CN106092625A - The industrial process fault detection method merged based on correction type independent component analysis and Bayesian probability - Google Patents

Abstract

The present invention relates to a kind of industrial process fault detection method merged based on correction type independent component analysis and Bayesian probability.Traditional fault detection method based on correction type independent component analysis needs to select the non-quadratic function of, to measure non-Gaussian system size.But, different industrial process datas or object can cause and be difficult to obtain abundant Heuristics in actual application and go to instruct the selection of non-quadratic function.To this, the inventive method, first against different non-quadratic functions, utilizes the normal data training of industrial process to obtain different correction type independent entry models；Then by Bayesian probability fusion method, the result of decision of these multiple Fault Models is carried out integrated, it is thus achieved that final probabilistic type monitoring index.Compared with the conventional method, the present invention can solve the model uncertain problem caused because of non-quadratic function multiformity, has taken into full account multiple model probability, has enhanced the reliability of Fault Model to a great extent.

Description

The industrial process fault inspection merged based on correction type independent component analysis and Bayesian probability Survey method

Technical field

The invention belongs to industrial process control field, particularly relate to a kind of general based on correction type independent component analysis and Bayes The industrial process fault detection method that rate merges.

Background technology

The production safety of modern industry process is had higher requirement by the market competition being growing more intense, timely and reliable Fault detection method become ingredient indispensable in whole production system.Owing to modern industry process is complicated and big Type trend, there will be different types of fault unavoidably in running.If fault warning cannot be triggered timely, it is possible to Cause operating accident, have a strong impact on the quality of product, even cause loss difficult to the appraisal on life and property.Therefore, how Set up relatively reliable and effective Fault Model, screen out the fault that production process occurs in time, be the most all One of problem that industrial quarters and academia are paid much attention to.

In existing fault detection method system, the fault detection method of data-driven has been developed as mainstream technology Means.Wherein, with pivot analysis (PCA) with independent component analysis (ICA) method as representative, by what extraction process data hid Useful information describes the essence of process operation, and whether monitor production process running status exception occurs on this basis.Phase Ratio is in PCA method, and ICA method is no longer required for process data approximation Gaussian distributed, and make use of the higher order statistical of data to believe Breath extracts the composition that hides of process data, is more suitable for processing the modeling of non-gaussian industrial process data and fault detection problem. But, traditional ICA method deposits some inevitable problems when setting up Fault Model.Firstly, since initial value Randomly generate, result in the uncertainty of set up model.Secondly, for the non-quadratic function of predictor non-Gaussian system degree Have three kinds can preferred form of this, this will also result in the uncertainty of institute's established model.Although, independent component analysis method (MICA) energy of correction type Preferably overcome first problem, but, the model uncertainty that the multiformity selected due to non-quadratic function is caused can reduce The accuracy of corresponding failure detection method and reliability.And want that finding a kind of non-quadratic function being suitable for various fault types is not Possible.If the failure detection result of the MICA model corresponding to different non-quadratic functions can be merged, i.e. consider institute Some model probabilities, this will significantly promote accuracy and the reliability of MICA method detection fault.

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..., x_n]^T, wherein, X ∈ R^n×m, n is number of training, and m is process measurement variable number, and R is set of real numbers, R^n×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 ∈ R^n×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 collected_mew∈R^m×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 BI_Q, 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.

Accompanying drawing explanation

Fig. 1 is the implementing procedure figure of method involved in the present invention.

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 BI_QWhether 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..., x_n]^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 ∈ R^n×M, concrete operations Step is as follows:

(1) calculateCovariance matrixWherein S ∈ R^m×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..., p_M]∈R^m×MAnd eigenvalue diagonal matrix D=diag (λ₁, λ₂..., λ_M)∈R^M×M；

(3) rightCarry out whitening processing, obtain

4th step: select kth non-quadratic function G from three kinds of non-quadratic functions_kAfter, call MICA iterative algorithm and ask for With G_kCorresponding 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 set_k, 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 G_kIndependent 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 c_i Initial value；

(3) vector c is updated according to the following formula_i:

c_i←E{Zg(c_i ^TZ)}-E{g′(c_i ^TZ)}c_i (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 updating_iCarry out orthogonal standardization the most according to the following formula:

$c_i\←c_i-{\mathrm{\Σ}}_{j=1}^{i-1}\left({c_i}^T{c}_i\right)c_j---\left(3\right)$

c_i←c_i/||c_i|| (4)

(5) repeat step (3)～(4) until vector c_iConvergence, and preserve vector c_i；

(6) arranging i=i+1, repeat the above steps (2)～(5) are until obtaining all d vector C=[c₁, c₂..., c_d]∈R^{M ×d}。

