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 for structures with parametric constraints

This paper presents a finite element (FE) model updating procedure applied to complex structures using an eigenvalue sensitivity‐based updating approach. The objective of the model updating is to reduce the difference between the calculated and the measured frequencies. The method is based on the first‐order Taylor‐series expansion of the eigenvalues with respect to some structural parameters selected to be adjusted. These parameters are assumed to be bounded by some prescribed regions which are determined according to the degrees of uncertainty that exist in the parameters. The changes of these parameters are found iteratively by solving a constrained optimization problem. The improvement of the current study is in the use of an objective function that is the sum of a weighted frequency error norm and a weighted perturbation norm of the parameters. Two weighting matrices are introduced to provide flexibility for individual tuning of frequency errors and parameters' perturbations. The proposed method is applied to a 1/150 scaled suspension bridge model. Using 11 measured frequencies as reference, the FE model is updated by adjusting ten selected structural parameters. The final updated FE model for the suspension bridge model is able to produce natural frequencies in close agreement with the measured ones. Copyright © 2000 John Wiley & Sons, Ltd.     

Improved parameter estimation for hydrological models using weighted object functions

This paper discusses the sensitivity of calibration of hydrological model parameters to different objective functions. Several functions are defined with weights depending upon the hydrological background. These are compared with an objective function based upon kriging. Calibration is applied to piezometric readings from the Isle of Goeree in the Netherlands. For a study on the permeability of the first aquifer, the kriging predictor yields weights that differ from using prior knowledge, and emphasizes more strongly spatially isolated points than commonly applied objective functions. It reduces the range of differences between measurements and model simulations, but the mean absolute error increases. For a study on the resistance of the top layer and of the aquitard, use of prior information in the objective functions leads to a reduction in standard deviations of the differences between measured and calculated values by 40–80%. Copyright © 1999 John Wiley & Sons, Ltd.     

Comparison of spectral and time domain calibration methods for precipitation‐discharge processes

Hydrological model parameter estimation is an important aspect in hydrologic modelling. Usually, parameters are estimated through an objective function minimization, quantifying the mismatch between the model results and the observations. The objective function choice has a large impact on the sensitivity analysis and calibration outcomes. In this study, it is assessed whether spectral objective functions can compete with an objective function in the time domain for optimization of the Soil and Water Assessment Tool (SWAT). Three empirical spectral objective functions were applied, based on matching (i) Fourier amplitude spectra, (ii) periodograms and (iii) Fourier series of simulated and observed discharge time series. It is shown that most sensitive parameters and their optimal values are distinct for different objective functions. The best results were found through calibration with an objective function based on the square difference between the simulated and observed discharge Fourier series coefficients. The potential strengths and weaknesses of using a spectral objective function as compared to utilising a time domain objective function are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

New lumped-mass-stick model based on modal characteristics of structures: development and application to a nuclear containment building

In this study, a new lumped-mass-stick model (LMSM) is developed based on the modal characteristics of a structure such as eigenvalues and eigenvectors. The simplified model, named the "frequency adaptive lumped-massstick model," hasonly a small number of stick elements and nodes to provide the same natural frequencies of the structure and is applied to a nuclear containment building. To investigate the numerical performance of the LMSM, a time history analysis is carried out on both the LMSM and the finite element model (FEM) for a nuclear containment building. A comparison of the results shows that the dynamic responses of the LMSM in terms of displacement and acceleration are almost identical to those of the FEM. In addition, the results in terms of floor response spectra at certain elevations are also in good agreement.     

