Methods and Object-Oriented Software for FE Reliability and Sensitivity Analysis with Application to a Bridge Structure

This paper addresses the growing demand for finite-element software with capabilities to incorporate uncertainty in the input parameters. Reliability and response sensitivity algorithms are implemented in the general-purpose finite-element software OpenSees, which employs an object-oriented programming approach to achieve a sustainable software with focus on maintainability and extensibility. The product is a comprehensive and freely available library of software tools for finite-element reliability and response sensitivity analysis. A numerical example involving a detailed model of a highway bridge with inelastic material behavior and 320 random variables is presented to demonstrate features of the methodology and the software. Importance vectors are employed to rank the input parameters according to their relative influence on the structural reliability. The required response sensitivities are obtained by an extensive implementation of the direct differentiation method.     

Nonlinear Finite-Element Analysis Software Architecture Using Object Composition

Object composition offers significant advantages over class inheritance to develop a flexible software architecture for finite-element analysis. Using this approach, separate classes encapsulate fundamental finite-element algorithms and interoperate to form and solve the governing nonlinear equations. Communication between objects in the analysis composition is established using software design patterns. Root-finding algorithms, time integration methods, constraint handlers, linear equation solvers, and degree of freedom numberers are implemented as interchangeable components using the Strategy pattern. The Bridge and Factory Method patterns allow objects of the finite-element model to vary independently from objects that implement the numerical solution procedures. The Adapter and Iterator patterns permit equations to be assembled entirely through abstract interfaces that do not expose either the storage of objects in the analysis model or the computational details of the time integration method. Sequence diagrams document the interoperability of the analysis classes for solving nonlinear finite-element equations, demonstrating that object composition with design patterns provides a general approach to developing and refactoring nonlinear finite-element software.     

Stream Sockets versus Web Services for High-Performance and Secure Structural Analysis in Internet Environments

The increased growth of internet use in the last several years has opened up new possibilities for structural engineering analysis, moving from personal computer oriented software to client–server distributed software. In this paper two client–server applications for structural engineering based on stream sockets and on web services are presented. These two technologies have been chosen to compare, in terms of performance and complexity, new internet protocols with traditional ways of implementing client–server applications. Moreover, special care has been taken in the security aspects as the internet has become much more susceptible to breaches of security. Therefore, two new applications based on the same technologies have been created that guarantee a secure use of structural software. Also, two different client applications are presented to emphasize the versatility and power of internet distributed technology—one as a stand-alone application and the other as an integrated commercial computer-aided design program.     

Handling of Constraints in Finite-Element Response Sensitivity Analysis

In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.     

Parameter Sensitivity and Importance Measures in Nonlinear Finite Element Reliability Analysis

Finite element reliability methods allow the analyst to define material, load, and geometry parameters as random variables to represent uncertainties in these model parameters. Approximate probabilistic analysis methods produce estimates of the response variance/covariances, probabilities of exceeding specified structural performance thresholds, and parameter importance measures. A necessary ingredient for such analysis is consistent, efficient, and accurate algorithms for computing finite element response sensitivities. In this paper, unified response sensitivity equations with respect to material, load, and geometry parameters are developed for the time- and space-discretized finite element model. The sensitivities with respect to nodal coordinates and global shape parameters in the presence of material and geometric nonlinearities represent an extension of previous work. Practical computer implementation issues are emphasized. The equations are implemented in the comprehensive, open-source, object-oriented finite element software OpenSees. Importance measures from reliability analysis, employing the sensitivity results, are presented to enable the investigation of the relative importance of uncertainty in the parameters of a finite element model. Two example applications demonstrate that the variability in nodal coordinates of a structure can be a significant source of uncertainty along with that in key material and load parameters.     

Finite-Element Analysis and Vibration Testing of a Two-Span Masonry Arch Bridge

This paper presents the analytical modeling, modal testing, and finite-element model updating for a two-span masonry arch bridge. An Ottoman masonry arch bridge built in the 19th century and located at Camlihemsin, Rize, Turkey is selected as an example. Analytical modal analysis is performed on the developed 3D finite-element model of the bridge to obtain dynamic characteristics. The ambient vibration tests are conducted under natural excitation such as human walking. The operational modal analysis is carried out using peak picking method in the frequency domain and stochastic subspace identification method in the time domain, and dynamic characteristics (natural frequencies, mode shapes, and damping ratios) are determined experimentally. Finite-element model of the bridge is updated to minimize the differences between analytically and experimentally estimated dynamic characteristics by changing boundary conditions. At the end of the study, maximum differences in the natural frequencies are reduced on average from 18 to 7% and a good agreement is found between analytical and experimental dynamic characteristics after finite-element model updating.     

