Flow Graph Method Research Articles

Stability and Dynamics Analysis of Time-Delay Fractional-Order Large-Scale Dual-Loop Neural Network Model With Cross-Coupling Structure.

In recent years, the analysis of the dynamics of annular neural networks has received extensive attention and achieved some achievements. However, most of the current research merely focuses on the single-ring, low-dimension, two rings sharing one neuron cases, without considering the rich coupling modes between rings. In this article, a large-scale time-delay fractional-order dual-loop neural network model with cross-coupling structure is established, in which two rings complete information interaction through two shared neurons. Moreover, the Caputo fractional derivative is introduced in this article to describe the neural network more accurately. First, the transmission time delay between each neuron is selected as the key parameter leading to the bifurcation, and the characteristic equation of the network is creatively derived using the Coates flow graph method. Subsequently, through the holistic element method and magnitude angle formula, we simplify the analytical process. Then, we obtain the stability and Hopf bifurcation criterion of the network. Finally, the conclusions of the theoretical analysis are verified by a series of numerical simulations. The results show that the stability region of the network is closely related to the fractional order, the number of neurons, the distribution of neurons, and the self-feedback coefficients. Moreover, the time delays have a significant effect on the amplitude and period of the Hopf bifurcation.

USAGE : Uncertain flow graph and spatio-temporal graph convolutional network-based saturation attack detection method

With the development of Software-Defined Networking (SDN), its security problems have attached interests from academia. The saturation attack targeted at the SDN switch is one of the most destructive problems in SDN. The saturation attack can destroy SDN networks by depleting the computation and storage resources of SDN switches. Currently, graph neural networks have already been used for detecting saturation attacks in SDN. When constructing the graph based on K-Nearest Neighbors (KNN) algorithm, the number of edges in the graph is fixed. That may fail on accurately representing the relationship among different nodes. In addition, when using the Graph Convolutional Network (GCN) to detect saturation attack against SDN, only a partial graph structure and node features will be learned, causing the flow graph nodes information cannot be fully utilized. To overcome these issues, in this work, we propose USAGE, an uncertain flow graph and spatio-temporal graph neural network-based saturation attack detection method. More specifically, USAGE designs the CRAM algorithm and EGG model. The CRAM algorithm is proposed to generate an uncertain flow graph for each network traffic flow, which can represent the uncertain relationship among different nodes. EGG is a spatio-temporal graph convolutional network model, which is proposed to detect saturation attacks. The evaluation results demonstrate that USAGE can generate a better graph than KNN and achieve high detection performance. Meanwhile, USAGE outperforms other methods in terms of TPR, TNR, accuracy, precision, recall, F-score, confusion matrix, ROC curves, and PR curves.

Exploration of bifurcation and stability in a class of fractional-order super-double-ring neural network with two shared neurons and multiple delays

Complex multi-ring coupling structures are common in real-world networks. However, the current work is mainly limited to unidirectional multi-ring or those sharing a neuron. This paper is devoted to the stability and Hopf bifurcation of a class of double-ring neural network with two shared neurons and multiple time delays, where n and m neurons are distributed on the double-ring, respectively. First, we obtain the characteristic equation of the network at the trivial equilibrium point by using the Coates flow graph method. Then, based on this, some sufficient conditions for the stability and Hopf bifurcation of the double-ring network under two connection modes are given. Finally, we provide some numerical examples to illustrate the validness of the theoretical results, and the influences of fractional order, network size and the distance between two shared neurons on Hopf bifurcation are also discussed.

Modelling and Analysis of Quadruple Asymmetrical Optical Micro-Ring Resonator for Biosensing Application

In this paper, modelling of an asymmetrical micro-ring resonator and its performance as an optical filter and optical sensor is analysed. Quadruple asymmetrical optical micro-ring resonator (QAOMRR) is mathematically modelled in Z-domain using delay line signal processing technique. The transmittance of the configuration is calculated using signal flow graph method. Vernier principle method is applied to achieve larger free spectral range (FSR). Also, the proposed QAOMRR in silicon-on-insulator (SOI) platform is used for biochemical sensing. The proposed QAOMRR offers a FSR of 3.155 THZ and Q- factor of 3875 as well as provide significant shift in resonant wavelength whenever any different analyte is present in biomolecules. Field investigation of the proposed QAOMRR is done using Finite Difference Time Domain (FDTD) method. The directional couplers are designed using FDTD simulations. The proposed method will be extremely useful for modelling analysis and design of different micro optical asymmetrical ring resonator configurations.

