SCIENCE CHINA Information Sciences, Volume 64 , Issue 3 : 132207(2021) https://doi.org/10.1007/s11432-019-2944-3

Fault detection for a class of linear systems with integral measurements

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  • ReceivedOct 31, 2019
  • AcceptedApr 30, 2020
  • PublishedFeb 7, 2021



This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61873149, 61733009, 61703244), and Research Fund for the Taishan Scholar Project of Shandong Province of China.


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  • Figure 1

    (Color online) The experimental setup of the three-tank system.

  • Table 1  

    Table 1Parameters of the three-tank system

    Symbol Value Description
    A 0.0154 ${\rm~m}^{2}$ Surface area of the tanks
    $S_{n}$ $5\times10^{-5}~{\rm~m}^{2}$ Surface area of the pipes
    $Q_{\rm~1max}$ 100 ${\rm~ml/s}$ Max flow rate of pump 1
    $Q_{\rm~2max}$ 100 ${\rm~ml/s}$ Max flow rate of pump 2
    $H_{\rm~max}$ 0.62 m Max height of tanks
    $az_1$ 0.46 Fluid constants for pipe 1
    $az_2$ 0.48 Fluid constants for pipe 2
    $az_3$ 0.58 Fluid constants for pipe 3

    Algorithm 1 Online fault detection algorithm

    Set $x(1)=[0~0~0]^\mathrm{T},~u(1)=[0~0~0]^\mathrm{T}$ as initial values of the system state and control input.

    Calculate $H_{os},~H_{us},~H_{ds},~H~_{fs}$ and $y_s,~u_s,~d_s,~f_s$ by using (H_os~ue) and (y-s).

    Calculate $P_s$ and $V_s$ according to Lemma 1 and SVD technique to ensure the solvability of (HHH).

    Update $r(k)$ by using (r3).

    Update $J_r(k)$ by using (Jr) and compare with $J_{\rm~th}$. As a result, the occurrence of a fault can be detected by applying (Jrth).

    Let $k=k+1$, and go to step 2 until the end of the process.