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.     

Flood forecasting with a watershed model: a new method of parameter updating

Abstract

Flood forecasting is of prime importance when it comes to reducing the possible number of lives lost to storm-induced floods. Because rainfall-runoff models are far from being perfect, hydrologists need to continuously update outputs from the rainfall-runoff model they use, in order to adapt to the actual emergency situation. This paper introduces a new updating procedure that can be combined with conceptual rainfall-runoff models for flood forecasting purposes. Conceptual models are highly nonlinear and cannot easily accommodate theoretically optimal methods such as Kalman filtering. Most methods developed so far mainly update the states of the system, i.e. the contents of the reservoirs involved in the rainfall-runoff model. The new parameter updating method proves to be superior to a standard error correction method on four watersheds whose floods can cause damage to the greater Paris area. Moreover, further developments of the approach are possible, especially along the idea of combining parameter updating with assimilation of additional data such as soil moisture data from field measurements and/or from remote sensing.     

两种识别结构模态参数时域法的对比研究

模态参数是有效评估结构安全状况的关键参数,在结构抗震加固和健康诊断领域得到广泛应用。与频域法相比较,时域法直接利用实测的振动信号识别模态参数,不需要进行频域变换,减少数据处理带来的误差,并且可以实现大型结构的在线识别,真实地反应结构的现状。以同济大学12层钢筋混凝土标准框架振动台模型试验完整数据为对象,在详细介绍ITD法和复指数法2种时域法理论的基础上,通过编程选取结构不同测点的振动加速度时程数据,识别了小震和强震工况下12层钢筋混凝土框架模型振动台试验模型的模态频率和阻尼比,并结合移动谱识别结构模态参数的时变特性。结果表明:ITD法和复指数法可有效地识别结构的模态参数,自振频率的识别精度较高,而阻尼比的离散度较大;小震工况频率变化值不大,而强震工况频率值较初始时刻有明显的下降,这与试验现象是吻合的,进一步说明移动谱与这2种时域法相结合可以反应结构在塑性阶段的参数时变特性。     

CONVEX MODEL FOR SEISMIC DESIGN OF STRUCTURES—II: DESIGN OF CONVENTIONAL AND ACTIVE STRUCTURES

The optimal design of the members of conventional structures or structures equipped with active bracing systems, known as active structures, is presented for uncertain excitations. Three approaches are used for obtaining the optimal structural design: (1) the time-history analysis of an actual earthquake record (AR), (2) the global energy-bound convex model adjusted with an excitation-specific reduction factor (RGEB), and (3) the global energy-bound convex model adjusted with an average reduction factor (ARGEB) for a set of excitations with common characteristics. The optimal structures obtained using the RGEB and ARGEB convex models have different sizes for their conventional members from the designs based on a time-history analysis of the actual earthquake (AR). The optimal design of the structure is carried out using a modified annealing algorithm. The advantage of using convex models to perform the optimization is that they represent a more general excitation than a single earthquake record. In addition, the RGEB and ARGEB convex models require considerably less computational effort since the constraints of the optimization become time-independent. A comparison between optimal designs of structures with conventional members only, and active structures indicates that the latter are more efficient by combining the conventional and active members.     

Cross-correlation coefficients and modal combination rules for non-classically damped systems

In stochastic analysis the knowledge of cross-correlation coefficients is required in order to combine the response of the modal Single-Degree-Of-Freedom (SDOF) oscillators for obtaining the nodal response. Moreover these coefficients play a fundamental role in the seismic analysis of structures when the response spectrum method is used. In fact they are used in some modal combination rules in order to obtain the maximum response quantities starting from the modal maxima. Herein a method for the evaluation of the cross-correlation coefficients for non-classically damped systems is presented. It is defined in the time domain instead of the frequency domain as usually encountered in the literature. Although non-classically damped structures possess complex eigenproperties, the great advantage in using this approach lies in the fact that the evaluation of these coefficients does not require complex quantities. Moreover a further particularization of the presented method allows a simple application of the spectrum analysis requiring only one response spectrum for an assigned damping ratio. Copyright © 1999 John Wiley & Sons, Ltd.     

