Adaptive robust control for seismically excited structures: The Chi‐Chi earthquake

Abstract

This paper proposes control for a seismically excited N story building. Intrinsic properties of the building's own robustness are analyzed by using an input‐to‐state stability method and solving a linear matrix inequality. Then frequency analysis on the base isolation gives guidelines for choosing parameters and also reveals the narrow flexibility of the base parameters. This frequency analysis, on the other hand, shows the need for a hybrid controller. Therefore a passive baseisolated building model is considered with an active hydraulic actuator. This passive and active combined hybrid controller is then designed using the backsteppping approach. The parametric uncertainties of both the building and the actuator are considered. Therefore an adaptive backstepping controller is designed. An H⁸ criterion is given to attenuate the effects of seismic excitation. Numerical simulations are carried out using the Chi‐Chi earthquake of Taiwan as an excitation source on a twelve story building. Results show that the hybrid system design is valid, with reasonable control force.     

A study on the performance of natural neighbour‐based Galerkin methods

In this paper we address the problem of improving natural element simulations in terms of computational cost. Several problems are discussed, that include an efficient natural neighbour search algorithm and a comparison of different natural neighbour‐based interpolation algorithms. In particular, we review the so‐called pseudo‐NEM, a moving least squares‐like approximation scheme that employs natural neighbours, and compare it with traditional Sibson and Laplace interpolation schemes in terms of both accuracy and computational cost. Some examples in linear Elasticity and visco‐plasticity are analysed in order to test the proposed schemes in engineering problems. Copyright © 2007 John Wiley & Sons, Ltd.     

A ‘best points’ interpolation method for efficient approximation of parametrized functions

We present an interpolation method for efficient approximation of parametrized functions. The method recognizes and exploits the low‐dimensional manifold structure of the parametrized functions to provide good approximation. Basic ingredients include a specific problem‐dependent basis set defining a low‐dimensional representation of the parametrized functions, and a set of ‘best interpolation points’ capturing the spatial‐parameter variation of the parametrized functions. The best interpolation points are defined as solution of a least‐squares minimization problem which can be solved efficiently using standard optimization algorithms. The approximation is then determined from the basis set and the best interpolation points through an inexpensive and stable interpolation procedure. In addition, an a posteriori error estimator is introduced to quantify the approximation error and requires little additional cost. Numerical results are presented to demonstrate the accuracy and efficiency of the method. Copyright © 2007 John Wiley & Sons, Ltd.     

A series of energy conserving algorithms for structural dynamics

Abstract

A series of step‐by‐step integration methods has been effectively developed which does not increase the total number of equations of motion and avoids the use of the derivatives of external force. The well‐known Newmark β method [16] with β = 1/4 is the lowest order of accuracy of this series of methods. All the algorithms of this series are unconditionally stable, without overshoot in displacement or in velocity, and they do not possess any numerical dissipations. The rapid changes of dynamic loading can be automatically overcome. It is also verified that the higher the order of the integration method, the more accurate. Consequently, the higher‐order algorithms of this series allow the use of a large time step in step‐by‐step dynamic analysis. Thus, they are competitive in dynamic analysis, especially when the response of a long duration is of interest.     

New minimum error rate algorithms for DFE

Abstract

We propose new adaptive minimum symbol error rate algorithms (MSER) for decision feedback equalization over M‐ary PAM channels. In addition, we take into consideration biased as well as unbiased estimates leading to two major versions respectively called biased MSER (BMSER) and unbiased MSER (UMSER). The exact forms of these algorithms are computationally complex and require channel parameter information and thus must be processed off‐line. We thus modify the exact forms into stochastic and simplified versions to reduce computation load. The stochastic version requires no channel information and hence can be processed on‐line, but at the cost of convergence rate. Merits and characteristics of various versions are discussed and compared.     

Analysis and optimal control of discrete time‐varying systems Via Hahn polynomials

Abstract

Recently, the problem of analysis and optimal control of discrete time‐invariant systems has been extensively studied using finite series expansion of discrete orthogonal polynomials. This paper is to extend the applicable scope of discrete orthogonal polynomials to discrete time‐varying systems. The finite set of Hahn polynomials {q_ik)], i=0, 1, …, N} is chosen as the finite series expansion basis due to its general form and useful properties. First, for treating the product of two discrete‐time functions by Hahn series expansion, a new algorithm is derived to compute the Hahn series expansion coefficients of products qi(k)q_j (k), i, j=0, 1, …, N. These Hahn coefficients are then used to establish a product operational matrix for relating the Hahn coefficient vector of a product function to those of its component functions. This product operational matrix, along with the relations for connecting the Hahn coefficient vectors of a discrete function x(k) and its time‐shifted x(k+1), is finally applied to derive computational algorithms for solving the problems of analysis and optimal control of discrete time‐varying systems via finite Hahn series. Computed results are provided to illustrate the applicability of the proposed algorithms.     

