Redundancy Matrix Research Articles

Structural Assessment of Architected Material Using the Redundancy Matrix and Experimental Testing

Structural Assessment of Architected Material Using the Redundancy Matrix and Experimental Testing

Multi-view [formula omitted]-means clustering algorithm based on redundant and sparse feature learning

In recent years, multi-view clustering has been widely concerned and studied. Being its data generally has high dimension and noise, how to effectively deal with redundant features in data from various views and improve the clustering effect is an important issue in multi-view clustering. In this paper, a robust multi-view clustering algorithm Multi-view K-means clustering algorithm based on redundant and sparse feature learning (RSFMVKM) considering redundancy and sparse feature learning is proposed, which can effectively reduce the dimensions of data from different views. Firstly, the K-means algorithm is extended to multi-view clustering, and the importance of each views is represented by learning the weight of each view. Secondly, the sparse feature representation is obtained by applying the norm constraint to the projection matrix in a single view, and the cosine similarity is used to depict the redundancy matrix, which can remove the redundant information and improve the clustering effect. Moreover, the proposed algorithm can effectively avoid the generation of empty classes, and the clustering index matrix is discrete, so the clustering results can be obtained directly. Finally, the proposed algorithm is compared with six state-of-the-art multi-view clustering algorithms on six public datasets, and the experimental results show that the algorithm is effective.

Efficient Computation of Redundancy Matrices for Moderately Redundant Truss and Frame Structures

Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal entries are required. The standard computation procedure has a high computational effort. Many structures fall in the category of moderately redundant, i.e., the ratio of the statical indeterminacy to the number of all load-carrying modes of all elements is less one half. This paper proposes a closed-form expression for redundancy contributions that is computationally efficient for moderately redundant systems. The expression is derived via a factorization of the redundancy matrix that is based on singular value decomposition. Several examples illustrate the behavior of the method for increasing size of systems and, where applicable, for increasing degree of statical indeterminacy.

A member redundancy index based on distributed static indeterminacy for optimum material distribution for structures with axially loaded members

Redundancy analysis in structural systems has been typically approached under particular loading conditions. Structural systems that are found to provide adequate levels of redundancy in light of such an approach may face serious threats resulting from accidental loads. Additionally, determining the degree of redundancy of a system as one unique global information ignores the spatial distribution of the redundancy in that system. Improper distribution of redundancy in the system may lead to the presence of superfluous material in parts of the system. One system measure that has been widely used to gage the level of redundancy in structures is the static indeterminacy. Hence, the redundancy matrix is an excellent tool that provides valuable insight into the distribution of the static indeterminacy among the structural members in the system; independently from any loads applied to the system. One of the essential components in the redundancy matrix is the distributed static indeterminacy. While providing satisfactory levels of redundancy in a system is encouraged, it is also necessary to optimize the material distribution in the system. Having members in the system that are highly, or even completely, redundant indicates an inefficient distribution of material and should be avoided. In this paper, a member redundancy index based on the distributed static indeterminacy is derived. This index can be used to efficiently distribute the material in the system in order to optimize its redundancy distribution.

Efficient Update of Redundancy Matrices for Truss and Frame Structures

Redundancy matrices provide insights into the load carrying behavior of statically indeterminate structures. This information can be employed for the design and analysis of structures with regard to certain objectives, for example reliability, robustness, or adaptability. In this context, the structure is often iteratively examined with the help of slight adjustments. However, this procedure generally requires a high computational effort for the recalculation of the redundancy matrix due to the necessity of costly matrix operations. This paper addresses this problem by providing generic algebraic formulations for efficiently updating the redundancy matrix (and related matrices). The formulations include various modifications like adding, removing, and exchanging elements and are applicable to truss and frame structures. With several examples, we demonstrate the interaction between the formulas and their mechanical interpretation. Finally, a performance test for a scaleable structure is presented.