Influence of lateral-load-resisting system on the earthquake response of structures—a system identification study

Analysis and comparison of the dynamic responses of three well instrumented (with accelerographs) high-rise buildings shaken during the 1984 Morgan Hill earthquake are presented. The buildings examined in the present work are (i) the Town Park Towers Apartment building, a 10-storey, concrete shear wall building; (ii) the Great Western Savings and Loan building, a 10-storey building with concrete frames and shear walls; and (iii) the Santa Clara County Office building, a 13-storey, moment-resistant steel frame building. The structures are located within 2 km of each other and, as may be confirmed by visual inspection of the recorded seismograms, experienced similar ground motions. One-dimensional and three-dimensional linear structural models are fitted to the observations using the modal minimization method' for structural identification, in order to determine optimal estimates of the parameters of the dominant modes of the buildings. The time-varying character of these parameters over the duration of the response is also investigated. Comparison of the recorded earthquake response of the structures reveals that the type of lateral-load-resisting system has an important effect on the dynamic behaviour of the structures because it controls the spacing of the characteristic modes on the frequency axis. The Santa Clara County Office building has closely spaced natural frequencies and exhibits strong torsional response and modal coupling. Its dynamic behaviour is contrasted with that of the Great Western Savings and Loan building which has well separated natural frequencies and exhibits small torsional response and no modal coupling. Strong modal coupling causes a beating-type phenomenon and makes earthquake response of structures different from that envisioned by codes.     

Response of non-classically damped structures in the modal subspace

The evaluation of the dynamic response of non-classically damped linear structures requires the solution of an eigenproblem with complex eigenvalues and modal shapes. Since in practice only a small number of complex modes are needed, the complex eigenvalue problem is solved in the modal subspace in which the generalized damping matrix is not uncoupled by classical real modes. It follows that the evaluation of the structural response requires in both cases the determination of complex modes by numerical techniques, which are not as robust as techniques currently used for the solution of the real eigenvalue problem, and the use of complex algebra. In the present paper an unconditionally stable step-by-step procedure is presented for the response of non-classically damped structures in the modal subspace without using complex quantities. The method is based on the evaluation of the fundamental operator in approximated form of the numerical procedure. In addition, the method can be easily modified to incorporate the modal superposition pseudo-static correction terms.     

Dynamic characteristics and seismic response of adjacent buildings linked by discrete dampers

Coupling adjacent buildings using discrete viscoelastic dampers for control of response to low and moderate seismic events is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristics, mainly modal damping ratio and modal frequency, of damper-linked linear adjacent buildings for practical use. Random seismic response of linear adjacent buildings linked by dampers is then determined by a combination of the complex modal superposition method and the pseudo-excitation method. This combined method can effectively and accurately determine random seismic response of non-classically damped systems in the frequency domain. Parametric studies are finally performed to identify optimal parameters of viscoelastic dampers for achieving the maximum modal damping ratio or the maximum response reduction of adjacent buildings. It is demonstrated that using discrete viscoelastic dampers of proper parameters to link adjacent buildings can reduce random seismic responses significantly. Copyright © 1999 John Wiley & Sons Ltd.     

Seismic signal analysis based on the dual-tree complex wavelet packet transform

We tried to apply the dual-tree complex wavelet packet transform in seismic signal analysis. The complex wavelet packet transform (CWPT) combine the merits of real wavelet packet transform with that of complex continuous wavelet transform (CCWT). It can not only pick up the phase information of signal, but also produce better “focalizing” function if it matches the phase spectrum of signals analyzed. We here described the dual-tree CWPT algorithm, and gave the examples of simulation and actual seismic signals analysis. As shown by our results, the dual-tree CWPT is a very effective method in analyzing seismic signals with non-linear phase. Foundation item: Cultural Heritage Protection Program of State Administration of Cultural Heritage (200001).     

A method for stochastic seismic response analysis of non-classically damped structures

A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression. The method is developed in the frequency domain, The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response), Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy, This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy~     

Forecasting streamflow by combination of a genetic input selection algorithm and wavelet transforms using ANFIS models

ABSTRACT

In this study, a data-driven streamflow forecasting model is developed, in which appropriate model inputs are selected using a binary genetic algorithm (GA). The process involves using a combination of a GA input selection method and two adaptive neuro-fuzzy inference systems (ANFIS): subtractive (Sub)-ANFIS and fuzzy C-means (FCM)-ANFIS. Moreover, the application of wavelet transforms coupled with these models is tested. Long-term data for the Lighvan and Ajichai basins in Iran are used to develop the models. The results indicate considerable improvements when GA selection and wavelet methods are used in both models. For example, the Nash-Sutcliffe efficiency (NSE) coefficient for Lighvan using FCM-ANFIS is 0.74. However, when GA selection is applied, the NSE is improved to 0.85. Moreover, when the wavelet method is added, the performance of new hybrid models shows noticeable enhancements. The NSE value of wavelet-FCM-ANFIS is improved to 0.97 for Lighvan basin.

