Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

On an isotropic porous solid cylinder:the analytical solution and sensitivity analysis of the pressure

Within this work,we perform a sensitivity analysis to determine the influence of the material input parameters on the pressure in an isotropic porous solid cylinder.We provide a step-by-step guide to obtain the analytical solution for a porous isotropic elastic cylinder in terms of the pressure,stresses,and elastic displacement.We obtain the solution by performing a Laplace transform on the governing equations,which are those of Biot's poroelasticity in cylindrical polar coordinates.We enforce radial boundary conditions and obtain the solution in the Laplace transformed domain before reverting back to the time domain.The sensitivity analysis is then carried out,considering only the derived pressure solution.This analysis finds that the time t,Biot's modulus M,and Poisson's ratio ν have the highest influence on the pressure whereas the initial value of pressure P_(0) plays a very little role.

Analysis of sensitivity to hydrate blockage risk in natural gas gathering pipeline

During the operational process of natural gas gathering and transmission pipelines,the formation of hydrates is highly probable,leading to uncontrolled movement and aggregation of hydrates.The continuous migration and accumulation of hydrates further contribute to the obstruction of natural gas pipelines,resulting in production reduction,shutdowns,and pressure build-ups.Consequently,a cascade of risks is prone to occur.To address this issue,this study focuses on the operational process of natural gas gathering and transmission pipelines,where a comprehensive framework is established.This framework includes theoretical models for pipeline temperature distribution,pipeline pressure distribution,multiphase flow within the pipeline,hydrate blockage,and numerical solution methods.By analyzing the influence of inlet temperature,inlet pressure,and terminal pressure on hydrate formation within the pipeline,the sensitivity patterns of hydrate blockage risks are derived.The research indicates that reducing inlet pressure and terminal pressure could lead to a decreased maximum hydrate formation rate,potentially mitigating pipeline blockage during natural gas transportation.Furthermore,an increase in inlet temperature and terminal pressure,and a decrease in inlet pressure,results in a displacement of the most probable location for hydrate blockage towards the terminal station.However,it is crucial to note that operating under low-pressure conditions significantly elevates energy consumption within the gathering system,contradicting the operational goal of energy efficiency and reduction of energy consumption.Consequently,for high-pressure gathering pipelines,measures such as raising the inlet temperature or employing inhibitors,electrical heat tracing,and thermal insulation should be adopted to prevent hydrate formation during natural gas transportation.Moreover,considering abnormal conditions such as gas well production and pipeline network shutdowns,which could potentially trigger hydrate formation,the installation of methanol injection connectors remains necessary to ensure production safety.

Explainable Neural Network for Sensitivity Analysis of Lithium-ion Battery Smart Production

Battery production is crucial for determining the quality of electrode,which in turn affects the manufactured battery performance.As battery production is complicated with strongly coupled intermediate and control parameters,an efficient solution that can perform a reliable sensitivity analysis of the production terms of interest and forecast key battery properties in the early production phase is urgently required.This paper performs detailed sensitivity analysis of key production terms on determining the properties of manufactured battery electrode via advanced data-driven modelling.To be specific,an explainable neural network named generalized additive model with structured interaction(GAM-SI)is designed to predict two key battery properties,including electrode mass loading and porosity,while the effects of four early production terms on manufactured batteries are explained and analysed.The experimental results reveal that the proposed method is able to accurately predict battery electrode properties in the mixing and coating stages.In addition,the importance ratio ranking,global interpretation and local interpretation of both the main effects and pairwise interactions can be effectively visualized by the designed neural network.Due to the merits of interpretability,the proposed GAM-SI can help engineers gain important insights for understanding complicated production behavior,further benefitting smart battery production.