Simulating Elliptic Low-pass Filter based on MOCCCII

Multiple output current-control current conveyer (MOCCCII) based Elliptic low-pass filter by using a simulating of RLC ladder prototype is presented in this work. The good performances of RLC ladder as well as low-sensitivity are inherited. Signal flow graph (SFG) method is applied to convert the RLC Elliptic ladder low-pass filter prototype to be the different function blocks. These function blocks can be realized by integrator and differentiator. Lossy integrator, lossless integrator and lossless differentiator realized from MOCCCII are straightforward replaced in SFG. Due to the tuning ability of MOCCCII, the proposed Elliptic low-pass filter can be tuned by adjusting the bias current (IB ). In addition, the frequency responses can be varied from 50kHz to 1MHz by tuning IB from 1μA to 100 μA to prove the electronic tuning performance of the proposed filter. The simulation results are carried out by PSpice that the performances are totally agreed with the theory.

Ultra-sensitive pressure sensor using double stage racetrack silicon micro resonator

Three layouts of add-drop double stage racetrack microring resonators (ADSRMRR) located on the centre of the flexible silicon diaphragm were introduced as microscale optomechanical pressure sensors. The light propagation through all of the proposed ADSRMRR layouts were simulated using the signal flow graph method and the variational finite difference time domain (varFDTD) analysis. To achieve optimum transmission, a formula was derived for a critical coupling coefficient in the presence of the coupling loss factor for each coupling region. The pressure was measured from a wavelength shift in the output drop port signals considering the change in the optical length of the ADSRMRR due to the diaphragm shear stress. The pressure sensitivity of 48.5 pm/kPa, 42.4 pm/kPa and 33.2 pm/kPa with the limit of detection of 4.1 × 10−2 kPa, 4.7 × 10−2 kPa and 6.0 × 10−2 kPa were measured for the symmetric-large layout, the asymmetric and the symmetric-small layout of ADSRMRR pressure sensor, respectively. We introduced the ratio of the total optical length rather the sum of the resonant mode numbers (R-ratio) as a key factor in designing of the microscale Vernier based-pressure sensors. It is found that, using an ADSRMRR layout with a higher R-ratio provides a higher sensitivity with a lower detection limit, which are required in altitude sensors in satellites, aircraft, and weather balloons.

Optimum light transmission via microring resonator under a lossy‐coupler critical coupling condition

AbstractThe optical transfer function is derived for add‐drop resonator (ADR) using the signal flow graph method. A critical coupling condition is calculated in the presence of loss in the coupling regions. Effect of critical coupling and coupler loss in the light transmission is studied. A limited area was determined for optimum optical transmission of ADR. We introduced a semi‐empirical equation to correlate the geometric design of coupling gap with the coupling strength parameters (coupling coefficient, k, and coupling loss, γ). Achieved results can be used in optical communication technology and the photonic sensor applications.

Modeling optical filters based on serially coupled microring resonators using radial basis function neural network

In this research for the first time by using radial basis function neural network (RBFNN), filters based on serially coupled microring resonators have been modeled. Also, signal flow graph (SFG) method based on Mason’s rule has been used to simulate filters. It has been represented when RBFNN has been learned, model can extract the outputs same as what was simulated by SFG method. It has been proved that RBFNN model can properly obtain results in several cases in which some parameters of filter like the order of filter; MRRs radius; coupling coefficients; and propagation loss have been changed. In these cases to design filter by an analytical method like the SFG, we need to obtain new transfer function. Obtaining novel transfer function would make filter designating complicated in terms of calculation and simulation time while the RBFNN can match with any change as fast as possible. The RBFNN has advantages of optimization ability, straightforward topological architecture, stable generalization ability, appropriate tolerance against input noise, online learning ability, accuracy in dynamically nonlinear approximation, predictability and fast and easy learning algorithms. These properties of RBFNN make it suitable to model pliable optical systems.

180° hybrid using a novel planar balun on suspended substrate for beam forming network applications

In this paper, a 180° hybrid consisting of a broadband balun and a T-junction in-phase power divider is proposed. The 180° hybrid is intended for operation in the C-band. The balun resembles a center tapped magnetic transformer where the coils are replaced by broadside-coupled lines. This new technique allows magnetic couplers to be realized by planar structures at microwave frequencies. The planar balun is broadband, and the size reduction is considerable. The broadside-coupled lines are on a suspended substrate. The proposed structure can be used in the beam forming networks of the multiple-beam antennas. It also prevents cross connections in the conventional beam forming networks. The planar balun is analyzed by the signal flow graph method. The scattering parameters of the 180° hybrid are calculated by the multiport connection method. Some design formulas for the construction of the balun are presented. The 3-dimensional model of the planar 180° hybrid is simulated by a full-wave simulator. Measurement results of the fabricated hybrid approve the simulation results. The 180° hybrid exhibits a relative bandwidth of 45% centered at 4.5 GHz. In the operating band, the amplitude and phase imbalance of the output ports are <0.6 dB and <10°, respectively.

