CN107703740A - A kind of robust interval sensor fault diagnosis method of bullet train critical system - Google Patents

A kind of robust interval sensor fault diagnosis method of bullet train critical system Download PDF

Info

Publication number
CN107703740A
CN107703740A CN201710554307.XA CN201710554307A CN107703740A CN 107703740 A CN107703740 A CN 107703740A CN 201710554307 A CN201710554307 A CN 201710554307A CN 107703740 A CN107703740 A CN 107703740A
Authority
CN
China
Prior art keywords
mrow
msub
msup
mtd
mtr
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201710554307.XA
Other languages
Chinese (zh)
Inventor
周东华
张峻峰
何潇
卢晓
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shandong University of Science and Technology
Original Assignee
Shandong University of Science and Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shandong University of Science and Technology filed Critical Shandong University of Science and Technology
Priority to CN201710554307.XA priority Critical patent/CN107703740A/en
Publication of CN107703740A publication Critical patent/CN107703740A/en
Pending legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Landscapes

  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Medicines Containing Antibodies Or Antigens For Use As Internal Diagnostic Agents (AREA)

Abstract

The invention discloses a kind of robust interval sensor fault diagnosis method of bullet train critical system, belong to field of signal processing, this method includes：Establish bullet train critical system discrete-time state-space model step；Design bullet train critical system robust Residual Generation device step；Design bullet train critical system robust interval Transducer-fault Detecting Method step；Design the separation of bullet train critical system robust interval sensor fault and method of estimation step.The effective guarantee of the present invention practical application request of bullet train critical system interval sensor fault diagnosis.