Uncertainty and sensitivity analysis of in-vessel phenomena under severe accident mitigation strategy based on ISAA-SAUP program

The phenomenology involved in severe accidents in nuclear reactors is highly complex.Currently,integrated analysis programs used for severe accident analysis heavily rely on custom empirical parameters,which introduce considerable uncertainty.Therefore,in recent years,the field of severe accidents has shifted its focus toward applying uncertainty analysis methods to quantify uncertainty in safety assessment programs,known as“best estimate plus uncertainty(BEPU).”This approach aids in enhancing our comprehension of these programs and their further development and improvement.This study concentrates on a third-generation pressurized water reactor equipped with advanced active and passive mitigation strategies.Through an Integrated Severe Accident Analysis Program(ISAA),numerical modeling and uncertainty analysis were conducted on severe accidents resulting from large break loss of coolant accidents.Seventeen uncertainty parameters of the ISAA program were meticulously screened.Using Wilks'formula,the developed uncertainty program code,SAUP,was employed to carry out Latin hypercube sampling,while ISAA was employed to execute batch calculations.Statistical analysis was then conducted on two figures of merit,namely hydrogen generation and the release of fission products within the pressure vessel.Uncertainty calculations revealed that hydrogen production and the fraction of fission product released exhibited a normal distribution,ranging from 182.784 to 330.664 kg and from 15.6 to 84.3%,respectively.The ratio of hydrogen production to reactor thermal power fell within the range of 0.0578–0.105.A sensitivity analysis was performed for uncertain input parameters,revealing significant correlations between the failure temperature of the cladding oxide layer,maximum melt flow rate,size of the particulate debris,and porosity of the debris with both hydrogen generation and the release of fission products.

A Bayesian multi-model inference methodology for imprecise momentindependent global sensitivity analysis of rock structures

Traditional global sensitivity analysis(GSA)neglects the epistemic uncertainties associated with the probabilistic characteristics(i.e.type of distribution type and its parameters)of input rock properties emanating due to the small size of datasets while mapping the relative importance of properties to the model response.This paper proposes an augmented Bayesian multi-model inference(BMMI)coupled with GSA methodology(BMMI-GSA)to address this issue by estimating the imprecision in the momentindependent sensitivity indices of rock structures arising from the small size of input data.The methodology employs BMMI to quantify the epistemic uncertainties associated with model type and parameters of input properties.The estimated uncertainties are propagated in estimating imprecision in moment-independent Borgonovo’s indices by employing a reweighting approach on candidate probabilistic models.The proposed methodology is showcased for a rock slope prone to stress-controlled failure in the Himalayan region of India.The proposed methodology was superior to the conventional GSA(neglects all epistemic uncertainties)and Bayesian coupled GSA(B-GSA)(neglects model uncertainty)due to its capability to incorporate the uncertainties in both model type and parameters of properties.Imprecise Borgonovo’s indices estimated via proposed methodology provide the confidence intervals of the sensitivity indices instead of their fixed-point estimates,which makes the user more informed in the data collection efforts.Analyses performed with the varying sample sizes suggested that the uncertainties in sensitivity indices reduce significantly with the increasing sample sizes.The accurate importance ranking of properties was only possible via samples of large sizes.Further,the impact of the prior knowledge in terms of prior ranges and distributions was significant;hence,any related assumption should be made carefully.

Calculations and Sensitivity Analysis of Chlorine-,NO_(x)-,and Bromine-Depleting Cycles of Stratospheric Ozone

This paper presents an engineering system approach using a 2D model of conservation of mass to study the dynamics of ozone and concerned chemical species in the stratosphere.By considering all fourteen photolysis,ozone-generating,and-depleting chemical reactions,the model calculated the transient,spatial changes of ozone under different physical-chemical-radiative conditions.Validation against the measured data demonstrated good accuracy,close match of our model with the observed ozone concentrations at both 20°S and 90°N locations.The deviation in the average concentration was less than 1% and in ozone profiles less than 17%.The impacts of various chlorine-(Cl),nitrogen oxides-(NO_(x)),and bromine-(Br)depleting cycles on ozone concentrations and distribution were investigated.The chlorine catalytic depleting cycle was found to exhibit the most significant impact on ozone dynamics,confirming the key role of chlorine in the problem of ozone depletion.Sensitivity analysis was conducted with levels of 25%,50%,100%,200%,and 400% of the baseline value.The combined cycles(Cl+NO_(x)+Br)showed the most significant influence on ozone behavior.The total ozone abundance above the South Pole could decrease by a small 3%,from 281 DU(Dubson Units)to 273 DU for the 25% level,or by a huge thinning of 60%to 114 DU for the 400% concentration level.When the level of chlorine gases increased beyond 200%,it would cause ozone depletion to a level of ozone hole(below 220 DU).The 2D Ozone Model presented in this paper demonstrates robustness,convenience,efficiency,and executability for analyzing complex ozone phenomena in the stratosphere.