(7) calculate corresponding to non-quadratic function G_kThe hybrid matrix A of MICA model_k∈R^m×dWith separation matrix W_k∈R^d×m, as Under:

A_k=PD^1/2C (5)

W_k=C^TD^-1/2P^T (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 Q_lim；

6th step: collect new process sampled data x_new∈R^m×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 Q_k, such 3 MICA models amount to and provide 3 groups corresponding to new samples dataMonitoring result；

$T_k^2={{\stackrel{\‾}{x}}_{new}}^T{W}^{T}W{\stackrel{\‾}{x}}_{new}---\left(7\right)$

$Q_k=\left|\right|{\stackrel{\‾}{x}}_{new}-AW{\stackrel{\‾}{x}}_{new}|{|}^2---\left(8\right)$

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 BI_Q, 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:

$P_{T_k^2}\left(F\right|{\stackrel{\‾}{x}}_{new})=\frac{P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|F)P_{T_k^2}\left(F\right)}{P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right)}---\left(9\right)$

Wherein, probabilityCalculation as follows:

$P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right)=P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|N)P_{T_k^2}\left(N\right)+P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|F)P_{T_k^2}\left(F\right)---\left(10\right)$

Wherein, N and F represents normal and fault condition, prior probability respectivelyWithValue α and 1-α, condition respectively ProbabilityWithCalculation as follows:

$P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|N)=\exp (-\frac{T_k^2}{T_{k,\lim }^2}),P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|F)=\exp (-\frac{T_{k,\lim }^2}{T_k^2})---\left(11\right)$

(2) it is calculated final probabilistic type index by equation below

${\mathrm{BI}}_{T^2}=\underset{k=1}{\overset{3}{\Σ}}\left\{\frac{P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|F)P_{T_k^2}\left(F\right|{\stackrel{\‾}{x}}_{new})}{{\mathrm{\Σ}}_{k=1}^3{P}_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|F)}\right\}---\left(12\right)$

(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 BI_Q, with above-mentioned fusion T²The mode of statistic is identical.

Secondly, fault decision-making is carried out:

By calculatedWith BI_QThe 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 ∈ R^960×33, it is standardized processing to it.

2. utilize PCA method to the data after standardizationCarry out whitening processing and obtain Z ∈ R^960×31。

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∈R^33×9With separation matrix W₁∈R^{9 ×33}.Then T is constructed²And Q statistical magnitude, and determine that it controls limit accordingly by KDE methodAnd Q_{1, lim}；

2) non-quadratic function G is selected₂Carry out MICA modeling, obtain corresponding hybrid matrix A₂∈R^33×9With separation matrix W₂∈R^{9 ×33}.Then T is constructed²And Q statistical magnitude, and determine that it controls limit accordingly by KDE methodAnd Q_{2, lim}；

3) non-quadratic function G is selected₃Carry out MICA modeling, obtain corresponding hybrid matrix A₃∈R^33×9With separation matrix W₃∈R^{9 ×33}.Then T is constructed²And Q statistical magnitude, and determine that it controls limit accordingly by KDE methodAnd Q_{3, 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 Q_k；

2) Bayesian probability fusion calculation is utilized to obtain probabilistic type monitoring indexWith BI_Q, 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.

Claims (3)

1. the industrial process fault detection method merged based on correction type independent component analysis and Bayesian probability, its feature exists In: said method comprising the steps of:

(1) sampled data under production process normal operating condition is collected, the training dataset of composition modeling: X=[x₁, x₁..., x_n]^T, wherein, X ∈ R^n×m, n is number of training, and m is process measurement variable number, and R is set of real numbers, R^n×mRepresent n × m The real number matrix of 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 data square Battle array

(3) utilize PCA method to data matrixCarry out whitening processing and obtain data matrix Z ∈ R^n×M, wherein, M≤m is matrix Z Middle variable number, specific implementation is as follows:

1. calculateCovariance matrixWherein S ∈ R^m×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..., p_M]∈R^m×MAnd eigenvalue diagonal matrix D=diag (λ₁, λ₂..., λ_M)∈R^M×M；

The most rightCarry out whitening processing, obtain

(4) from three kinds of non-quadratic functions, kth non-quadratic function G is selected_kAfter, call MICA iterative algorithm and ask for and G_kRelatively The MICA Fault Model answered, repeats this and operates until setting up three MICA models, wherein, k=1, and 2,3 are respectively three kinds not The label of same non-quadratic function；

