and analysis framework for guiding dynamics optimization and design of mechanical systems,and extending the applicability of the linear MSTMM to sensitivity analysis of transient dynamic responses.
基金supported by the National Natural Science Foundation of China(Grant Nos.42250103 and 42174090)the Opening Fund of Key Laboratory of Geological Survey and Evaluation of Ministry of Education(Grant No.GLAB2023ZR02)the Ministry of Science and Technology(MOST)Special Fund from the State Key Laboratory of Geological Processes and Mineral Resources(Grant No.MSFGPMR2022-4)。
文摘As a means of quantitative interpretation,forward calculations of the global lithospheric magnetic field in the Spherical Harmonic(SH)domain have been widely used to reveal geophysical,lithological,and geothermal variations in the lithosphere.Traditional approaches either do not consider the non-axial dipolar terms of the inducing field and its radial variation or do so by means of complicated formulae.Moreover,existing methods treat the magnetic lithosphere either as an infinitesimally thin layer or as a radially uniform spherical shell of constant thickness.Here,we present alternative forward formulae that account for an arbitrarily high maximum degree of the inducing field and for a magnetic lithosphere of variable thickness.Our simulations based on these formulae suggest that the satellite magnetic anomaly field is sensitive to the non-axial dipolar terms of the inducing field but not to its radial variation.Therefore,in forward and inverse calculations of satellite magnetic anomaly data,the non-axial dipolar terms of the inducing field should not be ignored.Furthermore,our results show that the satellite magnetic anomaly field is sensitive to variability in the lateral thickness of the magnetized shell.In particular,we show that for a given vertically integrated susceptibility distribution,underestimating the thickness of the magnetic layer overestimates the induced magnetic field.This discovery bridges the greatest part of the alleged gap between the susceptibility values measured from rock samples and the susceptibility values required to match the observed magnetic field signal.We expect the formulae and conclusions of this study to be a valuable tool for the quantitative interpretation of the Earth's global lithospheric magnetic field,through an inverse or forward modelling approach.
基金supported by the State Key Laboratory of Offshore Oil and Gas Exploitation, Open Fund Project (No. CCL2023RCPS0162RQN)the primary funding, National Natural Science Foundation of China (No. ZX20230400)
文摘Saline aquifers are considered as highly favored reservoirs for CO_(2)sequestration due to their favorable properties.Understanding the impact of saline aquifer properties on the migration and distribution of CO_(2)plume is crucial.This study focuses on four key parameters-permeability,porosity,formation pressure,and temperature-to characterize the reservoir and analyse the petrophysical and elastic response of CO_(2).First,we performed reservoir simulations to simulate CO_(2)saturation,using multiple sets of these four parameters to examine their significance on CO_(2)saturation and the plume migration speed.Subsequently,the effect of these parameters on the elastic properties is tested using rock physics theory.We established a relationship of compressional wave velocity(V_(p))and quality factor(Q_(p))with the four key parameters,and conducted a sensitivity analysis to test their sensitivity to V_(p) and Q_(p).Finally,we utilized visco-acoustic wave equation simulated time-lapse seismic data based on the computed V_(p) and Q_(p) models,and analysed the impact of CO_(2) saturation changes on seismic data.As for the above nu-merical simulations and analysis,we conducted sensitivity analysis using both homogeneous and heterogeneous models.Consistent results are found between homogeneous and heterogeneous models.The permeability is the most sensitive parameter to the CO_(2)saturation,while porosity emerges as the primary factor affecting both Q_(p) and V_(p).Both Q_(p) and V_(p) increase with the porosity,which contradicts the observations in gas reservoirs.The seismic simulations highlight significant variations in the seismic response to different parameters.We provided analysis for these observations,which serves as a valuable reference for comprehensive CO_(2)integrity analysis,time-lapse monitoring,injection planning and site selection.
