Recursive Transformation Research Articles

실시간 조종미계수 추정에 의한 무인비행기 조종면 고장검출

In case of an abnormal condition of control surface, the real-time estimation of aerodynamic derivatives are required for the reconfigurable control system to be flight for missions or return to the head office. The goal of this paper is to represent a technique of fault detection to the control surface as a base research to the fault tolerant control system for safety improvement of UAV. The real-time system identification for the fault detection to the control surface was applied with the recursive Fourier Transform and verified through the HILS and flight test. The failures of the control surface are detected by comparing the control derivatives in fault condition with the normal condition. As a result from the flight test, we have confirmed that the control derivatives of fault condition less than about 50% in the normal condition.

매개변수 추정 및 모델추종 적응제어기법을 이용한재형상 비행제어시스템 연구

*** † In this paper, a reconfigurable model following flight control method is proposed based on direct adaptive scheme using parameter estimation. Proposed method possesses fault detection and isolation capabilities as well as fault tolerance property. Adaptive control scheme updates the control gains to make the system output follow the reference output even when fault occurs. By adopting the parameter estimation method in frequency domain, system model changes due to fault can be estimated. The Fourier transformation and recursive Fourier transformation are used for system identification. With the help of Fourier transform, the proposed adaptive control algorithm guarantees the system stability and improves the system characteristics. To evaluate the performance of the proposed control method, numerical simulation is performed.

On the complexity of typechecking top-down XML transformations

We investigate the typechecking problem for XML transformations: statically verifying that every answer to a transformation conforms to a given output schema, for inputs satisfying a given input schema. As typechecking quickly turns undecidable for query languages capable of testing equality of data values, we return to the limited framework where we abstract XML documents as labeled ordered trees. We focus on simple top-down recursive transformations motivated by XSLT and structural recursion on trees. We parameterize the problem by several restrictions on the transformations (deleting, non-deleting, bounded width) and consider both tree automata and DTDs as input and output schemas. The complexity of the typechecking problems in this scenario ranges from PTIME to EXPTIME .

Lines And Circles: Images Of Time In A Panará Village

This article is an analysis of dual organization from the perspective of Panará people in central Brazil. It is suggested that the circular layout of villages with a central men's house can be read as instantiating distinct forms of temporality such that recursive transformation on the periphery is opposed to innovative transformation at the centre. Furthermore, I suggest that the tendency for innovation at the centre makes this the privileged space in which to encounter and incorporate people and things which come from the outside, beyond the circle of village houses. In this sense it may be more correct, as Lévi‐Strauss argued, to think of binary opposition as being a form of triadic organization. Finally, I argue that binary ways of organizing the world among the Panará are not based on the opposition of nature to culture but rather on the encounter between Panará and enemy‐others. As these categories have changed through history, so ways of instantiating the difference between selves and others among the Panará have also transformed.

Recursive filtering Radon-Ambiguity Transform algorithm for detecting multi-LFM signals

In multi-LFM signal condition, Radon-Ambiguity Transform (RAT) of the strong LFM component has strong suppression effect on that of the weak LFM component. A method named as Recursive Filtering RAT (RFRAT) algorithm is proposed for solving this problem. By fully using of the Maximum Likelihood (ML) estimation value of the frequency modulation rate got by RAT, RFRAT can detect the noisy multi-LFM signals out step by step. The merit of this new method is validated by an illustrative example in low Signal-to-Noise-Ratio (SNR) condition.

Wavelet analysis of images with thinning of the readings in checkerboard order

This paper discusses the wavelet transformation of an image, based on the thinning of its readings in checkerboard order. A recursive transformation algorithm is constructed, its features and basis functions are investigated, and filters are obtained that can be used with it. It is demonstrated that this transformation is efficient for constructing image contours.

Frege's unofficial arithmetic

AbstractI show that any sentence of nth-order (pure or applied) arithmetic can be expressed with no loss of compositionality as a second-order sentence containing no arithmetical vocabulary, and use this result to prove a completeness theorem for applied arithmetic. More specifically. I set forth an enriched second-order language L. a sentence of L (which is true on the intended interpretation of L), and a compositionally recursive transformation Tr defined on formulas of L, and show that they have the following two properties: (a) in a universe with at least ℶn−2 objects, any formula of nth-order (pure or applied) arithmetic can be expressed as a formula of L, and (b) for any sentence of is a second-order sentence containing no arithmetical vocabulary, and

A unified algebraic transformation approach for parallel recursive and adaptive filtering and SVD algorithms