Wavefield tomography based on local image correlations

The estimation of a velocity model from seismic data is a crucial step for obtaining a high‐quality image of the subsurface. Velocity estimation is usually formulated as an optimization problem where an objective function measures the mismatch between synthetic and recorded wavefields and its gradient is used to update the model. The objective function can be defined in the data‐space (as in full‐waveform inversion) or in the image space (as in migration velocity analysis). In general, the latter leads to smooth objective functions, which are monomodal in a wider basin about the global minimum compared to the objective functions defined in the data‐space. Nonetheless, migration velocity analysis requires construction of common‐image gathers at fixed spatial locations and subsampling of the image in order to assess the consistency between the trial velocity model and the observed data. We present an objective function that extracts the velocity error information directly in the image domain without analysing the information in common‐image gathers. In order to include the full complexity of the wavefield in the velocity estimation algorithm, we consider a two‐way (as opposed to one‐way) wave operator, we do not linearize the imaging operator with respect to the model parameters (as in linearized wave‐equation migration velocity analysis) and compute the gradient of the objective function using the adjoint‐state method. We illustrate our methodology with a few synthetic examples and test it on a real 2D marine streamer data set.     

Parameter identification of framed structures using an improved finite element model‐updating method—Part II: application to experimental data

In this study, we determine an updated finite element model of a reinforced concrete building—which was damaged from shaking during 1994 Northridge earthquake—using forced‐vibration test data and a novel model‐updating technique. Developed and verified in the companion paper (viz. BVLSrc, Earthquake Eng. Struct. Dyn. 2006; this issue), this iterative technique incorporates novel sensitivity‐based relative constraints to avoid ill conditioning that results from spatial incompleteness of measured data. We used frequency response functions and natural frequencies as input for the model‐updating problem. These data were extracted from measurements obtained during a white‐noise excitation applied at the roof of the building using a linear inertial shaker. Flexural stiffness values of properly grouped structural members, modal damping ratios, and translational and rotational mass values were chosen as the updating parameters, so that the converged results had direct physical interpretations, and thus, comparisons with common parameters used in seismic design and evaluation of buildings could be made. We investigated the veracity of the updated finite element model by comparing the predicted and measured dynamic responses under a second, and different type of forced (sine‐sweep) vibration, test. These results indicate that the updated model replicates the dynamic behaviour of the building reasonably well. Furthermore, the updated stiffness factors appear to be well correlated with the observed building damage patterns (i.e. their location and severity). Copyright © 2006 John Wiley & Sons, Ltd.     

Strict positive definiteness in geostatistics

Geostatistical modeling is often based on the use of covariance functions, i.e., positive definite functions. However, when interpolation problems have to be solved, it is advisable to consider the subset of strictly positive definite functions. Indeed, it will be argued that ensuring strict positive definiteness for a covariance function is convenient from a theoretical and practical point of view. In this paper, an extensive analysis on strictly positive definite covariance functions has been given. The closure of the set of strictly positive definite functions with respect to the sum and the product of covariance functions defined on the same Euclidean dimensional space or on factor spaces, as well as on partially overlapped lower dimensional spaces, has been analyzed. These results are particularly useful (a) to extend strict positive definiteness in higher dimensional spaces starting from covariance functions which are only defined on lower dimensional spaces and/or are only strictly positive definite in lower dimensional spaces, (b) to construct strictly positive definite covariance functions in space–time as well as (c) to obtain new asymmetric and strictly positive definite covariance functions.     

A new finite element model in studying earthquake triggering and continuous evolution of stress field

In this paper, a new finite element model (FEM) in consideration of regional stress field and an earthquake triggering factor C are proposed for studying earthquake triggering and stress field evolution in an earthquake sequence. The factor C is defined as a ratio between the shear stress and the frictional strength on a slip surface, and it can be used to tell if earthquake is triggered or not. The new FEM and the factor C are used to study the aftershock triggering of the 1976 Tangshan earthquake sequence. The results indicate that the effects of the stress field and the heterogeneity of the Tangshan earthquake fault zone on the aftershock triggering are very important. The aftershocks fallen in the earthquake triggering regions predicted by the new FEM are more than those fallen in the regions of ΔCFS⩾0 predicted by seismic dislocation theory. Supported by National Natural Science Foundation of China (Grant Nos. 40474013 and 40821062)     