Local and global sensitivity analysis for railway upgrading between hydrogen fuel cell and electrification

In the field of rail transit,the UK Department of Transport stated that it will realize a comprehensive transformation of UK railways by 2050,abandoning traditional diesel trains and upgrading them to new environmentally friendly trains.The current mainstream upgrade methods are electrification and hydrogen fuel cells.Comprehensive upgrades are costly,and choosing the optimal upgrade method for trams and mainline railways is critical.Without a sensitivity analysis,it is difficult for us to determine the influence relationship between each parameter and cost,resulting in a waste of cost when choosing a line reconstruction method.In addition,by analyzing the sensitivity of different parameters to the cost,the primary optimization direction can be determined to reduce the cost.Global higher-order sensitivity analysis enables quantification of parameter interactions,showing non-additive effects between parameters.This paper selects the main parameters that affect the retrofit cost and analyzes the retrofit cost of the two upgrade methods in the case of trams and mainline railways through local and global sensitivity analysis methods.The results of the analysis show that,given the current UK rail system,it is more economical to choose electric trams and hydrogen mainline trains.For trams,the speed at which the train travels has the greatest impact on the final cost.Through the sensitivity analysis,this paper provides an effective data reference for the current railway upgrading and reconstruction plan and provides a theoretical basis for the next step of train parameter optimization.

Machine learning based damage state identification:A novel perspective on fragility analysis for nuclear power plants considering structural uncertainties

Seismic fragility analysis(SFA)is known as an effective probabilistic-based approach used to evaluate seismic fragility.There are various sources of uncertainties associated with this approach.A nuclear power plant(NPP)system is an extremely important infrastructure and contains many structural uncertainties due to construction issues or structural deterioration during service.Simulation of structural uncertainties effects is a costly and time-consuming endeavor.A novel approach to SFA for the NPP considering structural uncertainties based on the damage state is proposed and examined.The results suggest that considering the structural uncertainties is essential in assessing the fragility of the NPP structure,and the impact of structural uncertainties tends to increase with the state of damage.Subsequently,machine learning(ML)is found to be superior in high-precision damage state identification of the NPP for reducing the time of nonlinear time-history analysis(NLTHA)and could be applied in the damage state-based SFA.Also,the impact of various sources of uncertainties is investigated through sensitivity analysis.The Sobol and Shapley additive explanations(SHAP)method can be complementary to each other and able to solve the problem of quantifying seismic and structural uncertainties simultaneously and the interaction effect of each parameter.

A logistic-Lasso-regression-based seismic fragility analysis method for electrical equipment considering structural and seismic parameter uncertainty

Damage to electrical equipment in an earthquake can lead to power outage of power systems.Seismic fragility analysis is a common method to assess the seismic reliability of electrical equipment.To further guarantee the efficiency of analysis,multi-source uncertainties including the structure itself and seismic excitation need to be considered.A method for seismic fragility analysis that reflects structural and seismic parameter uncertainty was developed in this study.The proposed method used a random sampling method based on Latin hypercube sampling(LHS)to account for the structure parameter uncertainty and the group structure characteristics of electrical equipment.Then,logistic Lasso regression(LLR)was used to find the seismic fragility surface based on double ground motion intensity measures(IM).The seismic fragility based on the finite element model of an±1000 kV main transformer(UHVMT)was analyzed using the proposed method.The results show that the seismic fragility function obtained by this method can be used to construct the relationship between the uncertainty parameters and the failure probability.The seismic fragility surface did not only provide the probabilities of seismic damage states under different IMs,but also had better stability than the fragility curve.Furthermore,the sensitivity analysis of the structural parameters revealed that the elastic module of the bushing and the height of the high-voltage bushing may have a greater influence.

Sensitivity analysis for stochastic user equilibrium with elastic demand assignment model

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.