Modal Testing, Finite-Element Model Updating, and Dynamic Analysis of an Arch Type Steel Footbridge

This paper describes an arch type steel footbridge, its analytical modeling, modal testing, finite-element model updating, and dynamic analysis. A modern steel footbridge which has an arch type structural system and is located on the Karadeniz coast road in Trabzon, Turkey is selected as an application. An analytical modal analysis is performed on the developed three-dimensional finite-element model of footbridge to provide analytical frequencies and mode shapes. Field ambient vibration tests on the footbridge deck under natural excitation such as human walking and traffic loads are conducted. The output-only modal parameter identification is carried out by using peak picking of the average normalized power spectral densities in the frequency domain and stochastic subspace identification in the time domain, and dynamic characteristics such as natural frequencies, mode shapes, and damping ratios are determined. The finite-element model of the footbridge is updated to minimize the differences between analytically and experimentally estimated modal properties by changing some uncertain modeling parameters such as material properties. Dynamic analyses of the footbridge before and after finite-element model updating are performed using the 1992 Erzincan earthquake record. At the end of the study, maximum differences in the natural frequencies are reduced from 22 to only 5% and good agreement is found between analytical and experimental dynamic characteristics such as natural frequencies and mode shapes by model updating. Also, maximum displacements and principal stresses before and after model updating are compared with each other.     

Graphical 3D Visualization of Highway Bridge Ratings

Aging highway infrastructure requires effective rating methodologies to prioritize bridges for rehabilitation and repair. To aid engineers in decision making regarding bridge maintenance, a three-dimensional (3D) visualization system is developed for rating reinforced concrete deck-girder bridge. Color codings show the most probable mode of failure for girder cross sections under combined moment-shear forces and allow an engineer to determine a rehabilitation strategy. The visualization system relies on 3D finite-element analyses using the open source framework OpenSees, making the system readily extensible to a wide range of bridge types and loading scenarios, as well as emergent reliability-based rating methodologies. Important features of the visualization system are emphasized, including the use of lighting and feature edge detection to improve the visual quality of a bridge model. Recent developments in scientific visualization are discussed for potential application to civil engineering problems.     

Finite-Element Model Updating for the Kap Shui Mun Cable-Stayed Bridge

This paper presents the implementation of the finite-element model updating for the Kap Shui Mun Bridge, a 430 m main span double-deck cable-stayed bridge in Hong Kong. The dynamic characteristics of the bridge have been studied through both three-dimensional finite-element prediction and field vibration measurement previously. In this paper, the developed finite-element model is updated based on the field measured dynamic properties. A comprehensive sensitivity study to demonstrate the effects of various structural parameters (including the connections and boundary conditions) on the modes of concern is first performed, according to which a set of structural parameters are then selected for adjustment. The finite-element model is updated in an iterative fashion so as to minimize the differences between the predicted and the measured natural frequencies. The final updated finite-element model for the Kap Shui Mun Bridge is able to produce natural frequencies in good agreement with the measured ones, and can be helpful for a more precise dynamic response prediction.     

Bayesian Modal Updating using Complete Input and Incomplete Response Noisy Measurements

The problem of identification of the modal parameters of a structural model using complete input and incomplete response time histories is addressed. It is assumed that there exist both input error (due to input measurement noise) and output error (due to output measurement noise and modeling error). These errors are modeled by independent white noise processes, and contribute towards uncertainty in the identification of the modal parameters of the model. To explicitly treat these uncertainties, a Bayesian framework is adopted and a Bayesian time-domain methodology for modal updating based on an approximate conditional probability expansion is presented. The methodology allows one to obtain not only the optimal (most probable) values of the updated modal parameters but also their uncertainties, calculated from their joint probability distribution. Calculation of the uncertainties of the identified modal parameters is very important if one plans to proceed with the updating of a theoretical finite-element model based on these modal estimates. The proposed approach requires only one set of excitation and corresponding response data. It is found that the updated probability density function (PDF) can be well approximated by a Gaussian distribution centered at the optimal parameters at which the posterior PDF is maximized. Numerical examples using noisy simulated data are presented to illustrate the proposed method.     