PetFMM—A dynamically load‐balancing parallel fast multipole library

Fast algorithms for the computation of N‐body problems can be broadly classified into mesh‐based interpolation methods, and hierarchical or multiresolution methods. To this latter class belongs the well‐known fast multipole method (FMM ), which offers ??(N) complexity. The FMM is a complex algorithm, and the programming difficulty associated with it has arguably diminished its impact, being a barrier for adoption. This paper presents an extensible parallel library for N‐body interactions utilizing the FMM algorithm. A prominent feature of this library is that it is designed to be extensible, with a view to unifying efforts involving many algorithms based on the same principles as the FMM and enabling easy development of scientific application codes. The paper also details an exhaustive model for the computation of tree‐based N‐body algorithms in parallel, including both work estimates and communications estimates. With this model, we are able to implement a method to provide automatic, a priori load balancing of the parallel execution, achieving optimal distribution of the computational work among processors and minimal inter‐processor communications. Using a client application that performs the calculation of velocity induced by N vortex particles in two dimensions, ample verification and testing of the library was performed. Strong scaling results are presented with 10 million particles on up to 256 processors, including both speedup and parallel efficiency. The largest problem size that has been run with the P etFMM library at this point was 64 million particles in 64 processors. The library is currently able to achieve over 85% parallel efficiency for 64 processes. The performance study, computational model, and application demonstrations presented in this paper are limited to 2D. However, the software architecture was designed to make an extension of this work to 3D straightforward, as the framework is templated over the dimension. The software library is open source under the PETS c license, even less restrictive than the BSD license; this guarantees the maximum impact to the scientific community and encourages peer‐based collaboration for the extensions and applications. Copyright © 2010 John Wiley & Sons, Ltd.     

Automated tracking of liquid velocities in a refractive index matched porous medium

Abstract

Particle tracking velocimetry is applied to flow inside a porous column at Reynolds number Re = 28. The column is composed of refractive‐index‐matched solid and liquid materials, allowing seeding particles to be tracked in a laser‐illuminated axial slice. To complement earlier results acquired for 7 mm spheres, we conduct new experiments with larger 12 mm spheres. By improving the image acquisition and analysis, we are able to process the new experiments using fully automated algorithms instead of manual tracking. As a result, greater vector yields, more accurate velocity data, and a more complete spatial coverage are achieved.     

A three‐noded shear‐flexible curved beam element based on coupled displacement field interpolations

An efficient shear‐flexible three‐noded curved beam element is proposed herein. The shear flexibility is based on Timoshenko beam theory and the element has three degrees of freedom, viz., tangential displacement (u), radial displacement (w) and the section‐rotation (θ). A quartic polynomial interpolation for flexural rotation ψ is assumed a priori. Making use of the physical composition of θ in terms of ψ and u, a novel way of deriving the polynomial interpolations for u and w is presented, by solving force‐moment and moment‐shear equilibrium equations simultaneously. The field interpolation for θ is then constructed from that of ψ and u. The procedure leads to high‐order polynomial field interpolations which share some of the generalized degrees of freedom, by means of coefficients involving material and geometric properties of the element. When applied to a straight Euler–Bernoulli beam, all the coupled coefficients vanish and the formulation reduces to classical quintic‐in‐w and quadratic‐in‐u element, with u, w, and ?w/?x as degrees of freedom. The element is totally devoid of membrane and shear locking phenomena. The formulation presents an efficient utilization of the nine generalized degrees of freedom available for the polynomial interpolation of field variables for a three‐noded curved beam element. Numerical examples on static and free vibration analyses demonstrate the efficacy and locking‐free property of the element. Copyright © 2001 John Wiley & Sons, Ltd.     

Singular‐ended spline interpolation for two‐dimensional boundary element analysis

A method of interpolation of the boundary variables that uses spline functions associated with singular elements is presented. This method can be used in boundary element method analysis of 2‐D problems that have points where the boundary variables present singular behaviour. Singular‐ended splines based on cubic splines and Overhauser splines are developed. The former provides C²‐continuity and the latter C¹‐continuity across element edges. The potentialities of the methodology are demonstrated analysing the dynamic response of a 2‐D rigid footing interacting with a half‐space. It is shown that, for a given number of elements at the soil–foundation interface, the singular‐ended spline interpolation increases substantially the displacement convergence rate and delivers smoother traction distributions. Copyright © 2000 John Wiley & Sons, Ltd.     

