Summary of the invention
In order to overcome the most methodical deficiency, the present invention provides a kind of based on correction type independent component analysis and Bayesian probability
The industrial process fault detection method merged.The present invention solves the technical scheme that above-mentioned technical problem used: a kind of based on
The industrial process fault detection method that correction type independent component analysis and Bayesian probability merge, comprises the following steps:
(1) sampled data under production process normal operating condition is collected, the training dataset of composition modeling: X=
[x1, x1..., xn]T, wherein, X ∈ Rn×m, n is number of training, and m is process measurement variable number, and R is set of real numbers, Rn×mRepresent n
The real number matrix of × m dimension, upper label T representing matrix transposition.
(2) being standardized data set X processing, the average making each measurand is 0, and variance is 1, obtains new number
According to matrix
(3) utilize PCA method to data matrixCarry out whitening processing and obtain data matrix Z ∈ Rn×M.Wherein, M≤m is
Variable number in matrix Z.
(4) for different non-quadratic functions, call MICA iterative algorithm and set up different MICA Fault Models, always
Three MICA models set up by meter;
(5) training data is constructed corresponding T2And Q statistical magnitude, and utilize and density Estimation (KDE) method respectively obtain T2With
The control limit that Q statistical magnitude is corresponding under the conditions of confidence alpha=99%;
(6) new process sampled data x is collectedmew∈Rm×1, and be standardized process and obtain
(7) it is respectively adopted different MICA models and it is carried out fault detect, i.e. set up statistic T2And Q, such 3
MICA model amounts to and provides 3 groups corresponding to new samples dataMonitoring result;
(8) by Bayesian inference, obtain 3 groups of monitoring results are merged with the form of probability, is i.e. divided
Dui Yingyu T2Probabilistic type monitoring index with Q statistical magnitudeWith BIQ, and make about new dataDetermine the most normally
Plan.
Compared with the conventional method, it is an advantage of the current invention that: the present invention utilizes each non-quadratic function to set up respectively accordingly
MICA model.Then, introduce Bayesian inference method and the monitoring result under different models is carried out integrated and probability fusion, with
Obtain last comprehensive monitoring index.Compared to existing method, the present invention can solve to cause because of non-quadratic function multiformity
Model uncertain problem, add the reliability and stability of Fault Model.Therefore, the present invention can be to a great extent
The upper reduction MICA method dependency to priori, strengthens the reliability of Fault Model, thus advantageously in industry
The enforcement of automatization.
Specific implementation method
The present invention will be described in detail with specific embodiment below in conjunction with the accompanying drawings.
As it is shown in figure 1, the invention discloses a kind of industry merged based on correction type independent component analysis and Bayesian probability
Procedure failure testing method.For industrial process fault detection problem, just collecting production process first with data collecting system
The often data set under running status, and it is standardized.Secondly, corresponding MICA is set up for different non-quadratic functions
Fault Model, and model parameter is preserved with standby.Then, new sampled data is calculated three groups of different monitorings systems
Metering T2And Q, and utilize Bayesian probability fusion method that difference monitoring result is integrated into probability level.Finally, according to probability
Monitoring indexWith BIQWhether occurrence transfinites is made the most normal decision-making of new data.The present invention is embodied as step such as
Under:
The first step: collect the sampled data under production process normal operating condition, the training dataset of composition modeling: X
=[x1, x1..., xn]T。
Second step: being standardized data set X processing, the average making each measurand is 0, and variance is 1, obtains new
Data matrix
3rd step: utilize PCA method to data matrixCarry out whitening processing and obtain data matrix Z ∈ Rn×M, concrete operations
Step is as follows:
(1) calculateCovariance matrixWherein S ∈ Rm×m;
(2) calculate all eigenvalues and the characteristic vector of matrix S, and reject the eigenvalue less than 0.0001 and characteristic of correspondence thereof
Vector, obtains eigenvectors matrix P=[p1, p2..., pM]∈Rm×MAnd eigenvalue diagonal matrix D=diag (λ1, λ2...,
λM)∈RM×M;
(3) rightCarry out whitening processing, obtain
4th step: select kth non-quadratic function G from three kinds of non-quadratic functionskAfter, call MICA iterative algorithm and ask for
With GkCorresponding MICA Fault Model, repeats this and operates until setting up three MICA models, wherein, k=1, and 2,3 respectively
It it is the label of three kinds of different non-quadratic functions.
