Signature Matrix Research Articles

A balancing approach to the realization of systems with internal passivity and reciprocity

This paper addresses the realization of positive real transfer functions which are symmetric with respect to some signature matrix. We show that a realization that is jointly internally reciprocal and internally passive can be achieved by positive real balancing.

Multiple Faults Isolation for Hybrid Systems with Unknown Fault Pattern

This work is concerned with multiple faults isolation for hybrid systems based on Global Analytical Redundancy Relationships (GARRs) approach. GARRs are derived from the Hybrid Bond Graph (HBG) model of a hybrid system with a specified causality assignment procedure. In this article, multiple faults are considered in a complex hybrid system and these faults can develop during a mode when the faults are not detectable. Once a fault is detected, a fault candidates set is generated from mode dependent-fault signature matrix (MD-FSM) tables and a set of fault pattern hypothesis is created from the fault candidates set for further refinement. Fault isolation is carried out using a multiple nonlinear least square optimization (MNLSO) algorithm. The developed technique can deal with multiple faults with unknown pattern. The fault could be of incipient or abrupt nature. The simulation results show the effectiveness of the proposed method.

Fault Diagnosis Using a Timed Discrete-Event Approach Based on Interval Observers: Application to Sewer Networks

This paper proposes a fault diagnosis method using a timed discrete-event approach based on interval observers that improves the integration of fault detection and isolation tasks. The interface between fault detection and fault isolation considers the activation degree and the occurrence time instant of the diagnostic signals using a combination of several theoretical fault signature matrices that store the knowledge of the relationship between diagnostic signals and faults. The fault isolation module is implemented using a timed discrete-event approach that recognizes the occurrence of a fault by identifying a unique sequence of observable events (fault signals). The states and transitions that characterize such a system can directly be inferred from the relation between fault signals and faults. The proposed fault diagnosis approach has been motivated by the problem of detecting and isolating faults of the Barcelona's urban sewer system limnimeters (level meter sensors). The results obtained in this case study illustrate the benefits of using the proposed approach in comparison with the standard fault detection and isolation approach.

Leakage Isolation using Pressure Sensitivity Analysis in Water Distribution Networks: Application to the Barcelona case study

Leaks are present to some extent in all water-distribution systems. This paper proposes a leakage localisation method based on the pressure measurements and pressure sensitivity analysis of nodes in a network. The sensitivity analysis using analytical tools is not a trivial job in a real network because the huge non-explicit non-línear systems of equation that describe its dynamics. Simulations of the network in presence and absence of leakage may provide an approximation of this sensitivity. This matrix is binarised using a threshold independent of the node. The binary matrix is assumed as a signature matrix for leakages. However, there is a trade-off between the resolution of the leakage isolation procedure and the number of available pressure sensors. In order to maximise the isolability with a reasonable number of sensors, an optimal sensor placement methodology, based on genetic algorithms, is also proposed. This methodology has been developed for Barcelona Network using Piccolo simulator. The sensor placement and the leakage detection and localization methodologies are applied to district management areas (DMA).

Pressure sensor distribution for leak detection in Barcelona water distribution network

This paper proposes a leakage detection method based on detecting significant discrepancies between pressure measurements and their estimations obtained from the simulation of a calibrated water distribution network model. Every sensor in the network will allow to detect a discrepancy in pressure due to leakage depending on its location. Then, a set of well distributed pressure sensors will generate a leakage signature that allows leakage localisation. This paper presents the methodology used in the Barcelona network for distributing properly the sensors for a good discrimination in the leakage localisation process. The methodology for sensor placement uses the pressure sensitivity matrix to the leakage presence. This matrix is normalised and binarised in order to be used as a leakage signature matrix using the standard model based fault diagnosis approach. Sensors may be installed in any node and leakages are simulated as a constant demand that can appear in any node too. The problem of deciding which are the best localisations for a small number of sensors in order to detect and localise leakages is an inverse problem that should be solved using optimisation. The resulting optimisation problem is of discrete nature and very huge for a real network. This type of problem is, in general, hard to solve and very time consuming. The use of GA (Genetic Algorithms) has been proved adequate according to the formulation of the signatures in the sensitivity matrix.

FRAMING SADDAM'S EXECUTION IN THE US PRESS

One of the major international events at the end of 2006 was the execution of former Iraqi President Saddam Hussein. The rushed execution sparked a controversy around the world and provided national media with an opportunity to frame the event in ways that resonate with their local audiences. This study focuses on the framing of the execution in the elite newspapers in the United States. Using a content analysis methodology, the study examines the news framing of the event in the US press. Of particular interest is the distributive and procedural justice frames used to describe Saddam's execution. In addition to dominant justice framing, the study also identifies the signature matrix of the coverage and the main interpretive packages comprising it.