Description

Robust intermittent sensor fault diagnosis method for high-speed train key system
Technical Field
The invention belongs to the field of signal processing, and particularly relates to a robust intermittent sensor fault diagnosis method for a key system of a high-speed train.
Background
The high-speed train is the system which is most closely related to passengers in the high-speed rail technology, and the safe and stable running of the high-speed train is the basis and the premise of the healthy and rapid development of the high-speed rail. The fault diagnosis technology is a key technology for guaranteeing the safe operation of the high-speed train. At present, a plurality of technical measures and systems are adopted by high-speed trains to improve the reliability and safety of train operation.
However, the existing high-speed train fault diagnosis technology has many limitations, such as mostly simple threshold comparison, and matching with strategic operation steps, redundant information which can be used for fault diagnosis is not sufficiently discovered; the diagnosis function depends heavily on the richness of the fault code table, only common faults existing in the fault code table can be diagnosed, and new faults generated in the actual operation of the train cannot be diagnosed; permanent faults are considered in the coping process, and intermittent sensor faults caused by electromagnetic interference and the like are not considered.
Based on the above situation, a robust intermittent sensor fault diagnosis method for a key system of a high-speed train is needed to implement real-time online diagnosis of the intermittent sensor fault of the key system of the high-speed train by a fault diagnosis system.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides the robust intermittent sensor fault diagnosis method for the key system of the high-speed train, which is reasonable in design, overcomes the defects of the prior art and has a good effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
a robust intermittent sensor fault diagnosis method for a key system of a high-speed train specifically comprises the following steps:
step 1: establishing a discrete time state space model of a key system of a high-speed train and identifying model parameters
Wherein,respectively, the system state, the control input and the measurement output; respectively, process noise and measurement noise;is a sensor failure; is a system parameter;is the parameter uncertainty; the following conditions are satisfied: the mean, covariance, and second moment of the initial state x (0) areP0，Σ0(ii) a The mean values of the noises w (k), v (k) are zero, and the covariance matrices are respectively sigmaw(k)，Σv(k)(ii) a Uncertainty of parameter Aδ(k),Bδ(k),Cδ(k) Has a mean value of zero and a covariance matrix of
Step 2: the method for designing the robust residual error generator of the key system of the high-speed train specifically comprises the following steps:
step 2.1: off-line computing gain matrix K (k)
K(k)＝G(k)Cc(k)TQ(k)-1, (2)；
Wherein,
step 2.2: computing robust residuals r (k) on-line
Wherein,
and step 3: the method for detecting the fault of the robust intermittent sensor of the key system of the high-speed train comprises the following steps:
step 3.1: calculating intermittent fault detection statistic TD(k)
Step 3.2: setting an intermittent fault detection false alarm rate Pfa
Pfa＝αfa, (12)；
Step 3.3: design intermittent Fault detection threshold JD
Wherein,
step 3.4: intermittent fault detection according to the following criteria
If TD(k-1)≤JD,TD(k)＞JDIf so, a fault occurs at the moment k, and the fault alarm indication quantity Ia＝1；
If TD(k-1)＞JD,TD(k)≤JDIf so, the fault disappears at the moment k, and the fault release indication quantity Ir＝1；
Accordingly, the fault alarm time and the fault release time of the ith intermittent fault are respectively
kalarm,i＝min(k|TD(k)＞JD,k≥krelease,i-1+1), (15)；
krelease,i＝min(k|TD(k)≤JD,k≥kalarm,i+1), (16)；
And 4, step 4: the method for designing the fault separation and estimation of the robust intermittent sensor of the key system of the high-speed train specifically comprises the following steps:
step 4.1: calculating intermittent fault separation statistic TI(i,j)
Wherein,
L(i,j)11＝G(i,j)11 TT(i)-1G(i,j)11, (18)；
L(i,j)12＝G(i,j)11 TT(i)-1G(i,j)12, (19)；
L(i,j)21＝G(i,j)12 TT(i)-1G(i,j)11, (20)；
L(i,j)22＝G(i,j)12 TT(i)-1G(i,j)12, (21)；
d(i,j)1＝G(i,j)11 TT(i)-1r(kalarm,i,krelease,i-1), (22)；
d(i,j)2＝G(i,j)12 TT(i)-1r(kalarm,i,krelease,i-1), (23)；
r(kalarm,i,krelease,i-1)＝[r(kalarm,i)Tr(kalarm,i+1)T… r(krelease,i-1)T], (24)；
T(i)＝diag(S(kalarm,i) S(kalarm,i+1) … S(krelease,i-1)), (26)；
G(i,j)11＝G(i,j){1:ny(krelease,i-kalarm,i),1}, (27)；
G(i,j)12＝G(i,j){1:ny(krelease,i-kalarm,i),2:ny}, (28)；