Calling MICA iterative algorithm, to set up the step of Fault Model as follows:
(1) independent entry number d needing to extract, and selected non-quadratic function G are setk, k=1,2,3, the most non-secondary
Function have following three kinds can preferred form of this:
G1(u)=log cosh (u), G2(u)=exp (-u2/ 2), G3(u)=u4 (1)
Wherein, u is function GkIndependent variable.
(2) when extract i-th (i=1,2 ..., d) during individual independent entry, choose M × M dimension unit matrix in i-th row as vector ci
Initial value;
(3) vector c is updated according to the following formulai:
ci←E{Zg(ci TZ)}-E{g′(ci TZ)}ci (2)
Wherein, g and g ' is single order and the second dervative of function G respectively, and E{} represents and asks for expected value;
(4) to the vectorial c after updatingiCarry out orthogonal standardization the most according to the following formula:
ci←ci/||ci|| (4)
(5) repeat step (3)~(4) until vector ciConvergence, and preserve vector ci;
(6) arranging i=i+1, repeat the above steps (2)~(5) are until obtaining all d vector C=[c1, c2..., cd]∈RM ×d。
(7) calculate corresponding to non-quadratic function GkThe hybrid matrix A of MICA modelk∈Rm×dWith separation matrix Wk∈Rd×m, as
Under:
Ak=PD1/2C (5)
Wk=CTD-1/2PT (6)
5th step: training data is constructed corresponding T2And Q statistical magnitude, and utilize and density Estimation (KDE) method respectively
To T2The control limit corresponding under the conditions of confidence alpha=99% is 99% with Q statistical magnitudeAnd Qlim;
6th step: collect new process sampled data xnew∈Rm×1, and be standardized process and obtain
7th step: be respectively adopted different MICA models and it is carried out fault detect, set up statistics the most respectively
AmountAnd Qk, such 3 MICA models amount to and provide 3 groups corresponding to new samples dataMonitoring result;
Wherein, | | | | represent the 2-norm calculating vector.
8th step: by Bayesian inference, obtain 3 groups of monitoring results are merged with the form of probability, to obtain final product
To corresponding respectively to T2Probabilistic type monitoring index with Q statistical magnitudeWith BIQ, and make about new dataThe most normal
Decision-making.Concrete implementation detail is further described as follows:
First, Bayesian probability fusion is carried out:
(A) to three groups of T2Statistic merges:
(1) new data is calculated according to the following formulaBelong to the probability of fault:
Wherein, probabilityCalculation as follows:
Wherein, N and F represents normal and fault condition, prior probability respectivelyWithValue α and 1-α, condition respectively
ProbabilityWithCalculation as follows:
(2) it is calculated final probabilistic type index by equation below
(B) three groups of Q statistical magnitude are merged
It is directed to Q statistical magnitude, first calculates new dataBelong to the probability of fault, conditional probability etc., then obtain final
Probabilistic type index BIQ, with above-mentioned fusion T2The mode of statistic is identical.
Secondly, fault decision-making is carried out:
By calculatedWith BIQThe concrete numerical value of index and probability control limit 1-α and contrast.If any one index
Numerical value is more than 1-α, then decision-making new dataFor fault sample;Otherwise, these dataFor normal sample and then new to the next one
The data that sampling obtains proceed fault detect.
Below in conjunction with the example of a concrete industrial process illustrate the present invention relative to the most methodical superiority with
Reliability.This process data comes from U.S.'s Tennessee-Yi Siman (TE) chemical process experiment, and prototype is Yi Siman Chemical Manufacture
One actual process flow process in workshop.At present, TE process is because of the complexity of its flow process, as a standard test platform by extensively
General for fault detect research.Whole TE process includes that 22 measurands, 12 performance variables and 19 composition measurements become
Amount.The data gathered are divided into 22 groups, including the data set under 1 group of nominal situation and 21 groups of fault datas.And at these
In fault data, having 16 is known fault type, such as cooling water inlet temperature or the change of feed constituents, valve viscous, anti-
Answering kinetics drift etc., also 5 fault types are unknown.In order to this process is monitored, choose as shown in table 1 33
Individual process variable, next combines this TE process and the present invention is embodied as step is explained in detail.