Representations of [formula omitted]-central [formula omitted]-Potapov functions in both nondegenerate and degenerate cases

Let J be an m × m signature matrix (i.e. J ∗ = J and J 2 = I m ) and let D : = { z ∈ C : | z | < 1 } . Denote P J ( D ) the class of all J -Potapov functions in D , i.e. the set of all meromorphic m × m matrix-valued functions f in D with J -contractive values at all points of D at which f is holomorphic. Further, denote P J , 0 ( D ) the subclass of all f ∈ P J ( D ) which are holomorphic at the origin. Let f ∈ P J , 0 ( D ) , and let f ( w ) = ∑ j = 0 ∞ A j w j be the Taylor series representation of f in some neighborhood of 0 . Then it was proved in [B. Fritzsche, B. Kirstein, U. Raabe, On the structure of J -Potapov sequences, Linear Algebra Appl., in press] that for each n ∈ N the matrix A n can be described by its position in a matrix ball depending on the sequence ( A j ) j = 0 n - 1 . The J -Potapov function f is called J -central if there exists some k ∈ N such that for each integer j ⩾ k the matrix A j coincides with the center of the corresponding matrix ball. In this paper, we derive left and right quotient representations of matrix polynomials for J -central J -Potapov functions in D . Moreover, we obtain recurrent formulas for the matrix polynomials involved in these quotient representations.

Equiangular tight frames

A survey on equiangular tight frames in the space $$ \mathbb{R}^n $$ is presented. Several equivalent definitions of a tight frame are given. The construction of the Mercedes–Benz frame, the well-known example of a tight frame on the plane, is generalized to the space $$ \mathbb{R}^n $$ . The existence problems for the Mercedes–Benz systems and other more general equiangular tight frames are discussed. It is shown that the Welch inequality becomes the equality only on equiangular tight frames (if they exist). Necessary and sufficient conditions for the existence of an equiangular tight (n,m)-frame are formulated in terms of the so-called signature matrices. All the main results are completely proved. Bibliography: 37 titles. Illustrations: 3 figures.

On the structure of J-Potapov sequences

Let J be an m × m signature matrix (i.e., J ∗ = J and J 2 = I m ) and let D ≔ { z ∈ C : | z | < 1 } . Denote P J , 0 ( D ) the set of all meromorphic m × m matrix-valued functions f in D which are holomorphic at 0 and take J-contractive values at all points of D at which f is holomorphic. Then it was proved in [B. Fritzsche, B. Kirstein, U. Raabe, On some interrelations between J-Potapov functions and J-Potapov sequences, OT Series, in press] that the Taylor coefficient sequences of the functions belonging to P J , 0 ( D ) are exactly the infinite J-Potapov sequences of complex m × m matrices. The main goal of this paper is to investigate the inner structure of infinite J-Potapov sequences. It turns out that such sequences have a clear geometric structure. Let ( A j ) j = 0 ∞ be a J-Potapov sequence. Then we will show that for each n ∈ N the matrix A n belongs to a certain matrix ball depending on the sequence ( A j ) j = 0 n - 1 . This observation leads us to the consideration of those J-Potapov sequences ( A j ) j = 0 ∞ for which there exists some k ∈ N such that for j ∈ { k , k + 1 , … } the matrix A j coincides with the center of the corresponding matrix ball. We will call these J-Potapov sequences J-central of order k . It turns out that J-central J-Potapov sequences have a recursive structure. We investigate connections between J-Potapov sequences and their J-Potapov–Ginzburg transforms, which are m × m Schur sequences. In particular, we derive formulas containing explicit interrelations between the parameters of the corresponding matrix balls. An essential consequence of these formulas is the observation that the concept of centrality is invariant with respect to J-Potapov–Ginzburg transform.