Editor D. Koutsoyiannis Associate editor E. Toth     

Development of a robust runoff-prediction model by fusing the Rational Equation and a modified SCS-CN method

Abstract

The objective of this study is to develop a Modified Rational Equation (MoRE) that combines the advantages of the Rational Equation (e.g. simplicity and global acceptance) and those of the standard US Department of Agriculture (USDA) Soil Conservation Service (SCS) curve number (CN) method (e.g. easy parameterization and extensive verification across the world). Herein, the hypothesis is that the MoRE is more accurate, consistent and robust than the SCS-CN method and its improved versions in predicting runoff in watersheds with limited data. The MoRE was designed to have a simple structure that is described by four intrinsic parameters: CN, permanent wilting point, field capacity and saturation soil moisture, and does not include initial abstraction as a variable. An evaluation of 77 USDA small agricultural watersheds indicated that CN of the MoRE has different physical meanings from CN of the SCS-CN method. The MoRE (mean Nash-Sutcliffe coefficient, E > 0.73) performed better than the SCS-CN (mean E < 0.32) and the four improved models (mean E < 0.56) in reproducing the runoff of the study watersheds. Performance of all six models varied greatly between watersheds, as well as between events, but was independent of watershed drainage area. However, the model performances tend to be better for watersheds and/or events with a runoff-to-rainfall ratio of between 0.1 and 0.3 than for those with a ratio outside this range. The MoRE has the most consistent and robust performance.

Editor D. Koutsoyiannis; Associate editor I. Nalbantis

Citation Wang, X., Liu, T., and Yang, W., 2012. Development of a robust runoff-prediction model by fusing the rational equation and a modified SCS-CN method. Hydrological Sciences Journal, 57 (6), 1118–1140.     

System identification of linear structures based on Hilbert–Huang spectral analysis. Part 2: Complex modes

A method, based on the Hilbert–Huang spectral analysis, has been proposed by the authors to identify linear structures in which normal modes exist (i.e., real eigenvalues and eigenvectors). Frequently, all the eigenvalues and eigenvectors of linear structures are complex. In this paper, the method is extended further to identify general linear structures with complex modes using the free vibration response data polluted by noise. Measured response signals are first decomposed into modal responses using the method of Empirical Mode Decomposition with intermittency criteria. Each modal response contains the contribution of a complex conjugate pair of modes with a unique frequency and a damping ratio. Then, each modal response is decomposed in the frequency–time domain to yield instantaneous phase angle and amplitude using the Hilbert transform. Based on a single measurement of the impulse response time history at one appropriate location, the complex eigenvalues of the linear structure can be identified using a simple analysis procedure. When the response time histories are measured at all locations, the proposed methodology is capable of identifying the complex mode shapes as well as the mass, damping and stiffness matrices of the structure. The effectiveness and accuracy of the method presented are illustrated through numerical simulations. It is demonstrated that dynamic characteristics of linear structures with complex modes can be identified effectively using the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Structural identification using linear models and earthquake records

The problem of determining linear models of structures from seismic response data is investigated using ideas from the theory of system identification. The approach is to determine the optimal estimates of the model parameters by minimizing a selected measure-of-fit between the responses of the structure and the model. Because earthquake records are normally available from only a small number of locations in a structure, and because of noise in the records, it is necessary in practice to estimate parameters of the dominant modes in the records, rather than the stiffness and damping matrices of the linear model. A new algorithm is developed to determine the optimal estimates of the modal parameters. After tests with simulated data, the method is applied to a multi-storey building using records from the 1971 San Fernando earthquake in California. New information is obtained concerning the properties of the lower modes of the building and the time-varying character of the equivalent linear parameters.     

