CN110232256B - KPLS (kernel principal component system) and RWFCM (wireless remote control unit) -based sewage treatment process monitoring method - Google Patents
KPLS (kernel principal component system) and RWFCM (wireless remote control unit) -based sewage treatment process monitoring method Download PDFInfo
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Abstract
The invention relates to the technical field of sewage treatment quality monitoring, and provides a KPLS and RWFCM-based sewage treatment process monitoring method. The method comprises the steps of firstly, collecting data samples of sewage treatment processes under normal working conditions and abnormal working conditions, respectively using data of sewage treatment operation variables and data of effluent quality variables as input and output data matrixes, and standardizing the two matrixes; then constructing a KPLS model and solving a score matrix; clustering the scoring matrix based on the RWFCM algorithm to obtain a membership matrix, and monitoring abnormal working conditions in the sewage treatment process according to the membership matrix; and finally, establishing a linear regression model of the membership matrix and the sample variable, solving the variable contribution matrix, and identifying abnormal working conditions in the sewage treatment process according to the variable contribution matrix. The invention can reduce the dimension of high-dimensional data and process nonlinear data, is insensitive to outliers, and can improve the timeliness and accuracy of monitoring and identifying the sewage treatment process.
Description
Technical Field
The invention relates to the technical field of sewage treatment quality monitoring, in particular to a sewage treatment process monitoring method based on KPLS and RWFCM.
Background
With the acceleration of the urbanization and industrialization process in China, the demand of the society on fresh water resources is increasing day by day, and the construction of municipal sewage treatment facilities needs to be accelerated to improve the municipal sewage treatment capacity. The activated sludge process is the main method for treating urban sewage at present. The activated sludge sewage purification mainly comprises 3 processes of initial adsorption, microorganism metabolism, flocculation formation and sedimentation, and the essence is that biodegradable organic matters in the sewage are adsorbed, decomposed and oxidized by utilizing the microorganism group in the activated sludge through a series of biochemical reactions, so that the biodegradable organic matters are separated from the sewage, and the aim of purifying the sewage is fulfilled.
At present, biochemical oxygen demand ([ BOD ]), chemical oxygen demand ([ COD ]), suspended matter ([ SS ]), ammonia nitrogen ([ NH ]), and total phosphorus ([ TP ]) are generally adopted as sewage discharge indexes. In the sewage treatment process, parameters such as water inlet flow, water inlet components, pollutant concentration, weather change and the like are passively accepted, and the life activities of microorganisms are influenced by various factors such as dissolved oxygen concentration, microorganism population, the pH value of sewage and the like, so that the long-term stable operation of the urban sewage treatment plant is very difficult to maintain. The failure of the sewage treatment plant easily causes the quality of the effluent not to reach the standard, increases the operation cost and causes environmental pollution. Therefore, if the abnormal working condition of the sewage treatment process cannot be detected in time, the correct judgment cannot be made and no powerful measures are taken in time for adjustment and correction, so that the irreversible loss of the sewage treatment process can be caused. Therefore, an operator can accurately judge the abnormal working condition by detecting the sewage treatment process, and timely and accurately take measures, so that the safety, stability and smooth operation of sewage treatment are ensured, and the quality of effluent is especially important.
The process monitoring method based on data driving is widely applied, wherein the multivariate statistical process monitoring method becomes one of research hotspots in the process monitoring field, and the research on the effluent quality monitoring of sewage treatment is promoted. The sewage treatment process is a complex nonlinear process, and historical fault data is not perfect, so that fault identification of fault variables is still a difficult problem in the sewage treatment effluent quality monitoring process.
The existing sewage treatment process monitoring method adopts a data mining method in recent years, and the main reason is that a large amount of data exists and can be widely used, and the data needs to be converted into useful information and knowledge urgently. Since sewage treatment process data has no classification identification and the occurrence of sewage treatment failures is not correlated much with time, it is not suitable to mine using classification or sequence pattern mining. The cluster analysis in the data mining technology is an unsupervised classification technology and can be well used for analyzing data with less prior knowledge, so that the cluster analysis technology is widely applied to sewage process monitoring.