step 4.2: setting intermittent fault separation error fraction
Step 4.3: design intermittent fault separation threshold JI(j)
Wherein,
step 4.4: intermittent fault separation according to the following criteria
If TI(i,j)＞JI(j) If yes, the sensor j has a fault;
if TI(i,j)≤JI(j) Then sensor j has no fault;
step 4.5: calculating intermittent fault estimates
Wherein,
the invention has the following beneficial technical effects:
the method and the device fully explore redundant information which can be used for fault diagnosis, can detect, separate and estimate the fault of the intermittent sensor on line in real time, do not depend on a fault code table, and effectively meet the actual application requirement of the fault diagnosis of the intermittent sensor of the key system of the high-speed train.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of a fault curve of an intermittent sensor of a key system of the high-speed train.
Fig. 3 is a schematic diagram of a fault detection result of an intermittent sensor of a key system of the high-speed train.
Fig. 4 is a schematic diagram of a fault separation result of an intermittent sensor of a key system of the high-speed train.
FIG. 5 is a schematic diagram of the fault estimation result of the intermittent sensor of the critical system of the high-speed train.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
a robust intermittent sensor fault diagnosis method for a key system of a high-speed train is disclosed, the flow of which is shown in figure 1, and the method specifically comprises the following steps:
step 1: establishing a discrete time state space model of a key system of a high-speed train and identifying model parameters
Wherein,respectively, the system state, the control input and the measurement output; respectively, process noise and measurement noise;is a sensor failure; is a system parameter;is the parameter uncertainty; the following conditions are satisfied: the mean, covariance, and second moment of the initial state x (0) areP0，Σ0(ii) a The mean values of the noises w (k), v (k) are zero, and the covariance matrices are respectively sigmaw(k)，Σv(k)(ii) a Uncertainty of parameter Aδ(k),Bδ(k),Cδ(k) Has a mean value of zero and a covariance matrix of
Step 2: the method for designing the robust residual error generator of the key system of the high-speed train specifically comprises the following steps:
step 2.1: off-line computing gain matrix K (k)
K(k)＝G(k)Cc(k)TQ(k)-1, (2)；
Wherein,
step 2.2: computing robust residuals r (k) on-line
Wherein,
and step 3: the method for detecting the fault of the robust intermittent sensor of the key system of the high-speed train comprises the following steps:
step 3.1: calculating intermittent fault detection statistic TD(k)
Step 3.2: setting an intermittent fault detection false alarm rate Pfa
Pfa＝αfa, (12)；
Step 3.3: design intermittent Fault detection threshold JD
Wherein,
step 3.4: intermittent fault detection according to the following criteria
If TD(k-1)≤JD,TD(k)＞JDIf so, a fault occurs at the moment k, and the fault alarm indication quantity Ia＝1；
If TD(k-1)＞JD,TD(k)≤JDIf so, the fault disappears at the moment k, and the fault release indication quantity Ir＝1；
Accordingly, the fault alarm time and the fault release time of the ith intermittent fault are respectively
kalarm,i＝min(k|TD(k)＞JD,k≥krelease,i-1+1), (15)；
krelease,i＝min(k|TD(k)≤JD,k≥kalarm,i+1), (16)；
The failure is shown in fig. 2, and the failure detection result is shown in fig. 3.
And 4, step 4: the method for designing the fault separation and estimation of the robust intermittent sensor of the key system of the high-speed train specifically comprises the following steps:
step 4.1: calculating intermittent fault separation statistic TI(i,j)
Wherein,
L(i,j)11＝G(i,j)11 TT(i)-1G(i,j)11, (18)；
L(i,j)12＝G(i,j)11 TT(i)-1G(i,j)12, (19)；
L(i,j)21＝G(i,j)12 TT(i)-1G(i,j)11, (20)；
L(i,j)22＝G(i,j)12 TT(i)-1G(i,j)12, (21)；
d(i,j)1＝G(i,j)11 TT(i)-1r(kalarm,i,krelease,i-1), (22)；
d(i,j)2＝G(i,j)12 TT(i)-1r(kalarm,i,krelease,i-1), (23)；
r(kalarm,i,krelease,i-1)＝[r(kalarm,i)Tr(kalarm,i+1)T… r(krelease,i-1)T], (24)；
T(i)＝diag(S(kalarm,i) S(kalarm,i+1) … S(krelease,i-1)), (26)；
G(i,j)11＝G(i,j){1:ny(krelease,i-kalarm,i),1}, (27)；
G(i,j)12＝G(i,j){1:ny(krelease,i-kalarm,i),2:ny}, (28)；
step 4.2: setting intermittent fault separation error fraction
Step 4.3: design intermittent fault separation threshold JI(j)
Wherein,
step 4.4: intermittent fault separation according to the following criteria
If TI(i,j)＞JI(j) If yes, the sensor j has a fault;
if TI(i,j)≤JI(j) Then sensor j has no fault;
step 4.5: calculating intermittent fault estimates
Wherein,
the results of fault isolation and fault estimation are shown in fig. 4 and 5, respectively.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.

