Explicit Pseudodynamic Algorithm with Improved Stability Properties

An explicit pseudodynamic algorithm with an improved stability property is proposed herein. This algorithm is shown to be unconditionally stable for any linear elastic systems and any instantaneous stiffness softening systems. The most attracting stability property is that it can have unconditional stability for the instantaneous hardening systems with the instantaneous degree of nonlinearity less than or equal to 2. This property has never been found among the currently available explicit algorithms. Hence, it may be applied to perform a general pseudodynamic test without considering the stability problem since it is rare for a civil engineering structure whose instantaneous degree of nonlinearity is greater than 2. This explicit algorithm can be implemented as a common explicit pseudodynamic algorithm, such as the use of the Newmark explicit method, since it does not involve any iteration procedure. In addition, it possesses comparable accuracy as that of a general second-order accurate integration method such as the Newmark explicit method. Both numerical and error propagation properties are analytically studied and numerical experiments are used to confirm these properties. Actual pseudodynamic tests attested to the feasibility of this proposed explicit pseudodynamic algorithm.     

Explicit Pseudodynamic Algorithm with Unconditional Stability

An unconditionally stable explicit pseudodynamic algorithm is proposed herein. This pseudodynamic algorithm can be implemented as simply as the very commonly used explicit pseudodynamic algorithms, such as the central difference method and the Newmark explicit method as reported in 1959. Thus, it can be used to perform pseudodynamic tests without using any iterative scheme or extra hardware that is generally needed by the currently available implicit pseudodynamic algorithms. This integration method is second-order accurate and the most promising property of this explicit pseudodynamic algorithm is its unconditional stability. In addition, it possesses much better error propagation properties when compared to the Newmark explicit method and the central difference method.     

Enhanced, Unconditionally Stable, Explicit Pseudodynamic Algorithm

In performing a pseudodynamic test, an explicit method is generally preferred over an implicit method since it involves no iteration procedure or extra hardware that is often needed for an implicit method. However, its integration time step is usually limited by stability. Hence, it is very promising for the pseudodynamic testing if an explicit method can have unconditional stability, which might eliminate the limitation on time step for the testing of a multiple degree of freedom system or a substructure system. Although an explicit pseudodynamic algorithm with unconditional stability has been successfully implemented and its superior characteristics have been identified, an enhanced unconditionally stable explicit pseudodynamic algorithm is further proposed. In this study, it is verified that both explicit pseudodynamic algorithms possess the same numerical characteristics in the step-by-step integration. However, the newly developed explicit pseudodynamic algorithm shows better error propagation properties when compared to that developed previously.     

Error Propagation in Implicit Pseudodynamic Testing of Nonlinear Systems

Error propagation analysis of an implicit pseudodynamic algorithm has been developed for linear elastic systems. However, these error propagation results might not be applicable to nonlinear systems. Since the pseudodynamic testing method aims at investigating the nonlinear behavior of a seismically loaded structure it is important to perform the error propagation analysis of the implicit pseudodynamic algorithm for nonlinear systems. A technique to conduct the nonlinear error propagation analysis of an implicit pseudodynamic algorithm is constructed and is illustrated by analyzing the constant average acceleration method. Theoretical results reveal that the numerical and error propagation properties for nonlinear systems are generally inherited from those of linear elastic systems although some properties are affected by the step degree of nonlinearity. It is verified that the most important property of unconditional stability is preserved for nonlinear systems for a complete pseudodynamic test procedure even if the convergence error is present. It is concluded that error propagation for the improved implementation is superior to that of the direct implementation and is consistent with that developed for linear elastic systems.     

A family of explicit algorithms for general pseudodynamic testing

A new family of explicit pseudodynamic algorithms is proposed for general pseudodynamic testing. One particular subfamily seems very promising for use in general pseudodynamic testing since the stability problem for a structure does not need to be considered. This is because this subfamily is unconditionally stable for any instantaneous stiffness softening system, linear elastic system and instantaneous stiffness hardening system that might occur in the pseudodynamic testing of a real structure. In addition, it also offers good accuracy when compared to a general second-order accurate method for both linear elastic and nonlinear systems.     