1. gather the process data under nominal situation, gather fault datas different in 21 simultaneously, and choose 960 normally
Data composition matrix X ∈ R960×33, it is standardized processing to it.
2. utilize PCA method to the data after standardizationCarry out whitening processing and obtain Z ∈ R960×31。
3. independent entry number d=9 of reservation, confidence alpha=99% are set, select different non-quadratic function to carry out MICA mould
Type is set up:
1) non-quadratic function G is selected1Carry out MICA modeling, obtain corresponding hybrid matrix A1∈R33×9With separation matrix W1∈R9 ×33.Then T is constructed2And Q statistical magnitude, and determine that it controls limit accordingly by KDE methodAnd Q1, lim;
2) non-quadratic function G is selected2Carry out MICA modeling, obtain corresponding hybrid matrix A2∈R33×9With separation matrix W2∈R9 ×33.Then T is constructed2And Q statistical magnitude, and determine that it controls limit accordingly by KDE methodAnd Q2, lim;
3) non-quadratic function G is selected3Carry out MICA modeling, obtain corresponding hybrid matrix A3∈R33×9With separation matrix W3∈R9 ×33.Then T is constructed2And Q statistical magnitude, and determine that it controls limit accordingly by KDE methodAnd Q3, lim。
4. obtain current new sampled data, and it is standardized process obtains
In order to verify that the present invention, relative to the most methodical superiority, chooses 21 kinds of faults and tests, equally to sampling
Data are standardized processing.
5. implement on-line monitoring process
1) utilize three kinds of different MICA Fault Models that new data is monitored, the statistic under structure corresponding model
And Qk;
2) Bayesian probability fusion calculation is utilized to obtain probabilistic type monitoring indexWith BIQ, and occurrence is controlled limit with probability
1-α contrasts, and decision-making current data is the most normal.
Table 1:TE process monitoring variable.
Sequence number |
Variable description |
Sequence number |
Variable description |
Sequence number |
Variable description |
1 |
Material A flow |
12 |
Separator liquid level |
23 |
D material inlet valve position |
2 |
Material D flow |
13 |
Separator pressure |
24 |
E material inlet valve position |
3 |
Material E flow |
14 |
Separator tower underflow amount |
25 |
A material inlet valve position |
4 |
Combined feed flow |
15 |
Stripper grade |
26 |
A and C material inlet valve position |
5 |
Circular flow |
16 |
Pressure of stripping tower |
27 |
Compressor cycle valve location |
6 |
Reactor feed |
17 |
Stripper bottom rate |
28 |
Emptying valve location |
7 |
Reactor pressure |
18 |
Stripper temperature |
29 |
Separator liquid phase valve location |
8 |
Reactor grade |
19 |
Stripper upper steam |
30 |
Stripper liquid phase valve location |
9 |
Temperature of reactor |
20 |
Compressor horsepower |
31 |
Stripper steam valve position |
10 |
Rate of evacuation |
21 |
Reactor cooled water outlet temperature |
32 |
Reactor condensate flow |
11 |
Separator temperature |
22 |
Separator cooling water outlet temperature |
33 |
Condenser cooling water flow |
Choose 18 typical faults (removing fault 3, fault 9 and fault 15) to be monitored, by mean failure rate verification and measurement ratio pair
The results are shown in Table 2 for ratio.Result shows that the inventive method has been obviously improved fault detect rate, improves fault detect effect.
Table 2: distinct methods is to the mean failure rate verification and measurement ratio of fault type in TE process 18.
Above-mentioned case study on implementation is only used for illustrating being embodied as rather than limiting the invention of the present invention.?
In the protection domain of spirit and claims of the present invention, any amendment that the present invention is made, both fall within the protection of the present invention
Scope.