Finite element model updating for structural damage detection using transmissibility data

This paper presents a new finite element model updating method for estimating structural parameters and detecting structural damage location and severity based on the structural responses(output-only data).The method uses the sensitivity relation of transmissibility data through a least-squares algorithm and appropriate normalization of the extracted equations.The proposed transmissibility-based sensitivity equation produces a more significant number of equations than the sensitivity equations based on the frequency response function(FRF),which can estimate the structural parameters with higher accuracy.The abilities of the proposed method are assessed by using numerical data of a two-story two-bay frame model and a plate structure model.In evaluating different damage cases,the number,location,and stiffness reduction of the damaged elements and the severity of the simulated damage have been accurately identified.The reliability and stability of the presented method against measurement and modeling errors are examined using error-contaminated data.The parameter estimation results prove the method’s capabilities as an accurate model updating algorithm.

An improved interval model updating method via adaptive Kriging models

Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample data.However,the surrogate model in IMU methods mostly adopts the one-time construction method.This makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU methods.Therefore,an improved IMU method via the adaptive Kriging models is proposed.This method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey numbers.These optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization(PSO)method to quantify the uncertain parameters,and the IMU is accomplished.During the construction of these adaptive Kriging models,the sample space is gridded according to sensitivity information.Local sampling is then performed in key subspaces based on the maximum mean square error(MMSE)criterion.The interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy requirements.The effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical shell.The results show that the updated results of the interval model are in good agreement with the experimental results.

Quantitative Identification of Delamination Damage in Composite Structure Based on Distributed Optical Fiber Sensors and Model Updating

Delamination is a prevalent type of damage in composite laminate structures.Its accumulation degrades structural performance and threatens the safety and integrity of aircraft.This study presents a method for the quantitative identification of delamination identification in composite materials,leveraging distributed optical fiber sensors and a model updating approach.Initially,a numerical analysis is performed to establish a parameterized finite element model of the composite plate.Then,this model subsequently generates a database of strain responses corresponding to damage of varying sizes and locations.The radial basis function neural network surrogate model is then constructed based on the numerical simulation results and strain responses captured from the distributed fiber optic sensors.Finally,a multi-island genetic algorithm is employed for global optimization to identify the size and location of the damage.The efficacy of the proposed method is validated through numerical examples and experiment studies,examining the correlations between damage location,damage size,and strain responses.The findings confirm that the model updating technique,in conjunction with distributed fiber optic sensors,can precisely identify delamination in composite structures.

Finite element model updating and validating of Runyang Suspension Bridge based on SHMS

Based on the finite element （FE） program ANSYS, a three-dimensional model for the Runyang Suspension Bridge （RSB） is established. The structural natural frequency, vibration mode, stress and displacement response under various load cases are given. A new method of FE model updating is presented based on the physical meaning of sensitivity and the penalty function concept. In this method, the structural model is updated by modifying the parameters of design, and validated by structural natural vibration characteristics, stress response as well as displacement response. The design parameters used for updating are bounded according to measured static response and engineering judgment. The FE model of RSB is updated and validated by the measurements coming from the structural health monitoring system （SHMS）, and the FE baseline model reflecting the current state of RSB is achieved. Both the dynamic and static results show that the method is effective in updating the FE model of long span suspension bridges. The results obtained provide an important research basis for damage alarming and health monitoring of the RSB.

Dynamic finite element model updating using meta-model and genetic algorithm

Current dynamic finite element model updating methods are not efficient or restricted to the problem of local optima. To circumvent these, a novel updating method which integrates the meta-model and the genetic algorithm is proposed. Experimental design technique is used to determine the best sampling points for the estimation of polynomial coefficients given the order and the number of independent variables. Finite element analyses are performed to generate the sampling data. Regression analysis is then used to estimate the response surface model to approximate the functional relationship between response features and design parameters on the entire design space. In the fitness evaluation of the genetic algorithm, the response surface model is used to substitute the finite element model to output features with given design parameters for the computation of fitness for the individual. Finally, the global optima that corresponds to the updated design parameter is acquired after several generations of evolution. In the application example, finite element analysis and modal testing are performed on a real chassis model. The finite element model is updated using the proposed method. After updating, root-mean-square error of modal frequencies is smaller than 2%. Furthermore, prediction ability of the updated model is validated using the testing results of the modified structure. The root-mean-square error of the prediction errors is smaller than 2%.