Assessment of robustness of hinged-bar systems

Typically in structural design, foreseeable loads are assumed in a dimensioning exercise. Structures can, however, be exposed to largely unforeseeable events such as intense environmental phenomena, accidents, malicious acts, and planning or execution errors. This circumstance determines the interest in the problem of structural robustness, which has been the subject of many recent works.
 This paper focuses on methods for assessing the robustness of hinged bar systems, considering truss structures as an example. They are the simplest in terms of computation, but make it possible to fully illustrate the proposed approach.
 First, the differences between progressive collapse (description of the process) and the disproportionate propagation of local failures (description of the state) are analyzed. The generalizing nature of the concept of robustness and its differences from the concept of invulnerability are pointed out.
 The paper considers the problem of measuring robustness. The known quantitative estimates of robustness are analyzed focusing on estimates that are invariant with respect to the stress state, as more general ones. The paper considers estimates that use such properties of the stiffness matrix as the condition number, or based on a comparison of the determinants of the original and changed stiffness matrices. It is pointed out that the degree of static indeterminacy can serve only as a necessary, but insufficient measure of robustness.
 The paper considers a well-known method of robustness assessment using a redundancy matrix determined by the forces that must be applied to assemble the system from elements with the length different from the design one. This method is opposed to the use of a projection matrix, the main diagonal elements of which indicate the degree of participation of the bars in ensuring robustness. The main properties of the idempotent projection matrix are considered. The paper illustrates the possibility of recalculating the projection matrix for the changed system with the help of the Jordan elimination step. A simple example demonstrates assembling and changing the projection matrix.
 In addition to the failure of the bar, the case of its damage (partial failure) is also considered, it is shown how it affects the change in the projector and the redistribution of internal forces.

RobustH∞output feedback control for type‐2Takagi‐Sugenofuzzy systems with multiple time‐delays and disturbances: A descriptor redundancy approach

AbstractTheH∞stability analysis and interval type‐2 Takagi‐Sugeno (T‐S) fuzzy control is studied for a class of interval type‐2 T‐S fuzzy systems. Firstly, the interval type‐2 T‐S fuzzy model is employed to approximate the system plant. Secondly, the delay‐dependent interval type‐2 T‐S fuzzy dynamic output feedback controller is designed. Thirdly, two classes of stability conditions in terms of linear matrix inequalities (LMIs) are derived, and the closed‐loop system is asymptotically stable and prescribedH∞performance is achieved. The delay‐dependent interval type‐2 T‐S fuzzy dynamic output feedback controller is designed to relax the control design conditions. The descriptor redundancy method is employed for avoiding the crossing vectors between the system gain matrices and controller gain matrices. The delay‐dependent Lyapunov functional with descriptor redundancy matrix is introduced, and the upper and lower membership functions information is considered. Some slack matrices are introduced via the upper and lower membership functions information to solve the obtained LMIs. Finally, simulation examples are performed to show the effectiveness of the proposed methods.

Self-Weighted Supervised Discriminative Feature Selection via Redundancy Minimization

Feature selection plays a key role in many machine learning problems. Especially as an important data preprocessing method, robust and pragmatic feature selection methods can be applied to extract meaningful features and eliminate redundant ones. As we all known, many feature selection methods select features by using some certain feature evaluation criteria to obtain the corresponding score for every feature, such that we can select high score features. Unfortunately, correlated features usually connect with each other, which may result in large correlations between top ranked features, such that the redundancy among the selected features is brought about. To solve this problem, we introduce the redundancy matrix A in the AGRM (a novel auto-weighted feature selection framework via global redundancy minimization) framework. Meanwhile, we introduce the adaptive redundancy matrix S and treat the redundancy matrix S as an optimizing variable, rather than setting the redundant matrix S as a prior. In addition, we propose a robust algorithm to efficiently address the constrained optimization problem. Finally, extensive experiments on six datasets show the superiority of our proposed method.