Claims (1)

1. A robust intermittent sensor fault diagnosis method for a key system of a high-speed train is characterized by comprising the following steps: the method specifically comprises the following steps:
step 1: establishing a discrete time state space model of a key system of a high-speed train and identifying model parameters
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>c</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>A</mi> <mi>&amp;delta;</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>c</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>B</mi> <mi>&amp;delta;</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>w</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>C</mi> <mi>&amp;delta;</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>v</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein,respectively, the system state, the control input and the measurement output; respectively, process noise and measurement noise;is a sensor failure; is a system parameter;is the parameter uncertainty; the following conditions are satisfied: the mean value of the initial state x (0),covariance, second moment ofP0，Σ0(ii) a The mean values of the noises w (k), v (k) are zero, and the covariance matrices are respectively sigmaw(k)，Σv(k)(ii) a Uncertainty of parameter Aδ(k),Bδ(k),Cδ(k) Has a mean value of zero and a covariance matrix of
Step 2: the method for designing the robust residual error generator of the key system of the high-speed train specifically comprises the following steps:
step 2.1: off-line computing gain matrix K (k)
K(k)＝G(k)Cc(k)TQ(k)-1, (2)；
Wherein,
<mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>A</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>A</mi> <mi>&amp;delta;</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>B</mi> <mi>&amp;delta;</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <mi>w</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
<mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <msub> <mi>C</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>C</mi> <mi>&amp;delta;</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <msub> <mi>&amp;Sigma;</mi> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <mi>v</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
<mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <msub> <mi>n</mi> <mi>x</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mi>x</mi> </msub> </mrow> </msub> <mo>-</mo> <mi>K</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
step 2.2: computing robust residuals r (k) on-line
<mrow> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein,
<mrow> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mn>0</mn> </msub> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
<mrow> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>B</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
<mrow> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
<mrow> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>K</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
and step 3: the method for detecting the fault of the robust intermittent sensor of the key system of the high-speed train comprises the following steps:
step 3.1: calculating intermittent fault detection statistic TD(k)
<mrow> <msub> <mi>T</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>r</mi> <msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mi>P</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>C</mi> <mi>&amp;delta;</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <mi>v</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Step 3.2: setting an intermittent fault detection false alarm rate Pfa
Pfa＝αfa, (12)；
Step 3.3: design intermittent Fault detection threshold JD
<mrow> <msub> <mi>J</mi> <mi>D</mi> </msub> <mo>=</mo> <msubsup> <mi>&amp;chi;</mi> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>f</mi> <mi>a</mi> </mrow> </msub> <mn>2</mn> </msubsup> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein,
<mrow> <mi>P</mi> <mo>{</mo> <msub> <mi>T</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&gt;</mo> <msubsup> <mi>&amp;chi;</mi> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>f</mi> <mi>a</mi> </mrow> </msub> <mn>2</mn> </msubsup> <mo>|</mo> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>~</mo> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mn>0</mn> <mrow> <msub> <mi>n</mi> <mi>y</mi> </msub> <mo>&amp;times;</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mi>P</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>C</mi> <mi>&amp;delta;</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <mi>v</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>)</mo> </mrow> <mo>}</mo> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>f</mi> <mi>a</mi> </mrow> </msub> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
step 3.4: intermittent fault detection according to the following criteria
If TD(k-1)≤JD,TD(k)＞JDIf so, a fault occurs at the moment k, and the fault alarm indication quantity Ia＝1；
If TD(k-1)＞JD,TD(k)≤JDIf so, the fault disappears at the moment k, and the fault release indication quantity Ir＝1；
Accordingly, the fault alarm time and the fault release time of the ith intermittent fault are respectively
kalarm,i＝min(k|TD(k)＞JD,k≥krelease,i-1+1), (15)；
krelease,i＝min(k|TD(k)≤JD,k≥kalarm,i+1), (16)；
And 4, step 4: the method for designing the fault separation and estimation of the robust intermittent sensor of the key system of the high-speed train specifically comprises the following steps:
step 4.1: calculating intermittent fault separation statistic TI(i,j)
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mi>I</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mi>d</mi> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>1</mn> </msub> <mo>-</mo> <mi>L</mi> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>12</mn> </msub> <mi>L</mi> <msup> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>22</mn> </msub> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>d</mi> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;times;</mo> <msup> <mrow> <mo>(</mo> <mi>L</mi> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>11</mn> </msub> <mo>-</mo> <mi>L</mi> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>12</mn> </msub> <mi>L</mi> <msup> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>22</mn> </msub> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>L</mi> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>21</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mi>d</mi> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>1</mn> </msub> <mo>-</mo> <mi>L</mi> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>12</mn> </msub> <mi>L</mi> <msup> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>22</mn> </msub> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>d</mi> <msub> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein,
L(i,j)11＝G(i,j)11 TT(i)-1G(i,j)11, (18)；
L(i,j)12＝G(i,j)11 TT(i)-1G(i,j)12, (19)；
L(i,j)21＝G(i,j)12 TT(i)-1G(i,j)11, (20)；
L(i,j)22＝G(i,j)12 TT(i)-1G(i,j)12, (21)；
d(i,j)1＝G(i,j)11 TT(i)-1r(kalarm,i,krelease,i-1), (22)；
d(i,j)2＝G(i,j)12 TT(i)-1r(kalarm,i,krelease,i-1), (23)；
