Transient Dynamic Nonlinear Analysis Using MIMD Computer Architectures

This paper presents research on the use of homogeneous parallel and heterogeneous distributed computers for finite-element analysis of transient dynamic problems using a message passing interface. The appropriate computer architectures are discussed, and this review is the basis for the development of a new definition of computational efficiency for heterogeneously distributed finite-element analysis. A code for the transient nonlinear analysis of reinforced concrete plates is profiled. It is demonstrated that although the code is efficient for homogeneous computing systems a new message passing procedure must be developed for heterogeneously distributed systems. A new algorithm is developed and tested on a heterogeneous system of workstations.     

Three-Dimensional Field-Scale Coupled Thermo-Hydro-Mechanical Modeling: Parallel Computing Implementation

An approach for the simulation of three-dimensional field-scale coupled thermo-hydro-mechanical problems is presented, including the implementation of parallel computation algorithms. The approach is designed to allow three-dimensional large-scale coupled simulations to be undertaken in reduced time. Owing to progress in computer technology, existing parallel implementations have been found to be ineffective, with the time taken for communication dominating any reduction in time gained by splitting computation across processors. After analysis of the behavior of the solver and the architecture of multicore, nodal, parallel computers, modification of the parallel algorithm using a novel hybrid message passing interface/open multiprocessing (MPI/OpenMP) method was implemented and found to yield significant improvements by reducing the amount of communication required. This finding reflects recent enhancements of current high-performance computing architectures. An increase in performance of 500% over existing parallel implementations on current processors was achieved for the solver. An example problem involving the Prototype Repository experiment undertaken by the Swedish Nuclear Fuel and Waste Management Co. [Svensk K?rnbr?nslehantering AB (SKB)] in ?sp?, Sweden, has been presented to demonstrate situations in which parallel computation is invaluable because of the complex, highly coupled nature of the problem.     

Consistent Finite-Element Response Sensitivity Analysis

This paper examines the important issue of response sensitivities of dynamic models of structural systems to both material and (discrete) loading parameters. Plasticity-based finite-element models of structural systems subjected to base excitation such as earthquake loading are considered. The two methods for computing the response sensitivities, namely, (1) discretizing in time the time continuous-spatially discrete response equations and differentiating the resulting time discrete-spatially discrete response equations with respect to sensitivity parameters, and (2) differentiating the time continuous-spatially discrete response equations with respect to sensitivity parameters and discretizing in time the resulting time continuous-spatially discrete response sensitivity equations, are clearly distinguished. The discontinuities in time of the response sensitivities arising due to material state transitions in the plasticity models, and their propagation from the quadrature point level to the global structural response level are discussed using a specific one-dimensional plasticity model. The procedure to obtain the exact sensitivities of the numerical nonlinear finite-element response, including proper capture of their discontinuities, is formalized. Application examples illustrating the concepts are presented at the end.     

Finite‐Element Calculations on Alliant FX/80

The finite‐element method has proven to be an invaluable tool for analysis and design of complex, high‐performance systems, such as those typically encountered in the aerospace or automotive industries. However, as the size of the finite‐element models of such systems increases, analysis computation time using conventional computers can become prohibitively high. Parallel processing computers provide the means to overcome these computation‐time limits, provided the algorithms used in the analysis can take advantage of multiple processors. The writers have examined several algorithms for linear and nonlinear static analysis, as well as dynamic finite‐element analysis. The performance of these algorithms on an Alliant FX/80 parallel supercomputer has been investigated. For single load‐case linear static analysis, the optimal solution algorithm is strongly problem dependent. For multiple load cases or nonlinear static analysis through a modified Newton‐Raphson method, decomposition algorithms are shown to have a decided advantage over element‐by‐element preconditioned conjugate gradient algorithms. For eigenvalue/eigenvector analysis, the subspace iteration algorithm with a parallel decomposition is shown to achieve a relatively high parallel efficiency.     

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.     

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.     

