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A novel scheme for multivariate statistical fault detection with application to the Tennessee Eastman process

  • * Corresponding author: Xianchao Xiu

    * Corresponding author: Xianchao Xiu

This work was supported in part by the National Natural Science Foundation of China under Grant 12001019

Abstract Full Text(HTML) Figure(11) / Table(2) Related Papers Cited by
  • Canonical correlation analysis (CCA) has gained great success for fault detection (FD) in recent years. However, it cannot preserve the prior information of the underlying process. To cope with these difficulties, this paper proposes an improved CCA-based FD scheme using a novel multivariate statistical technique, called sparse collaborative regression (SCR). The core of the proposed method is to take the prior information as a supervisor, and then integrate it with CCA. Further, the $ \ell_{2,1} $-norm is employed to reduce redundancy and avoid overfitting, which facilitates its interpretability. In order to solve the proposed SCR, an efficient alternating optimization algorithm is developed with convergence analysis. Finally, some experimental studies on a simulated example and the benchmark Tennessee Eastman process are conducted to demonstrate the superiority over the classical CCA in terms of the false alarm rate and fault detection rate. The detection results indicate that the proposed method is promising.

    Mathematics Subject Classification: Primary: 93C83, 90C25; Secondary: 62P30, 65K05.


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  • Figure 1.  Comparison of CCA and the proposed SCR

    Figure 2.  Detection strategy

    Figure 3.  Illustration of detection indices

    Figure 4.  Detection results for Type I

    Figure 5.  Detection results for Type II

    Figure 6.  Flowchart of the TE process

    Figure 7.  Detection results for IDV(2) in the TE process

    Figure 8.  Detection results for IDV(10) in the TE process

    Figure 9.  Detection results for IDV(18) in the TE process

    Figure 10.  Detection results for IDV(15) in the TE process

    Figure 11.  Relative differences

    Table 1.  The selected faults in TE process

    Fault No. Description Type
    IDV(1) A/C feed ratio step change
    IDV(2) component B step change
    IDV(3) feed D temperature step change
    IDV(4) RCW inlet temperature step change
    IDV(5) CCW inlet temperature step change
    IDV(6) feed A loss step change
    IDV(7) C header pressure loss step change
    IDV(8) feed A-C components random variation
    IDV(9) feed D temperature random variation
    IDV(10) feed C temperature random variation
    IDV(11) RCW inlet temperature random variation
    IDV(12) CCW inlet temperature random variation
    IDV(13) reaction kinetics slow drift
    IDV(14) RCW valve sticking
    IDV(15) CCW valve sticking
    IDV(16) unknown fault unknown
    IDV(17) unknown fault unknown
    IDV(18) unknown fault unknown
    IDV(19) unknown fault unknown
    IDV(20) unknown fault unknown
    IDV(21) unknown fault constant
     | Show Table
    DownLoad: CSV

    Table 2.  Detection results in term of FDR and FAR

    Fault No. CCA-r1 CCA-r2 SCR
    IDV(1) 99.75% 0.63% 99.88% 0.63% 99.88% 0.00%
    IDV(2) 96.50% 0.63% 97.50% 0.00% 99.50% 0.00%
    IDV(3) 11.13% 3.25% 13.00% 2.50% 32.75% 1.75%
    IDV(4) 100% 1.88% 99.88% 1.25% 100% 1.25%
    IDV(5) 100% 4.38% 100% 3.75% 100% 2.50%
    IDV(6) 100% 2.50% 100% 2.50% 100% 1.75%
    IDV(7) 100% 3.75% 96.88% 2.50% 100% 0.63%
    IDV(8) 96.50% 1.88% 97.50% 0.63% 99.75% 0.00%
    IDV(9) 8.75% 2.50% 9.75% 2.50% 12.63% 1.63%
    IDV(10) 86.88% 1.25% 89.50% 0.63% 96.75% 0.00%
    IDV(11) 76.50% 0.63% 76.88% 0.63% 85.13% 0.00%
    IDV(12) 99.13% 1.25% 99.75% 0.00% 100% 0.00%
    IDV(13) 95.75% 0.63% 95.13% 0.63% 99.75% 0.00%
    IDV(14) 100% 1.88% 99.88% 0.63% 100% 0.63%
    IDV(15) 13.13% 4.38% 16.88% 4.38% 48.50% 1.75%
    IDV(16) 93.00% 7.50% 94.38% 1.25% 97.38% 0.63%
    IDV(17) 94.13% 3.13% 97.63% 2.50% 98.25% 1.25%
    IDV(18) 90.88% 1.88% 92.50% 0.00% 95.75% 0.00%
    IDV(19) 92.00% 1.25% 92.50% 1.25% 92.50% 0.63%
    IDV(20) 86.88% 0.63% 87.13% 0.63% 92.13% 0.00%
    IDV(21) 44.63% 4.38% 61.50% 0.63% 72.38% 0.00%
     | Show Table
    DownLoad: CSV
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