CN110298385B - exergy information and incremental SVDD (singular value decomposition) based online early fault detection method - Google Patents

exergy information and incremental SVDD (singular value decomposition) based online early fault detection method Download PDF

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CN110298385B
CN110298385B CN201910486042.3A CN201910486042A CN110298385B CN 110298385 B CN110298385 B CN 110298385B CN 201910486042 A CN201910486042 A CN 201910486042A CN 110298385 B CN110298385 B CN 110298385B
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CN110298385A (en
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周猛飞
张强
刘志红
蔡亦军
潘海天
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Zhejiang University of Technology ZJUT
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Abstract

The invention provides a method based on
Figure DDA0002085413680000011
An online early failure detection method of information and increment SVDD. Based on
Figure DDA0002085413680000012
An online early fault detection method for describing SVDD by information and incremental support vector data comprises the steps of firstly standardizing process measurement data under normal working conditions to obtain a process training sample set and corresponding process training sample sets
Figure DDA0002085413680000013
An information value; calculating each measured variable and
Figure DDA0002085413680000014
screening out characteristic variables related to energy efficiency according to the accumulated mutual information contribution rate by using mutual information values between effects; establishing an SVDD initial model, and respectively carrying out self-adaptive updating of mutual information values and updating of an incremental SVDD model on newly added samples in the process to obtain an incremental SVDD state model under a normal working condition; and obtaining models in different states according to the measurement data in different states, and using the models for online early fault detection. The invention combines the advantages of an energy-based method and a data-based driving method, not only can solve the problem of time-varying characteristics of system parameters in the process, but also can effectively extract energy characteristic variables in the process, improve the speed and the precision of early fault detection and effectively realize the on-line detection of early faults.

Description

exergy information and incremental SVDD (singular value decomposition) based online early fault detection method
Technical Field
The invention relates to the field of on-line monitoring of early process faults, in particular to a method based on
Figure GDA0002980446300000012
An information and increment Support Vector Data Description (SVDD) online early fault detection method.
Background
The SVDD is a single-class classification algorithm based on a support domain, has intuitive data description and good popularization performance, can solve the problem that fault samples are difficult to obtain in the actual process, and is widely applied to the fields of fault diagnosis and the like. However, SVDD needs to solve the quadratic programming problem, the training complexity is high, and the training complexity is exponential to the number of samples. In the SVDD fault detection research, in order to reduce the SVDD computation complexity and improve the effectiveness of sample data, a feature sample is extracted by performing feature dimension reduction by using a statistical method, and then a SVDD classification model is established by using the feature sample to realize fault detection.
Figure GDA0002980446300000013
As a concept combining the first and second laws of thermodynamics, it can be used to better understand the process, quantify the direction of low efficiency and differentiate the quality of energy, it is a common concept in many fields such as physics, chemistry, mechanical mechanics, etc., and it adopts
Figure GDA0002980446300000014
The concept of (2) can also reduce data dimensionality. Based on
Figure GDA0002980446300000015
The information method can effectively reduce the modeling workload, increase the calculation efficiency, and maintain the similarity to a great extent while reducing the dimension of the model.
Figure GDA0002980446300000016
Is effective in chemical process system
Figure GDA0002980446300000017
The concrete expression of the information and the evaluation index of the overall energy quality of the process are based on
Figure GDA0002980446300000018
The information extraction method is to extract the information in the process
Figure GDA0002980446300000019
The effect is extracted, thereby achieving the effect of reducing the dimension.
However, in the actual industrial production process, the system process parameters change along with the advance of time, the fault characteristics change along with the change of the system process parameters, the fault detection model needs to train a new sample, at this time, the SVDD has to abandon the original trained model, new data needs to be retrained together with historical data, the algorithm complexity is known, and the calculation complexity of the algorithm increases exponentially along with the continuous update of the new data sample. Once a large amount of data samples are trained online, a large amount of computation time and storage space are wasted in the training process of the SVDD, so that the algorithm cannot meet the requirement of real-time updating of the system. Compared with the traditional batch SVDD, the incremental learning technology can inherit the learned knowledge and update the model according to the new data sample on the basis of the original model, so that the model knowledge has accumulativeness, and the time-varying problem of the actual process can be solved. Meanwhile, the historical energy characteristic variables cannot be applied to new process conditions and new data, and the energy characteristic variables need to be extracted from the sets of the historical data and the new data again. Typically, the most recent measured variable data highlights the characteristics of the current process system, while older historical data reflects system characteristics that are more distant from the most recent system state. Therefore, in order to reflect the current characteristics of the system in time, the influence of the historical data is reduced by adding weights to the historical data, and a forgetting factor can be added. In addition, the forgetting factor needs to be reasonably adjusted according to the change condition of the current system parameters. If the on-line extraction can be effectively carried out from the sample set
Figure GDA0002980446300000029
Information, the fault detection algorithm is used after the energy characteristic sample set is constructed, and the early fault detection efficiency can be obviously improved.
Disclosure of Invention
Aiming at the problem of time-varying characteristics of system parameters in the actual process and the problem that the screened energy characteristics are difficult to reflect the dynamic characteristics of the process, the invention respectively adopts an incremental learning algorithm and an energy characteristic extraction method based on a variable forgetting factor, and the method can adaptively extract the faults in the process
Figure GDA00029804463000000210
And meanwhile, an incremental detection model which is continuously updated can be established, so that an early fault detection method is provided.