Double-layer model updating for steel-concrete composite beam cable-stayed bridge based on GPS

In order to establish the relationship between the measured dynamic response and the health status of long-span bridges, a double-layer model updating method for steel-concrete composite beam cable-stayed bridges is proposed. Measured frequencies are selected as the first-layer reference data, and the mass of the bridge deck, the grid density, the modulus of concrete and the ballast on the side span are modified by using a manual tuning technique. Measured global positioning system （GPS） data is selected as the second-layer reference data, and the degradation of the integral structure stiffness EI of the whole bridge is taken into account for the second-layer model updating by using the finite element iteration algorithm. The Nanpu Bridge in Shanghai is taken as a case to verify the applicability of the proposed model updating method. After the first-layer model updating, the standard deviation of modal frequencies is smaller than 7%. After the second-layer model updating, the error of the deflection of the mid-span is smaller than 10%. The integral structure stiffness of the whole bridge decreases about 20%. The research results show a good agreement between the calculated response and the measured response.

OPTIMIZATION WITH QUADRATIC CONSTRAINT IN APPLICATION OF STRUCTURE DYNAMIC MODEL UPDATING

A model updating optimization algorithm under quadratic constraints is applied to structure dynamic model updating. The updating problems of structure models are turned into the optimization with a quadratic constraint. Numerical method is presented by using singular value decomposition and an example is given. Compared with the other method, the method is efficient and feasible.

DYNAMIC FINITE ELEMENT MODEL UPDATING BASED ON GLOBAL INFORMATION OF STRUCTURES

Finite element model updating method based on global information is proposed.Prior investigation upon design space of structural parameters is performed before updating usingstatistic analysis, including parameter screening using variance analysis and response surfacefitting using regression analysis. The parameter screening method selects the design parametersconsidering the result of hypothesis testing, which is a kind of global information. Meanwhile, thetraditional updating method considers local sensitivity which only gives the information at solepoint in the design space. Response surface fitting constructs a close-form multinomial whichdescribes the relationship between concerned structural feature and selected updating parameters. Itis an approximation to finite element models(FEM) and used as a substitution in the updatingiterations. The presented updating method can be applied without the restriction of linearassumption. In addition, there is no data exchange between the updating program and the finite-element analysis program in the updating iterations. This makes the method practical inengineering. An aircraft test structure, GARTEUR, is employed to verify the effectiveness of themethod. After updating, the error of modal frequencies is less than 3 percent.

Dynamic finite element model updating of prestressed concrete continuous box-girder bridge

The dynamic finite element model （FEM） of a prestressed concrete continuous box-girder bridge, called the Tongyang Canal Bridge, is built and updated based on the results of ambient vibration testing （AVT） using a real-coded accelerating genetic algorithm （RAGA）. The objective functions are defined based on natural frequency and modal assurance criterion （MAC） metrics to evaluate the updated FEM. Two objective functions are defined to fully account for the relative errors and standard deviations of the natural frequencies and MAC between the AVT results and the updated FEM predictions. The dynamically updated FEM of the bridge can better represent its structural dynamics and serve as a baseline in long-term health monitoring, condition assessment and damage identification over the service life of the bridge .