The fuzzy c-means clustering (FCM) algorithm is one of the classical clustering algorithms. FCM gives the uncertainty degree of the sample to the category, and establishes the uncertainty description of the sample to the category, which is more consistent with the description of the objective world. However, the data of the sewage treatment process has high dimensionality and nonlinearity and has outliers, and the traditional FCM algorithm cannot process the high dimensionality and nonlinearity data and is very sensitive to the outliers, so that the difficulty of process monitoring is increased, the reliability of fault detection is reduced, the quality of the sewage effluent is greatly influenced, and certain economic loss and even accidents are caused. Meanwhile, the clustering number of the FCM algorithm needs to be preset manually, and the method has great limitation in practical application.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a KPLS and RWFCM-based sewage treatment process monitoring method, which can reduce the dimension of high-dimensional data and process nonlinear data, is insensitive to outliers, can accurately and conveniently determine the clustering number, and improves the timeliness and accuracy of sewage treatment process monitoring and identification.
The technical scheme of the invention is as follows:
a KPLS and RWFCM based sewage treatment process monitoring method is characterized by comprising the following steps:
step 1: respectively collecting data samples of a normal working condition and a sewage treatment process containing an abnormal working condition, wherein the data samples of the sewage treatment process comprise m 1 Operation variable m of sewage treatment 2 A water outlet quality variable; adding the sewage treatment process data sample under the normal working condition before the sewage treatment process data sample under the abnormal working condition from the time angle to form a mixed data sample set; collecting m mixed data samples 1 Taking the data of the running variables of the sewage treatment as an input data matrix X, and concentrating the mixed data samples into m 2 Taking the data of the effluent quality variable as an output data matrix Y;
step 2: preprocessing an input data matrix X and an output data matrix Y; the preprocessing comprises the steps of calculating the mean value and the standard deviation of all variables in an input data matrix X and an output data matrix Y, and normalizing the input data matrix X and the output data matrix Y into data with zero mean value and unit standard deviation;
and 3, step 3: constructing a KPLS (kernel principal component analysis) model for monitoring the sewage treatment process, and mapping an input sample X in an input data matrix X to a high-dimensional feature space F: x → phi (X) belongs to F, a Gaussian kernel function is introduced to obtain a Gram matrix K of the input data matrix X, and the Gram matrix K is subjected to centralization processing;
and 4, step 4: determining the number of pivot elements by adopting a cross verification method, and solving a score matrix T;
and 5: clustering the score matrix T based on the RWFCM algorithm to obtain a membership matrix U, and monitoring abnormal working conditions of the sewage treatment process according to the membership matrix U: if the membership degree of the sample to the clustering center of the normal working condition sample at a certain moment is less than mu, the sewage treatment process generates an abnormality at the sample;
and 6: establishing a linear regression model of variables in the membership matrix U and the input data matrix X, solving a variable contribution matrix N by adopting a Lagrange multiplier method, and identifying abnormal working conditions of the sewage treatment process according to the variable contribution matrix N: if the contribution of the a-th variable to all clusters { η } a1 ,...,η ac Maximum of η ag If the variable a is a fault variable related to the g abnormal working condition; wherein c is the number of clusters, g belongs to { 1., c-1}, and the c-th cluster is the cluster of the normal working condition sample.
The sewage treatment process adopts an activated sludge method, raw sewage enters a biochemical tank part after primary treatment, after biological denitrification, one part of the raw sewage enters a secondary sedimentation tank for sedimentation after denitrification again through internal circulation reflux; the biochemical pool part comprises a biochemical pool l belonging to {1,2,3,4,5}, wherein the biochemical pool l belongs to 1 Belongs to {1,2} as an anoxic zone mainly completing the denitrification reaction process, a biochemical pool 2 Belongs to {3,4,5} as an aerobic zone mainly completing the nitration reaction process; in the step 1, m is 1 The operation variables of the sewage treatment comprise inflow, inflow ammonia nitrogen, active heterotrophic bacteria biomass in a biochemical pond I E {1,2,3,4,5}, easily biodegradable organic substrate in the biochemical pond I E {1,2,3,4,5}, and alkali in the biochemical pond I E {1,2,3,4,5}Biochemical and biochemical pool 1 Amount of nitronium in E {1,2}, biochemical pool l 2 Active autotrophic bacteria biomass in epsilon {3,4,5}, biochemical pond l 2 Ammonia nitrogen content in E {3,4,5}, biochemical pool l 2 The dissolved oxygen in the element {3,4,5 }; m is said 2 The quality variables of the effluent comprise biochemical oxygen demand, chemical oxygen demand, suspended matters and ammonia nitrogen amount of the effluent.
