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.

A Large-Scale Group Decision Making Model Based on Trust Relationship and Social Network Updating

With the development of big data and social computing,large-scale group decisionmaking(LGDM)is nowmerging with social networks.Using social network analysis(SNA),this study proposes an LGDM consensus model that considers the trust relationship among decisionmakers(DMs).In the process of consensusmeasurement:the social network is constructed according to the social relationship among DMs,and the Louvain method is introduced to classify social networks to form subgroups.In this study,the weights of each decision maker and each subgroup are computed by comprehensive network weights and trust weights.In the process of consensus improvement:A feedback mechanism with four identification and two direction rules is designed to guide the consensus of the improvement process.Based on the trust relationship among DMs,the preferences are modified,and the corresponding social network is updated to accelerate the consensus.Compared with the previous research,the proposedmodel not only allows the subgroups to be reconstructed and updated during the adjustment process,but also improves the accuracy of the adjustment by the feedbackmechanism.Finally,an example analysis is conducted to verify the effectiveness and flexibility of the proposed method.Moreover,compared with previous studies,the superiority of the proposed method in solving the LGDM problem is highlighted.

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.

AN UPDATING METHOD FOR LOCAL MODEL ERRORS

The location of model errors in a stiffness matrix by using test data has been investigated by the others.The present paper deals with the problem of updating stiffness elements in the erroneous areas. Firstly,a model that bears relation to erroneous elements only is derived.This model is termed local errors model,which reduces orders and computational loads compared with global stiffness matrix. Secondly,an inverse eigenvalue method is used to update model errors. The results of a numerical experiment demonstrate that the method is quite effective.

Updating ontologies and general rules

Inconsistencies or conflicts appearing in the integration of ontologies and general rules are handled by applying prioritizing and updating. First, a prioritized knowledge base is obtained by weighting information weight. Then, based on the idea ＂abandoning the old for the new＂, the weight of each rule is greater than that of the information in ontologies. If ontologies conflict with general rules, then a new knowledge-base without any inconsistency or conflict is obtained by using rules with big weight updating information in ontologies with small weight. Thus, current logic programming solvers and description logic reasoners are employed to implement the reasoning services, such as querying etc. Updating based on prioritizing is more suitable for handling inconsistencies than other approaches to introducing non-standard semantics if knowledge bases are dynamically evolving. Moreover, a consistent knowledge base can be always maintained in the dynamical environment by updating outdated information with new information based on weighting. Finally, this approach to dealing with inconsistencies is feasibly exemplified.

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.

Hierarchical Bayesian Calibration and On-line Updating Method for Influence Coefficient of Automatic Dynamic Balancing Machine

Measurement error of unbalance＇s vibration response plays a crucial role in calibration and on-line updating of influence coefficient（IC）. Focusing on the two problems that the moment estimator of data used in calibration process cannot fulfill the accuracy requirement under small sample and the disturbance of measurement error cannot be effectively suppressed in updating process, an IC calibration and on-line updating method based on hierarchical Bayesian method for automatic dynamic balancing machine was proposed. During calibration process, for the repeatedly-measured data obtained from experiments with different trial weights, according to the fact that measurement error of each sensor had the same statistical characteristics, the joint posterior distribution model for the true values of the vibration response under all trial weights and measurement error was established. During the updating process, information obtained from calibration was regarded as prior information, which was utilized to update the posterior distribution of IC combined with the real-time reference information to implement online updating. Moreover, Gibbs sampling method of Markov Chain Monte Carlo（MCMC） was adopted to obtain the maximum posterior estimation of parameters to be estimated. On the independent developed dynamic balancing testbed, prediction was carried out for multiple groups of data through the proposed method and the traditional method respectively, the result indicated that estimator of influence coefficient obtained through the proposed method had higher accuracy; the proposed updating method more effectively guaranteed the measurement accuracy during the whole producing process, and meantime more reasonably compromised between the sensitivity of IC change and suppression of randomness of vibration response.

Event-based incremental updating of spatio-temporal database

Based on the relationship among the geographic events, spatial changes and the database operations, a new automatic (semi-automatic) incremental updating approach of spatio-temporal database (STDB) named as (event-based) incremental updating (E-BIU) is proposed in this paper. At first, the relationship among the events, spatial changes and the database operations is analyzed, then a total architecture of E-BIU implementation is designed, which includes an event queue, three managers and two sets of rules, each component is presented in detail. The process of the E-BIU of master STDB is described successively. An example of building’s incremental updating is given to illustrate this approach at the end. The result shows that E-BIU is an efficient automatic updating approach for master STDB.

An intelligent procedure for updating deformation prediction of braced excavation in clay using gated recurrent unit neural networks

This paper aims to establish an intelligent procedure that combines the observational method with the existing deep learning technique for updating deformation of braced excavation in clay.The gated recurrent unit(GRU) neural network is adopted to formulate the forecast model and learn the potential rules in the field observations using the Nesterov-accelerated Adam(Nadam) algorithm.In the proposed procedure,the GRU-based forecast model is first trained based on the field data of previous and current stages.Then,the field data of the current stage are used as input to predict the deformation response of the next stage via the previously trained GRU-based forecast model.This updating process will loop up till the end of the excavation.This procedure has the advantage of directly predicting the deformation response of unexcavated stages based on the monitoring data.The proposed intelligent procedure is verified on two well-documented cases in terms of accuracy and reliability.The results indicate that both wall deflection and ground settlement are accurately predicted as the excavation proceeds.Furthermore,the advantages of the proposed intelligent procedure compared with the Bayesian/o ptimization updating are illustrated.

Automatic Road Change Detection and GIS Updating from High Spatial Remotely-Sensed Imagery

This paper presents a framework for road network change detection in order to update the Canadian National Topographic DataBase (NTDB). The methodology has been developed on the basis of road extraction from IRS\|pan images (with a 5.8 m spatial resolution) by using a wavelet approach. The feature matching and conflation techniques are used to road change detection and updating. Elementary experiments have showed that the proposed framework could be used for developing an operational road database updating system.

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.