Model updating of a bridge structure using vibration test data based on GMPSO and BPNN:case study

Model updating issues with high-dimensional and strong-nonlinear optimization processes are still unsolved by most optimization methods.In this study,a hybrid methodology that combines the Gaussian-white-noise-mutation particle swarm optimization(GMPSO),back-propagation neural network(BPNN)and Latin hypercube sampling(LHS)technique is proposed.In this approach,as a meta-heuristic algorithm with the least modification to the standard PSO,GMPSO simultaneously offers convenient programming and good performance in optimization.The BPNN with LHS establishes the meta-models for FEM to accelerate efficiency during the updating process.A case study of the model updating of an actual bridge with no distribution but bounded parameters was carried out using this methodology with two different objective functions.One considers only the frequencies of the main girder and the other considers both the frequencies and vertical displacements of typical points.The updating results show that the methodology is a sound approach to solve an actual complex bridge structure and offers good agreement in the frequencies and mode shapes of the updated model and test data.Based on the shape comparison of the main girder at the finished state with different objective functions,it is emphasized that both the dynamic and static responses should be taken into consideration during the model updating process.

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.

An improved optimal elemental method for updating finite element models

The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results.This situation occurs when the test modal model is incomplete,as is often the case in practice.An improved optimal elemental method is presented that defines a new objective function,and as a byproduct,circumvents the need for mass normalized modal shapes,which are also not readily available in practice.To solve the group of nonlinear equations created by the improved optimal method,the Lagrange multiplier method and Matlab function fmincon are employed.To deal with actual complex structures, the float-encoding genetic algorithm(FGA)is introduced to enhance the capability of the improved method.Two examples,a 7- degree of freedom(DOF)mass-spring system and a 53-DOF planar frame,respectively,are updated using the improved method. The example results demonstrate the advantages of the improved method over existing optimal methods,and show that the genetic algorithm is an effective way to update the models used for actual complex structures.

Finite element model updating for large span spatial steel structure considering uncertainties

In order to establish the baseline finite element model for structural health monitoring,a new method of model updating was proposed after analyzing the uncertainties of measured data and the error of finite element model.In the new method,the finite element model was replaced by the multi-output support vector regression machine(MSVR).The interval variables of the measured frequency were sampled by Latin hypercube sampling method.The samples of frequency were regarded as the inputs of the trained MSVR.The outputs of MSVR were the target values of design parameters.The steel structure of National Aquatic Center for Beijing Olympic Games was introduced as a case for finite element model updating.The results show that the proposed method can avoid solving the problem of complicated calculation.Both the estimated values and associated uncertainties of the structure parameters can be obtained by the method.The static and dynamic characteristics of the updated finite element model are in good agreement with the measured data.

Comparison of eigensensitivity and ANN based methods in model updating of an eight-story building

Analytical models prepared from field drawings do not generally provide results that match with experimental results.The error may be due to uncertainties in the property of materials,size of members and errors in the modelling process.It is important to improve analytical models using experimentally obtained data.For the past several years,data obtained from ambient vibration testing have been successfully used in many cases to update and match dynamic behaviors of analytical models with real structures.This paper presents a comparison between artificial neural network(ANN) and eigensensitivity based model updating of an existing multi-story building.A simple spring-mass analytical model,developed from the structural drawings of the building,is considered and the corresponding spring stiffness and lumped mass of all floors are chosen as updating parameters.The advantages and disadvantages of these updating methods are discussed.The advantage is that both methods ensure a physically meaningful model which canbe further employed in determining structural response and health monitoring.

Finite element model updating of existing steel bridge based on structural health monitoring

Based on the physical meaning of sensitivity,a new finite element(FE) model updating method was proposed. In this method,a three-dimensional FE model of the Nanjing Yangtze River Bridge(NYRB) with ANSYS program was established and updated by modifying some design parameters. To further validate the updated FE model,the analytical stress-time histories responses of main members induced by a moving train were compared with the measured ones. The results show that the relative error of maximum stress is 2.49% and the minimum relative coefficient of analytical stress-time histories responses is 0.793. The updated model has a good agreement between the calculated data and the tested data,and provides a current baseline FE model for long-term health monitoring and condition assessment of the NYRB. At the same time,the model is validated by stress-time histories responses to be feasible and practical for railway steel bridge model updating.