r(kalarm,i,krelease,i-1)＝[r(kalarm,i)Tr(kalarm,i+1)T…r(krelease,i-1)T], (24)；
<mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <msub> <mi>n</mi> <mi>y</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mo>(</mo> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>)</mo> <mi>Z</mi> <mo>(</mo> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>)</mo> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <msub> <mi>n</mi> <mi>y</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mi>Z</mi> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <msub> <mi>n</mi> <mi>y</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> <mi>e</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> <mi>Z</mi> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> <mi>e</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
T(i)＝diag(S(kalarm,i) S(kalarm,i+1) … S(krelease,i-1)), (26)；
G(i,j)11＝G(i,j){1:ny(krelease,i-kalarm,i),1}, (27)；
G(i,j)12＝G(i,j){1:ny(krelease,i-kalarm,i),2:ny}, (28)；
step 4.2: setting intermittent fault separation error fraction
<mrow> <msub> <mi>P</mi> <msubsup> <mi>f</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </msubsup> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <msubsup> <mi>f</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </msubsup> </msub> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>29</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Step 4.3: design intermittent fault separation threshold JI(j)
<mrow> <mi>P</mi> <mo>{</mo> <msub> <mi>T</mi> <mi>I</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>&gt;</mo> <msubsup> <mi>&amp;chi;</mi> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>f</mi> <mi>a</mi> </mrow> </msub> <mn>2</mn> </msubsup> <mo>|</mo> <msubsup> <mi>f</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> <mo>}</mo> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <msubsup> <mi>f</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </msubsup> </msub> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>30</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein,
<mrow> <msub> <mi>J</mi> <mi>I</mi> </msub> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <msubsup> <mi>f</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </msubsup> </msub> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
step 4.4: intermittent fault separation according to the following criteria
If TI(i,j)＞JI(j) If yes, the sensor j has a fault;
if TI(i,j)≤JI(j) Then sensor j has no fault;
step 4.5: calculating intermittent fault estimates
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>=</mo> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mo>{</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mn>1</mn> <msup> <mi>R</mi> <mo>+</mo> </msup> </msub> <mrow> <mo>(</mo> <mi>&amp;xi;</mi> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>-</mo> <msub> <mi>J</mi> <mi>I</mi> </msub> <mo>(</mo> <mn>1</mn> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mn>1</mn> <msup> <mi>R</mi> <mo>+</mo> </msup> </msub> <mrow> <mo>(</mo> <mi>&amp;xi;</mi> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mn>2</mn> </mrow> <mo>)</mo> <mo>-</mo> <msub> <mi>J</mi> <mi>I</mi> </msub> <mo>(</mo> <mn>2</mn> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <msub> <mn>1</mn> <msup> <mi>R</mi> <mo>+</mo> </msup> </msub> <mrow> <mo>(</mo> <mi>&amp;xi;</mi> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <msub> <mi>n</mi> <mi>y</mi> </msub> </mrow> <mo>)</mo> <mo>-</mo> <msub> <mi>J</mi> <mi>I</mi> </msub> <mo>(</mo> <msub> <mi>n</mi> <mi>y</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;times;</mo> <mi>arg</mi> <munder> <mi>max</mi> <mi>&amp;beta;</mi> </munder> <mi>ln</mi> <mrow> <mo>(</mo> <mi>p</mi> <mo>(</mo> <mrow> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>r</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> <mi>e</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>|</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>&amp;beta;</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mo>{</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mn>1</mn> <msup> <mi>R</mi> <mo>+</mo> </msup> </msub> <mrow> <mo>(</mo> <mi>&amp;xi;</mi> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>-</mo> <msub> <mi>J</mi> <mi>I</mi> </msub> <mo>(</mo> <mn>1</mn> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mn>1</mn> <msup> <mi>R</mi> <mo>+</mo> </msup> </msub> <mrow> <mo>(</mo> <mi>&amp;xi;</mi> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <mn>2</mn> </mrow> <mo>)</mo> <mo>-</mo> <msub> <mi>J</mi> <mi>I</mi> </msub> <mo>(</mo> <mn>2</mn> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <msub> <mn>1</mn> <msup> <mi>R</mi> <mo>+</mo> </msup> </msub> <mrow> <mo>(</mo> <mi>&amp;xi;</mi> <mo>(</mo> <mrow> <mi>i</mi> <mo>,</mo> <msub> <mi>n</mi> <mi>y</mi> </msub> </mrow> <mo>)</mo> <mo>-</mo> <msub> <mi>J</mi> <mi>I</mi> </msub> <mo>(</mo> <msub> <mi>n</mi> <mi>y</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;times;</mo> <mi>S</mi> <msup> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> <mi>e</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>h</mi> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> <mi>e</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>32</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein,
<mrow> <mi>S</mi> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> <mi>e</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> <mi>e</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <msub> <mi>n</mi> <mi>y</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mo>(</mo> <mi>l</mi> <mo>)</mo> <mi>Z</mi> <mo>(</mo> <mi>l</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mi>Q</mi> <msup> <mrow> <mo>(</mo> <mi>l</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <msub> <mi>n</mi> <mi>y</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mo>(</mo> <mi>l</mi> <mo>)</mo> <mi>Z</mi> <mo>(</mo> <mi>l</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>33</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
<mrow> <mi>h</mi> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> <mi>e</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> <mi>e</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <msub> <mi>n</mi> <mi>y</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>n</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>c</mi> </msub> <mo>(</mo> <mi>l</mi> <mo>)</mo> <mi>Z</mi> <mo>(</mo> <mi>l</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mi>Q</mi> <msup> <mrow> <mo>(</mo> <mi>l</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>r</mi> <mrow> <mo>(</mo> <mi>l</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>34</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
CN201710554307.XA 2017-07-10 2017-07-10 A kind of robust interval sensor fault diagnosis method of bullet train critical system Pending CN107703740A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710554307.XA CN107703740A (en) 2017-07-10 2017-07-10 A kind of robust interval sensor fault diagnosis method of bullet train critical system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710554307.XA CN107703740A (en) 2017-07-10 2017-07-10 A kind of robust interval sensor fault diagnosis method of bullet train critical system