Quantification of the redundancy distribution in truss and beam structures

The degree of statical indeterminacy as a fundamental property in structural mechanics is today mainly known as a property of a complete system without any information about its spatial distribution. The redundancy matrix provides information about the distribution of statical indeterminacy in the system and by this gives an additional valuable insight into the load-bearing behaviour. The derivation and definition of the redundancy matrix are presented based on truss systems and its mathematical properties and their mechanical interpretations are provided. The definition of the redundancy matrix is extended to other discrete systems like beam structures and a definition of the redundancy density is given for the continuous 1D case. Potential applications of the concept include robust design of structures, quantification of imperfection sensitivity as well as assessment of optimal actuator placement in adaptive structures.

Reversible Data Hiding in Encrypted Images using Chunk Encryption and Redundancy Matrix Representation

For reversible data hiding in encrypted images (RDHEI), the private information in the original image content is protected and the embedded secret data can be used to manage the encrypted image. Up to now, many RDHEI algorithms have been reported, however, these reported RDHEI algorithms cannot achieve a high embedding capacity. Therefore, this paper proposes a new RDHEI scheme, which will have improved performance. The main contributions of the proposed scheme include two points: chunk encryption (CE) and redundancy matrix representation (RMR). First, different from the encryption method of pixel-by-pixel encryption used in the previous RDHEI algorithms, CE is the method that uses the traditional exclusive-or (XOR) method to encrypt the original image in chunks. By using the CE method, redundancy will be retained in the encrypted chunks. Second, the RMR method is designed to generate available room for accommodating secret data in redundancy matrices, which are existed in some encrypted chunks. Experimental results show that the proposed scheme achieves a high embedding capacity and the directly decrypted images retain high quality.

Redundancy theory and evaluation index of cable–strut system

Redundancy theory of cable–strut system is developed for evaluation of structural design. This redundancy theory extends system-level redundancy to member-level redundancy and takes pre-force into account by introducing the second-order deformation of cable and strut. The linear and nonlinear redundancy matrices are derived through potential energy equations in the form of linear and nonlinear deformations, respectively. The characteristics of structural geometry, topology, and material property are included in both linear and nonlinear redundancy matrices. Nonlinear redundancy matrix is also related to pre-force. Two sets of redundancy-based indexes are proposed for evaluation of cable–strut system. The system-level index set is used to evaluate structural redundancy and the strengthening effect of the pre-force on the structural redundancy. The member-level index set is used to evaluate the distribution of redundancy and structural uniformity. Finally, three groups of 3-bar prisms and two groups of cable domes are designed and analyzed to verify the effectiveness of the proposed redundancy-based indexes. The results show that the two sets of redundancy-based indexes are able to reflect pre-force level and evenness of distribution of strain energy and thus can be used as structural evaluation indexes.

Using local redundancy to improve GNSS absolute positioning in harsh scenario

<p class="Abstract">In GNSS context, absolute positioning is a widespread operational mode, largely used in many field activities as automotive, aerospace and ships navigation. The functional model of absolute positioning, relating pseudorange measurements to unknowns, is well defined, while its stochastic model, defining the behavior of measurement error, is currently under investigation and is the core of this work.</p><p class="Abstract">A realistic model of measurement error can be used to define a weighting scheme, able to reduce the positioning errors; a weighted approach is mainly necessary in signal-degraded scenario, where pseudorange accuracies are significantly different and equally weighting all the measurements would yield very large errors.</p><p class="Abstract">The quality indicators, commonly adopted to define a pseudorange error model, are the signal-to-noise ratio and the satellite elevation angle. In this work, an additional indicator, the redundancy number, is introduced.</p><p class="Abstract">The redundancy numbers are the diagonal elements of the redundancy matrix and they represent the degree of controllability of the measurements; a large value of the redundancy number corresponds to a well-controlled measurement, while a small one corresponds to a leverage observation, with a high potential to influence the solution.</p>The benefits of using the proposed weighting schemes is demonstrated in urban canyon and with single (GPS only) or multiple (GPS/Glonass) constellations

Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors.

