Characteristic Matrices Research Articles

Practical technique for identifying characteristic matrices of railway vehicle carbodies based on stationary excitation tests

Practical technique for identifying characteristic matrices of railway vehicle carbodies based on stationary excitation tests

Characteristic matrices of compound operations of coverings and their relationships with rough sets

As the matrix can compactly represent numeric data, simplify problem formulation and reduce time complexity, it has many applications in most of the scientific fields. For this purpose, some types of generalized rough sets have been connected with matrices. However, covering-based rough sets which play an important role in data mining and machine learning are seldom connected with matrices. In this paper, we define three composition operations of coverings and study their characteristic matrices; Moreover, the relationships between the characteristic matrices and covering approximation operators are investigated. First, for a covering, an existing matrix representation of indiscernible neighborhoods called the type-1 characteristic matrix of the covering is recalled and a new matrix representation of neighborhoods called the type-2 characteristic matrix of the covering is proposed. Second, considering the importance of knowledge fusion and decomposition, we define three types of composition operations of coverings. Specifically, their type-1 and type-2 characteristic matrices are studied. Finally, we also explore the representable properties of covering approximation operators with respect to any covering generated by each composition operation. It is interesting to find that three types of approximation operators, which are induced by each type of composition operation of coverings, can be expressed as the Boolean product of a coefficient matrix and a characteristic vector. These interesting results suggest the potential for studying covering-based rough sets by matrix approaches.

A Second Pretabular Classical Relevance Logic

Pretabular logics are those that lack finite characteristic matrices, although all of their normal proper extensions do have some finite characteristic matrix. Although for Anderson and Belnap’s relevance logic R, there exists an uncountable set of pretabular extensions (Swirydowicz in J Symb Log 73(4):1249–1270, 2008), for the classical relevance logic $$ \hbox {KR} = \hbox {R} + \{(A\,\, \& \sim A)\rightarrow B\}$$ there has been known so far a pretabular extension: $${\mathcal L}$$ (Galminas and Mersch in Stud Log 100:1211–1221, 2012). In Section 1 of this paper, we introduce some history of pretabularity and some relevance logics and their algebras. In Section 2, we introduce a new pretabular logic, which we shall name $${\mathcal M}$$ , and which is a neighbor of $${\mathcal L}$$ , in that it is an extension of KR. Also in this section, an algebraic semantics, ‘ $${\mathcal M}$$ -algebras’, will be introduced and the characterization of $${\mathcal M}$$ to the set of finite $${\mathcal M}$$ -algebras will be shown. In Section 3, the pretabularity of $${\mathcal M}$$ will be proved.

Optimal Structure (k) Designs for Comparing Test Treatments with a Control

Mukerjee (1979) introduced structure (k) property of a factorial design. In this article, we introduce structure (k1), structure (k2) and structure (k1k2) properties of a factorial design. We establish properties of each of these structure designs in terms of the incidence and characteristic matrices of the designs. Furthermore, we develop methods of obtaining optimal R-type structure (k) designs and show that such designs are trace, A- and MV-optimal. The proposed methodologies are easy to follow and the construction of the designs comes out in a simple form.

Practical identification technique of characteristic matrices of structures from frequency response function

Practical identification technique of characteristic matrices of structures from frequency response function

The theory of parallel crc codes based on automaton models

A theoretical representation of the CRC codes with the aid of the finite automata in the Galois fields is proposed –linear finite-state machine (LFSM). We examined three types of LSC, which are distinguished by its characteristic matrices: type 1, type 2, and type 3. Three methods of the parallel CRC computation are proposed. The theorems are proven about the estimation of duration of the CRC computation by tuple-parallel method for three types of LFSM. We presented algorithms for the CRC tuple-parallel computation by the tables lookup for different types of LFSM and demonstrated their hardware implementation. For the symbolic-parallel and symbolic-tuple-parallel methods of CRC computation, symbolic LFSM over the non-binary Galois fields are applied. In contrast to the known approaches, which consider the problem of high speed only, present article stresses the need for taking into account a capability to detect errors with the aid of generator polynomials of the CRC codes. We proposed the Hamming codes and the Abramson codes in the binary and non-binary Galois fields for this purpose. Within the framework of single mathematical apparatus – theory of LFSM – it is possible to solve two important tasks simultaneously: to carry out mathematical substantiation of performance efficiency of the methods for parallel CRC computation and to estimate the detection and correction capability of the CRC codes based on LFSM graph models. Such comprehensive approach is relevant in the practice of various data transmission, storage and compression systems.