Bridge Model Updating Using Response Surface Method and Genetic Algorithm

A finite-element (FE) model of a structure is a highly idealized engineering model that may or may not truly reflect the physical structure. The purpose of model updating is to modify the FE model of a structure in order to obtain better agreement between the numerical and field-measured structure responses. In this paper, a new practical and user-friendly FE model updating method is presented. The new method utilizes the response surface method for the best experimental design of the parameters to be updated based on which numerical analysis can be performed in order to obtain explicit relationships between the structural responses and parameters from the simulation results. The parameters are then be updated using the genetic algorithm (GA) by minimizing an objective function. A numerical example of a simply supported beam has been used to demonstrate the concept. This method has also been applied to the model updating of an existing bridge. Results show that this method works well and achieves reasonable physical explanations for the updated parameters.     

Computer-Aided Site Layout Planning

This paper presents an interactive computer-aided site layout model to support site planning in a computer-aided design (CAD) environment and expands upon a model presented earlier by the writers. The developed model performs its task at two levels: Site representation, and site space analysis and allocation. The site representation is carried out using an open architecture supported by object-based concepts. The model offers three tiers of objects: (1) site objects, (2) construction objects, and (3) constraint objects. This structure facilitates the creation of new objects and reuse of domain knowledge, which allows for the gradual expansion and enrichment of the model’s knowledge base. At the space analysis and allocation level, the model introduces a geometric reasoning approach to analyze site space for finding an optimum or near-optimum location for facilities. This feature facilitates easy visualization of the site planning process and encourages user participation. The model is structured in three main modules: Database, Project Module, and Layout Control Module. The functionality of each module, along with their interconnectivity is described. The model is implemented using Visual Basic for Applications in AutoCAD environment and Microsoft Access. A numerical example of an actual site layout is presented to illustrate the functionality of the developed model.     

Ambient Vibration of Long-Span Cable-Stayed Bridge

The investigation of dynamic response for long-span cable-stayed bridges largely depends on a detailed understanding of their dynamic characteristics, such as the natural frequencies, mode shapes, and modal damping ratios. In this paper, the dynamic characteristics of a fairly long cable-stayed bridge in Hong Kong are studied using finite-element analysis and ambient vibration measurements. A three-dimensional finite-element model is first established for the bridge based on design drawings. The dynamic characteristics are then analyzed from the statically deformed configuration. Ambient vibration measurements are also conducted to obtain the dynamic characteristics of the bridge. Comparison between these two results shows that, for the most part, a total of 31 modes can be correlated with a reasonable agreement. However, the frequency differences of the higher modes can range between 15 and 30%. This implies that, if the measurement is more reliable, a finite-element model updating is necessary in order to achieve better correlation between these two results.     

Java Inspection Framework: Developing Field Inspection Support Systems for Civil Systems Inspection

In order to provide useful and practical computing support for inspectors in the field performing inspection activities, computer systems have to be designed and customized to recognize the specific task and context of the inspection. Unfortunately, the development of field inspection support systems is difficult and still suffers from a lack of more general design knowledge. Effort is wasted when implementing different applications that share some common aspects. This paper presents a partial solution to the difficult problem of developing field inspection support systems—a modular and customizable software environment to facilitate the construction of such applications.     

结构加速度频响函数模型修正的Kriging方法

为提高结构频响函数模型修正效率,提出将Kriging模型引入优化过程,代替有限元模型进行迭代运算.基于频响曲线对应频率点处的响应值之差构造目标函数,并结合初选设计参数进行实验设计.根据实验设计结果进行各参数的灵敏度分析,进而筛选出模型修正的待修正参数,基于该参数及其响应构造Kriging模型,经检验有效的Kriging模型将参与模型修正过程.以GARTEUR飞机模型为算例,基于加速度频响数据进行模型修正,修正后模型不仅能复现检验点处频响曲线,还能成功预测结构局部修改后的频响曲线,证明了Kriging方法应用于频响函数模型修正的有效性.      