Free spectral range analysis of double series microresonator system for all-optical corrosion sensor

A double series configuration of a microresonator is proposed to measure the amount of corrosion on iron metal. A numerical computation has been performed for analyzing the sensing operation in which the metal is attached to the waveguide as a top cladding material. The transparency peak profile and transfer function of the output transmission spectrum is obtained using a signal flow graph method and Mason’s rule. The output spectrum of the microresonator shows that the linear free spectral range (FSR) changes as the iron begins to oxidize, which affects the cladding index of the sensing system. The FSR changes with respect to the amount of corrosion present in iron metal. In addition, the microresonator is able to distinguish two different types of corrosion, which are hematite and magnetite. The sensitivities of the practical application design are obtained as 22.62 nm/RIU for magnetite and 7.17 nm/RIU for hematite detection. The FSR analysis is an alternative approach in all-optical sensing to wavelength shift. It is promising for applications in additional high-sensitivity all-optical corrosion sensors.

Performance optimization of an optical filter based on serially coupled microring resonators using a fuzzy logic system

The signal flow graph method based on Mason’s rule has been used to simulate a serially coupled triple microring resonator (SCTMRR) optical filter. One of the most important parameters of MRRs is the coupling coefficient. Therefore, calculating the optimum value of this parameter is one of the key challenges to design optical filters. The fuzzy logic system has been used to find mentioned coefficients. The fuzzy system inputs are the on–off ratio, shape factor (SF), and propagation loss parameters of the SCTMRR. The obtained results have been verified by comparison with authentic published works. It has been shown that to achieve minimum ripple and maximum SF of filter drop port response, the internal coupling coefficients should be smaller than the external ones. Just on the basis of fuzzy logic results, it has been proved that SF of the SCTMRR filter could not be >0.6.

Применение потоково-графовых методов в оптимизации расписания

Применение потоково-графовых методов в оптимизации расписания

Analysis of Electronic Circuits with the Signal Flow Graph Method

In this work a method called “signal flow graph (SFG)” is presented. A signal-flow graph describes a system by its signal flow by directed and weighted graph; the signals are applied to nodes and functions on edges. The edges of the signal flow graph are small processing units, through which the incoming signals are processed in a certain form. In this case, the result is sent to the outgoing node. The SFG allows a good visual inspection into complex feedback problems. Furthermore such a presentation allows for a clear and unambiguous description of a generating system, for example, a netview. A Signal Flow Graph (SFG) allows a fast and practical network analysis based on a clear data presentation in graphic format of the mathematical linear equations of the circuit. During creation of a SFG the Direct Current-Case (DC-Case) was observed since the correct current and voltage directions was drawn from zero frequency. In addition, the mathematical axioms, which are based on field algebra, are declared. In this work we show you in addition: How we check our SFG whether it is a consistent system or not. A signal flow graph can be verified by generating the identity of the signal flow graph itself, illustrated by the inverse signal flow graph (SFG−1). Two signal flow graphs are always generated from one circuit, so that the signal flow diagram already presented in previous sections corresponds to only half of the solution. The other half of the solution is the so-called identity, which represents the (SFG−1). If these two graphs are superposed with one another, so called 1-edges are created at the node points. In Boolean algebra, these 1-edges are given the value 1, whereas this value can be identified with a zero in the field algebra.

Analyzing a four quadrant dc-dc Luo converter by means of signal flow graph modeling technique

Abstract In this paper, the signal flow graph technique and Mason gain formula are applied for extracting small signal model and transfer functions from control to output and from input to output. In order to investigate a rather complex system, a four quadrant dc-dc Luo converter known as a second generation and high order power electronic converter is chosen for modeling and analyzing purposes. This converter has received the least attention and its dynamic modeling and analysis is not reported in literature. To get rid of complex equations in modeling high order converters, signal flow graph method is applied to manipulate the equations. Hence, the small signal models for two converters in different states are derived in detail and the obtained models are used to achieve the frequency responses and do stability analysis. The whole paper shows that using the proposed method, derivation of small signal models for all states and frequency domain analysis can be easily carried out in detail.