耦合有限单元法扩边的直流电阻率勘探无单元Galerkin法正演

本文分析了目前直流电阻率正演模拟中的无单元Galerkin法（EFGM）和有限单元法（FEM）的优缺点,针对采用第一类边界条件需要足够大的计算域时EFGM计算成本高的问题,在计算域外围区域采用FEM扩边,提出了直流电阻率的无单元Galerkin-有限单元耦合法（EFG-FE）.采用具有Kronecker delta函数性质的径向基点插值法（RPIM）构造EFGM形函数,在外围区域将EFGM与FEM直接耦合,无需其他处理手段,消除了传统EFGM与FEM耦合中存在的界面耦合困难.EFG-FE将模型计算域分割为EFGM区域和FEM区域,模型核心区域采用EFGM计算,发挥EFGM灵活性、适应性强和高精度的优点,使得模型建立简单方便,对任意复杂地电模型适应性强,同时获得高精度模拟结果.在模型计算域外围采用快速扩展的FEM单元网格进行剖分,利用其数值稳定性和高效性,使用少量FEM节点和单元网格将计算域大范围扩大满足第一类边界条件,同时不大幅增加计算成本,进而提高计算效率.最后,通过不同正演方法的模型算例的模拟结果对比,验证了本文提出的EFG-FE有效可行,其模拟结果具有很高的模拟精度,且相比于采用第三类边界条件的EFGM提高了计算效率,具有更好的模拟性能.

     

Assessment of rainfall‐runoff models based upon wavelet analysis

A basic hypothesis is proposed: given that wavelet‐based analysis has been used to interpret runoff time‐series, it may be extended to evaluation of rainfall‐runoff model results. Conventional objective functions make certain assumptions about the data series to which they are applied (e.g. uncorrelated error, homoscedasticity). The difficulty that objective functions have in distinguishing between different realizations of the same model, or different models of the same system, is that they may have contributed in part to the occurrence of model equifinality. Of particular concern is the fact that the error present in a rainfall‐runoff model may be time dependent, requiring some form of time localization in both identification of error and derivation of global objective functions. We explore the use of a complex Gaussian (order 2) wavelet to describe: (1) a measured hydrograph; (2) the same hydrograph with different simulated errors introduced; and (3) model predictions of the same hydrograph based upon a modified form of TOPMODEL. The analysis of results was based upon: (a) differences in wavelet power (the wavelet power error) between the measured hydrograph and both the simulated error and modelled hydrographs; and (b) the wavelet phase. Power difference and wavelet phase were used to develop two objective functions, RMSE(power) and RMS(phase), which were shown to distinguish between simulated errors and model predictions with similar values of the commonly adopted Nash‐Sutcliffe efficiency index. These objective functions suffer because they do not retain time, frequency or time‐frequency localization. Consideration of wavelet power spectra and time‐ and frequency‐integrated power spectra shows that the impacts of different types of simulated error can be seen through retention of some localization, especially in relation to when and the scale over which error was manifest. Theoretical objections to the use of wavelet analysis for this type of application are noted, especially in relation to the dependence of findings upon the wavelet chosen. However, it is argued that the benefits of localization and the qualitatively low sensitivity of wavelet power and phase to wavelet choice are sufficient to warrant further exploration of wavelet‐based approaches to rainfall‐runoff model evaluation. Copyright © 2006 John Wiley & Sons, Ltd.     

基于全局弱式无单元法直流电阻率正演模拟

全局弱式无单元法是在有限单元法基础上发展起来的一种数值模拟方法,它采用局部支持域内的节点信息来构造形函数实现局部精确逼近,摆脱了单元,仅依赖于节点信息,具有预处理简单、模拟精度高、灵活性强的特点,适用于复杂地电条件下直流电阻率正演模拟.本文采用RPIM构造直流电阻率全局弱式无单元法形函数,利用RPIM形函数推导了直流电阻率全局弱式无单元法方程.然后,编制了直流电阻率全局弱式无单元法正演模拟Fortran程序,利用该程序对典型的地电模型进行了正演模拟,并将正演结果与基于线性插值的FEM正演结果及解析解进行对比,结果表明采用RPIM形函数的全局弱式无单元法用于直流电阻率正演模拟的正确性及有效性,且在同等条件下,全局弱式无单元法模拟精度高于矩形剖分的FEM,更有利于指导电法勘探的数据解译;利用该程序对复杂地电模型进行了正演模拟,结果表明全局弱式无单元法对复杂地电模型模拟效果良好,适应性强,灵活性高,可任意加密节点提高模拟精度.