Fault Isolation Module Implementation using a Timed Discrete-Event Approach based on Interval Observers

This paper proposes a fault diagnosis method using a timed discrete-event approach based on interval observers which improves the integration of fault detection and isolation modules. The interface between fault detection and fault isolation considers the degree of fault signal activation and the occurrence time instants of the fault signals using a combination of several theoretical fault signature matrices which store the knowledge of the relationship between fault signals and faults. As a novelty, this paper illustrates the procedure to implement the fault isolation module using a timed discrete-event approach built on the grounds of an interval observer used to model the monitored system. In this way, the diagnosis result will be enhanced since the occurrence of a fault generates a unique sequence of observable events (fault signals) that will be recognized by the isolation module implemented as a timed discrete-event system. The states and transitions that characterize such a system can be inferred directly from the relation between fault signals and faults. The proposed fault diagnosis approach is applied to detect and isolate faults of the Barcelona's urban sewer system limnimeters (level meter sensors).

Fault Detection and Isolation in Sewer Networks

In this paper, the problem of fault detection and isolation (FDI) in sewer networks will be presented as well as a methodology to address it. In particular, the paper will focus on the case of faults in rain gauges and limnimeters (water level sensors in the sewers). The proposed model based FDI methodology is based on the use of interval methods (in order to enhance robustness) in fault detection and on the use of an isolation algorithm based on several fault signature matrices that considers additional information to the typical binary one. More precisely, fault signature matrices containing information about residual fault sensitivity and time/order of residual activation are used. To exemplify the FDI problem in sewer networks and the proposed FDI methodology, the Barcelona network is used as the case study. Such network has a telemetry system containing 22 rain gauges and more than 100 limnimeters used for the real-time control system. As additional topics discussed in the paper, the problem of reconstructing measurements from faulty sensors will also be addressed after the FDI system has located them. Also, some ideas on how to address the problem of faults in actuators embedding fault tolerance in the controller used for the global control of the network will be provided.

Model-based fault diagnosis in PEM fuel cell systems

In this work, a model-based fault diagnosis methodology for PEM fuel cell systems is presented. The methodology is based on computing residuals, indicators that are obtained comparing measured inputs and outputs with analytical relationships, which are obtained by system modelling. The innovation of this methodology is based on the characterization of the relative residual fault sensitivity. To illustrate the results, a non-linear fuel cell simulator proposed in the literature is used, with modifications, to include a set of fault scenarios proposed in this work. Finally, it is presented the diagnosis results corresponding to these fault scenarios. It is remarkable that with this methodology it is possible to diagnose and isolate all the faults in the proposed set in contrast with other well known methodologies which use the binary signature matrix of analytical residuals and faults.

Fault Diagnosis using a Timed Discrete Event Approach based on Interval Observers

This paper proposes a fault diagnosis method using a timed discrete-event approach based on interval observers which improves the integration of fault detection and isolation tasks. The interface between fault detection and fault isolation considers the degree of fault signal activation and the occurrence time of the diagnostic signals using a combination of several theoretical fault signature matrices which store the knowledge of the relationship between diagnostic signals and faults. As a novelty, this paper proposes to implement the fault isolation module using a timed discrete event approach in spite of using an analytical fault detection model. In this way, the diagnosis result will be enhanced since the occurrence of a fault generates a unique sequence of observable events (fault signals) that will be recognized by the isolation module implemented as a timed discrete event system. The states and transitions that characterize such a system can be inferred directly from the relation between fault signals and faults. The proposed fault diagnosis approach is applied to detect and isolate faults of the Barcelona's urban sewer system limnimeters (level meter sensors).

Decentralized distributed space-time trellis coding

In this paper, we introduce a new class of distributed space-time trellis codes (DSTTCs) for wireless networks with a large set of decode-and-forward relay nodes N. We consider the general case where each relay node is equipped with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> antennas and the destination node is equipped with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> antennas. It is assumed that at any given time only a small, a priori unknown subset of nodes S ∈ N is active and neither the relay nodes nor the destination node know which relay nodes are active. In the proposed scheme, each node is assigned a signature matrix and the signal transmitted by an active node is the product of the signature matrix and a space-time trellis code (STTC) matrix originally designed for N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> co-located antennas. It is shown that existing full-rank STTCs designed for N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ⩾ 2 co-located antennas are a favorable choice for the code matrix. Two practical designs for good deterministic signature matrix sets are provided and compared with random signature matrices. If the signature matrices are properly optimized, the proposed DSTTCs achieve a diversity order of d = min{N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> , N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> } if N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> nodes are active. Simulation results confirm that DSTTCs yield significant performance gains over distributed space-time block codes and distributed space-time filtering. Furthermore, equipping relay nodes with a second antenna can be highly beneficial especially if only few nodes can be active at any given time.