基金supported by the National Natural Science Foundation of China[grant numbers 42192553 and 41922036]the Fundamental Research Funds for the Central Universities–Cemac“GeoX”Interdisciplinary Program[grant number 020714380207]。
文摘While steady improvements have been achieved for the track forecasts of typhoons,there has been a lack of improvement for intensity forecasts.One challenge for intensity forecasts is to capture the rapid intensification(RI),whose nonlinear characteristics impose great difficulties for numerical models.The ensemble sensitivity analysis(ESA)method is used here to analyze the initial conditions that contribute to typhoon intensity forecasts,especially with RI.Six RI processes from five typhoons(Chaba,Haima,Meranti,Sarika,and Songda)in 2016,are applied with ESA,which also gives a composite initial condition that favors subsequent RI.Results from individual cases have generally similar patterns of ESA,but with different magnitudes,when various cumulus parameterization schemes are applied.To draw the initial conditions with statistical significance,sample-mean azimuthal components of ESA are obtained.Results of the composite sensitivity show that typhoons that experience RI in 24 h favor enhanced primary circulation from low to high levels,intensified secondary circulation with increased radial inflow at lower levels and increased radial outflow at upper levels,a prominent warm core at around 300 hPa,and increased humidity at low levels.As the forecast lead time increases,the patterns of ESA are retained,while the sensitivity magnitudes decay.Given the general and quantitative composite sensitivity along with associated uncertainties for different cumulus parameterization schemes,appropriate sampling of the composite sensitivity in numerical models could be beneficial to capturing the RI and improving the forecasting of typhoon intensity.
文摘Kangbao County is located in the northwest of Bashang in Hebei Province,which is a sub-arid area in the middle temperate zone,with a cold and arid climate and frequent disastrous weather.The meteorological data of Kangbao County Meteorological Station from 1994 to 2023 were selected,and the meteorological elements such as air pressure,temperature,precipitation,wind,relative humidity,sunshine,thunderstorm,hail,gale,rainstorm,fog,and snow cover were counted.The climate background analysis and high-impact weather analysis were carried out in combination with the topographic characteristics,geographical location,and climate characteristics.The results of meteorological sensitivity survey in the park showed that industries such as food,agriculture and new energy are very sensitive to temperature.During the visit to the enterprises in the park,it was found that heavy precipitation,snow,strong winds and hail had a great impact on many industries,and it was recommended to carry out long-term planning and reasonable design of buildings.It should pay close attention to forecasts and early warnings,formulate emergency plans for high-impact weather defense,and actively take preventive measures.
基金funded by the INTER program and cofunded by the Fond National de la Recherche,Luxembourg(FNR)and the Fund for Scientific Research-FNRS,Belgium(F.R.S-FNRS),T.0233.20-‘Sustainable Residential Densification’project(SusDens,2020–2024).
文摘The impact of different global and local variables in urban development processes requires a systematic study to fully comprehend the underlying complexities in them.The interplay between such variables is crucial for modelling urban growth to closely reflects reality.Despite extensive research,ambiguity remains about how variations in these input variables influence urban densification.In this study,we conduct a global sensitivity analysis(SA)using a multinomial logistic regression(MNL)model to assess the model’s explanatory and predictive power.We examine the influence of global variables,including spatial resolution,neighborhood size,and density classes,under different input combinations at a provincial scale to understand their impact on densification.Additionally,we perform a stepwise regression to identify the significant explanatory variables that are important for understanding densification in the Brussels Metropolitan Area(BMA).Our results indicate that a finer spatial resolution of 50 m and 100 m,smaller neighborhood size of 5×5 and 3×3,and specific density classes—namely 3(non-built-up,low and high built-up)and 4(non-built-up,low,medium and high built-up)—optimally explain and predict urban densification.In line with the same,the stepwise regression reveals that models with a coarser resolution of 300 m lack significant variables,reflecting a lower explanatory power for densification.This approach aids in identifying optimal and significant global variables with higher explanatory power for understanding and predicting urban densification.Furthermore,these findings are reproducible in a global urban context,offering valuable insights for planners,modelers and geographers in managing future urban growth and minimizing modelling.
基金Dalian Municipal Natural Science Foundation under Grant No.2019RD01。
文摘Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting multi-hazard dynamic responses to super high-rise structures has significant engineering and scientific value. This study performed a parametric global sensitivity analysis (GSA) for multi-hazard dynamic response prediction of super high-rise structures using the multiple-degree-of-freedom shear (MFS) model. Polynomial chaos Kriging (PCK) was introduced to build a surrogate model that allowed GSA to be combined with Sobol’ indices. Monte Carlo simulation (MCS) is also conducted for the comparison to verify the accuracy and efficiency of the PCK method. Parametric sensitivity analysis is performed for a wide range of aleatory uncertainty (intensities of coupled multi-hazard), epistemic uncertainty (bending stiffness, k_(m);shear stiffness, kq;density, ρ;and damping ratio, ξ), probability distribution types, and coefficients of variation. The results indicate that epistemic uncertainty parameters, k_(m), ρ, and ξ dramatically affect the multi-hazard dynamic responses of super high-rise structures;in addition, Sobol’ indices between the normal and lognormal distributions are insignificant, while the variation levels have remarkably influenced the sensitivity indices.