Two-Dimensional Fast-Response Flood Modeling: Desktop Parallel Computing and Domain Tracking

Emergency flood management is enhanced by using models that can estimate the timing and location of flooding. Typically, flood routing and inundation prediction is accomplished by using one-dimensional (1D) models. These have been the models of choice because they are computationally simple and quick. However, these models do not adequately represent the complex physical processes present for shallow flows located in the floodplain or in urban areas. Two-dimensional (2D) models developed on the basis of the full hydrodynamic equations can be used to represent the complex flow phenomena that exist in the floodplain and are, therefore, recommended by the National Research Council for increased use in flood analysis studies. The major limitation of these models is the increased computational cost. Two-dimensional flood models are prime candidates for parallel computing, but traditional methods/equipment (e.g., message passing paradigm) are more complex in terms of code refactoring and hardware setup. In addition, these hardware systems may not be available or accessible to modelers conducting flood analyses. This paper presents a 2D flood model that implements multithreading for use on now-prevalent multicore computers. This desktop parallel computing architecture has been shown to decrease computation time by 14 times on a 16-processor computer and, when coupled with a wet cell tracking algorithm, has been shown to decrease computation by as much as 310 times. These accomplishments make high-fidelity flood modeling more feasible for flood inundation studies using readily available desktop computers.     

Vibration-based Damage Detection of Structures by Genetic Algorithm

Vibration-based methods are being rapidly applied to detect structural damage. The usual approaches incorporate sensitivity analysis and the optimization algorithm to minimize the discrepancies between the measured vibration data and the analytical data. However, conventional optimization methods are gradient based and usually lead to a local minimum only. Genetic algorithms explore the region of the whole solution space and can obtain the global optimum. In this paper, a genetic algorithm with real number encoding is applied to identify the structural damage by minimizing the objective function, which directly compares the changes in the measurements before and after damage. Three different criteria are considered, namely, the frequency changes, the mode shape changes, and a combination of the two. A laboratory tested cantilever beam and a frame are used to demonstrate the proposed technique. Numerical results show that the damaged elements can be detected by genetic algorithm, even when the analytical model is not accurate.     

Reliability-Based Optimum Design of Glulam Cable-Stayed Footbridges

This work presents a procedure for finding the reliability-based optimum design of cable-stayed bridges. The minimization problem is stated as the minimization of stresses, displacements, reliability, and bridge cost. A finite-element approach is used for structural analysis. It includes a direct analytic sensitivity analysis module, which provides the structural behavior responses to changes in the design variables. An equivalent multicriteria approach is used to solve the nondifferential, nonlinear optimization problem, turning the original problem into sequential minimization of unconstrained convex scalar functions, from which a Pareto optimum is obtained. Examples are given illustrating the procedure.     

A general multilevel SEM framework for assessing multilevel mediation.

Several methods for testing mediation hypotheses with 2-level nested data have been proposed by researchers using a multilevel modeling (MLM) paradigm. However, these MLM approaches do not accommodate mediation pathways with Level-2 outcomes and may produce conflated estimates of between- and within-level components of indirect effects. Moreover, these methods have each appeared in isolation, so a unified framework that integrates the existing methods, as well as new multilevel mediation models, is lacking. Here we show that a multilevel structural equation modeling (MSEM) paradigm can overcome these 2 limitations of mediation analysis with MLM. We present an integrative 2-level MSEM mathematical framework that subsumes new and existing multilevel mediation approaches as special cases. We use several applied examples and accompanying software code to illustrate the flexibility of this framework and to show that different substantive conclusions can be drawn using MSEM versus MLM. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Numerical Approximations of Design Points in Reliability Analysis under Parametric Changes

Traditional approaches for repeatedly updating reliability estimates, as needed in reliability-based optimal designs or real-time system control, require the iterative application of a reliability method. This paper explores a new strategy for repeatedly estimating reliability under frequent parameter variations. The central idea is to update the design point in the parameter domain, rather than in the traditional random variable domain, by evaluating several parametric sensitivity measures which are systems of nonlinear first-order ordinary differential equations relating the design point to parameter changes. Four numerical algorithms for evaluating the sensitivity measures are developed using the Euler and the improved Euler algorithms. Two solution procedures are applied. One procedure solves for the updated design point directly, while the other solves for both the unit normal vector at the design point and the reliability index separately, and evaluates the product of these to determine the updated design point. The numerical techniques are thoroughly compared with the classical Hasofer and Lind-Rackwitz and Fiessler (HL-RF) algorithm in five numerical examples regarding efficiency and accuracy. It is found that they are efficient and robust under given conditions.     