Genetic algorithm based LQR vibration wireless control of laminated plate using photostrictive actuators

A photostrictive type of opto-electromechanical actuator activated by high-energy lights can introduce actuation and control effects without hard-wired connections.This paper addresses the controllability aspect in wireless vibration control of plate structures via photostrictive actuators.A modal force index,which has taken into account the mode number,the spatial distribution,and the dimension of the actuator,is chosen as an objective function to determine the optimal locations of photostrictive actuators.A linear methodology is proposed in this paper and the vibration equation is written in the standard state-space form.A binary-coded GA based combined optimal placement and LQR(linear quadratic regulator) control scheme has been incorporated,which maximizes the modal force index,the closed loop damping and minimizes input light intensity to the actuators.In the present method only three weighting factors have been used to search optimal Q and R matrices using GA,which reduces chromosome length and hence minimizes computational time.Numerical results demonstrate that the use of strategically positioned actuator patches can effectively control the fundamental modes that dominate the structural vibration.     

Broken ergodicity in magnetohydrodynamic turbulence

Turbulent magnetofluids appear in various geophysical and astrophysical contexts, in phenomena associated with planets, stars, galaxies and the universe itself. In many cases, large-scale magnetic fields are observed, though a better knowledge of magnetofluid turbulence is needed to more fully understand the dynamo processes that produce them. One approach is to develop the statistical mechanics of ideal (i.e. non-dissipative), incompressible, homogeneous magnetohydrodynamic (MHD) turbulence, known as “absolute equilibrium ensemble” theory, as far as possible by studying model systems with the goal of finding those aspects that survive the introduction of viscosity and resistivity. Here, we review the progress that has been made in this direction. We examine both three-dimensional (3-D) and two-dimensional (2-D) model systems based on discrete Fourier representations. The basic equations are those of incompressible MHD and may include the effects of rotation and/or a mean magnetic field B _o. Statistical predictions are that Fourier coefficients of the velocity and magnetic field are zero-mean random variables. However, this is not the case, in general, for we observe non-ergodic behavior in very long time computer simulations of ideal turbulence: low wavenumber Fourier modes that have relatively large means and small standard deviations, i.e. coherent structure. In particular, ergodicity appears strongly broken when B _o?=?0 and weakly broken when B _o?≠?0. Broken ergodicity in MHD turbulence is explained by an eigenanalysis of modal covariance matrices. This produces a set of modal eigenvalues inversely proportional to the expected energy of their associated eigenvariables. A large disparity in eigenvalues within the same mode (identified by wavevector k ) can occur at low values of wavenumber k?=?| k |, especially when B _o?=?0. This disparity breaks the ergodicity of eigenvariables with smallest eigenvalues (largest energies). This leads to coherent structure in models of ideal homogeneous MHD turbulence, which can occur at lowest values of wavenumber k for 3-D cases, and at either lowest or highest k for ideal 2-D magnetofluids. These ideal results appear relevant for unforced, decaying MHD turbulence, so that broken ergodicity effects in MHD turbulence survive dissipation. In comparison, we will also examine ideal hydrodynamic (HD) turbulence, which, in the 3-D case, will be seen to differ fundamentally from ideal MHD turbulence in that coherent structure due to broken ergodicity can only occur at maximum k in numerical simulations. However, a nonzero viscosity eliminates this ideal 3-D HD structure, so that unforced, decaying 3-D HD turbulence is expected to be ergodic. In summary, broken ergodicity in MHD turbulence leads to energetic, large-scale, quasistationary magnetic fields (coherent structures) in numerical models of bounded, turbulent magnetofluids. Thus, broken ergodicity provides a large-scale dynamo mechanism within computer models of homogeneous MHD turbulence. These results may help us to better understand the origin of global magnetic fields in astrophysical and geophysical objects.     

A new simplified approach for assessing nonlinear seismic response of plan-asymmetric structures considering soil-structure interaction

