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Related Concept Videos

Fault Types01:18

Fault Types

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When analyzing a single line-to-ground fault from phase A to ground at a three-phase bus, it is important to consider the fault impedance. This impedance is zero for a bolted fault, equal to the arc impedance for an arcing fault, and represents the total fault impedance for a transmission-line insulator flashover. To derive sequence and phase currents, fault conditions are translated from the phase domain to the sequence domain.
For line-to-line faults occurring between phases B and C, the...
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The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as the volume tends to zero. More practically, divergence measures how much a vector field spreads out or diverges from a given point. For an outgoing flux, conventionally, the divergence is positive. The diverging point is often called the "source" of the field. Meanwhile, the negative divergence of a vector field at a point means that the vector...
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The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
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The seminal work of Ohno in 1970 popularized the idea of gene duplication and divergence. DNA sequence comparison studies reveal that a large portion of the genes in bacteria, archaebacteria, and eukaryotes was  generated by gene duplication and divergence, indicating its critical role in evolution.
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The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
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Related Experiment Video

Updated: Feb 10, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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An improved incipient fault detection method based on Kullback-Leibler divergence.

Hongtian Chen1, Bin Jiang1, Ningyun Lu1

  • 1College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, 169 Shengtai West Road, Jiang Ning District, Nanjing, 211106, China.

ISA Transactions
|May 27, 2018
PubMed
Summary

This study introduces an advanced incipient fault detection method using Kullback-Leibler (KL) divergence. It effectively identifies subtle anomalies in systems by comparing probability density functions (PDFs), outperforming existing techniques.

Keywords:
Electrical drive systemsIncipient fault detectionKullback-Leibler (KL) divergencePrincipal component analysis (PCA)

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Area of Science:

  • Engineering
  • Statistics
  • Machine Learning

Background:

  • Traditional multivariate fault detection methods struggle with detecting subtle anomalies.
  • Statistical process control often relies on predefined thresholds that may not adapt to system variations.
  • Accurate incipient fault detection is crucial for preventing catastrophic failures in complex systems.

Purpose of the Study:

  • To develop an improved method for incipient fault detection using Kullback-Leibler (KL) divergence.
  • To enhance the detection of slight anomalous behaviors in multivariate systems.
  • To provide a robust and adaptable fault detection framework for non-Gaussian systems.

Main Methods:

  • Utilized Kullback-Leibler (KL) divergence for comparing online and reference probability density functions (PDFs).
  • Employed Principal Component Analysis (PCA) to define evaluation functions in principal and residual subspaces.
  • Analyzed robust performance against varying Signal-to-Noise Ratios (SNR) and applied nonlinear projections.

Main Results:

  • The proposed method successfully detected three types of incipient faults in a numerical example.
  • Demonstrated superior performance compared to several existing fault detection methods.
  • Successfully applied to incipient fault detection in a non-Gaussian electrical drive system.

Conclusions:

  • The KL divergence-based method offers a significant improvement for incipient fault detection.
  • The approach is robust and effective even in non-Gaussian environments.
  • This methodology provides a valuable tool for early anomaly detection in industrial systems.