The step 3 comprises the following steps:
step 3.1: the KPLS model for monitoring the sewage treatment process is constructed as
Φ＝TP 1 '+Φ r
Y＝TQ'+Y r
Step 3.2: mapping input samples X in an input data matrix X to a high-dimensional feature space F: x → phi (X) belongs to F, a Gaussian kernel function is introduced to obtain a Gram matrix K of the input data matrix X, the Gram matrix K is subjected to centralized processing, and a KPLS model is converted into a kernel-based modeling model
K＝TP 2 '+E
Y＝TQ'+Y r
Wherein, the element of the ith row and the jth column of the Gram matrix K is K ij ＝k(x i ,x j )＝<Φ(x i ),Φ(x j )>，x i 、x j Respectively, the ith input sample X in the input data matrix X i J-th input sample x j ，k(x i ,x j ) Is a Gaussian kernel function, i, j belongs to {1, 2., n }, and n is the number of samples in the input data matrix X; t is high dimensional data phi = { phi (x) i ) I ∈ {1,2,.., n } } score matrix, T = [ T ] } 1 ,...,t A ]A is the number of pivot elements, P 1 ＝[p 11 ,...,p 1A ]、P 2 ＝[p 21 ,...,p 2A ]、Q＝[q 1 ,...,q A ]A load matrix phi, a Gram matrix K, and an output data matrix Y r 、E、Y r Respectively are the modeling residual errors of the matrix phi, the Gram matrix K and the output data matrix Y.
In the step 4, determining the number of the principal elements A by adopting a cross verification method, and solving a scoring matrix T, wherein the method comprises the following steps:
step 4.1: let u be any column of the output data matrix Y;
and 4.2: calculating a score vector: t = Ku;
step 4.3: normalizing the score vector t: i t | → 1;
step 4.4: and (3) performing regression on each column in the output data matrix Y on the score vector t: q = Y't;
step 4.5: calculating a new score for the output data matrix Y: u = Yq;
step 4.6: and (3) carrying out normalization processing on the u vector: l u | | → 1;
step 4.7: judging whether u converges: if yes, jumping to step 4.8; if not, jumping to step 4.2;
step 4.8: updating the matrix: k = (I-tt ') K (I-tt '), Y = Y-tq ', repeat steps 4.2 through 4.7, and perform the calculation of the next score vector until a score vectors are all extracted; wherein I is an identity matrix.
In the step 3, the Gram matrix after the centralization processing
Wherein E is n Is an n × n identity matrix, 1 n Is n-dimensional all 1 column vector, 1' n Is 1 n The transposed matrix of (2).