Based on
Figure GDA00029804463000000211
The online early fault detection method of the information and increment SVDD comprises the following steps:
(1) collecting process measurement variables and
Figure GDA00029804463000000212
the effect sample is standardized to obtain
Figure GDA0002980446300000021
And Y0(ii) a The method comprises the following steps of performing data preprocessing on a sample, wherein the preprocessing is mainly performed by adopting data standardization, and the specific implementation steps are as follows:
for training sample data x1,x2,…xNSample xiThe calculation formula of the normalization process is as follows:
Figure GDA0002980446300000022
wherein x isi、
Figure GDA0002980446300000023
Respectively representing the ith original off-line sample and the normalized sample, wherein theta is the arithmetic mean of all sample data, and sigma is the variance of all samples. Through standardization processing, detection errors caused by variable measuring ranges can be eliminated;
(2) in the calculation step 1
Figure GDA0002980446300000024
And Y0With different measured variables from each other
Figure GDA00029804463000000213
Mutual information value of effects
Figure GDA0002980446300000025
Screening and selecting according to the principle of accumulated mutual information contribution rate
Figure GDA00029804463000000214
Efficient most relevant set of energy feature sample set X0The detailed steps for establishing the energy characteristic sample are as follows:
in order to reduce the influence of the sample size on mutual information estimation, a K-nearest neighbor method is adopted to calculate a mutual information value between two variables:
Figure GDA0002980446300000026
wherein N is the number of total samples, k is the number of neighbors, sxAnd syAre respectively represented as
Figure GDA0002980446300000027
And Y0The number of nearest neighbor samples in the subspace, phi (·) is a digamma function. Meanwhile, in order to ensure that the mutual information can effectively extract the energy information, the cumulative mutual information contribution degree of the selected g measurement variables can be as follows:
Figure GDA0002980446300000028
CPMI indicates that the first g features are included
Figure GDA00029804463000000215
Effect information accounting system
Figure GDA00029804463000000216
The ratio of the effective information is generally used to determine the number of features to be screened. Since the mutual information of each feature is greater than 0, the CPMI monotonically increases within the value range of the number of the screened features. In order to achieve relatively good feature dimension reduction effect, CPMI is required to be larger than a specified control limit;
(3) energy feature sample set X obtained in step 20And constructing an initial SVDD model gamma0The detailed steps for establishing the model are as follows:
given a training set x1,x2,…,xN]Where N is the number of samples. a and R represent the center and radius of the hypersphere, respectively. According to the principle of minimizing the structural risk, the hypersphere radius minimization problem can be described as the following quadratic programming problem with inequality constraint, and simultaneously, a relaxation variable xi is introducediAnd a penalty factor C:
Figure GDA0002980446300000031
for the quadratic programming problem with the constraint condition, a lagrangian multiplier can be introduced, the quadratic programming problem is often easier to solve after being converted into a dual form, and a kernel function can be introduced to project an original space to a high-dimensional space so as to solve the nonlinear problem:
Figure GDA0002980446300000032
solving by a quadratic programming Optimization (SMO) algorithm to obtain an optimal solution alphaiThereby obtaining an initial SVDD modeType gamma0The model parameters of (1);
(4) introducing incremental samples
Figure GDA0002980446300000033
And Y1Then, self-adaptively updating the mutual information value corresponding to the incremental sample according to the energy feature extraction rule based on the variable forgetting factor
Figure GDA0002980446300000034
Screening out an energy feature set of the incremental sample according to a feature dimension reduction principle
Figure GDA0002980446300000035
The self-adaptive energy feature extraction method comprises the following steps:
after mutual information values corresponding to the newly added data samples are added with a forgetting factor rho, the newly added measurement samples at the t +1 th time
Figure GDA0002980446300000036
And corresponding
Figure GDA00029804463000000312
Effect data sample Yt+1The mutual information value between the two is as follows:
Figure GDA0002980446300000037
where rho epsilon (0, 1)]，
Figure GDA0002980446300000038
Representing the column vector formed by the characteristics of the jth measured variable in the t +1 th new sample, m refers to the number of the measured variables,
Figure GDA0002980446300000039
H(Yt+1)、
Figure GDA00029804463000000310
respectively representing the information entropy of the variable and the joint entropy value between the two.
The variable forgetting factor method can adaptively adjust the size of the current forgetting factor according to the parameter change of the time-varying system, and the variable forgetting factor ρ of the mutual information value of the newly added sample at the (k + 1) th time is as follows:
Figure GDA00029804463000000311
Figure GDA0002980446300000041
in the formula CPMIt+1The cumulative mutual information contribution rate g of the characteristic sample corresponding to the t +1 th newly added datat+1The value is selected according to the cumulative mutual information contribution rate of the current sample, CPMIt+1The value is typically greater than 0.85. Finally, the CPMI from the current sample sett+1Screening out a new energy feature set
Figure GDA0002980446300000042
(5) According to the initial SVDD model gamma of step 30And step 4) energy characteristic sample
Figure GDA0002980446300000043
Updating to obtain an incremental SVDD model gamma1The specific steps of incremental updating are as follows:
1) statistics and statistical limits;
given sample set X ═ X1,x2,…,xN]The dual form of the SVDD hypersphere radius optimization problem is as follows:
Figure GDA0002980446300000044
wherein
Figure GDA0002980446300000045
Delta is the optimal compensation factor and the kernel function can be recorded as Kij＝K(xi,xj) (ii) a From the KKT condition, W is the optimum solution for alphaiThe first derivative of δ needs to satisfy the following condition:
Figure GDA0002980446300000046
Figure GDA0002980446300000047
wherein Ω (x)i) Is a sample discriminant function of SVDD.
