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13
A SignalFlowGraph Approach to Online Gradient Calculation
 Neural Computation
, 2000
"... A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple oneinput, on ..."
Abstract

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A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple oneinput, oneoutput transformation, as in an electrical circuit. Even if graph representations are popular in the neural network community, they are often used for qualitative description rather than for rigorous representation and computational purposes. In this article, a method for both online and batchbackward gradient computation of a system output or cost function with respect to system parameters is derived by the SFG representation theory and its known properties. The system can be any causal, in general nonlinear and timevariant, dynamic system represented by an SFG, in particular any feedforward, timedelay, or recurrent neural network. In this work, we use discretetime notation, but the same theory holds for the continuoustime case. The gradient is obtained in a straightforward way by the analysis of two SFGs, the original one and its adjoint (obtained from the first by simple transformations), without the complex chain rule expansions of derivatives usually employed. This method can be used for sensitivity analysis and for learning both offline and online. Online learning is particularly important since it is required by many real applications, such as digital signal processing, system identification and control, channel equalization, and predistortion. 1
A Model Based Approach to Constructing Performance Degradation Monitoring Systems
"... Abstract—Enterprises that are tightly choreographed require ongoing knowledge of their member systems capabilities in order to adapt and maintain effective operations. Member system capabilities are derived from knowing the current performance levels of the member systems functionalities. The perfor ..."
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Abstract—Enterprises that are tightly choreographed require ongoing knowledge of their member systems capabilities in order to adapt and maintain effective operations. Member system capabilities are derived from knowing the current performance levels of the member systems functionalities. The performance degradation curves for the member systems functionalities must be continually monitored. There are several basic stakeholders in the performance degradation curves. Operations can use them to manage the aggregate mission performance. The operator can use them to adapt the vehicle to the mission. Sustainment, anticipatory logistics, and maintenance clearly have a need for this information. By contrast, loosely coupled or uncoupled enterprises require less knowledge of degraded performance; though they still require knowledge of complete loss of performance,
1 A Linear System Approach to QoS Control
, 2004
"... We present a novel service discipline, called linear service discipline, to serve multiple QoS queues sharing a bandwidth resource and analyze its properties. The linear server makes the output traffic and the queueing dynamics of individual queues as a linear function of its input traffic. In parti ..."
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We present a novel service discipline, called linear service discipline, to serve multiple QoS queues sharing a bandwidth resource and analyze its properties. The linear server makes the output traffic and the queueing dynamics of individual queues as a linear function of its input traffic. In particular, if input traffic is Gaussian, the distributions of queue length and output traffic are also Gaussian with their mean and variance being a function of input mean and input power spectrum (equivalently, autocorrelation function of input). Important QoS measures including buffer overflow probability and queueing delay distribution are also expressed as a function of input mean and input power spectrum. Based on these analytical results, a simple measurementbased QoS control scheme is proposed and evaluated. This study points out a new direction for networkwide traffic management based on linear system theories by letting us view the queueing process at each node as a linear filter. Index Terms Quality of service, service discipline, Gaussian traffic, linear system, measurementbased traffic control I.
A Hierarchical Modelbased approach to Systems Health Management
"... provides the ability to maintain system health and performance over the life of a system. For safetycritical systems, ISHM must maintain safe operations while increasing availability by preserving functionality and minimizing downtime. This paper discusses a modelbased approach to ISHM that combin ..."
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provides the ability to maintain system health and performance over the life of a system. For safetycritical systems, ISHM must maintain safe operations while increasing availability by preserving functionality and minimizing downtime. This paper discusses a modelbased approach to ISHM that combines fault detection, isolation and identification, faultadaptive control, and prognosis into a common framework. At the core of this framework are a set of component oriented physical system models. By incorporating physics of failure models into component models the dynamic behavior of a failing or degrading system can be derived by simulation. Current state information predicts future behavior and performance of the system to guide decision making on system operation and maintenance. 1,2 We demonstrate our approach on the fluid loop of a secondary
RELIABILITY
, 2004
"... www.elsevier.com/locate/ress Characteristics of organizational culture at the maintenance units of two Nordic nuclear power plants Teemu Reiman a,*, Pia Oedewald a, Carl Rollenhagen b ..."