The topic of indoor positioning and indoor navigation by using observations from smartphone sensors is very challenging as the determined trajectories can be subject to significant deviations compared to the route travelled in reality. Especially the calculation of the direction of movement is the critical part of pedestrian positioning approaches such as Pedestrian Dead Reckoning (“PDR”). Due to distinct systematic effects in filtered trajectories, it can be assumed that there are systematic deviations present in the observations from smartphone sensors. This article has two aims: one is to enable the estimation of partial redundancies for each observation as well as for observation groups. Partial redundancies are a measure for the reliability indicating how well systematic deviations can be detected in single observations used in PDR. The second aim is to analyze the behavior of partial redundancy by modifying the stochastic and functional model of the Kalman filter. The equations relating the observations to the orientation are condition equations, which do not exhibit the typical structure of the Gauss-Markov model (“GMM”), wherein the observations are linear and can be formulated as functions of the states. To calculate and analyze the partial redundancy of the observations from smartphone-sensors used in PDR, the system equation and the measurement equation of a Kalman filter as well as the redundancy matrix need to be derived in the Gauss-Helmert model (“GHM”). These derivations are introduced in this article and lead to a novel Kalman filter structure based on condition equations, enabling reliability assessment of each observation.

Self-weighted discriminative feature selection via adaptive redundancy minimization

Abstract In this paper, a novel self-weighted orthogonal linear discriminant analysis (SOLDA) method is firstly proposed, such that optimal weight can be automatically achieved to balance both between-class and within-class scatter matrices. Since correlated features tend to have similar rankings, multiple adopted criteria might lead to the state that top ranked features are selected with large correlations, such that redundant information is brought about. To minimize associated redundancy, an original regularization term is introduced to the proposed SOLDA problem to penalize the high-correlated features. Different from other methods and techniques, we optimize redundancy matrix as a variable instead of setting it as a priori, such that correlations among all the features can be adaptively evaluated. Additionally, a brand new recursive method is derived to achieve the selection matrix heuristically, such that closed form solution can be obtained with holding the orthogonality. Consequently, self-weighted discriminative feature selection via adaptive redundancy minimization (SDFS-ARM) method can be summarized, such that non-redundant discriminative features could be selected correspondingly. Eventually, the effectiveness of the proposed SDFS-ARM method is further validated by the empirical results.

Multi-label regularized quadratic programming feature selection algorithm with Frank–Wolfe method

Feature selection is an effective pre-processing step to remove possible redundant and irrelevant features for various machine learning paradigms, which can help build a more understandable machine learning based component in hybrid expert systems. Single-label quadratic programming feature selection (QPFS) model is formulated as a QP problem with a unit simplex constraint to both minimize feature-feature redundancy and maximize feature-label relevance simultaneously. Since its redundancy matrix is desired not to be positive semi-definite and then estimated by Nystrom low-rank approximation method, its performance depends greatly on under-sampling rate and random permutation. In this paper, without any approximation, we extend this model to construct a regularized version (rQPFS), resulting in a strictly convex QP problem, to achieve a globally optimal subset of features. To reduce the increment of computational time for entire redundancy matrix, Frank–Wolfe method with a sub-linear convergence rate and its special cases for strictly convex function and unit simplex constraint are applied to solve our rQPFS efficiently. Furthermore, to tackle multi-label FS paradigm, pruned problem transformation trick is used to evaluate feature-label relevance to describe label correlations sufficiently. The detailed experimental study on eight data sets shows that our proposed method performs the best, compared with six state-of-the-art multi-label FS methods, according to six instance-based performance evaluation measures.