Linearly Implicit Time Integration Methods for Real-Time Dynamic Substructure Testing

The simulation in real time of heterogeneous systems has to guarantee that the time integration of the equations of motion is always successfully completed within an a priori fixed sampling time interval. Therefore, numerical and/or physical substructures as well as numerical solution methods have to be adapted to the needs of real-time simulations. Monolithic stable numerical methods are implicit and cannot be easily used in real-time applications because of their iterative strategies necessary to solve the nonlinear corrector equations. As an alternative, in the present paper, we consider linearly implicit Rosenbrock-based L-stable real-time (LSRT) compatible algorithms with both two-stage and three-stage. Moreover, other linearly implicit structural integrators used nowadays to perform coupled simulations in real time are introduced too. Successively, typical properties of monolithic algorithms are shown when large time steps are employed. The loss of stability and the reduction of accuracy of these algorithms, when applied to coupled systems caused by kinematically closed loops, are analyzed in-depth through a split-inertia substructured system. In this respect, the benefits of the L-stability property are shown. Finally, the performance of the algorithms under investigation appears in a number of more realistic tests considering both nonstiff and stiff substructures.     

Explicit Integration Method for Extended-Period Simulation of Water Distribution Systems

Extended-period simulation of incompressible and inertialess flow in water distribution systems is normally done using numerical integration techniques, although regression methods are also sometimes employed. A new method for extended-period simulation, called the explicit integration (EI) method, is proposed. The method is based on the premise that a complex water distribution system can be represented by a number of simple base systems. The simple base systems are selected in such a way that their dynamic equations can be solved through explicit integration. In this paper a simple base system consisting of a fixed-head reservoir feeding a tank through a single pipeline is analyzed. It is then illustrated how a complex water distribution system can be decoupled into simple base systems and its dynamic behavior simulated using a stepwise procedure. The EI method is compared to the commonly used Euler numerical integration method using two example networks. It is shown that the accuracy of the EI method is considerably better than that of the Euler method for the same computational effort.     

Influence of Implicit Integration Scheme on Prediction of Shear Band Formation

Implicit integration schemes for elastoplastic constitutive equations have been developed in recent years as an alternative to explicit schemes. The consistent tangent constitutive matrix Dcon that results from implicit schemes makes the global stiffness matrix consistent with the implicit integration procedure and differs from the traditional continuum tangent constitutive matrix Dep that results from explicit schemes. Onset of strain localization and shear banding has been traditionally predicted using the continuum tangent constitutive matrix. It is shown that different criteria for onset of shear-band formation are obtained depending on whether Dcon or Dep is used. It is shown that shear band prediction using Dcon is step-size dependent, and that the use of Dcon influences the predicted onset of strain localization in frictional materials. An analytical equation for prediction of the onset of shear-band formation using Dcon for the Mohr–Coulomb model is developed, and a numerical example is presented.     

Development of Direct Integration Algorithms for Structural Dynamics Using Discrete Control Theory

In structural dynamics, integration algorithms are often used to obtain the solution of temporally discretized equations of motion at selected time steps. Various time integration algorithms have been developed in the time domain using different methods. In order for an integration algorithm to be reliable it must be stable and accurate. A discrete transfer function is used to study the properties of integration algorithms. A pole mapping rule from control theory in conjunction with a discrete transfer function is used to develop new integration algorithms for obtaining solutions to structural dynamics problems. A new explicit integration algorithm, called the CR (Chen and Ricles) algorithm, is subsequently developed based on the proposed method. The properties of the algorithm are investigated and compared with other well established algorithms such as the Newmark family of integration algorithms. By assigning proper stable poles to the discrete transfer function the newly developed CR explicit algorithm is unconditionally stable and has the same accuracy as the Newmark method with constant acceleration. In addition, the CR algorithm is based on expressions for displacement and velocity that are both explicit in form, making it an appealing integration algorithm for solving structural dynamics problems.     

Equivalent Linearization for the Nonstationary Response Analysis of Nonlinear Systems with Random Parameters

This paper presents an approach for analyzing nonlinear systems with parameter uncertainty subjected to stochastic excitation. The uncertain parameters are modeled as time-independent random variables. A general solution procedure based on equivalent linearization is presented. The set of orthogonal polynomials associated with the probability density function is used as the solution basis for the response moments. In addition, the instantaneous equivalent stiffness and damping matrices are approximated as quadratic random functions. The resulting Liapunov system with explicit random coefficients can then be converted into a deterministic system using the method of weighted residuals. Applications to single-degree-of-freedom uncertain systems are given and the accuracy of the results is validated.     