As can be seen from equation (10), the KKT condition of SVDD generally divides the training sample set into three categories: an intra-sphere non-support vector R, a standard support vector S, and a boundary support vector E. For new sample x just addeduThe model parameters need to be changed to make the extended sample set reach the KKT condition again, so as to obtain a new optimal solution, where the model coefficients change as:
Figure GDA0002980446300000048
wherein alpha isuIs the new sample x just addeduCorresponding Lagrange multiplier, Δ αuFor the variance of Lagrange multiplier of new sample, Delta alphajAnd adding the Lagrange multiplier variable quantity of the original sample set for the new sample. The standard support vector model coefficient variance can be written as:
Figure GDA0002980446300000049
let T equal to K-1For samples in the E, R set, its κi≡ 0, known from formula (13):
Figure GDA00029804463000000513
order to
Figure GDA0002980446300000052
In the formula (I), the compound is shown in the specification,
Figure GDA0002980446300000053
is a model boundary sensitivity factor, for samples within the S set, which
Figure GDA0002980446300000054
When the compound is brought into the formula (12), the following components are included:
Figure GDA0002980446300000055
2) sample attribute migration;
the sample attribute migration is based on the delta sample model coefficient variation Δ αuAnd adjusting the change of the original sample model coefficient to enable the extended sample set to satisfy the KKT condition again so as to tend to a new equilibrium state. In the process of migrating the attributes of the incremental samples, the attributes all meet delta alphau>0, six different sample attribute migration scenarios are introduced below:
①κsattribute value set corresponding to standard support vector set
Figure GDA0002980446300000056
The s-th number in (1) can be calculated by the formula (14)sIf it satisfies the upper limit Δ αs≤C-αsThen Δ αuAnd kappasSame number, xsChange from standard support vector to boundary support vector:
Figure GDA0002980446300000057
wherein λ is a migration factor.
If delta alphasAt a lower limit Δ αs≥-αsThen, delta αuAnd kappasOpposite sign, xsSupported by a standardVector becomes the intra-sphere non-support vector:
Figure GDA0002980446300000058
③ for the non-support vector x in the ballrThen there is dr>0，
Figure GDA0002980446300000059
The r-th element as the non-SVM sensitization factor set in the sphere can be calculated according to the formula (16) to obtain delta dr. If Δ dr<0, intra-sphere non-support vector xrWould become the standard support vector:
Figure GDA00029804463000000510
support vector x for boundarieseThen there is dr<0, the e-th element of the set of non-SVM sensitivity factors within the sphere can be represented as
Figure GDA00029804463000000511
Can be calculated to obtain
Figure GDA00029804463000000512
If Δ de>0, boundary support vector xeWould become the standard support vector:
Figure GDA0002980446300000061
commonly set increment sample xuWhen d is zerouIf x is greater than or equal to 0, the sample x is considereduAnd the model sample coefficients are not required to be updated if the target class samples are within the sphere. When d isu<0, incremental sample xuThen it becomes the standard support vector:
Figure GDA0002980446300000062
alpha in the incremental SVDD model training processuThe upper bound value is a penalty factor C when alpha isuWhen C is less than or equal to C, increment sample alphauWill become a boundary support vector with delta coefficient variation of:
λma＝C-αu (22)
in incremental SVDD, let Δ αmax＝min{λsp,λsm,λrs,λes,λu,λmaAs incremental samples alphauThe coefficient variation of the original model sample obtained by the equation (14) is delta alphai；
3) Updating a T matrix;
the T matrix model in equation (13) also needs to be updated in the incremental iteration process, and in order to reduce the complexity of calculating the inverse matrix, the following update strategy is adopted. For an arbitrary sample xl∈R∪E∪{xuBecome the standard support vector with T +1 updates of the process Tt+1Comprises the following steps:
Figure GDA0002980446300000063
when the standard supports vector xlWhen leaving set S, Tt+1Comprises the following steps:
Figure GDA0002980446300000064
(6) continuously introducing an incremental sample, and dynamically updating an incremental SVDD model gamma t times according to the steps 4) and 5)t. And for different fault state samples, calculating the incremental SVDD model gamma of different fault statesth；
(7) To online test sample set
Figure GDA0002980446300000065
Data standardization and energy feature extraction are carried out, and h fault state models corresponding to the data standardization and the energy feature extraction are calculatedRelative distance gamma of the moldh(xhi) Based on the principle of minimum relative distance, the fault state category corresponding to the sample is detected and identified, and the detailed steps are as follows:
the relative distance-based discrimination method can strengthen the discrimination rule and improve the fault state detection rate of the algorithm by dividing by the radius of the hypersphere in each fault state model. The relative distance can not only detect the fault, but also judge the severity of the fault. Using relative distance as criterion:
Figure GDA0002980446300000071
compared with the prior art, the invention has the beneficial effects that:
the invention combines the advantages of an energy-based method and a data-based driving method, not only can solve the problem of time-varying characteristics of system parameters in the process, but also can effectively extract energy characteristic variables in the process, improve the speed and the precision of early fault detection and effectively realize the on-line detection of early faults.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of a commercial propylene rectification column;
FIG. 3 is a graph comparing incremental and batch model training times;
FIGS. 4 a-4 c are online early failure detection results of a prior SVDD method, wherein FIG. 4a is the sample's performance on a normal state model, FIG. 4b is the sample's performance on a moderate degradation state model, and FIG. 4c is the sample's performance on a severe degradation state model;
FIGS. 5 a-5 c are online early failure detection results of the incremental SVDD method, wherein FIG. 5a is the sample's performance on the normal state model, FIG. 5b is the sample's performance on the moderate degradation state model, and FIG. 5c is the sample's performance on the severe degradation state model;
fig. 6a to 6c are online early failure detection results of the method of the present invention, wherein fig. 6a is the representation of a sample on a normal state model, fig. 6b is the representation of a sample on a moderate degradation state model, and fig. 6c is the representation of a sample on a severe degradation state model.