基金jointly funded by the National Natural Science Foundation of China(Grant No.42161024)the Central Financial Forestry and Grassland Science and Technology Extension Demonstration Project(2025)(Grant No.Xin[2025]TG 09)。
文摘Accurate quantification of carbon and water fluxes dynamics in arid and semi-arid ecosystems is a critical scientific challenge for regional carbon neutrality assessments and sustainable water resource management.In this study,we developed a multi-flux global sensitivity discriminant index(D_(sen))by integrating the Biome-BGCMuSo model with eddy covariance flux observations.This index was combined with a Bayesian optimization algorithm to conduct parameter optimization.The results demonstrated that:(1)Sensitivity analysis identified 13 highly sensitive parameters affecting carbon and water fluxes.Among these,the canopy light extinction coefficient(k)and the fraction of leaf N in Rubisco(FLNR)exhibited significantly higher sensitivity to carbon fluxes(GPP,NEE,Reco;D_(sen)>10%)compared to water flux(ET).This highlights the strong dependence of carbon cycle simulations on vegetation physiological parameters.(2)The Bayesian optimization framework efficiently converged 30 parameter spaces within 50 iterations,markedly improving carbon fluxes simulation accuracy.The Kling-Gupta efficiency(KGE)values for Gross Primary Production(GPP),Net Ecosystem Exchange(NEE),and Total Respiration(Reco)increased by 44.94%,69.23%and 123%,respectively.The optimization prioritized highly sensitive parameters,underscoring the necessity of parameter sensitivity stratification.(3)The optimized model effectively reproduced carbon sink characteristics in mountain meadows during the growing season(cumulative NEE=-375 g C/m^(2)).It revealed synergistic carbon-water fluxes interactions governed by coupled photosynthesis-stomatal pathways and identified substrate supply limitations on heterotrophic respiration.This study proposes a novel multi-flux sensitivity index and an efficient optimization framework,elucidating the coupling mechanisms between vegetation physiological regulation(k,FLNR)and environmental stressors(VPD,SWD)in carbonwater cycles.The methodology offers a practical approach for arid ecosystem model optimization and provides theoretical insights for grassland management through canopy structure regulation and water-use efficiency enhancement.
基金supported by the National Natural Science Foundation of China(Nos.52306036,52325602 and U2441279)the National Science and Technology Major Project,China(Nos.Y2022-Ⅱ-0003-0006 and Y2022-Ⅱ-0002-0005)supported by the Project of National Key Laboratory of Science and Technology on Aero-Engine Aero-thermodynamics,China(Nos.6142702200101 and 2024-CXPT-GF-JJ-88-0103)。
文摘This paper presents a sensitivity analysis method for analyzing the key factors affecting the stability problem of the transonic compressors.The adjoint method is integrated into the meridional stability model,a linear stability prediction model utilized to analyze the flow stability problem of the compressor,and the sensitivity analysis method is further developed for the flow stability problem of the compressor.The study selects the NASA Rot or 37,a transonic compressor,as the research object to verify the proposed method and explore the sensitive factors leading to the stall inception.The results of sensitivity analysis to both the flow parameters and the external source terms reveal that the stall inception is sensitive to the base flow field at the rotor tip and the stability margin of the compressor can be enhanced by improving the flow field at this region.Physical explanations are presented and discussed to correlate the three-dimensional flow field to the results obtained via the employed analysis method,which shows that flow structures and characteristics near the end-wall region,especially the tip leakage flow or the tip leakage vortex and its interaction with the shock wave,contribute to the stall inception.
基金support from the National Natural Science Foundation of China(Grant Nos.52174123&52274222).
文摘This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.
基金supported by the Talent Project of Tianchi Young-Doctoral Program in Xinjiang Uygur Autonomous Region of China(No.51052401510)Natural Science Foundation General Project(Grant Number 2025D01C36)of the Xinjiang Uyghur Autonomous Region of China+1 种基金This study received financial support from the National Natural Science Foundation of Xinjiang Province(Grant Nos.2022TSYCTD0019 and 2022D01D32)the China Scholarship Council(CSC)(Grant No.2021SLJ009915).