An innovative approximate method is presented to consider the plan asymmetry, nonlinear structural behaviour and soil-structure interaction (SSI) effects simultaneously. The proposed method so-called Flexible base 2DMPA (F2MPA) is an extension of 2 degrees of freedom modal pushover analysis (2DMPA) approach to consider foundation flexibility in seismic response analysis of plan asymmetric structures which itself were developed based on Uncoupled Modal Response History Analysis method for inelastic fixed-base asymmetric structures. In F2MPA for each mode shape using 2DMPA procedure, the elastic and inelastic properties of 2DOF modal systems corresponding to the fixed-base structure are initially derived. Then in each time step, displacements and inelastic restoring forces of the superstructure are computed from modal equations of the flexibly-supported structure. In each time step, the nonlinear secant stiffness matrix corresponding to the n-th MDOF modal equations of soil-structure system is updated using the corresponding modal 2DOF system of fixed-base structure. To update the transformed modal stiffness matrix of the SSI system, this matrix is partitioned and it is assumed that the non-linear variation of the superstructure can be estimated from the variation of modal stiffness matrix of the fixed-base structure. Accuracy of the proposed method was verified on an 8-story asymmetric-plan building under different seismic excitations. The results obtained from F2MPA method were compared with those obtained by nonlinear response history analysis of the asymmetric soil-structure system as a reference response. It was shown that the proposed approach could predict the results of the nonlinear time history analysis with a good accuracy. The main advantage of F2MPA is that this method is much less time-consuming and useful for the practical aims such as massive analysis of a nonlinear structure under different records with multiple intensity levels.     

基于振型的结构平面规则性界定方法

为研究结构平面规则性的界定方法,首先分析了平面规则结构的振型序列特征并验证了其稳定性。以L型结构为例,通过将规则结构的振型序列特征与L型结构的振型序列特征对比,得到了不同L型结构的平面规则性界定曲线,指出了凸出部分的横向长度与横向总长度之比、凸出部分的纵向长度与纵向总长度之比和结构高度是影响L型结构平面规则与否的重要因素,并建议平面不规则结构位移比限值取1.3。提出了基于振型的结构平面规则性界定方法,即:与平面规则结构的振型序列相比,平面不规则结构的振型序列中不利振型（扭转振型、包含扭转的耦合振型及局部振型等需考虑空间效应的振型）会提前。通过对一实际结构进行计算分析,验证了基于振型的结构平面规则性界定方法的优越性和正确性。     

Improved dynamic correction method in seismic analysis of both classically and non‐classically damped structures

A step‐by‐step approximate procedure taking into consideration high‐frequency modes, usually neglected in the modal analysis of both classically and non‐classically damped structures, is presented. This procedure can be considered as an extension of traditional modal correction methods, like the mode‐acceleration method and the dynamic correction method, which are very effective for structural systems subjected to forcing functions described by analytical laws. The proposed procedure, herein called improved dynamic correction method, requires two steps. In the first step, the number of differential equations of motion are reduced and consequently solved by using the first few undamped mode‐shapes. In the second step, the errors due to modal truncation are reduced by correcting the dynamic response and solving a new set of differential equations, formally similar to the original differential equations of motion. The difference between the two groups of differential equations lies in the forcing vector, which is evaluated in such a way as to correct the effects of modal truncation on applied loads. Copyright © 2001 John Wiley & Sons, Ltd.     

Multivariate approach for chlorophyll-a and suspended matter retrievals in Case II type waters using hyperspectral data

Abstract

Remote sensing has become promising in providing temporal and spatial information on biogeodynamics in large and open freshwater bodies. In optically complex environments, such as in the Western Basin of Lake Erie (WBLE), the water contains multiple biogeochemical constituents or colour producing agents (CPAs), such as phytoplankton, suspended matter and dissolved organic carbon; identifying and analysing such in-water constituents is crucial for understanding and assessing many biogeochemical processes. For example, concentrations of chlorophyll-a and total suspended matter can be used as proxies to assess phytoplankton dynamics and particulate loading. However, quantitative estimation of their concentrations from satellite observations is complicated when working with mixed spectral signatures. Hyperspectral remote sensing is fast emerging as a key technology for advanced and improved understanding of optically complex waters. This study estimates concentrations of chlorophyll-a and total suspended matter (TSM) in the WBLE by applying the partial least squares (PLS) method to a full range (400–900 nm) of continuous narrow spectral bands. The PLS method models the covariance between hyperspectral bands and CPAs, and identifies the optimal bands that characterize most of the variance in the CPAs. This method avoids the curse of dimensionality and the effects of multi-collinearity, a challenge that is associated with new-generation hyperspectral satellite sensors. Validation parameters for the PLS-based models produced R² of 0.84 for chlorophyll-a (RMSE = 1.18 μg/L), and R² of 0.90 for TSM (RMSE = 1.26 mg/L), illustrating the potential of the PLS method for isolating and extracting absorption features characterizing the various CPAs in optically complex Case II type waters.

Editor Z.W. Kundzewicz Associate editor Not assigned