Detailed Description
The invention will now be described in detail with reference to the plant examples and the accompanying drawings, in order to provide a thorough understanding of the effectiveness of the process and method of the invention as applied and practiced by way of example.
Based on
Figure GDA0002980446300000072
The information and increment SVDD online early fault detection method has the following specific implementation mode:
the industrial propylene rectifying tower is used as a research object, the feeding of the tower mainly comprises propane and propylene, the relative volatility of the propane and the propylene is close to 1, and in order to achieve a better separation effect, the two towers are connected in series for operation. The flow of a commercial propylene rectification column is shown in FIG. 2. The No. 1 propylene rectifying tower is equivalent to a stripping section in the rectifying process, the tower is provided with 77 layers of tower plates, and the tower bottom discharge is used as circulating propane under the condition of flow control. And pumping tower kettle materials of the No. 2 propylene rectifying tower into the top of the No. 1 propylene rectifying tower through a reflux pump to serve as the top reflux of the No. 1 propylene rectifying tower. The propylene product is passed through an overhead cooler and then to a propylene product guard bed to remove some of the oxide impurities. The industrial rectification case is based on ASPEN simulation of a propylene rectification tower of a certain plant, and the propylene rectification process is simulated by using Aspen Tech 8.4 software. In order to simulate the scaling fault of the heat exchanger in the rectification process, a double-material-flow heat exchanger module with detailed calculation is adopted in the process, the total heat transfer coefficient is calculated according to the membrane coefficient and the pipe wall resistance calculated by the geometric structure, and the condenser scaling factor is selected to generate step change to simulate the early fault of the rectification process. If the fouling factor of the condenser is increased, the heat transfer efficiency is reduced, the heat flux of the heat exchanger is reduced, and the process is effective
Figure GDA0002980446300000089
Is wasted and the waste is generated,
Figure GDA00029804463000000810
the effect will be reduced。
Figure GDA00029804463000000811
The effect is taken as an index for measuring the effective energy utilization efficiency of the process, and the early failure condition of the rectification process can be obviously reflected, so that the step change of the fouling factor of the condenser is adopted to indicate whether the early failure occurs or not. During the simulation, the fouling factor parameter of the condenser of column 2 was varied from 0 to 8.6X 10-3(sqm K)/Watt to simulate early failure during rectification.
(1) Collecting process measurement variables and
Figure GDA00029804463000000812
the effect sample is standardized to obtain
Figure GDA0002980446300000081
And Y0(ii) a The method comprises the following steps of performing data preprocessing on a sample, wherein the preprocessing is mainly performed by adopting data standardization, and the specific implementation steps are as follows:
for training sample data x1,x2,…xNSample xiThe calculation formula of the normalization process is as follows:
Figure GDA0002980446300000082
wherein x isi、
Figure GDA0002980446300000083
Respectively representing the ith original off-line sample and the normalized sample, wherein theta is the arithmetic mean of all sample data, and sigma is the variance of all samples. Through standardization processing, detection errors caused by variable measuring ranges can be eliminated;
(2) in the calculation step 1
Figure GDA0002980446300000084
And Y0With different measured variables from each other
Figure GDA00029804463000000813
Mutual information value of effects
Figure GDA0002980446300000085
Screening and selecting according to the principle of accumulated mutual information contribution rate
Figure GDA00029804463000000814
Efficient most relevant set of energy feature sample set X0The detailed steps for establishing the energy characteristic sample are as follows:
in order to reduce the influence of the sample size on mutual information estimation, a K-nearest neighbor method is adopted to calculate a mutual information value between two variables:
Figure GDA0002980446300000086
wherein N is the number of total samples, k is the number of neighbors, sxAnd syAre respectively represented as
Figure GDA0002980446300000087
And Y0The number of nearest neighbor samples in the subspace, phi (·) is a digamma function. Meanwhile, in order to ensure that the mutual information can effectively extract the energy information, the cumulative mutual information contribution degree of the selected g measurement variables can be as follows:
Figure GDA0002980446300000088
CPMI indicates that the first g features are included
Figure GDA00029804463000000815
Effect information accounting system
Figure GDA00029804463000000816
The ratio of the effective information is generally used to determine the number of features to be screened. Since the mutual information of each feature is greater than 0, the CPMI monotonically increases within the value range of the number of the screened features. To achieveThe relatively good characteristic dimension reduction effect needs to ensure that the CPMI is larger than the specified control limit, and the control limit is usually 85%;
(3) energy feature sample set X obtained in step 20And constructing an initial SVDD model gamma0The detailed steps for establishing the model are as follows:
given a training set x1,x2,…,xN]Where N is the number of samples. a and R represent the center and radius of the hypersphere, respectively. According to the principle of minimizing the structural risk, the hypersphere radius minimization problem can be described as the following quadratic programming problem with inequality constraint, and simultaneously, a relaxation variable xi is introducediAnd a penalty factor C:
Figure GDA0002980446300000091
for the quadratic programming problem with the constraint condition, a lagrangian multiplier can be introduced, the quadratic programming problem is often easier to solve after being converted into a dual form, and a kernel function can be introduced to project an original space to a high-dimensional space so as to solve the nonlinear problem:
Figure GDA0002980446300000092
solving by a quadratic programming Optimization (SMO) algorithm to obtain an optimal solution alphaiThereby obtaining an initial SVDD model gamma0The model parameters of (1);
(4) introducing incremental samples
Figure GDA0002980446300000093
And Y1Then, self-adaptively updating the mutual information value corresponding to the incremental sample according to the energy feature extraction rule based on the variable forgetting factor
Figure GDA0002980446300000094
Screening out energy characteristics of incremental samples according to a characteristic dimension reduction principleCollection
Figure GDA0002980446300000095
The self-adaptive energy feature extraction method comprises the following steps:
after mutual information values corresponding to the newly added data samples are added with a forgetting factor rho, the newly added measurement samples at the t +1 th time
Figure GDA0002980446300000096
And corresponding
Figure GDA00029804463000000912
Effect data sample Yt+1The mutual information value between the two is as follows:
Figure GDA0002980446300000097
where rho epsilon (0, 1)]，
Figure GDA0002980446300000098
Representing the column vector formed by the characteristics of the jth measured variable in the t +1 th new sample, m refers to the number of the measured variables,
Figure GDA0002980446300000099
H(Yt+1)、
Figure GDA00029804463000000910
respectively representing the information entropy of the variable and the joint entropy value between the two.
The variable forgetting factor method can adaptively adjust the size of the current forgetting factor according to the parameter change of the time-varying system, and the variable forgetting factor ρ of the mutual information value of the newly added sample at the (k + 1) th time is as follows:
Figure GDA00029804463000000911
Figure GDA0002980446300000101
in the formula CPMIt+1The cumulative mutual information contribution rate g of the characteristic sample corresponding to the t +1 th newly added datat+1The value is selected according to the cumulative mutual information contribution rate of the current sample, CPMIt+1The value is typically greater than 0.85. Finally, the CPMI from the current sample sett+1Screening out a new energy feature set
Figure GDA0002980446300000102
(5) According to the initial SVDD model gamma of step 30And step 4) energy characteristic sample
Figure GDA0002980446300000103
Updating to obtain an incremental SVDD model gamma1The specific steps of incremental updating are as follows:
1) statistics and statistical limits;
given sample set X ═ X1,x2,…,xN]The dual form of the SVDD hypersphere radius optimization problem is as follows:
Figure GDA0002980446300000104
wherein
Figure GDA0002980446300000105
Delta is the optimal compensation factor and the kernel function can be recorded as Kij＝K(xi,xj) (ii) a From the KKT condition, W is the optimum solution for alphaiThe first derivative of δ needs to satisfy the following condition:
Figure GDA0002980446300000106
Figure GDA0002980446300000107
wherein Ω (x)i) Is a sample discriminant function of SVDD.
As can be seen from equation (10), the KKT condition of SVDD generally divides the training sample set into three categories: an intra-sphere non-support vector R, a standard support vector S, and a boundary support vector E. For new sample x just addeduThe model parameters need to be changed to make the extended sample set reach the KKT condition again, so as to obtain a new optimal solution, where the model coefficients change as:
Figure GDA0002980446300000108
wherein alpha isuIs the new sample x just addeduCorresponding Lagrange multiplier, Δ αuFor the variance of Lagrange multiplier of new sample, Delta alphajAnd adding the Lagrange multiplier variable quantity of the original sample set for the new sample. The standard support vector model coefficient variance can be written as:
Figure GDA0002980446300000109
let T equal to K-1For samples in the E, R set, its κi≡ 0, known from formula (13):
Figure GDA00029804463000001113
order to
Figure GDA0002980446300000112
In the formula (I), the compound is shown in the specification,
Figure GDA0002980446300000113
is a model boundary sensitivity factor, for samples within the S set, which
Figure GDA0002980446300000114
When the compound is brought into the formula (12), the following components are included:
Figure GDA0002980446300000115
2) sample attribute migration;
the sample attribute migration is based on the delta sample model coefficient variation Δ αuAnd adjusting the change of the original sample model coefficient to enable the extended sample set to satisfy the KKT condition again so as to tend to a new equilibrium state. In the process of migrating the attributes of the incremental samples, the attributes all meet delta alphau>0, six different sample attribute migration scenarios are introduced below:
①κsattribute value set corresponding to standard support vector set
Figure GDA0002980446300000116
The s-th number in (1) can be calculated by the formula (14)sIf it satisfies the upper limit Δ αs≤C-αsThen Δ αuAnd kappasSame number, xsChange from standard support vector to boundary support vector:
Figure GDA0002980446300000117
wherein λ is a migration factor.