Product function combination design based on functional redundancy analysis

Function combination designs integrate multiple product functions into a single product carrier. In this article, we proposed a function combination design method based on the functional redundancy analysis of parent products for the conceptual design process. According to the design task, we analyzed each parent product function carrier, established an expression model of functional elements based on the functional basis approach, and constructed a functional structure of the parent product based on relationships among energy, material, and signal flow. Then, we established a product function redundancy matrix and carrier redundancy matrix, and obtained redundancy functions and the principle structure carrier. We constructed a function carrier matrix for function combination products, sought the appropriate principle, established a design structure matrix, analyzed the coupling relationship between the principle scheme and structure carrier, and obtained a conceptual scheme of combination products through operations including reuse, variant, removal, and increase. Moreover, we used a sticker removal machine as an example to verify the validity of our function combination method.

Ka-band redundant and reconfiguration matrix for EuroSkyWay multimedia satellite

This paper presents the design, manufacture, integration and measured performance of a redundancy and reconfiguration matrix developed for the transmit section of the EuroSkyWay multimedia satellit...

Sufficient conditions of the redundancy-transform for the blind single channel identification

A subspace method to blindly estimate finite impulse response channels has been considered using redundancy-transform in transmitters. We find sufficient conditions for channel identifiability and observe that channels can be identified without restrictions on their zeros if we properly choose a redundancy matrix to satisfy certain conditions. From these conditions, we also derive another method called the orthogonal subchannel method. This method also can guarantee identifiability of channels without restrictions on their zeros.

Spatial declustering weights

Because of autocorrelation and spatial clustering, all data within a given dataset have not the same statistical weight for estimation of global statistics such mean, variance, or quantiles of the population distribution. A measure of redundancy (or nonredundancy) of any given regionalized random variable Z(uα)within any given set (of size N) of random variables is proposed. It is defined as the ratio of the determinant of the N X Ncorrelation matrix to the determinant of the (N - 1) X (N - 1)correlation matrix excluding random variable Z(uα).This ratio measures the increase in redundancy when adding the random variable Z(uα)to the (N - 1 )remainder. It can be used as declustering weight for any outcome (datum) z(uα). When the redundancy matrix is a kriging covariance matrix, the proposed ratio is the crossvalidation simple kriging variance. The covariance of the uniform scores of the clustered data is proposed as a redundancy measure robust with respect to data clustering.

Linear constraint relations in biochemical reaction systems: I. Classification of the calculability and the balanceability of conversion rates

Measurements provide the basis for process monitoring and control as well as for model development and validation. Systematic approaches to increase the accuracy and credibility of the empirical data set are therefore of great value. In (bio)chemical conversions, linear conservation relations such as the balance equations for charge, enthalpy, and/or chemical elements, can be employed to relate conversion rates. In a pactical situation, some of these rates will be measured (in effect, be calculated directly from primary measurements of, e.g., concentrations and flow rates), as others can or cannot be calculated from the measured ones. When certain measured rates can also be calculated from other measured rates, the set of equations, the accuracy and credibility of the measured rates can indeed be improved by, respectively, balancing and gross error diagnosis. The balanced conversion rates are more accurate, and form a consistent set of data, which is more suitable for further application (e.g., to calculate nonmeasured rates) than the raw measurements. Such an approach has drawn attention in previous studies. The current study deals mainly with the problem of mathematically classifying the conversion rates into balanceable and calculable rates, given the subset of measured rates. The significance of this problem is illustrated with some examples. It is shown that a simple matrix equation can be derived that contains the vector of measured conversion rates and the redundancy matrix R. Matrix R plays a predominant role in the classification problem. In supplementary articles, significance of the redundancy matrix R for an improved gross error diagnosis approach will be shown. In addition, efficient equations have been derived to calculate the balanceable and/or calculable rates. The method is completely based on matrix algebra (principally different from the graph-theoretical approach), and it is easily implemented into a computer program. (c) 1994 John Wiley & Sons, Inc.