Research on the iterative method for model updating based on the frequency response function

Model reduction technique is usually employed in model updating process. In this paper, a new model updat- ing method named as cross-model cross-frequency response function （CMCF） method is proposed and a new iterative method associating the model updating method with the mo- del reduction technique is investigated. The new model up- dating method utilizes the frequency response function to avoid the modal analysis process and it does not need to pair or scale the measured and the analytical frequency re- sponse function, which could greatly increase the number of the equations and the updating parameters. Based on the traditional iterative method, a correction term related to the errors resulting from the replacement of the reduction ma- trix of the experimental model with that of the finite element model is added in the new iterative method. Comparisons be- tween the traditional iterative method and the proposed itera- tive method are shown by model updating examples of solar panels, and both of these two iterative methods combine the CMCF method and the succession-level approximate reduc- tion technique. Results show the effectiveness of the CMCF method and the proposed iterative method .

Model Updating for High Speed Aircraft in Thermal Environment Using Adaptive Weighted-Sum Methods

Model updating for aircraft in a high temperature environment(HTE)is proposed based on the hierarchical method.With this method,the problem can be decomposed into temperature field updating and dynamic structural updating.In order to improve the estimation accuracy,the model updating problem is turned into a multi-objective optimization problem by constructing the objective function which combined with residues of modal frequency and effective modal mass.Then the metamodeling,support vector regression(SVR)is introduced to improve the optimization efficiency,and the solution can be determined by adaptive weighted-sum method(AWS).Finally,the proposed method is tested on a finite element(FE)model of a reentry vehicle model.The results show that the multi-objective model updating method in HTE can identify the input parameters of the temperature field and structure with good accuracy.

Finite Element Model Updating for Structural Health Monitoring

This paper provides a model updating approach to detect,locate,and char-acterize damage in structural and mechanical systems by examining changes in mea-sured vibration responses.Research in vibration-based damage identification has been rapidly expanding over the last few decades.The basic idea behind this technology is that modal parameters(notably frequencies,mode shapes,and modal damping)are functions of the physical properties of the structure(mass,damping,and sifies).Therefore,changes in the physical properties will cause changes in the modal proper-ties which could be obtained by structural health monitoring(SHM).Updating is a process fraught with numerical difficulties.These arise from inaccuracy in the model and imprecision and lack of information in the measurements,mainly taken place in joints and critical points.The motivation for the development of this technology is.presented,methods are categorized according to various criteria such as the level of damage detection provided from vibration testing,natural frequency and mode shape readings are then obtained by using modal analysis techniques,which are used for updating structural parameters of the associated finite element model The experi-mental studies for the laboratory tested bridge model show that the proposed model.updating using ME scope technique can provide reasonable model updating results.

Performance Comparison of Two Meta-Model for the Application to Finite Element Model Updating of Structures

To investigate the application of meta-model for finite element( FE) model updating of structures,the performance of two popular meta-model,i. e.,Kriging model and response surface model( RSM),were compared in detail. Firstly,above two kinds of meta-model were introduced briefly. Secondly,some key issues of the application of meta-model to FE model updating of structures were proposed and discussed,and then some advices were presented in order to select a reasonable meta-model for the purpose of updating the FE model of structures. Finally,the procedure of FE model updating based on meta-model was implemented by updating the FE model of a truss bridge model with the measured modal parameters. The results showed that the Kriging model was more proper for FE model updating of complex structures.

A novel Q-based online model updating strategy and its application in statistical process control for rubber mixing

To overcome the large time-delay in measuring the hardness of mixed rubber, rheological parameters were used to predict the hardness. A novel Q-based model updating strategy was proposed as a universal platform to track time-varying properties. Using a few selected support samples to update the model, the strategy could dramat- ically save the storage cost and overcome the adverse influence of low signal-to-noise ratio samples. Moreover, it could be applied to any statistical process monitoring system without drastic changes to them, which is practical for industrial practices. As examples, the Q-based strategy was integrated with three popular algorithms （partial least squares （PIE）, recursive PIE （RPLS）, and kernel PIE （KPIE）） to form novel regression ones, QPLS, QRPIE and QKPLS, respectively. The applications for predicting mixed rubber hardness on a large-scale tire plant in east China prove the theoretical considerations.