Error Modeling and Sensitivity Analysis of a Parallel Robot with SCARA(Selective Compliance Assembly Robot Arm) Motions

Parallel robots with SCARA（selective compliance assembly robot arm） motions are utilized widely in the field of high speed pick-and-place manipulation. Error modeling for these robots generally simplifies the parallelogram structures included by the robots as a link. As the established error model fails to reflect the error feature of the parallelogram structures, the effect of accuracy design and kinematic calibration based on the error model come to be undermined. An error modeling methodology is proposed to establish an error model of parallel robots with parallelogram structures. The error model can embody the geometric errors of all joints, including the joints of parallelogram structures. Thus it can contain more exhaustively the factors that reduce the accuracy of the robot. Based on the error model and some sensitivity indices defined in the sense of statistics, sensitivity analysis is carried out. Accordingly, some atlases are depicted to express each geometric error’s influence on the moving platform’s pose errors. From these atlases, the geometric errors that have greater impact on the accuracy of the moving platform are identified, and some sensitive areas where the pose errors of the moving platform are extremely sensitive to the geometric errors are also figured out. By taking into account the error factors which are generally neglected in all existing modeling methods, the proposed modeling method can thoroughly disclose the process of error transmission and enhance the efficacy of accuracy design and calibration.

Separation of Comprehensive Geometrical Errors of a 3-DOF Parallel Manipulator Based on Jacobian Matrix and Its Sensitivity Analysis with Monte-Carlo Method

Parallel kinematic machines （PKMs） have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.

Nonlinear Mathematical Modeling and Sensitivity Analysis of Hydraulic Drive Unit

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Quantitative investigation on micro-parameters of cemented paste backfill and its sensitivity analysis

The mechanical properties of cemented paste backfill(CPB) depend heavily on its pore structural characteristics and micro-structural changes. In order to explore the variation mechanisms of macro-mechanical characteristics and micro-structure of CPB. CPB specimens with different mass concentrations prepared from the full tailings of Xianglushan Tungsten Ore were micro-tests. Moreover, acquired pore digital images were processed by using the pores(particles) and cracks analysis system(PCAS), and a sensitivity analysis was performed. The results show that as the mass concentration of CPB increases from 70% to 78%, the porosity, the average pore area and the number of pores drop overall, leading to a decline in the pores opening degree and enhancing the mechanical characteristics. As the mass concentration of CPB increases, the trend of fractal dimension, probability entropy and roundness is reduced, constant and increased, which can result in an enhancement of the uniformity, an unchanged directionality and more round pores. According to the definition of sensitivity, the sensitivities of various micro-parameters were calculated and can be ranked as porosity > average pore area > number of pores > roundness > fractal dimension > probability entropy.

Global analysis of sensitivity of bioretention cell design elements to hydrologic performance

Analysis of sensitivity of bioretention cell design elements to their hydrologic performances is meaningful in offering theoretical guidelines for proper design. Hydrologic performance of bioretention cells was facilitated with consideration of four metrics： the overflow ratio, groundwater recharge ratio, ponding time, and runoff coefficients. The storm water management model （SWMM） and the bioretention infiltration model RECARGA were applied to generating runoff and outflow time series for calculation of hydrologic performance metrics. Using a parking lot to build a bioretention cell, as an example, the Morris method was used to conduct global sensitivity analysis for two groups of bioretention samples, one without underdrain and the other with underdrain. Results show that the surface area is the most sensitive element to most of the hydrologic metrics, while the gravel depth is the least sensitive element whether bioretention cells are installed with underdrain or not. The saturated infiltration rate of planting soil and the saturated infiltration rate of native soil are the other two most sensitive elements for bioretention cells without underdrain, while the saturated infiltration rate of native soil and underdrain size are the two most sensitive design elements for bioretention cells with underdrain.