Vibrations of a Mindlin plate subjected to a pair of inertial loads moving in opposite directions

A Mindlin plate subjected to a pair of inertial loads traveling at a constant high speed in opposite directions along arbitrary trajectory, straight or curved, is presented. The masses represent vehicles passing a bridge or track plates. A numerical solution is obtained using the space–time finite element method, since it allows a clear and simple derivation of the characteristic matrices of the time-stepping procedure. The transition from one spatial finite element to another must be energetically consistent. In the case of the moving inertial load the classical time-integration schemes are methodologically difficult, since we consider the Dirac delta term with a moving argument. The proposed numerical approach provides the correct definition of force equilibrium in the time interval. The given approach closes the problem of the numerical analysis of vibration of a structure subjected to inertial loads moving arbitrarily with acceleration. The results obtained for a massless and an inertial load traveling over a Mindlin plate at various speeds are compared with benchmark results obtained for a Kirchhoff plate. The pair of inertial forces traveling in opposite directions causes displacements and stresses more than twice as large as their corresponding quantities observed for the passage of a single mass.

Managing requirements for the development of a novel elbow rehabilitation device

The development of new technologies for healthcare must take into consideration customer requirements from different stakeholders. The Voice of the Customer must be identified, analyzed and organized. This study aims to present a new approach of managing requirements from different product value chain stakeholders for a novel elbow rehabilitation device development. The Customer Value Chain Analysis tool was used to identify the product value chain stakeholders and the Quality Function Deployment tool to analyze and prioritize these requirements. The development is described in accordance with the engineering requirement process adapted to this case: 1) elicitation: the requirements come from the literature; benchmarking; questionnaires applied to all parties identified by Customer Value Chain Analysis application; 2) analyses: requirements were understood, and their overlaps, conflicts and prioritization were done by means of Quality Function Deployment (quality, product and part characteristics matrices); and 3) documentation: the identified construct of requirements were: ergonomics, functions, aesthetics, handling, materials, components/elements. The main parts that must be prioritized were: arm support, forearm support, support shaft, joystick, and support base. The association of these two tools is a novel and successful approach of identify different product value chain stakeholders and prioritize technical requirements for health product development.

An Algorithm for Identifying Symmetric Variables in the Canonical Reed–Muller Algebra System

To simplify the process for identifying 12 types of symmetric variables in the canonical Reed–Muller (CRM) algebra system, we propose a new symmetry detection algorithm based on AND-XOR expansion. By analyzing the relationships between the coefficient matrices of sub-functions and the order coefficient subset matrices based on AND-XOR expansion around two arbitrary logical variables, the constraint conditions of the order coefficient subset matrices are revealed for 12 types of symmetric variables. Based on the proposed constraints, the algorithm is realized by judging the order characteristic square value matrices. The proposed method avoids the complicated process for separating the AND–XOR expansion coefficients into different groups in the Reed–Muller transform methods and solves the problem of completeness in the RM type decomposition map method. The application results show that, compared with traditional methods the new algorithm is an optimal detection method in terms of applicability of the number of logical variables, detection types, and complexity of the identification process. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. Experimental results show that the proposed algorithm is convenient and efficient.

Attenuation and diffusion produced by small-radius curvatures in POFs.

Our aim is to characterize curvatures using a methodology previously applied to other localized disturbances in plastic optical fibers (POFs). The effects of several curvature radii and turn angles have been analyzed, so that for each condition, angular dependent attenuation and diffusion are obtained from experimental measurements to construct a matrix that accounts for the global effects of power loss and mode mixing introduced by the curvature over the angular power distribution. Power loss as a function of bend radius was calculated using the characteristic matrices and compared to experimental results to validate the model. This curvature model can be a useful tool to predict the impact of bends on transmission properties as is demonstrated in the example of a small network in a domestic environment.