Multigrid Preconditioner for Unstructured Nonlinear 3D FE Models

Multigrid and multigrid-preconditioned conjugate-gradient solution techniques applicable for unstructured 3D finite-element models that may involve sharp discontinuities in material properties, multiple element types, and contact nonlinearities are developed. Their development is driven by the desire to efficiently solve models of rigid pavement systems that require explicit modeling of spatially varying and discontinuous material properties, bending elements meshed with solid elements, and separation between the slab and subgrade. General definitions for restriction and interpolation operators applicable to models composed of multiple, displacement-based isoparametric finite-element types are proposed. Related operations are used to generate coarse mesh element properties at integration points, allowing coarse-level coefficient matrices to be computed by a simple assembly of element stiffness matrices. The proposed strategy is shown to be effective on problems involving spatially varying material properties, even in the presence of large variations within coarse mesh elements. Techniques for solving problems with nodal contact nonlinearities using the proposed multigrid methods are also described. The performance of the multigrid methods is assessed for model problems incorporating irregular meshes and spatially varying material properties, and for a model of two rigid pavement slabs subjected to thermal and axle loading that incorporates nodal contact conditions and both solid and bending elements.     

A method for judging measures of stochastic dependence: Further comments on the current controversy.

A large number of reports have been published on stochastic independence (SI) between implicit and explicit measures of memory. This is often taken to imply that different memory systems mediate implicit and explicit memory performance. In these cases, SI is inferred from contingency analysis of overall success rates in 2 memory tasks when the performance in 1 or both of the tasks is, to a large extent, mediated by factors other than memory. Typically, the difference between performance with studied and nonstudied items is not large in implicit memory tasks. It is argued that this must be taken into account when evaluating the contingency analysis. A method is presented for estimating the relevant joint and conditional probabilities, assuming that the aspects of performance in the 2 tasks that are related to memory are dependent to the maximum possible extent. The method is applied to a number of published studies, and it is shown that the difference between these estimated probabilities and those given by SI is too small to allow any conclusion to be drawn about memory systems from contingency analysis of data reported in these studies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The cognitive and neural architecture of sequence representation.

The authors theorize that 2 neurocognitive sequence-learning systems can be distinguished in serial reaction time experiments, one dorsal (parietal and supplementary motor cortex) and the other ventral (temporal and lateral prefrontal cortex). Dorsal system learning is implicit and associates noncategorized stimuli within dimensional modules. Ventral system learning can be implicit or explicit. It also allows associating events across dimensions and therefore is the basis of cross-task integration or interference, depending on degree of cross-task correlation of signals. Accordingly, lack of correlation rather than limited capacity is responsible for dual-task effects on learning. The theory is relevant to issues of attentional effects on learning; the representational basis of complex, sequential skills; hippocampal- versus basal ganglia-based learning; procedural versus declarative memory; and implicit versus explicit memory. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Implicit memory: Retention without remembering.

Explicit measures of human memory, such as recall or recognition, reflect conscious recollection of the past. Implicit tests of retention measure transfer (or priming) from past experience on tasks that do not require conscious recollection of recent experiences for their performance. The article reviews research on the relation between explicit and implicit memory. The evidence points to substantial differences between standard explicit and implicit tests, because many variables create dissociations between these tests. For example, although pictures are remembered better than words on explicit tests, words produce more priming than do pictures on several implicit tests. These dissociations may implicate different memory systems that subserve distinct memorial functions, but the present argument is that many dissociations can be understood by appealing to general principles that apply to both explicit and implicit tests. Phenomena studied under the rubric of implicit memory may have important implications in many other fields, including social cognition, problem solving, and cognitive development. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Memory systems do not divide on consciousness: Reinterpreting memory in terms of activation and binding.

There is a popular hypothesis that performance on implicit and explicit memory tasks reflects 2 distinct memory systems. Explicit memory is said to store those experiences that can be consciously recollected, and implicit memory is said to store experiences and affect subsequent behavior but to be unavailable to conscious awareness. Although this division based on awareness is a useful taxonomy for memory tasks, the authors review the evidence that the unconscious character of implicit memory does not necessitate that it be treated as a separate system of human memory. They also argue that some implicit and explicit memory tasks share the same memory representations and that the important distinction is whether the task (implicit or explicit) requires the formation of a new association. The authors review and critique dissociations from the behavioral, amnesia, and neuroimaging literatures that have been advanced in support of separate explicit and implicit memory systems by highlighting contradictory evidence and by illustrating how the data can be accounted for using a simple computational memory model that assumes the same memory representation for those disparate tasks. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Classical conditioning of autonomic fear responses is independent of contingency awareness.