Publications (1)

Publication Number Publication Date
CN107703740A true CN107703740A (en) 2018-02-16

Family

ID=61170641

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710554307.XA Pending CN107703740A (en) 2017-07-10 2017-07-10 A kind of robust interval sensor fault diagnosis method of bullet train critical system

Country Status (1)

Country Link
CN (1) CN107703740A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109325310A (en) * 2018-10-25 2019-02-12 山东科技大学 A kind of bullet train intermittent fault detection method based on the multiple side's T control figure
CN109839264A (en) * 2019-03-13 2019-06-04 山东科技大学 High-speed train braking system intermittent fault detection method under closed loop

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6317698B1 (en) * 1999-04-06 2001-11-13 Ford Global Technologies, Inc. Observer for transfer case fault detection in a four-wheel drive system
US20050114023A1 (en) * 2003-11-26 2005-05-26 Williamson Walton R. Fault-tolerant system, apparatus and method
CN102253663A (en) * 2011-03-25 2011-11-23 清华大学 Leakage fault diagnose method and system thereof for networked three-container water tank system
CN102436179A (en) * 2011-11-25 2012-05-02 中国电力科学研究院 Design method of robustness fault detection filter of linear uncertain system
CN104360679A (en) * 2014-10-21 2015-02-18 南京航空航天大学 Train suspension system fault diagnosis and fault-tolerant control method based on dynamic actuator
CN105867360A (en) * 2016-06-14 2016-08-17 江南大学 Initial value prediction iterative learning fault diagnosis algorithm of electromechanical control system
CN106525466A (en) * 2016-10-14 2017-03-22 清华大学 Robust filtering method and system for a key part of motor train unit braking system