In this paper, a unified algebraic transformation approach is presented for designing parallel recursive and adaptive digital filters and singular value decomposition (SVD) algorithms. The approach is based on the explorations of some algebraic properties of the target algorithms' representations. Several typical modern digital signal processing examples are presented to illustrate the applications of the technique. They include the cascaded orthogonal recursive digital filter, the Givens rotation-based adaptive inverse QR algorithm for channel equalization, and the QR decomposition-based SVD algorithms. All three examples exhibit similar throughput constraints. There exist long feedback loops in the algorithms' signal flow graph representation, and the critical path is proportional to the size of the problem. Applying the proposed algebraic transformation techniques, parallel architectures are obtained for all three examples. For cascade orthogonal recursive filter, retiming transformation and orthogonal matrix decompositions (or pseudo-commutativity) are applied to obtain parallel filter architectures with critical path of five Givens rotations. For adaptive inverse QR algorithm, the commutativity and associativity of the matrix multiplications are applied to obtain parallel architectures with critical path of either four Givens rotations or three Givens rotations plus two multiply-add operations, whichever turns out to be larger. For SVD algorithms, retiming and associativity of the matrix multiplications are applied to derive parallel architectures with critical path of eight Givens rotations. The critical paths of all parallel architectures are independent of the problem size as compared with being proportional to the problem size in the original sequential algorithms. Parallelism is achieved at the expense of slight increase (or the same for the SVD case) in the algorithms' computational complexity.

Transforming loops to recursion for multi-level memory hierarchies

Recently, there have been several experimental and theoretical results showing significant performance benefits of recursive algorithms on both multi-level memory hierarchies and on shared-memory systems. In particular, such algorithms have the data reuse characteristics of a blocked algorithm that is simultaneously blocked at many different levels. Most existing applications, however, are written using ordinary loops. We present a new compiler transformation that can be used to convert loop nests into recursive form automatically. We show that the algorithm is fast and effective, handling loop nests with arbitrary nesting and control flow. The transformation achieves substantial performance improvements for several linear algebra codes even on a current system with a two level cache hierarchy. As a side-effect of this work, we also develop an improved algorithm for transitive dependence analysis (a powerful technique used in the recursion transformation and other loop transformations)that is much faster than the best previously known algorithm in practice.

A spectral recursive transformation method for electromagnetic waves in generalized anisotropic layered media

A transition-matrix method is commonly used to deal with the problems of plane wave scattering from and the Green's function for multilayered generalized anisotropic media. The boundary conditions at the source interfaces are matched numerically. This method, although rigorous analytically, causes numerical singularities in the matrix inversion when the spectral fields are highly attenuating. A recursive variable transformation method is developed to deal with the exponentially growing or decaying terms associated with the spectral matrix method. The proposed scheme is suitable for numerical analysis of generalized anisotropic layers including uniaxial and biaxial materials, biased ferrites, magnetoplasmas, chiral and bi-anisotropic materials without increasing computer time. Applications of the recursive method are highlighted through examples of radiation and scattering from a three-layer ferrite structure and a conductor-backed magnetoplasma layer.

Robust Estimation in the Presence of Noise Uncertainty and Unmodeled Dynamics

ABSTRACT This paper considers robust identification for discrete-time stochastic system consisting of a modeled part which is described with ARMAX process and unmodeled dynamics. The noise distribution belongs to a specified class of distributions and such assumption introduces in recursive algorithm nonlinear transformation of prediction error. Under the standard conditions imposed on the modeled system part, it is shown that the estimation error converges to a limit which explicitly depends on the unmodeled dynamics.

Adaptive Estimation in the Panel Data Error Component Model with Heteroskedasticity of Unknown Form

The authors show that the adaptive estimation result for the heteroskedasticity of an unknown form time-series (or cross-section) model can be generalized to the panel data error components model. The authors give recursive transformations that change the error term of a random effects model and the first differenced error term of a fixed effects model into classical errors. They also propose a modified Breusch-Pagan test for testing the random individual effects. Monte Carlo evidence suggests that the proposed estimator performs adequately in small samples. Copyright 1994 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Bayes inference in regression models with ARMA (p, q) errors

We develop practical and exact methods of analyzing ARMA(p, 4) regression error models in a Bayesian framework by using the Gibbs sampling and Metropolis-Hastings algorithms, and we prove that the kernel of the proposed Markov chain sampler converges to the true density. The procedures can be applied to pure ARMA time series models and to determine features of the likelihood function by choosing appropriate diffuse priors. Our results are unconditional on the initial observations. We also show how the algorithm can be further simplified for the important special cases of stationary AR(p) and invertible MA(q) models. Recursive transformations developed in this paper to diagonalize the covariance matrix of the errors should prove useful in frequentist estimation. Examples with simulated and actual economic data are presented. KPJ~ ~~ourls: Gibbs sampling; Metropolis-Hastings algorithm; Data augmentation; Time series; ARMA processes; Markov chain; Bayesian statistics

Computer-aided detection of clustered microcalcifications: an improved method for grouping detected signals.