The role of contingency awareness in classical conditioning experiments using human subjects is currently under debate. This study took a novel approach to manipulating contingency awareness in a differential Pavlovian conditioning paradigm. Complex sine wave gratings were used as visual conditional stimuli (CS). By manipulating the fundamental spatial frequency of the displays, we were able to construct pairs of stimuli that varied in discriminability. One group of subjects was given an “easy” discrimination, and another was exposed to a “difficult” CS+ and CS–. A 3rd group was exposed to a stimulus that was paired with the unconditional stimulus (UCS) 50% of the time and served as a control. Skin conductance response (SCR) and continuous UCS expectancy data were measured concurrently throughout the experiment. Differential UCS expectancy was found only in the easy discrimination group. Differential SCRs were found in the easy discrimination group as well as in the difficult discrimination group, but not in the 50% contingency control. The difficult discrimination group did not exhibit differential UCS expectancy but did show clear differential SCR. These observations support a dual process interpretation of classical conditioning whereby conditioning on an implicit level can occur without explicit knowledge about the contingencies. The role of contingency awareness in classical conditioning experiments using human subjects is currently under debate. This study took a novel approach to manipulating contingency awareness in a differential Pavlovian conditioning paradigm. Complex sine wave gratings were used as visual conditional stimuli (CS). By manipulating the fundamental spatial frequency of the displays, we were able to construct pairs of stimuli that varied in discriminability. One group of subjects was given an “easy” discrimination, and another was exposed to a “difficult” CS+ and CS–. A 3rd group was exposed to a stimulus that was paired with the unconditional stimulus (UCS) 50% of the time and served as a control. Skin conductance response (SCR) and continuous UCS expectancy data were measured concurrently throughout the experiment. Differential UCS expectancy was found only in the easy discrimination group. Differential SCRs were found in the easy discrimination group as well as in the difficult discrimination group, but not in the 50% contingency control. The difficult discrimination group did not exhibit differential UCS expectancy but did show clear differential SCR. These observations support a dual process interpretation of classical conditioning whereby conditioning on an implicit level can occur without explicit knowledge about the contingencies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Understanding implicit and explicit attitude change: A systems of reasoning analysis.

There is considerable controversy about how to conceptualize implicit and explicit attitudes, reflecting substantial speculation about the mechanisms involved in implicit and explicit attitude formation and change. To investigate this issue, the current work examines the processes by which new attitudes are formed and changed and how these attitudes predict behavior. Five experiments support a systems of reasoning approach to implicit and explicit attitude change. Specifically, explicit attitudes were shaped in a manner consistent with fast-changing processes, were affected by explicit processing goals, and uniquely predicted more deliberate behavioral intentions. Conversely, implicit attitudes reflected an associative system characterized by a slower process of repeated pairings between an attitude object and related evaluations, were unaffected by explicit processing goals, uniquely predicted spontaneous behaviors, and were exclusively affected by associative information about the attitude object that was not available for higher order cognition. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Regression analysis of the log odds ratio: a method for retrospective studies

Quantification of the dependence of the odds ratio on concomitant variables associated with each of several 2 X 2 tables, using a regression model proposed by Zelen [1971], is an important tool for retrospective studies in epidemiology, An "exact" analysis may be based on the conditional likelihood obtained by fixing all the marginal totals. A symptotically this approach is equivalent to use of an unconditional log-linear model. The method is used to reanalyze data reported by Kneale [1971] on the relationship between obstetric radiation and childhood cancer.     

A modified EM algorithm for estimation in generalized mixed models

Application of the EM algorithm for estimation in the generalized mixed model has been largely unsuccessful because the E-step cannot be determined in most instances. The E-step computes the conditional expectation of the complete data log-likelihood and when the random effect distribution is normal, this expectation remains an intractable integral. The problem can be approached by numerical or analytic approximations; however, the computational burden imposed by numerical integration methods and the absence of an accurate analytic approximation have limited the use of the EM algorithm. In this paper, Laplace's method is adapted for analytic approximation within the E-step. The proposed algorithm is computationally straightforward and retains much of the conceptual simplicity of the conventional EM algorithm, although the usual convergence properties are not guaranteed. The proposed algorithm accommodates multiple random factors and random effect distributions besides the normal, e.g., the log-gamma distribution. Parameter estimates obtained for several data sets and through simulation show that this modified EM algorithm compares favorably with other generalized mixed model methods.