Seismic response comparison and sensitivity analysis of pile foundation in liquefiable and non-liquefiable soils

Case history investigations have shown that pile foundations are more critically damaged in liquefiable soils than non-liquefiable soils.This study examines the differences in seismic response of pile foundations in liquefiable and non-liquefiable soils and their sensitivity to numerical model parameters.A two-dimensional finite element(FE)model is developed to simulate the experiment of a single pile foundation centrifuge in liquefiable soil subjected to earthquake motions and is validated against real-world test results.The differences in soil-pile seismic response of liquefiable and non-liquefiable soils are explored.Specifically,the first-order second-moment method(FOSM)is used for sensitivity analysis of the seismic response.The results show significant differences in seismic response for a soil-pile system between liquefiable and non-liquefiable soil.The seismic responses are found to be significantly larger in liquefiable soil than in non-liquefiable soil.Moreover,the pile bending moment was mainly affected by the kinematic effect in liquefiable soil,while the inertial effect was more significant in non-liquefiable soil.The controlling parameters of seismic response were PGA,soil density,and friction angle in liquefiable soil,while the pile bending moment was mainly controlled by PGA,the friction angle of soil,and shear modulus of loose sand in non-liquefiable soil.

Parameter identification and global sensitivity analysis of Xin'anjiang model using meta-modeling approach

Parameter identification, model calibration, and uncertainty quantification are important steps in the model-building process, and are necessary for obtaining credible results and valuable information. Sensitivity analysis of hydrological model is a key step in model uncertainty quantification, which can identify the dominant parameters, reduce the model calibration uncertainty, and enhance the model optimization efficiency. There are, however, some shortcomings in classical approaches, including the long duration of time and high computation cost required to quantitatively assess the sensitivity of a multiple-parameter hydrological model. For this reason, a two-step statistical evaluation framework using global techniques is presented. It is based on （1） a screening method （Morris） for qualitative ranking of parameters, and （2） a variance-based method integrated with a meta-model for quantitative sensitivity analysis, i.e., the Sobol method integrated with the response surface model （RSMSobol）. First, the Morris screening method was used to qualitatively identify the parameters＇ sensitivity, and then ten parameters were selected to quantify the sensitivity indices. Subsequently, the RSMSobol method was used to quantify the sensitivity, i.e., the first-order and total sensitivity indices based on the response surface model （RSM） were calculated. The RSMSobol method can not only quantify the sensitivity, but also reduce the computational cost, with good accuracy compared to the classical approaches. This approach will be effective and reliable in the global sensitivity analysis of a complex large-scale distributed hydrological model.

Dynamical Behavior and Sensitivity Analysis of a Delayed Coronavirus Epidemic Model

Mathematical delay modelling has a significant role in the different disciplines such as behavioural,social,physical,biological engineering,and bio-mathematical sciences.The present work describes mathematical formulation for the transmission mechanism of a novel coronavirus(COVID-19).Due to the unavailability of vaccines for the coronavirus worldwide,delay factors such as social distance,quarantine,travel restrictions,extended holidays,hospitalization,and isolation have contributed to controlling the coronavirus epidemic.We have analysed the reproduction number and its sensitivity to parameters.If,R_(covid)>1then this situation will help to eradicate the disease and if,R_(covid)>1 the virus will spread rapidly in the human beings.Well-known theorems such as Routh Hurwitz criteria and Lasalle invariance principle have presented for stability.The local and global stabilizes for both equilibria of the model have also been presented.Also,we have analysed the effect of delay reason on the reproduction number.In the last,some very useful numerical consequences have presented in support of hypothetical analysis.

Finite Element Model Updating of Bridge Structures Based on Sensitivity Analysis and Optimization Algorithm

The dynamic characteristics of bridge structures, such as the natural frequencies, mode shapes and model damping ratio, are the basis of structural dynamic computation, seismic analysis, vibration control and structural health condition monitoring. In this paper, a three-dimensional finite-element model is established for a highway bridge over a railway on No.312 National Highway and the ambient test is carried out in site, the dynamic characteristics of the bridge are studied using the finite-element analysis and ambient vibration measurements. Comparison between the theoretical and experimental results shows that the frequency differences of the modes range between 0.44% and 8.77%. If the measurement is more reliable, the finite element model updating is necessary. Thus, a set of design variables is selected based on sensitivity analysis, then the finite element model of the bridge is updated based on optimization algorithm. The results of model updating show that the proposed updating method in this paper is more simple and effective, the updated finite element model can reflect the dynamic characteristics of the bridge better, the analytical results can provide the theoretical basis for damage identification and health condition monitoring of the bridge.