A computerized scheme for the automated detection of clustered microcalcifications from digital mammograms is being developed. This scheme is one part of an overall package for computer-aided diagnosis (CAD), the purpose of which is to assist radiologists in detecting and diagnosing breast cancer. One important step in the computer detection scheme is to group or cluster microcalcifications, since clustered microcalcifications are more clinically significant than are isolated microcalcifications. Previously a "growing" technique in which signals (possible microcalcifications) were clustered by grouping those that were within some predefined distance from the center of the growing cluster was used. In this paper, a new technique for grouping signals, which consists of two steps, is introduced. First, signals that may be several pixels in area are reduced to single pixels by means of a recursive transformation. Second, the number of signals (nonzero pixels) within a small region, typically 3.2 x 3.2 mm, are counted. Only if three or more signals are present within such a region are they preserved in the output image. In this way, isolated signals are eliminated. Furthermore, this method can eliminate falsely detected clusters, which were identified by a previous detection scheme, based on the spatial distribution of signals within the cluster. The differences in performance of the CAD scheme for detecting clustered microcalcifications using the old and new clustering techniques was measured using 78 mammograms, containing 41 clusters.(ABSTRACT TRUNCATED AT 250 WORDS)

Recursive operations in image algebra

The image algebra, developed by Ritter et al. at the University of Florida, is an algebraic structure for image processing. The three commonly used high-level image-template operations provided by the image algebra are the generalized convolution ⊕, the additive maximum or generalized lattice convolution {ie23-1}, and the multiplicative maximum {ie23-2}. These are used to realize various nonrecursive image transformations, including morphological transformations. Along with nonrecursive transformations, a class of recursive transformations, such as IIR filters, adaptive dithering, and predictive coding, are also widely used in signal and image processing. In this paper the notions of recursive templates and recursive template operations are introduced; these allow the image algebra to express a set of linear and nonlinear recursive transformations. Algebraic properties of these recursive operations are given, providing a mathematical basis for recursive template composition and decomposition. Finally, applications of recursive template operations in specifying some image processing algorithms are presented.

Decomposition of the density of states via the recursion method

A scheme for a fast decomposition of the total density of states evaluated by the recursion method is presented. It is suggested that all the projected densities can be obtained in a single recursion calculation instead of applying the complete recursion procedure to each projection separately. The proposed scheme appears to be exact for the correct choice of the initial vector of the recursion transformation. It is shown that when the random initial vector approach to the total density of states is implemented, good results can be obtained, in particular for calculating the partial densities of states. The applicability and efficiency of the proposed method are demonstrated on two model systems. A simple criterion of reliability is formulated. Possible ways to eliminate spurious effects caused by the random initial vector approach are discussed.

Comparative study of dynamic analysis techniques in vehicle simulation

Several dynamic analysis techniques are compared with a planar vehicle model. Cartesian formulation, suspension superelement technique, velocity transformation, and recursive formula are compared. The relation between the recursive formula and velocity transformation is investigated. When those techniques are applied to a planar vehicle with two independent suspensions, the efficiency of those methods was compared. The computational efficiency of the recursive formula was higher than those of other methods for the specific planar vehicle example.

Recursive transformation matrices for linear dynamic system models

In time series analyses and forecasting, dynamic linear models of canonical form are quite often used, specially in Generalised Exponentially Weighted Regression (GEWR) type models, introduced by Harrison and Akram (1982) and Akram (1984). This form is convenient, but usually not attractive for operation since the meaning of the parameters is not clear. To overcome this problem one needs a system of dynamic linear models in diagonal or any other meaningful form similar to canonical form. This is obtained by reparameterisation of a model to a desired form by similarity transformation of one system to another system through a transformation matrix. A general analytical expression for the elements of this matrix and its inverse, specially in case of canonical to diagonal transformation, is not known. One needs to compute these elements each time a transformation is sought. To ease this cumbersome problem a general recursive form of transformation matrix along with its inverse is presented for canonical to diagonal transformation. This general result apart from simplifying the process of transformation of linear dynamic systems helps us to reparameterise the models to a desired form.

Computational Approach To Large Quam Dynamical Problems

The organizational structure is described for a new program that permits computa tions on a variety of quantum mechanical problems in chemical dynamics and spec troscopy. Particular attention was devoted to developing and using algorithms that exploit the capabilities of current vector supercomputers. A key component in this procedure is the recursive transformation of the large sparse Hamiltonian matrix into a much smaller tridiagonal matrix. An ap plication to time-dependent laser-mole cule energy transfer is presented. Rate of energy deposition in the multimode mole cule for systematic variations in the mo lecular intermode coupling parameters is emphasized.

Density of localized states near the band edge of disordered systems.

The band-tail density of states for the tight-binding model with Gaussian distribution of site energies is calculated numerically in one, two, and three dimensions by use of the recursive transformation method. Our results confirm the band-tail scaling properties as predicted by the Halperin-Lax theory but indicate that in 3D, the near-tail behavior displayed by the model is qualitatively distinct from the simple exponential as deduced from experimental data. Implications are discussed.