A unified approach to optimization of structural members under general constraints

A unified numerical approach, based on a control parameterization technique, for solving structural crosssectional optimization problems is presented. The key factor to the unified formulation lies in the framing of the objective functional and the constraints into the same unified canonical form. Consequently, the different types of objective functionals, geometrical and performance constraints can be treated in the same way, thus paving the path for the problems to be solved under a single approach using a general purpose software. To demonstrate this versatile approach, several illustrative examples of cross-sectional shape optimization of structural members under a variety of constraints were examined.     

A unified approach to pattern recognition

The paper is an outline of a new approach to pattern recognition developed by the author. A fuller introduction to the approach will appear soon.⁽¹⁾ Within the proposed framework the two principal approaches to pattern recognition—vector and syntactic—are unified.     

A unified approach to layout wirability

We consider the problem of wiring planar knock-knee mode layouts. We present a systematic approach to this problem and develop a unified framework that also applies to layouts using grids that are more general than the usual square grid, and determine all possible grids that satisfy some natural regularity criteria. We develop some specific techniques for wiring of layouts in the square grid. As one of the applications of these techniques, we give a simple characterization of two-layer wirability of an arbitrary layout.On leave from the Institute of Computer Science, Polish Academy of Sciences, P.O. Box 22, 00-901 Warsaw, Poland. W. Lipski tragically died on May 30, 1985.The work of F. P. Preparata was supported in part by the Semiconductor Research Corporation under Contract SRC RSCH 84-06-049.     

A unified approach to smoothing formulas

Based on various approaches, several different solutions to the smoothing problem have been given. The relationships between these solutions are not immediate, although they solve the same problem. Making use of a certain framework from scattering theory, we derive two families of solutions, with equations evolving forwards and backwards in time, respectively. Within these families three major previous approaches are obtained as special cases, and their relationships are clarified. The set of solutions also contains as a fourth special case a (new) backwards analog of the innovations solution. The Mayne-Fraser two-filter formula belongs to the set of backwards solutions, and within this framework certain difficulties with its interpretation can be resolved.     

A unified approach to optimal feature selection

The optimum finite set of linear observables for discriminating two Gaussian stochastic processes is derived using classical methods and distribution function theory. The results offer a new, accurate information-theoretic strategy and are superior to well-known conventional methods using statistical distance measures.     

A unified approach to deadbeat systems design

This paper is concerned with the design of a discrete-time regulator by using an observer in conjunction with a state feedback law. Previous techniques have been examined, modified, and simplified to a unified procedure. For example, in the initial step, Krylov's transformation is used which has never been applied explicitly. In the second step, an alternate use of Krylov's transformation is demonstrated to design feedback laws that achieve eigenvalue placement. In the final stage of the controller design, the combination of the observer and the state feedback law is clearly seen. Two new matrix identities are derived and applied in the transfer function manipulation.     

A unified reanalysis approach for structural analysis,design, and optimization

This study presents a unified reanalysis approach for structural analysis, design, and optimization that is based on the Combined Approximations (CA) method. The method is suitable for various analysis models (linear, nonlinear, elastic, plastic, static, dynamic), different types of structures (trusses, frames, grillages, continuum structures), and all types of design variables (cross-sectional, material, geometrical, topological). The calculations are based on results of a single exact analysis. The computational effort is usually much smaller than that needed to carry out a complete analysis of modified designs. Accurate results are achieved by low-order approximations for significant changes in the design. It is possible to improve the accuracy by considering higher-order terms, and exact solutions can be achieved in certain cases. The solution steps are straightforward, and the computational procedures presented can readily be used with general finite element systems. Typical results are demonstrated by numerical examples.     

A unified approach to reducts in dominance-based rough set approach

The Dominance-based Rough Set Approach (DRSA), which is an extension of the Rough Set Approach (RSA), analyzes a sorting problem for a given data set. Attribute reduction is one of major topics in RSA as well as DRSA. By attribute reduction, we can find an important attribute set, which is called a reduct. In this paper, we propose a new approach to reducts in DRSA. A few kinds of reducts have been already proposed in DRSA, therefore, we clarify relations among the proposed and previous ones. We prove that they are consolidated into four kinds. Moreover, we show that all kinds of reducts can be enumerated based on two discernibility matrices.     

A unified approach to synthesis of linear systems

A simple procedure for direct synthesis of linear feedback systems which is applicable to either continuous or sampled data processes is derived. Given the transfer function of the process to be controlled and constraints on desired closed-loop dynamics, the procedure yields an exact analytical solution for the transfer function of the required compensator without recourse to graphical techniques. Suitable constraints include specification of any or all closed-loop poles and/or specification of the position, velocity, or acceleration error constant. Design for specified rise time, overshoot, mean-squared error, etc., may be accomplished by using an iterative routine. The procedure is ideally suited for implementation by digital computer and has been applied to a simulated adaptive flight control system which required that the entire compensator design procedure be executed by a computer without the aid of human intervention.     

A unified approach to ranking in probabilistic databases

Ranking is a fundamental operation in data analysis and decision support and plays an even more crucial role if the dataset being explored exhibits uncertainty. This has led to much work in understanding how to rank the tuples in a probabilistic dataset in recent years. In this article, we present a unified approach to ranking and top-k query processing in probabilistic databases by viewing it as a multi-criterion optimization problem and by deriving a set of features that capture the key properties of a probabilistic dataset that dictate the ranked result. We contend that a single, specific ranking function may not suffice for probabilistic databases, and we instead propose two parameterized ranking functions, called PRF ^ω and PRF ^e, that generalize or can approximate many of the previously proposed ranking functions. We present novel generating functions-based algorithms for efficiently ranking large datasets according to these ranking functions, even if the datasets exhibit complex correlations modeled using probabilistic and/xor trees or Markov networks. We further propose that the parameters of the ranking function be learned from user preferences, and we develop an approach to learn those parameters. Finally, we present a comprehensive experimental study that illustrates the effectiveness of our parameterized ranking functions, especially PRF ^e, at approximating other ranking functions and the scalability of our proposed algorithms for exact or approximate ranking.     