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www.elsevier.com/locate/ress Characteristics of organizational culture at the maintenance units of two Nordic nuclear power plants Teemu Reiman a,*, Pia Oedewald a, Carl Rollenhagen b
Equivalent Circuits and Signal Flow Graphs to the SmallSignal Analysis of Active Circuits
"... Abstruct Smallsignal Thevenin and Norton equivalent circuits seen looking into each terminal of the BJT and the FET are described. The application of these! circuits to writing by inspection the expressions for gain, input resistance, and output resistance of multistage amplifiers is demonstrated. ..."
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Abstruct Smallsignal Thevenin and Norton equivalent circuits seen looking into each terminal of the BJT and the FET are described. The application of these! circuits to writing by inspection the expressions for gain, input resistance, and output resistance of multistage amplifiers is demonstrated. The application of the circuits to the noise analysis of devices is illustrated by the calculation of the noise input voltage and current of the BJT and the noise input voltage of the MOSFET. The circuits are useful for the analysis of feedback amplifiers where Mason’s signal flow graph can he used to solve the simultaneous equations that are obtained. Several examples are presented which illustrate flowgraph solutions for feedback circuits. I.
Analysis of the Modified MOS Wilson Current Mirror: A Pedagogical Exercise in Signal Flow Graphs, Mason's Gain Rule, and DrivingPoint Impedance Techniques
, 2001
"... A pedagogical analysis of the modified MOS Wilson current mirror using signal flow graphs (SFGs), Mason's gain rule, and drivingpoint impedance (DPI) techniques is presented as an exercise for undergraduate electrical engineering students learning to analyze transistorlevel circuits with mult ..."
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A pedagogical analysis of the modified MOS Wilson current mirror using signal flow graphs (SFGs), Mason's gain rule, and drivingpoint impedance (DPI) techniques is presented as an exercise for undergraduate electrical engineering students learning to analyze transistorlevel circuits with multiplefeedback loops. While students often prefer the SFG representation for single feedback loops, they often abandon it in favor of the more familiar nodal analysis methods for multiple loops. Yet these methods can be long and cumbersome and contribute little to intuition. In an attempt to preserve the intuitive grasp of tradeoffs, this paper presents an exercise of several wellestablished analytical techniques for generating and analyzing SFGs. The modified Wilson current mirror is used to compare three analytical approaches: 1) fundamental laws with bruteforce algrebra, 2) fundamental laws with Mason's gain rule, and 3) DPI technique with Mason's gain rule. The concepts reinforced in this paper include: 1) tradeoffs between gain and other quantities such as output resistance or bandwidth, 2) how Mason's gain rule simplifies the analyses of closedloop gain, and 3) how DPI techniques simplify the generation of SFGs.
LETTER Communicated by Andrew Back A SignalFlowGraph Approach to Online Gradient Calculation
"... A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple oneinput, on ..."
Abstract
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A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple oneinput, oneoutput transformation, as in an electrical circuit. Even if graph representations are popular in the neural network community, they are often used for qualitative description rather than for rigorous representation and computational purposes. In this article, a method for both online and batchbackward gradient computation of a system output or cost function with respect to system parameters is derived by the SFG representation theory and its known properties. The system can be any causal, in general nonlinear and timevariant, dynamic system represented by an SFG, in particular any feedforward, timedelay, or recurrent neural network. In this work, we use discretetime notation, but the same theory holds for the continuoustime case. The gradient is obtained in a straightforward way by the analysis of two SFGs, the original one and its adjoint (obtained from the first by simple transformations), without the complex chain rule expansions of derivatives usually employed. This method can be used for sensitivity analysis and for learning both offline and online. Online learning is particularly important since it is required by many real applications, such as digital signal processing, system identification and control, channel equalization, and predistortion. 1