文摘Roll coating is a vital industrial process used in printing,packaging,and polymer film production,where maintaining a uniform coating is critical for product quality and efficiency.This work models non-isothermal Carreau fluid flow between a rotating roll and a stationary wall under fixed boundary constraints to evaluate how non-Newtonian and thermal effects influence coating performance.The governing equations are transformed into non-dimensional form and simplified using lubrication approximation theory.Approximate analytical solutions are obtained via the perturbation technique,while numerical results are computed using both the finite difference method and the BVPMidrich technique.Furthermore,Response surface methodology(RSM)is employed for optimization and sensitivity analysis.Analytical and numerical results show strong agreement(<1%deviation).The model predicts coating thickness 0.55≤λ≤0.64,power input 1.05≤P_(w)≤1.99,and separation force 0.91≤S_(f)≤1.82 for 0.1≤We≤0.9 and 0.01≤F≤0.09.Increasing We enhances the coating thickness and power input but reduces velocity and separation force.The findings provide physical insight into elastic and viscous effects in roll coating,providing insight for optimizing coating uniformity,minimizing wear,improving industrial coating processes,and extending substrate lifespan.
基金supported by the National Key Research and Development Program of China(No.2022YFC3701205)the National Natural Science Foundation of China(No.41975173)the Science and Technology Development Fund of the Chinese Academy of Meteorological Sciences(No.2021KJ011)。
文摘In recent years,incidents of simultaneous exceedance of PM_(2.5)and O_(3) concentrations,termed PM_(2.5)and O_(3) co-pollution events,have frequently occurred in China.This study conducted atmospheric circulation analysis on two typical co-pollution events in Beijing,occurring from July 22 to July 28,2019,and from April 25 to May 2,2020.These events were categorized into pre-trough southerly airflow type(Type 1)and post-trough northwest flow type(Type 2).Subsequently,sensitivity analyses using the GRAPES-CUACE adjoint model were performed to quantify the contributions of precursor emissions from Beijing and surrounding areas to PM_(2.5)and O_(3) concentrations in Beijing for two types of co-pollution.The results indicated that the spatiotemporal distribution of sensitive source region varied among different circulation types.Primary PM_(2.5)(PPM_(2.5))emissions from Hebei contributed the most to the 24-hour average PM_(2.5)(24-h PM_(2.5))peak concentration(41.6%-45.4%),followed by Beijing emissions(31%-35.7%).The maximum daily 8-hour average ozone peak concentration was primarily influenced by the emissions from Hebei and Beijing,with contribution ratios respectively of 32.8%-44.8% and 29%-42.1%.Additionally,NO_(x)emissions were the main contributors in Type 1,while both NO_(x)and VOCs emissions contributed similarly in Type 2.The iterative emission reduction experiments for two types of co-pollution indicated that Type 1 required emission reductions in NO_(x)(52.4%-71.8%)and VOCs(14.1%-33.8%)only.In contrast,Type 2 required combined emission reductions in NO_(x)(37.0%-65.1%),VOCs(30.7%-56.2%),and PPM_(2.5)(31%-46.9%).This study provided a reference for controlling co-pollution events and improving air quality in Beijing.
基金supported by the Natural Science BasicResearch Program of Shaanxi,China(No.2021JC-14)。
文摘The water hammer problem is an important issue in the dynamics of liquid propulsion system.This paper aims to use the Lattice Boltzmann Method(LBM)with entropy limiter to study the water hammer problems in propellant feedlines.The dynamic characteristics of valve-closing water hammer and filling water hammer are investigated by this method,and the sensitivity of filling water hammer is analyzed with a single factor sensitivity analysis with 8 factors and 9 levels and a multi-factor sensitivity analysis with L_(27)(3^(13))orthogonal experiment based on range method.It is found that the solving result of LBM with entropy limiter is basically in good agreement with finite volume method,and using the entropy limiter can eliminate numerical oscillations when solving valve-closing water hammer problems and solve the numerical"blow up"when solving filling water hammer problems.It can be seen that the dynamic characteristics of valve-closing water hammer are relatively simple,while there are many factors that affect the filling water hammer and the degree of these effects varies.The effects on the maximum water hammer pressure are relatively uniform,but those on the water hammer response time vary greatly through the skewness analysis.