If delta alphasAt a lower limit Δ αs≥-αsThen, delta αuAnd kappasOpposite sign, xsFrom the standard support vector to the intra-sphere non-support vector:
Figure GDA0002980446300000118
③ for the non-support vector x in the ballrThen there is dr>0，
Figure GDA0002980446300000119
The r-th element as the set of non-SVM sensitivity factors within the sphere, according to the formula(16) Can calculate to obtain delta dr. If Δ dr<0, intra-sphere non-support vector xrWould become the standard support vector:
Figure GDA00029804463000001110
support vector x for boundarieseThen there is dr<0, the e-th element of the set of non-SVM sensitivity factors within the sphere can be represented as
Figure GDA00029804463000001111
Can be calculated to obtain
Figure GDA00029804463000001112
If Δ de>0, boundary support vector xeWould become the standard support vector:
Figure GDA0002980446300000121
commonly set increment sample xuWhen d is zerouIf x is greater than or equal to 0, the sample x is considereduAnd the model sample coefficients are not required to be updated if the target class samples are within the sphere. When d isu<0, incremental sample xuThen it becomes the standard support vector:
Figure GDA0002980446300000122
alpha in the incremental SVDD model training processuThe upper bound value is a penalty factor C when alpha isuWhen C is less than or equal to C, increment sample alphauWill become a boundary support vector with delta coefficient variation of:
λma＝C-αu (22)
in incremental SVDD, let Δ αmax＝min{λsp,λsm,λrs,λes,λu,λmaAsIncremental sample alphauThe coefficient variation of the original model sample obtained by the equation (14) is delta alphai；
3) Updating a T matrix;
the T matrix model in equation (13) also needs to be updated in the incremental iteration process, and in order to reduce the complexity of calculating the inverse matrix, the following update strategy is adopted. For an arbitrary sample xl∈R∪E∪{xuBecome the standard support vector with T +1 updates of the process Tt+1Comprises the following steps:
Figure GDA0002980446300000123
when the standard supports vector xlWhen leaving set S, Tt+1Comprises the following steps:
Figure GDA0002980446300000124
(6) continuously introducing an incremental sample, and dynamically updating an incremental SVDD model gamma t times according to the steps 4) and 5)t. And for different fault state samples, calculating the incremental SVDD model gamma of different fault statesth；
(7) To online test sample set
Figure GDA0002980446300000125
Carrying out data standardization and energy feature extraction, and calculating the relative distance gamma of the h fault state modelsh(xhi) Based on the principle of minimum relative distance, the fault state category corresponding to the sample is detected and identified, and the detailed steps are as follows:
the relative distance-based discrimination method can strengthen the discrimination rule and improve the fault state detection rate of the algorithm by dividing by the radius of the hypersphere in each fault state model. The relative distance can not only detect the fault, but also judge the severity of the fault. Using relative distance as criterion:
Figure GDA0002980446300000131
the most essential difference between the incremental SVDD and the SVDD is structural inheritance, so the training time of the incremental SVDD is shorter than that of the traditional SVDD, as shown in fig. 3. According to the results, as the number of samples is continuously increased, the difference between the training time of the SVDD model and the incremental SVDD is larger and larger. The reason is that the traditional SVDD algorithm has to put the last training sample and the newly added sample together for retraining to solve the secondary optimization problem, so that the historical samples are repeatedly trained, and meanwhile, the samples which are just added are not reasonably screened; different from the batch-type SVDD, the inheritability of the structure brings the advantage that the incremental SVDD can update the model by using the last training result, and the incremental SVDD selectively performs learning training on the incremental samples, so that the training time can be obviously reduced.
The method of the invention is compared with the SVDD method and the incremental SVDD online early detection rate, and the detection results are shown in Table 1. Comparing the detection results of the SVDD method and the incremental SVDD method, the difference between the incremental algorithm and the non-incremental algorithm in the fault detection rate is not obvious. The incremental SVDD has smaller hypersphere space and more training data dimension and sample number than the non-incremental SVDD, thereby showing that the incremental SVDD can selectively reserve the samples which are most likely to be the support vectors, and shortening the training time without reducing the fault detection rate. That is to say, the incremental algorithm does not sacrifice the classification capability to improve the training speed of the model, which indicates that the incremental algorithm is more suitable for the problem of system dynamic change. The results in table 1 and fig. 4, 5, 6 also show that the algorithm failure detection rate without energy feature extraction is lower than the algorithm failure detection rate with energy feature extraction, demonstrating that the algorithm based on energy feature extraction has a lower failure detection rate
Figure GDA0002980446300000133
The feature dimension reduction technology for information extraction can effectively eliminate irrelevant noise information and extract fault change features, and improves the classification performance of the model, so that the actual production process is guided to a certain extent.