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6317698B1 (en) * 1999-04-06 2001-11-13 Ford Global Technologies, Inc. Observer for transfer case fault detection in a four-wheel drive system
US20050114023A1 (en) * 2003-11-26 2005-05-26 Williamson Walton R. Fault-tolerant system, apparatus and method
CN102253663A (en) * 2011-03-25 2011-11-23 清华大学 Leakage fault diagnose method and system thereof for networked three-container water tank system
CN102436179A (en) * 2011-11-25 2012-05-02 中国电力科学研究院 Design method of robustness fault detection filter of linear uncertain system
CN104360679A (en) * 2014-10-21 2015-02-18 南京航空航天大学 Train suspension system fault diagnosis and fault-tolerant control method based on dynamic actuator
CN105867360A (en) * 2016-06-14 2016-08-17 江南大学 Initial value prediction iterative learning fault diagnosis algorithm of electromechanical control system
CN106525466A (en) * 2016-10-14 2017-03-22 清华大学 Robust filtering method and system for a key part of motor train unit braking system

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
秦利国等: "一种基于鲁棒残差生成器的故障估计方法", 《上海交通大学学报》 *
鄢镕易等: "一类存在参数摄动的线性随机系统的鲁棒间歇故障诊断方法", 《自动化学报》 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109325310A (en) * 2018-10-25 2019-02-12 山东科技大学 A kind of bullet train intermittent fault detection method based on the multiple side's T control figure
CN109325310B (en) * 2018-10-25 2023-05-05 山东科技大学 High-speed train intermittent fault detection method based on multiple T-square control diagram
CN109839264A (en) * 2019-03-13 2019-06-04 山东科技大学 High-speed train braking system intermittent fault detection method under closed loop

Similar Documents

Publication Publication Date Title
CN107272651B (en) A kind of Robust Detection Method of Braking System for Multiple Units interval multiplying property sensor fault
CN104483962B (en) The online fault detection method of batch process based on multidirectional orthogonal locality preserving projections
CN110879372B (en) Traction system main loop earth fault diagnosis method and system based on feature correlation
CN105976578A (en) High-speed train axle temperature dynamic alarm threshold setting method based on monitoring data
CN111351664A (en) Bearing temperature prediction and alarm diagnosis method based on LSTM model
CN103776654A (en) Method for diagnosing faults of multi-sensor information fusion
CN107703740A (en) A kind of robust interval sensor fault diagnosis method of bullet train critical system
CN112947392B (en) Flight control system actuator and sensor composite tiny fault estimation method based on robust observer
CN111222247A (en) Early fault early warning method for rotary machine
CN108415402B (en) Consider the EMU robust filtering fault detection method of event-driven and output saturation
CN105043761A (en) Locomotive locking shaft fault diagnosis method
CN106959397A (en) A kind of method for designing of small fault diagnostic system for high ferro inverter
CN108170955B (en) Robust state monitoring and fault detection method considering saturation effect of random sensor
Pang et al. An integrated LSTM-AM and SPRT method for fault early detection of forced-oxidation system in wet flue gas desulfurization
CN105989435A (en) Method for estimating equipment maintenance period based on RCM theory
CN110146757B (en) Electromagnetic valve structural fault diagnosis method for ECAS system
CN102778889A (en) Intermittent fault fault-tolerance analyzing method of spacecraft attitude control system
CN110187206B (en) Fault detection method for suspension system in non-Gaussian process under complex working condition
Sang et al. Incipient fault detection for air brake system of high-speed trains
CN107356282A (en) Bullet train robust interval Transducer-fault Detecting Method in the case of resolution limitations
CN110058124A (en) The intermittent fault detection method of Linear Discrete Time-delay Systems
CN108874741A (en) A kind of relay valve leakage failure detection method based on SPRT algorithm
CN109325310B (en) High-speed train intermittent fault detection method based on multiple T-square control diagram
CN104977357B (en) Steel rail crack sound emission signal extracting and denoising method based on kalman filtering
CN106874589A (en) A kind of alarm root finding method based on data-driven

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20180216

RJ01 Rejection of invention patent application after publication