Cost‐effective algorithms for processor arrays with reconfigurable bus systems

Abstract

A processor array with a reconfigurable bus system (abbreviated to PARBS) is a computation model which consists of a processor array and a reconfigurable bus system. It is a very powerful computation model in that it possesses the ability to solve many problems efficiently. However, most existing efficient algorithms on PARBS's use a large number of processors to solve problems. For example, to determine the maximum (minimum) of n data items in O(l) time, O(n ²) processors are required [12]. To solve the all‐pairs shortest paths and the minimum spanning tree problems in O(log n) time, O(n ⁴) processors are required [20]. These networks will therefore become very expensive for large n. In this paper, we introduce the concept of iterative‐PARBS, which is similar to the FOR‐loop construct in sequential programming languages. The iterative‐PARBS is a building block through which the processing data can be routed several times. We can think of it as a “hardware subroutine.’’ Based on this scheme, it is possible to explore more cost‐effective, time‐efficient parallel algorithms for use in a PARBS. The following new results are derived in this study: 1. The minimum (maximum) of n data items can be determined in O(l) time on a PARBS with O(n ^1+? ) processors for any fixed 8 > 0.

2. The all‐pairs shortest paths and the minimum spanning tree problems can be solved in O (log n) time on a PARBS with O(n ^3+? ) processors for any fixed 8 > 0.

     

“Changes or not” is the question: The meaning of posttraumatic stress reactions one year after the Taiwan chi‐chi earthquake

Abstract

“Resource gains” and “resource losses”, based on the Conservation of Resources Theory, are equally important in trauma recovery. This study was to investigate their influence on the severity of post‐traumatic stress reactions and psychosocial adjustment patterns of the residents in two severely damaged townships. Five hundred and fifty six adults (157 males and 399 females) were assessed in terms of objective and subjective threat (of losses), subjective evaluations of changes in life domains and coping resources, and severity of post‐traumatic symptoms one year after the Earthquake. The results showed that those who reported “No Change”, compared to those were either “better” or “worse”, had the least severity of PTSD symptoms. The subjective evaluation of changes in life domains and subjective threat were positively associated with changes in coping resources, but not the severity of PTSD symptoms. Results are discussed from the viewpoint of Cox's Stress Model and Wu's Life‐Energy Stress Model, and it is suggested that successful coping might be accompanied by PTSD symptoms. Reconsideration and expansion of the meaning of “changed vs. unchanged” following a traumatic experience is also discussed.     

Forced convective heat and mass transfer of a water droplet (effects of vapour concentration)

Abstract

Numerically controlled flame cutting machines used in shipyards are generally equipped only with line‐segment and circle‐arc moving capabilities. This paper attacks the problem of how to approximate a given curve of arbitrary shape by a sequence of line‐segments and circle‐arcs. The given curve is represented by the cubic spline interpolation curve formed by a set of net points on the curve. An efficient method based on the nature of cubic spline is then provided to approximate the interpolation curve by a sequence of linesegments and circle‐arcs. This method has been practically employed by the China Shipbuilding Co. in production line. In order to save storage and expedite the approximation, an effective method is also provided for selecting a near minimal set of net points whose cubic spline interpolation curve can adequately represent the actual given curve. Although the techniques are developed for shipbuilding purpose, they can find applications in other fields.     

Polytope finite elements

In this paper, finite elements based on arbitrary convex and non‐convex polytopes are introduced. Polytopes in combination with natural element coordinates (NECs) permit a uniform element formulation of interpolation functions that are independent of the dimension of space, localization and the number of vertices. NECs based on the natural neighbor interpolation are restricted to the polytope and can be understood as an extension of the barycentric coordinates on simplexes. The differentiation and integration of these interpolation functions on the basis of NECs is essential for finite element approximations. The accuracy of the finite element interpolation or approximation can be controlled by either applying the h‐version or by utilizing the p‐version of the finite element method (FEM). Advantages in the handling of hanging nodes are discussed. Furthermore, we present construction methods for Lagrangian as well as for hierarchical interpolation functions based on NECs. Numerical experiments on different convex and non‐convex decompositions will show the usability, accuracy and convergence of the developed polytope FEM. Copyright © 2007 John Wiley & Sons, Ltd.     

Precipitation of secondary phases in super duplex stainless steel ZERON100 isothermally aged

Abstract

In the present paper the results of secondary phases determination and quantification in ZERON100 duplex steel, heat treated at 850–1000°C for 180–2400 s, are presented. During the isothermal heat treatments, at 850°C, the χ phase is the only phase to precipitate at α/γ boundaries and triple points, while at 900 and 950°C, χ phase is the first phase to precipitate after 180 s, followed by σ phase 300 s later. At all the temperatures the total amount of secondary phases is ～3% after <600 s aging.     

Further considerations of a 1‐subcycle parallel thinning algorithm

Abstract

In this paper, we present two improved versions of a pseudo 1‐subcycle parallel thinning algorithm which we proposed earlier [1] and describe a two‐stage structure to realize the 1‐subcycle parallel algorithm.