TABLE 1 detection rates of different methods in early failure states
Figure GDA0002980446300000132
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms set forth in the embodiments but rather by the equivalents thereof as may occur to those skilled in the art upon consideration of the present inventive concept.

Claims (1)

1. Based on
Figure FDA0002980446290000019
The online early fault detection method of the information and increment SVDD comprises the following steps:
1) collecting process measurement variables and
Figure FDA00029804462900000110
the effect sample is standardized to obtain
Figure FDA0002980446290000011
And Y0(ii) a The method comprises the following steps of preprocessing a sample by data standardization, wherein the preprocessing comprises the following specific implementation steps:
for training sample data x1,x2,…xNSample xiThe calculation formula of the normalization process is as follows:
Figure FDA0002980446290000012
wherein x isi、
Figure FDA0002980446290000013
Respectively represent the ith original separationLine samples and normalized samples, theta is the arithmetic mean of all sample data, and sigma is the variance of all samples;
2) in the calculation step 1)
Figure FDA0002980446290000014
And Y0With different measured variables from each other
Figure FDA00029804462900000112
Mutual information value of effects
Figure FDA0002980446290000015
Screening and selecting according to the principle of accumulated mutual information contribution rate
Figure FDA00029804462900000111
Efficient most relevant set of energy feature sample set X0The detailed steps for establishing the energy characteristic sample are as follows:
in order to reduce the influence of the sample size on mutual information estimation, a K-nearest neighbor method is adopted to calculate a mutual information value between two variables:
Figure FDA0002980446290000016
wherein N is the number of total samples, k is the number of neighbors, sxAnd syAre respectively represented as
Figure FDA0002980446290000017
And Y0The number of nearest neighbor samples in the subspace, phi (·) is a digamma function; meanwhile, in order to ensure that the mutual information can effectively extract the energy information, the cumulative mutual information contribution degree of the selected g measurement variables can be as follows:
Figure FDA0002980446290000018
CPMI represents pre-stageg features comprising
Figure FDA00029804462900000113
Effect information accounting system
Figure FDA00029804462900000114
The proportion of the effective information is used for determining the number of the screened features; because the mutual information of each feature is greater than 0, the CPMI is monotonically increased within the value range of the screened feature number; in order to achieve relatively good feature dimension reduction effect, CPMI is required to be larger than a specified control limit;
3) the energy characteristic sample set X obtained in the step 2)0And constructing an initial SVDD model gamma0The detailed steps for establishing the model are as follows:
given a training set x1,x2,…,xN]Wherein N is the number of samples; a and R represent the center and radius of the hypersphere, respectively. According to the principle of minimizing the structural risk, the hypersphere radius minimization problem can be described as the following quadratic programming problem with inequality constraint, and simultaneously, a relaxation variable xi is introducediAnd a penalty factor C:
Figure FDA0002980446290000021
for the quadratic programming problem with the constraint condition, a lagrangian multiplier can be introduced, the quadratic programming problem is often easier to solve after being converted into a dual form, and a kernel function can be introduced to project an original space to a high-dimensional space so as to solve the nonlinear problem:
Figure FDA0002980446290000022
obtaining an optimal solution alpha through solving a quadratic programming optimization algorithm SMO algorithmiThereby obtaining an initial SVDD model gamma0The model parameters of (1);
4) introducing incremental samples
Figure FDA0002980446290000023
And Y1Then, self-adaptively updating the mutual information value corresponding to the incremental sample according to the energy feature extraction rule based on the variable forgetting factor
Figure FDA0002980446290000024
Screening out an energy feature set of the incremental sample according to a feature dimension reduction principle
Figure FDA0002980446290000025
The self-adaptive energy feature extraction method comprises the following steps:
after mutual information values corresponding to the newly added data samples are added with a forgetting factor rho, the newly added measurement samples at the t +1 th time
Figure FDA0002980446290000026
And corresponding
Figure FDA00029804462900000213
Effect data sample Yt+1The mutual information value between the two is as follows:
Figure FDA0002980446290000027
where rho epsilon (0, 1)]，
Figure FDA0002980446290000028
Representing the column vector formed by the characteristics of the jth measured variable in the t +1 th new sample, m refers to the number of the measured variables,
Figure FDA0002980446290000029
H(Yt+1)、
Figure FDA00029804462900000210
individual watchThe information entropy of the argument and the joint entropy value between the two;
the variable forgetting factor method can adaptively adjust the size of the current forgetting factor according to the parameter change of the time-varying system, and the variable forgetting factor ρ of the mutual information value of the newly added sample at the (k + 1) th time is as follows:
Figure FDA00029804462900000211
Figure FDA00029804462900000212
in the formula CPMIt+1The cumulative mutual information contribution rate g of the characteristic sample corresponding to the t +1 th newly added datat+1The value is selected according to the principle of the accumulated mutual information contribution rate of the current sample; finally, the CPMI from the current sample sett+1Screening out a new energy feature set
Figure FDA0002980446290000031
