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<p>Sensors are critical for data acquisition in thermal, chemical, and other nonlinear parabolic distributed parameter systems (DPSs). However, accurate sensor fault estimation is hindered by the coupling of the nonlinear term with spatiotemporal dynamics, as well as the neglect of model reduction errors and external disturbances. To overcome these challenges, this paper proposes a robust sensor fault estimation framework for nonlinear DPSs. Specifically, the infinite-dimensional DPSs are first decomposed into finite-dimensional ordinary differential equations (ODEs) using the spectral method. Both model reduction errors and external disturbances are then incorporated into an enhanced transformation model and sliding mode observer, enabling precise fault detection, isolation, and estimation. Leveraging the Lyapunov direct method and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> theory, the stability and robustness of the estimation errors are rigorously guaranteed under environmental uncertainties. Finally, the method is validated through simulations on the heat transfer process and the Fisher equation, demonstrating its effectiveness in handling time-invariant and time-varying, and single- and multi-sensor faults in noisy industrial scenarios.</p>

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Sensor fault diagnosis framework for nonlinear parabolic distributed parameter systems

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Liqun Chen,
  • Meiyang Ren,
  • Kui Wang,
  • Wenjing Shen,
  • Yu Zhou,
  • Peng Wei

摘要

Sensors are critical for data acquisition in thermal, chemical, and other nonlinear parabolic distributed parameter systems (DPSs). However, accurate sensor fault estimation is hindered by the coupling of the nonlinear term with spatiotemporal dynamics, as well as the neglect of model reduction errors and external disturbances. To overcome these challenges, this paper proposes a robust sensor fault estimation framework for nonlinear DPSs. Specifically, the infinite-dimensional DPSs are first decomposed into finite-dimensional ordinary differential equations (ODEs) using the spectral method. Both model reduction errors and external disturbances are then incorporated into an enhanced transformation model and sliding mode observer, enabling precise fault detection, isolation, and estimation. Leveraging the Lyapunov direct method and \(H_\infty \) H ∞ theory, the stability and robustness of the estimation errors are rigorously guaranteed under environmental uncertainties. Finally, the method is validated through simulations on the heat transfer process and the Fisher equation, demonstrating its effectiveness in handling time-invariant and time-varying, and single- and multi-sensor faults in noisy industrial scenarios.