(5) training data is constructed corresponding T²And Q statistical magnitude, and utilize and density Estimation (KDE) method respectively obtain T²Unite with Q The control limit that metering is corresponding under the conditions of confidence alpha=99%；

(6) new process sampled data x is collected_new∈R^m×1, and be standardized process and obtain

(7) it is respectively adopted different MICA models and it is carried out fault detect, be i.e. constructed as follows shown statisticAnd Q_k, this 3 MICA models of sample amount to and provide 3 groups corresponding to new samples dataMonitoring result:

$T_k^2={{\stackrel{\‾}{x}}_{new}}^T{W}^{T}W{\stackrel{\‾}{x}}_{new}---\left(1\right)$

$Q_k=\left|\right|{\stackrel{\‾}{x}}_{new}-AW{\stackrel{\‾}{x}}_{new}|{|}^2---\left(2\right)$

Wherein, | | | | represent the 2-norm calculating vector；

(8) by Bayesian inference, obtain 3 groups of monitoring results are merged with the form of probability, i.e. obtains probabilistic type Monitoring indexWith BI_Q, and make about new dataThe most normal decision-making.

The industrial process fault detect merged based on correction type independent component analysis and Bayesian probability the most according to claim 1 Method, it is characterised in that described step (4) particularly as follows: first, can select non-quadratic function G preferred form of this from following three kinds_k, That is:

G₁(u)=log cosh (u), G₂(u)=exp (-u²/ 2), G₃(u)=u⁴ (3)

Wherein, u is the independent variable of function G；Secondly, for different non-quadratic function G_k, call MICA iterative algorithm and set up fault The step of detection model is as follows:

1. independent entry number d needing to extract, and selected non-quadratic function G are set_k；

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 c_i's Initial value；

Update vector c the most according to the following formula_i:

c_i←E{Zg(c_i ^TZ)}-E{g′(c_i ^TZ)}c_i (4)

Wherein, g and g ' is function G respectively_kSingle order and second dervative, E{} represents and asks for expected value；

4. to the vectorial c after updating_iCarry out orthogonal standardization the most according to the following formula:

$c_i\←c_i-{\mathrm{\Σ}}_{j=1}^{i-1}\left({c_i}^T{c}_i\right)c_j---\left(5\right)$

c_i←c_i/||c_i|| (6)

3.～4. 5. step is repeated until vector c_iConvergence, and preserve vector c_i；

2.～5. 6. arranging i=i+1, repeat the above steps is until obtaining all d vector C=[c₁, c₂..., c_d]∈R^M×d；

7. calculate corresponding to non-quadratic function G_kThe hybrid matrix A of MICA model_k∈R^m×dWith separation matrix W_k∈R^d×m, as follows:

A_k=PD^1/2C (7)

W_k=C^TD^-1/2P^T (8)

And preservation matrix A_kWith W_kWith standby.

The industrial process fault detect merged based on correction type independent component analysis and Bayesian probability the most according to claim 1 Method, it is characterised in that described step (8) particularly as follows:

First, Bayesian probability fusion is carried out:

(A) to three groups of T²Statistic merges:

Calculate new data the most according to the following formulaBelong to the probability of fault:

$P_{T_k^2}\left(F\right|{\stackrel{\‾}{x}}_{new})=\frac{P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|F)P_{T_k^2}\left(F\right)}{P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right)}---\left(9\right)$

Wherein, probabilityCalculation as follows:

$P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right)=P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|N)P_{T_k^2}\left(N\right)+P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|F)P_{T_k^2}\left(F\right)---\left(10\right)$

Wherein, N and F represents normal and fault condition, prior probability respectivelyWithValue α and 1-α, condition respectively ProbabilityWithCalculation as follows:

$P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|N)=\exp (-\frac{T_k^2}{T_{k,\lim }^2}),P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|F)=\exp (-\frac{T_{k,\lim }^2}{T_k^2})---\left(11\right)$

2. it is calculated final probabilistic type index by equation below

${\mathrm{BI}}_{T^2}=\underset{k=1}{\overset{3}{\mathrm{\Σ}}}\left\{\frac{P_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|F)P_{T_k^2}\left(F\right|{\stackrel{\‾}{x}}_{new})}{{\mathrm{\Σ}}_{k=1}^3{P}_{T_k^2}\left({\stackrel{\‾}{x}}_{new}\right|F)}\right\}---\left(12\right)$

(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 general Rate type index BI_Q, with above-mentioned fusion T²The mode of statistic is identical；

Secondly, fault decision-making is carried out:

By calculatedWith BI_QThe 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.