The step 5 comprises the following steps:
step 5.1: clustering the score matrix T based on the RWFCM algorithm, and constructing an RWFCM target function of
Wherein, the first and the second end of the pipe are connected with each other,
is the ith row vector of the scoring matrix T,
input sample x in m1 dimension i Corresponding toA-dimensional new sample u after dimensionality reduction ij Is a sample
For the jth clustering center v j Degree of membership of s ij Is a sample
Likelihood of belonging to jth cluster, membership matrix U = (U) ij ) n×c Cluster center matrix V = (V) j ) c×A And c is the number of clusters; m is in the range of [1, + ∞]Is a blur index;
is a sample
With the jth cluster center v j Mahalanobis distance between them, S j Is a fuzzified covariance matrix, S j Is a positive definite matrix;
as a penalty term, η j P is a probability index as a penalty factor; c clustering centers obtained by clustering the score matrix T comprise clustering centers of normal working condition samples and clustering centers of c-1 abnormal working condition samples;
step 5.2: solving a membership matrix U:
step 5.2.1: initializing RWFCM algorithm parameters: determining the clustering number c, setting a fuzzy index m and a probability index p, setting an algorithm termination limit epsilon and a maximum iteration count, initializing the iteration count k =1, and randomly initializing a membership matrix U (k) ＝(u ij (k) ) n×c Randomly initializing a cluster center matrix V (k) ＝(v j (k) ) c×A Randomly initializing a fuzzy covariance matrix set S (k) ＝(S j (k) ) n×n×c ；
Step 5.2.2: u is to be ij (k) 、v j (k) 、S j (k) Substituting into formula
Computing a likelihood matrix B for the (k + 1) th iteration (k+1) ＝(s ij (k+1) ) n×c ；
Step 5.2.3: will s ij (k+1) 、v j (k) 、S j (k) Substitution formula
Calculating membership degree matrix U of k +1 iteration (k+1) ＝(u ij (k+1) ) n×c ；
Step 5.2.4: will u ij (k+1) 、s ij (k+1) Substitution formula
Calculating a clustering center matrix of the (k + 1) th iteration as V (k+1) ＝(v j (k+1) ) c×A ；
Step 5.2.5: will u ij (k+1) 、s ij (k+1) 、v j (k+1) Substituting into formula
Calculating the fuzzification covariance matrix set S of the (k + 1) th iteration (k+1) ＝(S j (k+1) ) n×n×c (ii) a Wherein, γ j Is a lagrange multiplier;
step 5.2.6: if | | | U (k+1) -U (k) If | | is less than epsilon or the iteration times k is more than count, stopping iteration to obtain a final membership matrix U, and entering the step 5.3; otherwise, letting k = k +1, and returning to step 5.2.2;
step 5.3: monitoring abnormal working conditions in the sewage treatment process according to the membership matrix U: if the ith sample
Membership degree of clustering center of normal working condition sampleIf the value is less than mu, the sewage treatment process is abnormal at the ith sample; if the sewage treatment process is abnormal, entering the step 6; and if the sewage treatment process is not abnormal, ending the monitoring method of the sewage treatment process based on KPLS and RWFCM.
In the step 5.2.1, determining the cluster number c includes:
computing input samples X in an input data matrix X i Point density value D of i Is composed of
Wherein, the first and the second end of the pipe are connected with each other,
r d is the effective radius of the neighborhood density,
computing the constructor S (j) as
The image of the structural function S (j) is drawn, and the number of slopes of the image of the structural function S (j) is defined as the cluster number c.
The step 6 comprises the following steps:
step 6.1: establishing a linear regression model of the variables in the membership matrix U and the input data matrix X as
Wherein N is 0 ＝(η 0j ) 1×c Is a constant term of ∈ ij For the error term, it is assumed that: e (. Epsilon.) ij )＝0，Var(ε ij )＝δ 2 δ is a constant; x is a radical of a fluorine atom ia For the ith input sample X in the input data matrix X i The value of the a variable of (a);
contribution matrix, η, for variables aj Is a regression coefficient, eta aj The contribution of the a variable to the j cluster;
step 6.2: solving a variable contribution matrix N by adopting a Lagrange multiplier method:
step 6.2.1: initializing each parameter: setting an algorithm termination limit tau and a maximum iteration number T, initializing the iteration number k =1, and randomly initializing a variable contribution matrix
Step 6.2.2: will eta aj (k) Substitution formula
Calculate N for the k +1 th iteration 0 (k+1) ＝(η 0j (k+1) ) 1×c ；
Step 6.2.3: will eta 0j (k+1) Substitution formula
Computing the variable contribution matrix for the (k + 1) th iteration
Step 6.2.4: if N (k+1) -N (k) If | is less than tau or the iteration times k is more than T, stopping iteration and entering the step 6.3; otherwise, let k = k +1, return to step 6.2.2;
step 6.3: and (3) identifying abnormal working conditions in the sewage treatment process according to the variable contribution matrix N: if the contribution of the a-th variable to all clusters { η } a1 ,...,η ac The maximum value in (j) is η ag If the variable a is a fault variable related to the g abnormal working condition, judging that the variable a is a fault variable related to the g abnormal working condition; wherein g belongs to { 1., c-1}, and the c-th cluster is a cluster of normal working condition samples.