A unified approach to the definition of random sequences

Using the concept of test functions, we develop a general framework within which many recent approaches to the definition of random sequences can be described. Using this concept we give some definitions of random sequences that are narrower than those proposed in the literature. We formulate an objection to some of these concepts of randomness. Using the notion of effective test function, we formulate a thesis on the true concept of randomness.     

A unified approach to content-based and fault-tolerant music recognition

In this paper, we propose a unified approach to fast index-based music recognition. As an important area within the field of music information retrieval (MIR), the goal of music recognition is, given a database of musical pieces and a query document, to locate all occurrences of that document within the database, up to certain possible errors. In particular, the identification of the query with regard to the database becomes possible. The approach presented in this paper is based on a general algorithmic framework for searching complex patterns of objects in large databases. We describe how this approach may be applied to two important music recognition tasks: The polyphonic (musical score-based) search in polyphonic score data and the identification of pulse-code modulation audio material from a given acoustic waveform. We give an overview on the various aspects of our technology including fault-tolerant search methods. Several areas of application are suggested. We describe several prototypic systems we have developed for those applications including the notify! and the audentify! systems for score- and waveform-based music recognition, respectively.     

A unified approach to the linear camera calibration problem

The camera calibration process relates camera system measurements (pixels) to known reference points in a three-dimensional world coordinate system. The calibration process is viewed as consisting of two independent phases: the first is removing geometrical camera distortion so that rectangular calibration grids are straightened in the image plane, and the second is using a linear affine transformation as a map between the rectified camera coordinates and the geometrically projected coordinates on the image plane of known reference points. Phase one is camera-dependent, and in some systems may be unnecessary. Phase two is concerned with a generic model that includes 12 extrinsic variables and up to five intrinsic parameters. General methods handling additional constraints on the intrinsic variables in a manner consistent with explicit satisfaction of all six constraints on the orthogonal rotation matrix are presented. The use of coplanar and noncoplanar calibration points is described     

A unified approach to shaft calculations using a microcomputer

This paper describes a program written for a microcomputer which allows shaft (or beam) calculations to be made for a wide range of geometrical, loading and support conditions. Expressions for generalized support conditions are developed including support flexibility and unloaded support misalignment. The program, occupying 6100 bytes of memory without problem data statements, is shown applied to a simple flexible support problem and to a complex paper-making machine shaft mounted on 21 supports.     

A structural approach to reversible computation

Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on simulations of low-level machine models. By contrast, we develop a more structural approach. We show how high-level functional programs can be mapped compositionally (i.e. in a syntax-directed fashion) into a simple kind of automata which are immediately seen to be reversible. The size of the automaton is linear in the size of the functional term. In mathematical terms, we are building a concrete model of functional computation. This construction stems directly from ideas arising in Geometry of Interaction and Linear Logic—but can be understood without any knowledge of these topics. In fact, it serves as an excellent introduction to them. At the same time, an interesting logical delineation between reversible and irreversible forms of computation emerges from our analysis.     

A feature-based approach to structural design

Despite the continuing improvements in computeraided design (CAD) systems and improvements in geometric modeling, most CAD systems are used as advanced drafting and drawing management tools by structural designers. A computer model of a structural design usually is generated by creating a detailed geometric model of the primitive components of the design and then attaching attributes, such as physical properties and loading conditions, to the various geometric components to reveal the structural characteristics of those components. Thisbottom-up approach has been inherited from early drafting techniques and contrasts sharply with a structural designer's natural way of thinking and reasoning about the design. Geometric features, on the other hand, provide high-level abstractions of design information and can be tailored to a designer's specific engineering needs. In this paper the advantages of using feature-based techniques in structural CAD systems are discussed. These techniques provide better modeling primitives for users and superior data models for CAD systems for reasoning about the geometry, topology, and engineering properties of a structure.     

A structural approach to robust control

We consider the problem of stabilizing linear stationary parametrically uncertain systems with a guaranteed stability margin. The methodology of our approach is based on the synthesis of superstable closed systems, done with the procedures derived from the block control principle and their modifications, the procedures consisting of sequential establishment of local connections in elementary blocks that provide for the superstability of each block and the closed system as a whole in the new coordinate basis. The fact that the notion of superstability is formulated in terms of the elements of the system matrix based on inequalities lets us provide for robust stability for all admissible values of indefinite parameters in such systems. The robust control algorithms that we have developed are applicable to a practically significant class of linear systems which, given that parameters change in known ranges, preserve structural controllability properties defined by the nominal system.     

A unified approach to adapt scientific visualization systems to third-party solvers

This paper presents a new unified approach to adapt scientific visualization systems to third-party solvers implemented on different software and hardware platforms. This approach allows building multiplatform visualization systems, enables automatic conversion of input and output data from any solver into a rendering-compatible format, and provides real-time generation of high-quality images. The automated adaptation of visualization systems to third-party solvers is based on ontological engineering methods. Multiplatform portability is provided by the automatic generation of a graphical user interface (GUI) for each particular operating system and by preprocessing the data to be rendered by using heuristic-based tools, which ensures compatibility with different hardware and software platforms, including desktop computers and mobile devices. In addition, an original anti-aliasing algorithm is proposed to ensure high quality of resulting images. Based on the proposed approach, a multiplatform scientific visualization system called SciVi is developed, which is successfully used for solving various real-world scientific visualization problems from different application domains.