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The transfer function is a fundamental concept in the analysis and design of linear time-invariant (LTI) systems. It offers a concise way to understand how a system responds to different inputs in the frequency domain. It serves as a bridge between the time-domain differential equations that describe system dynamics and the frequency-domain representation that facilitates easier manipulation and analysis.
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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
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Transfer Across Different Machines by Transfer Function Estimation.

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Summary
This summary is machine-generated.

This study introduces a new method for estimating the transfer function, including phase, for rotating machinery. This improves the transferability of digital twin models for prognostic health monitoring across different machines.

Keywords:
adaptive clutter separation (ACS)autoregressive moving-average (ARMA) modelminimum phasetransfer across different machines (TDM)transfer function estimationzeros and poles

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Area of Science:

  • Engineering
  • Data Science
  • Mechanical Engineering

Background:

  • Digital twins are advanced tools for prognostic health monitoring.
  • Transferring digital twins to new rotating machinery is challenging due to vibration signal distortion caused by transfer functions.
  • Existing transfer function estimation algorithms often omit phase information.

Purpose of the Study:

  • To highlight the significance of accurate transfer function estimation for successful digital twin implementation across diverse machines.
  • To present a novel algorithm for estimating the complete transfer function, including phase, for gear signals.
  • To validate the proposed algorithm's effectiveness using both simulated and measured data.

Main Methods:

  • Development of a new algorithm for transfer function estimation.
  • Inclusion of phase information in the transfer function estimation process.
  • Validation using simulated transfer functions and measured vibration signals from rotating machinery.

Main Results:

  • The proposed algorithm successfully estimates the transfer function with phase information.
  • Demonstrated the feasibility of the method on gear signals.
  • Validated the algorithm's performance against simulated and real-world data.

Conclusions:

  • Accurate transfer function estimation, including phase, is crucial for effective digital twin deployment in rotating machinery.
  • The novel algorithm offers a significant advancement for transfer function estimation, enabling better cross-machine digital twin applications.
  • This work contributes to the advancement of prognostic health monitoring through enhanced digital twin transferability.