Design of Asymmetric Parallel-Cascaded Micro-Ring Resonator Using Transfer Matrix and Signal Flow-Graph Methods

Asymmetric parallel-cascaded micro-ring resonator (APCMR) is proposed. The proposed device is composed of two or more micro-ring-resonators with different diameter. The proposed device is designed using transfer matrix combined with signal flow graph methods. The designed device with crosstalk less than and equal -10 dB can be obtained by setting coupling coefficient. The proposed device can be used for optical filters and sensors.

THE ANALYSIS OF PHASE, DISPERSION AND GROUP DELAY IN INGAASP/INP MICRORING RESONATOR

The Vernier operation with signal flow graph (SFG) is a graphical approach for analyzing the intricate photonic circuits mathematically and quick calculation of optical transfer function. Analysis of a cascaded microring resonators (CMRR) made of InGaAsP/InP semiconductor is presented using the signal flow graph (SFG) method which enables modelling the transfer function of the passive CMRR. These passive filters are mostly characterized by their frequency response. The theoretical calculations of the system is performed by the Vernier effects analysis. Two MRRs with radius of 100 µm which are vertically coupled together are used to generate resonant peaks. Here, the phase, dispersion and group delay of the generated signals are analyzed.

Design and modeling of flower like microring resonator

This paper presents a novel multi-channel optical filter structure. The proposed design is based on using a set of microring resonators (MRRs) in new formation, named flower like arrangement. It is shown that instead of using 18 MRRs, by using only 5 MRRs in recommended formation, same filtering operation can be achieved. It is shown that with this structure, six filters and four integrated demultiplexers (DEMUXs) are obtained. The simplicity, extensibility and compactness of this structure make it usable in wavelength division multiplexing (WDM) networks. Filter's characteristics such as shape factor (SF), free spectral range (FSR) and stopband rejection ratio can be designed by adjusting microrings' radii and coupling coefficients. To model this structure, signal flow graph method (SFG) based on Mason's rule is used. The modeling method is discussed in depth. Furthermore, the accuracy and applicability of this method are verified through examples and comparison with other modeling schemes.

Flow-Graph and Markovian Methods for Cyber Security Analysis

A flow-graph depicts the interrelationships among cyber security and security threats/incidents (i.e., internal, external, and accidental). Using a flow-graph, the manner in which security threats may affect systems can be investigated. This paper reports analytical approaches to analyze time to security threats and probability of security threat occurrence. Considering embedded threat detection functions in a safe-guard unit, the proposed approaches use the flow-graph concept, and Markovian method to calculate time to security threat occurrence and its probability. The threat detection functions are featured by incident detection and recovery mechanisms. The results of this study can be used by all parties (public and private sector organizations, service providers, IT, and insurance companies) to better deal with cyber security issues with respect to utilizing technology, investment, and insurance. An illustrative example is demonstrated to present the application of the approach.

Buck-Boost DC-DC Converter Control by Using the Extracted Model from Signal Flow Graph Method

In this paper, the signal flow graph technique and Mason gain formula are applied for extracting the model and transfer functions from control to output and from input to output of a buck-boost converter. In order to investigate a controller necessity for the converter of assumed parameters, the frequency and time domain analysis are done and the open loop system characteristics are verified and the needed closed loop controlled system specifications are determined. Finally designing a controller for the mentioned converter system based on the extracted model is discussed. Then, a modern control design method is employed for regulator design. For this purpose, a full state feedback control for pole placement is applied. The simulation results are used to show the performance of the proposed modeling and regulation method.

Active Damping-Based Control for Grid-Connected $LCL$ -Filtered Inverter With Injected Grid Current Feedback Only

An LCL-type filter is widely used in the grid-connected inverter. However, with only injected grid current control, the current harmonics and low bandwidth caused by the resonance peak cannot be tolerated. The active damping (AD) method with an extra feedback provides a high rejection of the resonance so that the dynamic is improved; however, the high-precision sensing circuit for the extra feedback increases the cost. In this paper, with the signal flow graph and response-fitting methods, an AD method based on the feedback of the injected grid current has been proposed. Then, the novel closed-loop current control requires accurately sensing the injected grid current only, while no observation is needed. Compared with the extra feedback methods, the cost and the complexity are reduced while the reliability is improved. Based on the study of the relation between the controller and the system dynamic, a straightforward design has been proposed. The robustness, harmonic rejection, and digital implementation have been studied. Compared with the conventional control methods, the proposed one promises the satisfactory performance with both analog and digital implementations. Simulations and experiments have verified the proposed control and design strategies.