     

Suspended load estimation using L1-fuzzy regression,L2-fuzzy regression and MARS-fuzzy regression models

ABSTRACT

The problem of estimation of suspended load carried by a river is an important topic for many water resources projects. Conventional estimation methods are based on the assumption of exact observations. In practice, however, a major source of natural uncertainty is due to imprecise measurements and/or imprecise relationships between variables. In this paper, using the Multivariate Adaptive Regression Splines (MARS) technique, a novel fuzzy regression model for imprecise response and crisp explanatory variables is presented. The investigated fuzzy regression model is applied to forecast suspended load by discharge based on two real-world datasets. The accuracy of the proposed method is compared with two well-known parametric fuzzy regression models, namely, the fuzzy least-absolutes model and the fuzzy least-squares model. The comparison results reveal that the MARS-fuzzy regression model performs better than the other models in suspended load estimation for the particular datasets. This comparison is done based on four goodness-of-fit criteria: the criterion based on similarity measure, the criterion based on absolute errors and the two objective functions of the fuzzy least-absolutes model and the fuzzy least-squares model. The proposed model is general and can be used for modelling natural phenomena whose available observations are reported as imprecise rather than crisp.

Editor D. Koutsoyiannis; Associate editor H. Aksoy     

Automatic calibration of HEC‐HMS using single‐objective and multi‐objective PSO algorithms

This study presents single‐objective and multi‐objective particle swarm optimization (PSO) algorithms for automatic calibration of Hydrologic Engineering Center‐ Hydrologic Modeling Systems rainfall‐runoff model of Tamar Sub‐basin of Gorganroud River Basin in north of Iran. Three flood events were used for calibration and one for verification. Four performance criteria (objective functions) were considered in multi‐objective calibration where different combinations of objective functions were examined. For comparison purposes, a fuzzy set‐based approach was used to determine the best compromise solutions from the Pareto fronts obtained by multi‐objective PSO. The candidate parameter sets determined from different single‐objective and multi‐objective calibration scenarios were tested against the fourth event in the verification stage, where the initial abstraction parameters were recalibrated. A step‐by‐step screening procedure was used in this stage while evaluating and comparing the candidate parameter sets, which resulted in a few promising sets that performed well with respect to at least three of four performance criteria. The promising sets were all from the multi‐objective calibration scenarios which revealed the outperformance of the multi‐objective calibration on the single‐objective one. However, the results indicated that an increase of the number of objective functions did not necessarily lead to a better performance as the results of bi‐objective function calibration with a proper combination of objective functions performed as satisfactorily as those of triple‐objective function calibration. This is important because handling multi‐objective optimization with an increased number of objective functions is challenging especially from a computational point of view. Copyright © 2012 John Wiley & Sons, Ltd.     

Selection of calibration objective fonctions in the context of rainfall-ronoff modelling in a Sudanese savannah area

Abstract

In the context of rainfall-runoff modelling carried out on the Sudanese savannah area in the northwest of the Ivory Coast, attempts are being made to reconstitute the flow at the outlets of catchments in 10 day time steps. By using algorithms with automatic fitting procedures for the parameters, it appeared necessary to make a choice concerning the calibration objective functions to be used. The paper presents the algorithms, data and objective functions that have been used. The results obtained from the calibrations made have been analysed. That analysis was done principally with the help of a comparative evaluation modulus which takes into account elements other than the value of the objective function alone and which enables the quality of the results to be picked out from a hydrological point of view. At the conclusion of the analysis, the objective function defined by Nash seems to stand out quite clearly in relation to the other formulae examined.     