Parallel Algorithms for Integrated Structural/Control Optimization

Optimization of combined structural and control systems is a complex problem requiring an inordinate amount of computer‐processing time, especially the solution of the eigenvalue problem of a general unsymmetric square real matrix with complex eigenvalues and eigenvectors, which is frequently used in such problem. The few algorithms presented in the literature thus far have been applied to small structures with a few members and controllers only. Parallel processing on new‐generation multiprocessor computers provides an opportunity to solve large‐scale problems. In this paper, the integrated structural and control optimization problem is formulated by including constraints on displacements, stresses, and closed‐loop eigenvalues and the corresponding damping factors. Then, parallel algorithms are presented for integrated optimization of structures on shared‐memory multiprocessors such as the Cray YMP 8/864 supercomputer. In particular, parallel algorithms are presented for the solution of complex eigenvalue problems encountered in structural control problems using the method of matrix iteration for dominant eigenvalue(s). The solution is divided into two parts. The first part is the iteration for dominant eigenvalue(s) and the corresponding eigenvector(s) and the second part is the reduction of the matrix to obtain the smaller eigenvalue(s) and the corresponding eigenvector(s).     

Grid-Enabled Simulation-Optimization Framework for Environmental Characterization

Many engineering and environmental problems that involve the determination of unknown system characteristics from observation data can be categorized as inverse problems. A common approach undertaken to solve such problems is the simulation-optimization approach where simulation models are coupled with optimization or search methods. Simulation-optimization approaches, particularly in environmental characterization involving natural systems, are computationally expensive due to the complex three-dimensional simulation models required to represent these systems and the large number of such simulations involved. Emerging grid computing environments (e.g., TeraGrid) show promise for improving the computational tractability of these approaches. However, harnessing grid resources for most computational applications is a nontrivial problem due to the complex hierarchy of heterogeneous and geographically distributed resources involved in a grid. This paper reports and discusses the development and evaluation of a grid-enabled simulation-optimization framework for solving environmental characterization problems. The framework is designed in a modular fashion that simplifies coupling with simulation model executables, allowing application of simulation-optimization approaches across problem domains. The framework architecture utilizes standard communications protocols and the message passing interface with an application programming interface to establish a connection between a centralized search application and simulation models running on TeraGrid resources. Sets of performance and scalability results for solving a groundwater source history reconstruction (SHR) problem are presented. The results show that for a given set of resources, parameters controlling the granularity at various levels of parallelism play an important role in the overall parallel performance. A production run for solving the SHR problem using three geographically distributed grid resources indicates that even in a cross-site grid environment a factor of 90 speedup is possible using 140 computer processors.     

Transit Route Network Design Using Parallel Genetic Algorithm

A transit route network design (TRND) problem for urban bus operation involves the determination of a set of transit routes and the associated frequencies that achieve the desired objective. This can be formulated as an optimization problem of minimizing the total system cost, which is the sum of the operating cost and the generalized travel cost. A review of previous approaches to solve this problem reveals the deficiency of conventional optimization techniques and the suitability of genetic algorithm (GA) based models to handle such combinatorial optimization problems. Since GAs are computationally intensive optimization techniques, their application to large and complex problems is limited. The computational performance of a GA model can be improved by exploiting its inherent parallel nature. Accordingly, two parallel genetic algorithm (PGA) models are proposed in this study. The first is a global parallel virtual machine (PVM) parallel GA model where the fitness evaluation is done concurrently in a parallel processing environment using PVM libraries. The second is a global message passing interface (MPI) parallel GA model where an MPI environment substitutes for the PVM libraries. An existing GA model for TRND for a large city is used as a case study. These models are tested for computation time, speedup, and efficiency. From the study, it is observed that the global PVM model performed better than the other model.     