Knowledge reduction of dynamic covering decision information systems when varying covering cardinalities

In covering-based rough set theory, non-incremental approaches are time-consuming for performing knowledge reduction of dynamic covering decision information systems when the cardinalities of coverings change as a result of object immigration and emigration. Because computing approximations of sets is an important step for knowledge reduction of dynamic covering decision information systems, efficient approaches to calculating the second and sixth lower and upper approximations of sets using the type-1 and type-2 characteristic matrices, respectively, are essential. In this paper, we provide incremental approaches to computing the type-1 and type-2 characteristic matrices of dynamic coverings whose cardinalities vary with the immigration and emigration of objects. We also design incremental algorithms to compute the second and sixth lower and upper set approximations. Experimental results demonstrate that the incremental approaches effectively improve the efficiency of set approximation computation. Finally, we employ several examples to illustrate the feasibility of the incremental approaches for knowledge reduction of dynamic covering decision information systems when increasing the cardinalities of coverings.

Knowledge reduction of dynamic covering decision information systems caused by variations of attribute values

In practical situations, it is time-consuming to conduct knowledge reduction of dynamic covering decision information systems caused by variations of attribute values with the non-incremental approaches. In this paper, motivated by the need for knowledge reduction of dynamic covering decision information systems, we introduce incremental approaches to computing the type-1 and type-2 characteristic matrices for constructing the second and sixth lower and upper approximations of sets in dynamic covering approximation spaces caused by revising attribute attributes. We also employ several examples to explain how to compute the second and sixth lower and upper approximations of sets in dynamic covering approximation spaces. Then we propose the incremental algorithms for computing the second and sixth lower and upper approximations of sets and employ experimental results to illustrate the incremental algorithms are effective to calculate the second and sixth lower and upper approximations of sets in dynamic covering approximation spaces. Finally, we give two examples to show how to conduct knowledge reduction of dynamic covering decision information systems caused by altering attribute values.

In-process cutting tool remaining useful life evaluation based on operational reliability assessment

In this paper, a method for evaluating the remaining useful life of an individual cutting tool while the tool is in process is proposed. The method is based on the operational reliability of a cutting tool which is used to assess its ability to complete a machining operation. Sensitive features extracted from force, vibration and acoustic emission signals are used to form characteristic matrices. Based on the kernel principal component analysis method, subspace matrices can be developed by reducing redundant information. The principal angle between the matrices of the normal state and the running state in the subspace is calculated. The cosine value of the minimum principal angle is used to assess the tool operational reliability. The remaining useful life of a cutting tool can be evaluated when the operational reliability assessment result is one of the back propagation neural network model’s input parameters together with some machining parameters. A chaotic genetic algorithm is used to optimize the initial weights and thresholds of the model with improved ergodicity and recurrence properties. The chaotic variables are introduced to improve the global searching ability and convergence speed. A case study is presented to validate the performance of the proposed method. The remaining useful life of an individual cutting tool can be evaluated quantitatively without the need of large samples and probability or statistic techniques.

A two-dimensional Riemann solver with self-similar sub-structure – Alternative formulation based on least squares projection

Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The self-similar formulation of Balsara [16] proves especially useful for this purpose. While that work is based on a Galerkin projection, in this paper we present an analogous self-similar formulation that is based on a different interpretation. In the present formulation, we interpret the shock jumps at the boundary of the strongly-interacting state quite literally. The enforcement of the shock jump conditions is done with a least squares projection (Vides, Nkonga and Audit [67]). With that interpretation, we again show that the multidimensional Riemann solver can be endowed with sub-structure. However, we find that the most efficient implementation arises when we use a flux vector splitting and a least squares projection. An alternative formulation that is based on the full characteristic matrices is also presented. The multidimensional Riemann solvers that are demonstrated here use one-dimensional HLLC Riemann solvers as building blocks.Several stringent test problems drawn from hydrodynamics and MHD are presented to show that the method works. Results from structured and unstructured meshes demonstrate the versatility of our method. The reader is also invited to watch a video introduction to multidimensional Riemann solvers on http://www.nd.edu/~dbalsara/Numerical-PDE-Course.