The purpose of the first improved algorithm is to produce the P8ET (perfect 8‐curve excluding T‐junction)‐type thin line which is well‐defined in general. This algorithm involves local branches containing T‐junctions or quasi T‐junctions. The second improved algorithm obtains an isotropic skeleton of an L‐shape pattern, such that the visual quality of a skeleton is more satisfactory. In this algorithm, another set of thinning conditions especially designed is also involved.

We also describe a two‐stage structure which consists of a thinning table and a control unit. The thinning table is used to provide the attributes of an input 3×3 local pattern. The control unit is used to check the removal of the center “1” pixel of this local pattern. The inputs of the control unit also comprise the outputs of other neighboring thinning tables. This structure can exactly implement the original 1‐subcycle parallel algorithm. The above‐mentioned algorithms have been implemented on this realized structure in this paper.

Several experiments confirm that the improved algorithms can produce the desired effective thin line, and also show that the realized structure is feasible and practicable.     

Spectral density variation mapping of cerebral waves by three‐dimensional interpolation techniques

This work focuses on interpolation methods which are proposed as solutions to the EEG source localization. First, a low pass and a high pass filter were applied to the EEG signal in order to remove EEG artifacts. Then, classical interpolation techniques such as three‐dimensional (3D) K‐nearest neighbor and 3D spline were implemented. The major contribution of this article is to develop a new interpolation method called 3D multiquadratic technique which is based on the Euclidean distances between the electrodes. A substitution of the Euclidean distance by the corresponding arc length was realized to promote the 3D spherical multiquadratic interpolation. Based on measured EEG recordings from 19 electrodes mounted on the scalp, these interpolation methods (3D K‐nearest neighbor, 3D spline, 3D multiquadratic and spherical multiquadratic) were applied to EEG recordings of 15 healthy subjects at rest and with closed eyes. The aim of EEG interpolation is to reach the maximum of the spatial resolution of EEG mapping by predicting the brain activity distribution of 109 virtual points located on the scalp surface. The evaluation of the different interpolation methods was achieved by measuring the means of the normalized root mean squared error (NRMSE) and processing time. The results showed that the multiquadratic and 3D spline interpolation methods gave the minimum normalized root mean squared error, but the multiquadratic method was characterized by the minimal processing time compared with 3D K‐nearest neighbor, 3D spline, and 3D spherical multiquadratic methods. Finally, a Spectral density variation mapping of different cerebral waves (delta, theta, alpha and beta) with 128 electrodes was generated by applying the Fast Fourier Transform (FFT). © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 191–198, 2015     

Assessment of explicit and semi‐explicit classes of model‐based algorithms for direct integration in structural dynamics

The ‘model‐based’ algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in earthquake engineering, an experimental method where the system response is simulated by dividing it into a physical and an analytical domain. The term ‘model‐based’ indicates that the algorithmic parameters are functions of the complete model of the system to enable unconditional stability to be achieved within the framework of an explicit formulation. These two features make the model‐based algorithms also potential candidates for computations in structural dynamics. Based on the algorithmic difference equations, these algorithms can be classified as either explicit or semi‐explicit, where the former refers to the algorithms with explicit difference equations for both displacement and velocity, while the latter for displacement only. The algorithms pertaining to each class are reviewed, and a new family of second‐order unconditionally stable parametrically dissipative semi‐explicit algorithms is presented. Numerical characteristics of these two classes of algorithms are assessed under linear and nonlinear structural behavior. Representative numerical examples are presented to complement the analytical findings. The analysis and numerical examples demonstrate the advantages and limitations of these two classes of model‐based algorithms for applications in structural dynamics. Copyright © 2015 John Wiley & Sons, Ltd.     

An optimal algorithm for multiplication in F256/F4

Applying an interpolation algorithm invented by D. V. Chudnovsky and G. V. Chudnovsky to the Fermat-curvex ³ + y³ = 1 overF ₄, we present a bilinear algorithm for the multiplication in theF ₄-algebraF ₂₅₆ which requires 8 essential multiplications.     

Topology optimization with incompressible materials under small and finite deformations using mixed u/p elements

This paper focuses on topology optimization utilizing incompressible materials under both small‐ and finite‐deformation kinematics. To avoid the volumetric locking that accompanies incompressibility, linear and nonlinear mixed displacement/pressure (u/p) elements are utilized. A number of material interpolation schemes are compared, and a new scheme interpolating both Young's modulus and Poisson's ratio (E ‐ν interpolation) is proposed. The efficacy of this proposed scheme is demonstrated on a number of examples under both small‐ and finite‐deformation kinematics. Excessive mesh distortions that may occur under finite deformations are dealt with by extending a linear energy interpolation approach to the nonlinear u/p formulation and utilizing an adaptive update strategy. The proposed optimization framework is demonstrated to be effective through a number of representative examples.