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Signal-flow graphs offer a streamlined and intuitive approach to representing control systems, providing an alternative to traditional block diagrams. These graphs use branches to symbolize systems and nodes to represent signals, effectively illustrating the relationships and interactions within the system.
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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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Network Function of a Circuit01:25

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Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
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The Power Flow Problem and Solution01:26

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Power flow problem analysis is fundamental for determining real and reactive power flows in network components, such as transmission lines, transformers, and loads. The power system's single-line diagram provides data on the bus, transmission line, and transformer. Each bus k in the system is characterized by four key variables: voltage magnitude Vk​, phase angle δk​, real power Pk​, and reactive power Qk​. Two of these four variables are inputs, while the...
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Related Experiment Video

Updated: Aug 16, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Published on: September 8, 2023

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Hypergraph and network flow-based quality function deployment.

János Abonyi1, Tímea Czvetkó1

  • 1ELKH-PE Complex Systems Monitoring Research Group, University of Pannonia, Egyetem str. 10, H-8200 Veszprém, Hungary.

Heliyon
|December 26, 2022
PubMed
Summary

This study enhances Quality Function Deployment (QFD) by integrating operations research methods. New approaches optimize development actions, improve decision-making, and visually identify interactions for better product development.

Keywords:
HypergraphLinear programmingMinimum cost flowProduct developmentQuality function deployment

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Area of Science:

  • Operations Research
  • Product Development
  • Quality Management

Background:

  • Quality Function Deployment (QFD) translates customer needs into product characteristics.
  • Traditional QFD overlooks the direct impact of development parameter interactions on customer satisfaction.
  • This limits the optimization of development actions under constraints.

Purpose of the Study:

  • To enhance QFD by optimizing development parameter selection under capacity or cost constraints.
  • To directly implement cross-relationships between development parameters.
  • To visually identify interactions between development parameters and customer requirements.

Main Methods:

  • Formulating QFD as a network flow problem using linear optimization for benefit maximization.
  • Applying minimum cost flow approach for cost minimization.
  • Representing QFD as a hypergraph to analyze interactions using centrality metrics.

Main Results:

  • Linear optimization maximized customer satisfaction.
  • Minimum cost flow approach minimized total development costs.
  • Hypergraph representation effectively identified indirect interactions between development parameters and customer needs.

Conclusions:

  • Integrating operations research methods significantly improves QFD's decision-making reliability.
  • The proposed approaches offer distinct advantages for different development strategies.
  • Visualizing interactions aids in a more comprehensive understanding of product development dynamics.