Some developments on phase coordinates line modeling based on Idempotent decomposition

Abstract Time-domain transmission line models remains a topic of ongoing research. The state of the art consists in using the Method of Characteristics (MoC) with a rational approximation of the characteristic admittance and propagation function matrices. The so-called universal line model (ULM) stands as among the most accurate phase-domain line models using MoC. However, it might present unstable responses due to large residue-pole ratios which amplifies the error associated with the interpolation scheme of the reflected current wave. In this work we investigate the possibility of using Idempotent Decomposition as an alternative for a full-frequency-dependent transmission line model suitable for the analysis of underground cables and overhead lines. An overview of the basic structure of time-domain transmission line modeling is presented. Results indicate that the separation of the propagation function into the sum of products of an Idempotent matrix with the corresponding exponential time-delay function avoids the stability problems related to large residue-pole ratios. A proposition to group Idempotent matrices with similar time-delays to reduce the order of the rational approximation of the propagation function matrix is also analyzed. Four test cases were considered including two previously reported cases where unstable simulation responses were found using ULM with a simple interpolation scheme. A Numerical Laplace Transform (NLT) approach was used to compare the time-domain responses. While results indicate that the Idempotent decomposition can be used to model underground cables, there is some accuracy loss in the rational approximation of the propagation function in the case of overhead transmission lines when a large number of phases is involved.

Experiments with nonstationary bilinear finite state machines

For nonstationary bilinear finite state machines over the field GF(p), we prove existence criteria of synchronizing, homing and diagnostic sequences formulated in terms of characteristic matrices of the finite state machines. For synchronizing sequences, we propose a method to construct them.

Reversible elementary cellular automaton with rule number 150 and periodic boundary conditions over 𝔽p

The study of the reversibility of elementary cellular automata with rule number 150 over the finite state set 𝔽p and endowed with periodic boundary conditions is done. The dynamic of such discrete dynamical systems is characterized by means of characteristic circulant matrices, and their analysis allows us to state that the reversibility depends on the number of cells of the cellular space and to explicitly compute the corresponding inverse cellular automata.

Characterization Based Design Under Dual State Vectors

This paper presents an automated design that is capable of generating large number of possible design concepts of hybrid combined mechanisms by given only the kinematic functions in requirement specifications. A hybrid mechanism is captured with considering its intrinsic multiple loop kinematic behavior being viewed as several kinematic state transformations. The input and output kinematic characteristic states of a subsystem or a basic mechanism unit are represented by qualitative dual state vectors related by characteristic matrix. Each element of the matrix defines a relative transformation and the operation rules of these transformations are defined. The subsystem characteristic matrix is the product of characteristic matrices of the serialized transformation units or addition of the paralleled. The dual state vectors of all available mechanism units are identified and the combination pattern decomposition rules for subsystem are established. Each set of such basic mechanism units and unit connections is the kinematic-to-structural representation of hybrid mechanism. By successive decomposition of logical hybrid connections, a thorough design process for hybrid mechanism is established. Then, the characteristic matrix of a subsystem can be successively decomposed into various sets of characteristic matrices of basic mechanism units. Due to this modularization of kinematic components and connection patterns, a hybrid system is described in functional hierarchy at two levels as the physical mechanism units and logical combination units which facilitate to map kinematic space to characteristic space till to dual state vector routing operations. This laid a ground work for hybrid mechanism design and examples are given to illustrate the proposed design principles.

Free Vibration Analysis of a Sloping-frame: Closed-form Solution versus Finite Element Solution and Modification of the Characteristic Matrices

Free Vibration Analysis of a Sloping-frame: Closed-form Solution versus Finite Element Solution and Modification of the Characteristic Matrices

Application of Frequency-Partitioning Fitting to the Phase-Domain Frequency-Dependent Modeling of Overhead Transmission Lines

This paper shows that a previously proposed linear-system identification method based on frequency partitioning and adaptive weighting can be successfully applied to the phase-domain frequency-dependent modeling of overhead transmission lines for electromagnetic transient simulations. As the framework of the phase-domain modeling, the universal line model is used, and the frequency responses of the characteristic admittance and propagation function matrices are realized by linear equivalents obtained by the identification method mentioned before, instead of the well-known Vector Fitting method. In this paper, numerical techniques to enhance the identification method for this phase-domain line modeling application are also presented. For validation, the proposed approach is applied to modeling an existing 500-kV double-circuit transmission line. The effectiveness of the numerical techniques for enhancements are shown through the modeling process, and transient waveforms obtained by the proposed approach are compared with those by the rigorous Laplace transform method and with a field-test result.