文摘In this study,the multi-scale(meso and macro)modelling was used to predict the electric response of the material.Porosity was introduced through a sugar-templating process to enhance compressibility and sensitivity.Mean-field homogenization was employed to predict the electrical conductivity of the nanocomposites,which was validated experimentally through I–V characterisation,confirming stable Ohmic behavior.The homogenised material parameters were incorporated into COMSOLMultiphysics to simulate diaphragmdeflection and capacitance variation under applied pressure.Experimental results showed a linear and stable capacitance response at the force magnitude of 0–7 N.The Graphene nanoplatelets(GnP)–Polydimethylsiloxane(PDMS)sensor demonstrated superior sensitivity(0.0032 pF/N)compared to the CNT–PDMS sensor(0.0019 pF/N),attributed to improved filler dispersion and higher effective surface area of GnP.Finite element simulations were further conducted to evaluate stress distribution in a GnP–PDMS-based capacitive sensor integrated into a shoe insole for gait analysis.The results correlated well with experimental capacitance changes,validating the sensor’s mechanical reliability and pressure sensitivity.This comparative study establishes the GnP–PDMS composite as a more effective candidate for low-cost,biocompatible,and high-performance flexible pressure sensors in wearable biomedical and gait monitoring applications.
文摘Correction to:Nuclear Science and Techniques(2025)36:111 https://doi.org/10.1007/s41365-025-01681-9.In the sentence beginning‘The weights of the parameters used for the…’in this article,the text‘RCSs’should have read‘SCRs’.In Table 7 of this article,the column header ρ_fuel was incorrect and should have read CPv_fuel.For completeness and transparency,the old incorrect version and the corrected version of Table 7 are displayed below.
基金funded by the Ministry of Higher Education,Science and Technology,Republic of Indonesia through the Indonesia Collaborative Research(Riset Kolaborasi Indonesia)grant(Number:01319/UN4.22/PT.01.03/2025)。
文摘The Toraja Highlands,encompassing Tana Toraja and North Toraja,form the strategic upper reaches of the Saddang Watershed in South Sulawesi,where steep terrain,active land-cover change,and high ecological sensitivity converge.This study addresses the need for an objective and validated ecological sensitivity map to support sustainable mountain watershed management.We construct an ecological sensitivity index based on principal component analysis using four key indicators:land cover,vegetation density(NDVI),slope,and rainfall,and evaluate its reliability through multi-source validation.Inputs integrate national elevation models,Landsat 8 imagery,and satellite-derived rainfall.Rainfall represents a multi-year climatology for 2015–2024,whereas land cover and NDVI reflect recent surface conditions derived from a cloud-free 2024 composite.The resulting sensitivity zonation indicates that 41.10%of Tana Toraja and 67.11%of North Toraja fall into the very high sensitivity class,concentrated on steep slopes and intensively converted landscapes.Eventbased spatial cross-validation against independent landslide records yields overall accuracies of 67.65%and 66.67%,while field verification produces Kappa values of 0.847 and 0.871.Stakeholder appraisal further corroborates the mapped patterns.Together,these convergent lines of evidence identify priority areas for reforestation,soil conservation,slope stabilization,and sustainable watershed management.The transparent and reproducible workflow supports evidence-based risk reduction and resilience building in the upper reaches of the Saddang Watershed.
基金The Scientific Innovation Research of College Graduates in Jiangsu Province(No.CXLX13_110)the Young Scientists Fund of National Natural Science Foundation of China(No.51408253)the Young Scientists Fund of Huaiyin Institute of Technology(No.491713328)
文摘This paper puts forward a rigorous approach for a sensitivity analysis of stochastic user equilibrium with the elastic demand （SUEED） model. First, proof is given for the existence of derivatives of output variables with respect to the perturbation parameters for the SUEED model. Then by taking advantage of the gradient-based method for sensitivity analysis of a general nonlinear program, detailed formulae are developed for calculating the derivatives of designed variables with respect to perturbation parameters at the equilibrium state of the SUEED model. This method is not only applicable for a sensitivity analysis of the logit-type SUEED problem, but also for the probit-type SUEED problem. The application of the proposed method in a numerical example shows that the proposed method can be used to approximate the equilibrium link flow solutions for both logit-type SUEED and probit-type SUEED problems when small perturbations are introduced in the input parameters.