Statistical Sensitivity Analysis of Lattice Space Structures

This paper presents a statistical sensitivity analysis for shape distortions of space structures. The approach is based on a statistical shape‐distortion analysis on the structural errors and an adjoint method of sensitivity analysis. The statistical shape‐distortion analysis allows the stochastic errors to be represented by member‐length tolerances. The sensitivity analysis is performed to predict the effects of member‐length errors for lattice space antennas on the surface accuracy. The formulas presented in this paper give an effective approach to predict the effects of member‐length errors on the shape distortions, to obtain effective structural elements to correct the shape distortions, and to design tolerance errors of the structural elements. Numerical examples for statically determinate and indeterminate two‐dimensional truss beams have been demonstrated to identify the members contributing most to the errors. These results show that the errors of the longitudinal elements of the structure are important for designing accurate truss structures. Moreover, the validity and effectiveness of the present approach have been investigated.     

Novel Cellular Automata Approach to Optimal Water Distribution Network Design

This paper proposes a novel heuristic-based and cellular automata-inspired approach to the optimal design of water distribution networks. The design of water distribution networks is of central importance to the water industry, but many networks cannot be optimally designed by traditional techniques due to their complexity. Genetic algorithms have become a state-of-the-art technique for this purpose but are hampered by the fact that they are population based and require a large number of model evaluations to achieve good solutions. The proposed approach uses a parallel, localist, heuristic-based algorithm to optimally design water distribution networks requiring only a limited number of model evaluations. The algorithm is applied to a well-known simple test network and two real water distribution systems in the U.K. The results indicate that the proposed cellular approach is a viable alternative to genetic algorithm approaches while using only a fraction of the computational time required by its evolutionary counterpart.     

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.     

3D structural information as a guide to protein engineering using genetic selection

A great variety of protein systems have been investigated in the past year using structure-guided evolutionary strategies. On the basis of available 3D structural information, critical regions of proteins have been targeted for randomizing mutagenesis and active variants of the corresponding genes have been selected. These approaches help characterize structural and mechanistic features of proteins and have important implications for design.     

Robust Parallel Algorithms for Solution of Riccati Equation

Robust and efficient parallel-vector algorithms are presented for the solution of the Riccati equations encountered in optimal control problems on shared-memory multiprocessor machines. The algorithms have been implemented on a Cray YMP 8∕8128 and applied to three large problems resulting from a continuous bridge structure, a 21-story space truss structure, and a 12-story space moment-resisting building structure. Efficiency of the algorithms is presented in terms of millions of floating point operations per second (MFLOPS) and the speedup. The MFLOPS for the largest example resulting from the 12-story space frame structure is a high 206.0. The speedup due to parallel processing only (for the same example), using seven processors, is 6.33. When vectorization is combined with parallel processing a very significant speedup of 54.4 is obtained using seven processors. The algorithms developed in this research find applications in the complex integrated control∕structural optimization problem. Further, the writers are currently using them to develop large adaptive∕smart structures.     

Software Framework for Parameter Updating and Finite-Element Response Sensitivity Analysis

The finite-element software framework OpenSees is extended with parameter updating and response sensitivity capabilities to support client applications such as reliability, optimization, and system identification. Using software design patterns, member properties, applied loadings, and nodal coordinates can be identified and repeatedly updated in order to create customized finite-element model updating applications. Parameters are identified using a Chain of Responsibility software pattern, where objects in the finite-element model forward a parameterization request to component objects until the request is handled. All messages to identify and update parameters are passed through a Facade that decouples client applications from the finite-element domain of OpenSees. To support response sensitivity analysis, the Strategy design pattern facilitates multiple approaches to evaluate gradients of the structural response, whereas the Visitor pattern ensures that objects in the finite-element domain make the proper contributions to the equations that govern the response sensitivity. Examples demonstrate the software design and the steps taken by representative finite-element model updating and response sensitivity applications.