Sparsely spread CDMA—a statistical mechanics-based analysis

Sparse code division multiple access (CDMA), a variation on the standard CDMA method in which the spreading (signature) matrix contains only a relatively small number of nonzero elements, is presented and analysed using methods of statistical physics. The analysis provides results on the performance of maximum likelihood decoding for sparse spreading codes in the large system limit. We present results for both cases of regular and irregular spreading matrices for the binary additive white Gaussian noise channel (BIAWGN) with a comparison to the canonical (dense) random spreading code.

Direct and inverse asymptotic scattering problems for Dirac-Krein systems

The asymptotic scattering matrix s e(λ) for a Dirac-Krein system with signature matrix J = diag{ I p ,-I p }, integrable potential, and the boundary condition u 1(0, λ) = u 2(0, λ)e(λ) with a coefficient e(λ) that belongs to the Schur class of holomorphic contractive p × p matrix-valued functions in the open upper half-plane is defined. The inverse asymptotic scattering problem for a given s e is analyzed by Krein’s method. Earlier studies by Krein and others focused on the case in which e = I p (or a constant unitary matrix).

Prognostic Testing in Uveal Melanoma by Transcriptomic Profiling of Fine Needle Biopsy Specimens

Many uveal melanoma patients die of metastasis despite ocular treatment. Transcriptomic profiling of enucleated tumors can identify patients at high metastatic risk. Because most uveal melanomas do not require enucleation, a biopsy would be required for this analysis. Here, we establish the feasibility of transcriptomic analysis of uveal melanomas from fine needle aspirates. Transcriptomic profiles were analyzed from postenucleation "mock" needle biopsies and matching tumors from eight enucleated eyes and from fine needle aspirates in 17 uveal melanomas before radiotherapy. Predictive accuracy was assessed using a weighted voting classifier optimized for probe set selection using a minimal redundancy/maximum relevance algorithm. Transcriptomic profiles from mock biopsies were highly similar to those from their matching tumor samples (P < 0.0001). Transcriptomic profiles from fine needle aspirates clustered into two classes with discriminating probe sets that overlapped significantly with those for our published classification (P < 0.00001). No loss of predictive accuracy was identified among eight needle aspirates obtained from a distant location. Thus, it is feasible to obtain RNA of adequate quality and quantity to perform transcriptomic analysis on uveal melanoma samples obtained by fine needle biopsy. This method can be applied to specimens obtained from distant geographic locations and can stratify uveal melanoma patients based on metastatic risk.

A Setup for Active Fault Diagnosis

A setup for active fault diagnosis (AFD) of parametric faults in dynamic systems is formulated in this note. It is shown that it is possible to use the same setup for both open loop systems, closed-loop systems based on a nominal feedback controller as well as for closed-loop systems based on a reconfigured feedback controller. This will make the proposed AFD approach very useful in connection with fault tolerant control (FTC). The setup will make it possible to let the fault diagnosis part of the fault tolerant controller remain unchanged after a change in the feedback controller. The setup for AFD is based on the Youla-Jabr-Bongiorno-Kucera (YJBK) parameterization of all stabilizing feedback controllers and the dual YJBK parameterization. It is shown that the AFD is based directly on the dual YJBK transfer function matrix. This matrix will be named the fault signature matrix when it is used in connection with AFD

The number of equivalence classes of symmetric sign patterns

This paper shows that the number of sign patterns of totally non-zero symmetric n -by- n matrices, up to conjugation by permutation and signature matrices and negation, is equal to the number of unlabelled graphs on n vertices.

Detectors and Asymptotic Analysis for Bandwidth-Efficient Space–Time Multiple-Access Systems

In this paper, a narrowband multiple-channel transmission scheme with multiple transmit antennas is proposed and analyzed. The channelization is based on space-time signature matrices, which do not expand bandwidth, unlike conventional schemes such as code-division or time-division multiplexing. The channels can be used by multiple independent users in an uplink or downlink scenario (multiple access or broadcast channels, respectively), or by one user in a multiplexing scenario. The data transmitted on each channel is convolutionally encoded, interleaved, and then space-time block encoded before space-time channelization. Each channel has a unique interleaver and space-time signature, but the convolutional encoder and space-time block code encoder can be identical across channels. It is shown that asymptotic single-user-like performance can be achieved with optimal detection and decoding in a Rayleigh fading channel. Practical receiver algorithms are developed based on the iterative (turbo) detection technique. The simulation results demonstrate that these suboptimal receivers achieve single-user performance at moderate signal-to-noise ratios, and moderate user loads. In the single-user multiplexing case, a significant performance gain over single-channel transmission with the same data rate is obtained.