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.

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 .

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.

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 .

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.

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.

Damage Identification of General Overhead Travelling Crane Structure Based on Model Updating by Sensitivity

A model based damage identification was proposed by facilitating parameter sensitivity analysis and applied to a general overhead travelling crane.As updating reference data,experimental modal frequency was obtained by operational modal analysis(OMA)under ambient excitation.One dimensional damage function was defined to identify the damage by bending stiffness.The results showed that the model updating method could locate the damage and quantitatively describe the structure.The average error of eigenvalues between updated model analysis and the experimental results was less than 4% which proved the accuracy reliable.The comparison of finite element analysis and the test results of the deflection under the capacity load further verified the feasibility of this 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.

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.

PRINCIPAL COMPONENT DECOMPOSITION BASED FINITE ELEMENT MODEL UPDATING FOR STRAIN-RATE-DEPENDENCE NONLINEAR DYNAMIC PROBLEMS

Thin wail component is utilized to absorb impact energy of a structure. However, the dynamic behavior of such thin-walled structure is highly non-linear with material, geometry and boundary non-linearity. A model updating and validation procedure is proposed to build accurate finite element model of a frame structure with a non-linear thin-walled component for dynamic analysis. Design of experiments （DOE） and principal component decomposition （PCD） approach are applied to extract dynamic feature from nonlinear impact response for correlation of impact test result and FE model of the non-linear structure. A strain-rate-dependent non-linear model updating method is then developed to build accurate FE model of the structure. Computer simulation and a real frame structure with a highly non-linear thin-walled component are employed to demonstrate the feasibility and effectiveness of the proposed approach.

Dynamical Model Updating Based on Modal Tests with Changed Structure

A new approach to modifying the stiffness and mass matrices of finite element models is presented to improve the calculation precision.By measuring the mode frequencies and shapes of both of the original and the new structures with changed stiffness and mass,the stiffness and mass matrices of the finite element model can be updated through matrices calculation and solving algebra equations.Taking a multi-freedom model as an example,the relation between the number of the modes and the correction precision of stiffness and mass matrix elements is researched.The facility and precision of the method are totally confirmed especially when the modeling error is known limited to a definite local range.The feasibility of the approach is proven by an effective engineering application to the model updating of a wing piece used in flutter test.

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.

Digital twin-assisted gearbox dynamic model updating toward fault diagnosis

One of the core challenges of intelligent fault diagnosis is that the diagnosis model requires numerous labeled training datasets to achieve satisfactory performance.Generating training data using a virtual model is a potential solution for addressing such a problem,and the construction of a high-fidelity virtual model is fundamental and critical for data generation.In this study,a digital twin-assisted dynamic model updating method for fault diagnosis is thus proposed to improve the fidelity and reliability of a virtual model,which can enhance the generated data quality.First,a virtual model is established to mirror the vibration response of a physical entity using a dynamic modeling method.Second,the modeling method is validated through a frequency analysis of the generated signal.Then,based on the signal similarity indicator,a physical–virtual signal interaction method is proposed to dynamically update the virtual model in which parameter sensitivity analysis,surrogate technique,and optimization algorithm are applied to increase the efficiency during the model updating.Finally,the proposed method is successfully applied to the dynamic model updating of a single-stage helical gearbox;the virtual data generated by this model can be used for gear fault diagnosis.

Finite element model updating of a tied-arch bridge using Douglas-Reid method and Rosenbrock optimization algorithm

Condition assessment of bridges has become increasingly important. In order to accurately simulate the real bridge, finite element （FE） model updating method is often applied. This paper presents the calibration of the FE model of a reinforced concrete tied-arch bridge using Douglas-Reid method in combination with Rosenbrock optimization algorithm. Based on original drawings and topographic survey, a FE model of the investigated bridge is created. Eight global modes of vibration of the bridge are identified by ambient vibration tests and the frequency domain decomposition technique. Then, eight structural parameters are selected for FE model updating procedure through sensitivity analysis. Finally, the optimal structural parameters are identified using Rosenbrock optimization algorithm. Results show that although the identified parameters lead to a perfect agreement between approximate and measured natural frequencies, they may not be the optimal variables which minimize the differences between numerical and experimental modal data. However, a satisfied agreement between them is still presented. Hence, FE model updating based on Douglas-Reid method and Rosenbrock optimization algorithm could be used as an alternative to other complex updating procedures.

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.

Dynamic parametric modeling-based model updating strategy of aeroengine casings

For accurate Finite Element(FE)modeling for the structural dynamics of aeroengine casings,Parametric Modeling-based Model Updating Strategy(PM-MUS)is proposed based on efficient FE parametric modeling and model updating techniques regarding uncorrelated/correlated mode shapes.Casings structure is parametrically modeled by simplifying initial structural FE model and equivalently simulating mechanical characteristics.Uncorrelated modes between FE model and experiment are reasonably handled by adopting an objective function to recognize correct correlated modes pairs.The parametrized FE model is updated to effectively describe structural dynamic characteristics in respect of testing data.The model updating technology is firstly validated by the detailed FE model updating of one fixed–fixed beam structure in light of correlated/uncorrelated mode shapes and measured mode data.The PM-MUS is applied to the FE parametrized model updating of an aeroengine stator system(casings)which is constructed by the proposed parametric modeling approach.As revealed in this study,(A)the updated models by the proposed updating strategy and dynamic test data is accurate,and(B)the uncorrelated modes like close modes can be effectively handled and precisely identify the FE model mode associated the corresponding experimental mode,and(C)parametric modeling can enhance the dynamic modeling updating of complex structure in the accuracy of mode matching.The efforts of this study provide an efficient dynamic model updating strategy(PM-MUS)for aeroengine casings by parametric modeling and experimental test data regarding uncorrelated modes.

Estimation of failure probability in braced excavation using Bayesian networks with integrated model updating

A probabilistic model is proposed that uses observation data to estimate failure probabilities during excavations.The model integrates a Bayesian network and distanced-based Bayesian model updating.In the network,the movement of a retaining wall is selected as the indicator of failure,and the observed ground surface settlement is used to update the soil parameters.The responses of wall deflection and ground surface settlement are accurately predicted using finite element analysis.An artificial neural network is employed to construct the response surface relationship using the aforementioned input factors.The proposed model effectively estimates the uncertainty of influential factors.A case study of a braced excavation is presented to demonstrate the feasibility of the proposed approach.The update results facilitate accurate estimates according to the target value,from which the corresponding probabilities of failure are obtained.The proposed model enables failure probabilities to be determined with real-time result updating.

Stochastic model updating using distance discrimination analysis

This manuscript presents a stochastic model updating method, taking both uncertainties in models and variability in testing into account. The updated finite element（FE） models obtained through the proposed technique can aid in the analysis and design of structural systems. The authors developed a stochastic model updating method integrating distance discrimination analysis（DDA） and advanced Monte Carlo（MC） technique to（1） enable more efficient MC by using a response surface model,（2） calibrate parameters with an iterative test-analysis correlation based upon DDA, and（3） utilize and compare different distance functions as correlation metrics. Using DDA, the influence of distance functions on model updating results is analyzed. The proposed stochastic method makes it possible to obtain a precise model updating outcome with acceptable calculation cost. The stochastic method is demonstrated on a helicopter case study updated using both Euclidian and Mahalanobis distance metrics. It is observed that the selected distance function influences the iterative calibration process and thus, the calibration outcome, indicating that an integration of different metrics might yield improved results.