5) The initial SVDD model gamma according to the step 3)0And step 4) energy characteristic sample
Figure FDA0002980446290000032
Updating to obtain an incremental SVDD model gamma1The specific steps of incremental updating are as follows:
5-1) statistics and statistical limits;
given sample set X ═ X1,x2,…,xN]The dual form of the SVDD hypersphere radius optimization problem is as follows:
Figure FDA0002980446290000033
wherein
Figure FDA0002980446290000034
Delta is the optimal compensation factor and the kernel function can be recorded as Kij＝K(xi,xj) (ii) a From the KKT condition, W is the optimum solution for alphaiThe first derivative of δ needs to satisfy the following condition:
Figure FDA0002980446290000035
Figure FDA0002980446290000036
wherein Ω (x)i) A sample discrimination function for SVDD;
as can be seen from equation (10), the KKT condition of SVDD generally divides the training sample set into three categories: an intra-sphere non-support vector R, a standard support vector S and a boundary support vector E; for new sample x just addeduThe model parameters need to be changed to make the extended sample set reach the KKT condition again, so as to obtain a new optimal solution, where the model coefficients change as:
Figure FDA0002980446290000037
wherein alpha isuIs the new sample x just addeduCorresponding Lagrange multiplier, Δ αuFor the variance of Lagrange multiplier of new sample, Delta alphajThe Lagrange multiplier variation of the original sample set after the new sample is added; the standard support vector model coefficient variance can be written as:
Figure FDA0002980446290000041
let T equal to K-1For samples in the E, R set, its κi≡ 0, known from formula (13):
Figure FDA0002980446290000042
order to
Figure FDA0002980446290000043
In the formula (I), the compound is shown in the specification,
Figure FDA0002980446290000044
is a model boundary sensitivity factor, for samples within the S set, which
Figure FDA0002980446290000045
When it is carried into formula (12):
Figure FDA0002980446290000046
5-2) sample attribute migration;
the sample attribute migration is based on the delta sample model coefficient variation Δ αuAdjusting the change of the original sample model coefficient to enable the extended sample set to satisfy the KKT condition again so as to tend to a new equilibrium state; in the process of migrating the attributes of the incremental samples, the attributes all meet delta alphau>0, the sample attribute migration cases are divided into the following six types:
①κsattribute value set corresponding to standard support vector set
Figure FDA0002980446290000047
The s-th number in (1) can be calculated by the formula (14)sIf it satisfies the upper limit Δ αs≤C-αsThen Δ αuAnd kappasSame number, xsChange from standard support vector to boundary support vector:
Figure FDA0002980446290000048
wherein λ is a migration factor;
if delta alphasAt a lower limit Δ αs≥-αsThen, delta αuAnd kappasOpposite sign, xsFrom the standard support vector to the intra-sphere non-support vector:
Figure FDA0002980446290000049
③ for the non-support vector x in the ballrThen there is dr>0，
Figure FDA00029804462900000410
The r-th element as the non-SVM sensitization factor set in the sphere can be calculated according to the formula (16) to obtain delta dr(ii) a If Δ dr<0, intra-sphere non-support vector xrWould become the standard support vector:
Figure FDA0002980446290000051
support vector x for boundarieseThen there is dr<0, the e-th element of the set of non-SVM sensitivity factors within the sphere can be represented as
Figure FDA0002980446290000052
Can be calculated to obtain
Figure FDA0002980446290000053
If Δ de>0, boundary support vector xeWould become the standard support vector:
Figure FDA0002980446290000054
commonly set increment sample xuWhen d is zerouIs more than or equal to 0Then the sample x is considereduIf the target class sample is the intra-sphere target class sample, the model sample coefficient does not need to be updated; when d isu<0, incremental sample xuThen it becomes the standard support vector:
Figure FDA0002980446290000055
alpha in the incremental SVDD model training processuThe upper bound value is a penalty factor C when alpha isuWhen C is less than or equal to C, increment sample alphauWill become a boundary support vector with delta coefficient variation of:
λma＝C-αu (22)
in incremental SVDD, let Δ αmax＝min{λsp,λsm,λrs,λes,λu,λmaAs incremental samples alphauThe coefficient variation of the original model sample obtained by the equation (14) is delta alphai；
5-3) updating the T matrix;
the T matrix model in the formula (13) also needs to be updated in the incremental iteration process, and in order to reduce the complexity of calculating an inverse matrix, the following updating strategy is adopted; for an arbitrary sample xl∈R∪E∪{xuBecome the standard support vector with T +1 updates of the process Tt+1Comprises the following steps:
Figure FDA0002980446290000056
when the standard supports vector xlWhen leaving set S, Tt+1Comprises the following steps:
Figure FDA0002980446290000061
6) continuously introducing incremental samples, and dynamically updating t times of incremental SVDD model gamma according to step 4) and step 5)t(ii) a And forCalculating the incremental SVDD model gamma of different fault states by using the same fault state sampleth；
7) To online test sample set
Figure FDA0002980446290000062
Carrying out data standardization and energy feature extraction, and calculating the relative distance gamma of the h fault state modelsh(xhi) Based on the principle of minimum relative distance, the fault state category corresponding to the sample is detected and identified, and the detailed steps are as follows:
the discrimination method based on the relative distance can strengthen the judgment rule and improve the fault state detection rate of the algorithm by dividing the radius of the hypersphere in each fault state model; the relative distance can not only detect the fault, but also judge the severity of the fault; using relative distance as criterion:
Figure FDA0002980446290000063
。
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