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SCIENCE CHINA Information Sciences, Volume 64 , Issue 7 : 172214(2021) https://doi.org/10.1007/s11432-020-3001-7

New health-state assessment model based on belief rule base with interpretability

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  • ReceivedFeb 20, 2020
  • AcceptedJun 29, 2020
  • PublishedMay 20, 2021

Abstract


Acknowledgment

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61773388, 61702142, 61751304, 61833016, 61867001), China Postdoctoral Science Foundation (Grant Nos. 2015M570847, 2016T90938), Key Research and Development Plan of Hainan (Grant No. ZDYF2019007), Natural Science Foundation of Hainan (Grant No. 2019CXTD405), and Guangxi Key Laboratory of Trusted Software (Grant No. KX202050).


References

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  • Figure 1

    (Color online) The relationship between $P({\bf{\Omega~}})$ and $D({\bf{\Omega~}},{{\bf{\Omega~}}^0})$.

  • Figure 2

    (Color online) 2000 points generated by using (9) with $\kappa~=~1,2$ and (7). (a) The point distribution when $\kappa~=~1$;protect łinebreak (b) the point distribution when $\kappa~=~2$; (c) the point distribution generated by (7).

  • Figure 3

    (Color online) Conflict belief distributions of (a) W-shape, (b) U-shape, and (c) V-shape in the health-state assessment.

  • Figure 4

    (Color online) The structure of the health-state assessment model based on interpretable BRB.

  • Figure 5

    (Color online) The replacement operation.

  • Figure 6

    (Color online) The original vibration data and features. (a) The original vibration data; (b) kurtosis; (c) skewness.

  • Figure 7

    (Color online) (a) The estimated health state and (b) the corresponding belief degrees.

  • Figure 8

    (Color online) The errors between model outputs (BRB1, BRB2, FRB, ELM) and the actual health state. (a) The errors of BRB1, FRB, and ELM; (b) the errors of BRB1 and BRB2.

  • Figure 9

    (Color online) The rule weights in BRB0, BRB1, and BRB2.

  • Figure 10

    (Color online) The belief distributions in BRB0, BRB1, and BRB2.

  • Table 1  

    Table 1Referential values of attributes and output

    Attribute $\delta_i$ L M H VH Output N S M SE
    $K$ 1 0.1 2.4 5.2 9.2 Health state 0 0.25 0.75 1
    $S$ 1 0 0.8 1.4 2.9
  • Table 2  

    Table 2The initial rules

    Number${\theta~_k}$$K~\wedge~S$Health state levels Health Number${\theta~_k}$$K~\wedge~S$Health state levels Health
    ${\textstyle{{\{~\rm~N,~~~S,~~M,~~SE\}~}~\over~{\{~{\beta~_1},{\beta~_2},{\beta~_3},{\beta~_4}\}~}}}$ state ${\textstyle{{\{\rm~N,~~~S,~~M,~~SE\}~}~\over~{\{~{\beta~_1},{\beta~_2},{\beta~_3},{\beta~_4}\}~}}}$ state
    1 0.7 L $\wedge$ L 0.00, 0.10, 0.53, 0.37 0.7925 91 H $\wedge$ L 0.00, 0.40, 0.60, 0.00 0.55
    2 0.8 L $\wedge$ M 0.00, 0.00, 0.00, 1.00 1 100.7 H $\wedge$ M 0.00, 0.75, 0.25, 0.00 0.375
    3 0.7 L $\wedge$ H 0.00, 0.00, 0.30, 0.70 0.925 111 H $\wedge$ H 0.15, 0.85, 0.00, 0.00 0.2125
    4 0.8 L $\wedge$ VH 0.20, 0.60, 0.20, 0.00 0.3 121 H $\wedge$ VH 0.80, 0.20, 0.00, 0.00 0.05
    5 1 M $\wedge$ L 0.00, 0.00, 0.90, 0.10 0.775 130.8 VH $\wedge$ L 0.85, 0.15, 0.00, 0.00 0.0375
    6 0.7 M $\wedge$ M 0.00, 0.00, 0.00, 1.00 1 141 VH $\wedge$ M 0.40, 0.60, 0.00, 0.00 0.15
    7 0.7 M $\wedge$ H 0.00, 0.00, 0.75, 0.25 0.8125 151 VH $\wedge$ H 0.90, 0.10, 0.00, 0.00 0.025
    8 1 M $\wedge$ VH 0.10, 0.70, 0.20, 0.00 0.325 160.7 VH $\wedge$ VH 1.00, 0.00, 0.00, 0.00 0
  • Table 3  

    Table 3The initial referential values of health state

    The parameter Value The parameter Value The parameter Value
    Maximum generation $G$ 100 The zoom factor $F$ $[0.2,05]$ Population size $\lambda$ 50
    Covariance matrix ${\boldsymbol{\sigma~}}~=~\kappa~*~{\boldsymbol~I}$ $\kappa~=~0.1$ The crossover rate $Cr$ 0.2
  • Table 4  

    Table 4The optimized rules

    Number ${\theta~_k}$ $K~\wedge~S$ Health state levels ${\textstyle{{\{\rm~N,~S,~M,~SE\}~}~\over~{\{~{\beta~_1},{\beta~_2},{\beta~_3},{\beta~_4}\}~}}}$ Health state $[0,1]$
    1 0.69 L $\wedge$ L 0.020, 0.068, 0.505, 0.407 0.80275
    2 0.96 L $\wedge$ M 0.000, 0.007, 0.031, 0.962 0.987
    3 0.62 L $\wedge$ H 0.027, 0.081, 0.234, 0.658 0.85375
    4 0.8 L $\wedge$ VH 0.20, 0.60, 0.20, 0.00 0.3
    5 1.00 M $\wedge$ L 0.016, 0.048, 0.868, 0.068 0.731
    6 0.61 M $\wedge$ M 0.000, 0.000, 0.019, 0.981 0.99525
    7 0.60 M $\wedge$ H 0.002, 0.009, 0.727, 0.262 0.8095
    8 0.91 M $\wedge$ VH 0.104, 0.644, 0.141, 0.111 0.37775
    9 1.00 H $\wedge$ L 0.000, 0.119, 0.639, 0.242 0.751
    10 0.60 H $\wedge$ M 0.108, 0.770, 0.119, 0.003 0.28475
    11 1.00 H $\wedge$ H 0.232, 0.768, 0.000, 0.000 0.192
    12 0.98 H $\wedge$ VH 0.980, 0.017, 0.003, 0.000 0.0065
    13 0.8 VH $\wedge$ L 0.85, 0.15, 0.00, 0.00 0.0375
    14 1 VH $\wedge$ M 0.40, 0.60, 0.00, 0.00 0.15
    15 0.99 VH $\wedge$ H 0.903, 0.086, 0.008, 0.003 0.0305
    16 1.00 VH $\wedge$ VH 0.943, 0.045, 0.007, 0.005 0.0215
  • Table 5  

    Table 5MSEs generated by five models

    BRB0 BRB1 BRB2 FRB ELM
    MSE 0.0114 0.0054 0.0051 0.0092 0.0064
  • Table 6  

    Table 6Average MSEs generated by using three optimization algorithms

    AlgorithmMSESatisfy interpretability constraint in Eq. (12)Be consistent with initial judgement
    PSO-I0.0049YESYES
    GA-I0.0057YESYES
    SA-I0.0052YESYES
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