结构双层多重调谐质量阻尼器(DMTMD)控制策略的鲁棒性评价

基于定义的二类优化目标函数,评价双层多重调谐质量阻尼器(DMTMD)控制策略对漂移频率系数(DFR)摄动的鲁棒性。数值研究表明,使用第二类优化准则设计的DMTMD、双重调谐质量阻尼器(DTMD)和多重调谐质量阻尼器(MTMD)比使用第一类优化准则设计的DMTMD、DTMD和MTMD具有更高的对DFR摄动的鲁棒性。而且,使用第二类优化准则设计的总数为4的DMTMD、DTMD和总数为11的MTMD具有近似相同的对DFR摄动的鲁棒性。     

Dynamic model updating using a combined genetic‐eigensensitivity algorithm and application in seismic response prediction

A reliable computational model is necessary for evaluating the state and predicting the future performance of existing structures, especially after exposure to damaging effects such as an earthquake. A major problem with the existing iterative‐based model updating methods is that the search might be trapped in local optima. The genetic algorithms (GAs) offer a desirable alternative because of their ability in performing a robust search for the global optimal solution. This paper presents a GA‐based model updating approach using a real‐coding scheme for global model updating based on dynamic measurement data. An eigensensitivity method is employed to further fine‐tune the GA updated results in case the sensitivity problem arises due to restricted measurement information. The application on shear‐type frames reveals that with a limited amount of modal data, namely the lowest three natural frequencies and the first mode shape, it is possible to achieve satisfactory updating by the GA alone for cases involving a limited number of parameters (storey stiffness herein). With the incorporation of the eigensensitivity algorithm, the updating capability is extended to a sufficiently large number of parameters. In case the modal data contain errors, the GA is also shown to be able to update the model to a satisfactory accuracy, provided the required amount of modal data is available. An example is given in which a 6‐DOF stick model for an actual six‐storey RC frame is updated using the measured dynamic properties. The effectiveness of the updating is evaluated by comparing the measured and predicted seismic response using the updated model. Copyright © 2005 John Wiley & Sons, Ltd.     

Modelling of groundwater flow in heterogeneous porous media by finite element method

The HySuf‐FEM code (Hydrodynamic of Subsurface Flow by Finite Element Method) is proposed in this article in order to estimate the spatial variability of the transmissivity values of the Berrechid aquifer (Morocco). The calibration of the model is based on the hydraulic head, hydraulic conductivity and recharge. Three numerical tests are used to validate the model and verify its convergence. The first test case consists in using the steady analytical solution of the Poisson equation. In the second, the model has been compared with the hydrogeological system which is characterized by an unconfined monolayer (isotropic layer) and computed by using PMWIN‐MODFLOW software. The third test case is based on the comparison between the results of HySuf‐FEM and the multiple cell balance method in the aquifer system with natural boundaries case. Good agreement between the Hydrodynamic of Subsurface Flow, the numerical tests and the spatial distribution of the thickening of the hydrogeological system is deduced from the analysis and the interpretations of hydrogeological wells. Copyright © 2011 John Wiley & Sons, Ltd.     

剪切波分裂分析系统SAM(2007)——软件系统

地震各向异性是一种普遍现象,利用剪切波分裂可以研究地壳介质的地震各向异性特性,这是地震学研究中的一个前沿课题。本文介绍了基于SAM(2003R)发展的剪切波分裂系统分析方法软件——SAM(2007)。SAM(2007)在保留原软件系统优点的基础上,修改和发展了新的功能,在资料预处理、数据分析和结果输出等方面都进行了更新或发展,增加了地震定位模块,使新的软件系统更适用于国内的区域地震台网或流动台网资料的处理和分析。     

B-Spline impulse response functions (BIRF) for transient SSI analysis of rigid foundations

This work presents a simplified, yet accurate model of rigid foundation-soil systems for the dynamic analysis of structures including SSI effects. The simplified model is based on closed form solutions that reproduce the characteristic B-spline impulse response functions (BIRF) of 3D continuous soil-foundation systems, as obtained from rigorous boundary element method (BEM) analysis. The proposed simplified model is used within the framework of B-spline impulse response techniques and can be coupled directly to other solution techniques, such as the finite element method (FEM). Validation and application studies demonstrate the accuracy and versatility of the simplified model for the direct time domain solution of dynamic SSI problems involving rigid square surface foundations of any size. The proposed model, although simplified, demonstrates similar high accuracy to that of more rigorous solutions based on domain discretizations.