Object-Oriented Paradigm in Programming for Computer-Aided Analysis of Structures

The concept of object-oriented programming (OOP) has redefined the design and development of large-scale codes worldwide and is now the order of the day in the software industry. Although OOP offers enormous potential in the scientific software business, this innovative programming technique has yet to find a niche in the development of structural engineering software. The present paper is an attempt to highlight the superior programming capability offered by the OOP approach in computer-aided analysis and design of civil engineering structures. The paper presents a brief theoretical background on the important basic and advanced concepts of OOP within the context of structural engineering. The paper explains the relevant fundamentals of object-oriented modeling and design in structural engineering for the orientation of civil engineering professionals who are new to the concept of OOP. The paper provides simple examples of object-oriented programs for elementary structural analysis to illustrate implementation of the OOP paradigm for computational structural analysis. User-code fragments with accompanying commentary are included to provide more detailed directions to structural engineers who wish to adopt the OOP paradigm. The paper also includes a brief review of the evolution that the computational programming paradigm has undergone over the past few decades to cope with the increasing complexity of software. A comparison of currently prevalent programming paradigms is presented to illustrate the relative advantages of OOP for large-scale software applications in structural engineering.     

Failure Analysis of Transmission Line Towers

Transmission line towers, though designed per code provisions, may fail during mandatory testing required in many countries. Different types of premature failures that were observed during full-scale testing of transmission line towers at Tower Testing and Research Station, Structural Engineering Research Centre, Chennai (CSIR-SERC) are studied, and the results are discussed in detail. The failures are modeled using finite-element software, and the analytical results and the test results are compared with various code provisions. The nonlinear finite-element analysis program NE-Nastran was used to model the elastoplastic behavior of towers. Bracing members with slenderness ratios above 170 become ineffective, even though they have to carry insignificant forces. Importance of design assumptions and connection detailing in overall performance of towers were studied. Nonlinear finite-element analysis is useful in understanding the system behavior and for prediction of the failure pattern and ultimate load. Based on the test results, the importance of studying these failures is highlighted and significant conclusions were drawn.     

Directing Exploration with 3D FEM Sensitivity and Data Uncertainty

Quantitatively directed exploration (QDE) employs a first-order Taylor series expansion to combine sensitivity of a 3D finite-element model (FEM) and uncertainty in geologic data to calculate the variance in project performance, which is employed to direct exploration. This approach is made practical by calculating model sensitivity with direct differentiation of the engineering analysis code, thus producing sensitivity with a single model run rather than multiple runs required by parameter perturbation. Uncertainty in subsurface data is computed through two different extrapolation methods for comparison: kriging and conditional probability (Bayesian updating). Although either of these methods can be employed in QDE, conditional probability is required to quantifiably terminate exploration. The QDE framework is applicable to any subsurface analysis that employs a 3D FEM. A case study illustrates the QDE approach, where settlement is the performance criterion, and layer interface elevations are the uncertain geologic data. Additional boring locations identified by QDE were placed where a combination of model sensitivity and subsurface uncertainty was the greatest, thus directing exploration toward the building footprint and away from existing sampled points.     

Linking Nonlinear System Identification with Nonlinear Dynamic Simulation under OpenSees: Some Justifications and Implementations

This study seeks to bridge the gap between nonlinear system identification and nonlinear dynamic finite-element analysis. Motivated by the needs in earthquake simulation, it is first investigated under which conditions and to what degree the prediction of maximum lateral drift and base shear requires accurate nonlinear hysteretic moment-rotation joint models. A series of simulations is carried out using a simple but typical steel frame under two different earthquake ground motion time histories scaled up to various levels. As one of the two major classes of models in nonlinear system identification, nonparametric models are proposed to be implemented into OpenSees. A methodology with details is provided to effectively implement feedforward neural networks with one hidden layer as a new one-dimensional nonlinear smooth material model directly from a MATLAB environment to OpenSees. The same methodology can be applied to benefit the implementation of other parametric and nonparametric models with linear parameterization. Numerical examples are provided. Challenges are discussed and future work is identified.