The beneficial effects of the invention are as follows:
(1) The KPLS algorithm and the RWFCM algorithm are combined, the KPLS model and the RWFCM model are constructed to describe the normal production process, prior knowledge of abnormal working conditions in the sewage treatment process is not needed, and only normal working condition data are used as marking data. Firstly, based on a data driving method, a Gaussian kernel function is adopted, standardized process variables are projected to a high-dimensional feature space, a KPLS model for monitoring the sewage treatment process is established in the high-dimensional feature space, after the number of principal elements is determined by a cross verification method, dimension reduction is carried out on high-dimensional input data, a score matrix T is obtained and is used as input data of cluster analysis in an RWFCM algorithm, and the problems that the FCM cannot process nonlinear data and is sensitive to outliers are solved while the purpose of dimension reduction is achieved.
(2) The invention calculates the constructor based on the density function and solves the cluster number according to the constructor, thereby accurately and conveniently determining the cluster number and solving the limitation problem that the cluster number of the RWFCM algorithm needs to be preset manually.
(3) According to the invention, the scoring matrix T is clustered based on the RWFCM algorithm to obtain the membership matrix U, abnormal working conditions are monitored in the sewage treatment process according to the membership matrix U, the occurrence time of the abnormal working conditions can be monitored through the sample membership, and the number of the abnormal working conditions can be identified. According to the method, the membership matrix U and the linear regression model of the sewage treatment process variable are established, the Lagrange multiplier method is adopted to solve the linear regression model to obtain the variable contribution matrix N, the abnormal working condition identification is carried out on the sewage treatment process according to the variable contribution matrix N, and the fault variable related to each abnormal working condition can be identified through the contribution of the variable to the clustering. The invention has high timeliness and accuracy for monitoring and identifying abnormal working conditions in the sewage treatment process, can facilitate operators to monitor the sewage treatment process, accurately judge the fluctuation of the effluent quality of sewage treatment, and timely take measures to treat and correct, thereby ensuring the stable, efficient and safe operation of sewage plants and ensuring the effluent quality.
Drawings
FIG. 1 is a flow chart of a KPLS and RWFCM based wastewater treatment process monitoring method of the present invention;
FIG. 2 is a schematic diagram illustrating the membership of a monitoring sample to a clustering center of a normal condition sample according to an embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating the membership of a monitoring sample to the clustering center of a type 1 abnormal condition sample according to an embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating the membership of a monitoring sample to a cluster center of a sample under a type 2 abnormal condition in an embodiment of the present invention;
FIG. 5 is a diagram illustrating a clustering effect of the score matrix T according to an embodiment of the present invention;
fig. 6 is a schematic diagram illustrating the contribution of each sample variable to each cluster in the embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and specific embodiments.
Fig. 1 shows a flow chart of the KPLS and RWFCM-based sewage treatment process monitoring method of the present invention. The invention discloses a sewage treatment process monitoring method based on KPLS and RWFCM, the method is characterized by comprising the following steps:
step 1: respectively collecting data samples of a normal working condition and a sewage treatment process containing an abnormal working condition, wherein the data samples of the sewage treatment process comprise m 1 Operation variable m of sewage treatment 2 A water outlet quality variable; adding the sewage treatment process data sample under the normal working condition before the sewage treatment process data sample under the abnormal working condition from the time angle to form a mixed data sample set; collecting m mixed data samples 1 Taking the data of the running variable of the sewage treatment as an input data matrix X, and concentrating the mixed data sample into m 2 The data of the water quality variable is used as an output data matrix Y.
In this embodiment, the sewage treatment process employs an activated sludge process. The activated sludge process flow is generally divided into primary treatment, secondary treatment and tertiary treatment according to the treatment degree. The raw sewage is treated in the first stage and then enters the biochemical tank for biological denitrification, one part of the raw sewage is subjected to denitrification again through internal circulation reflux, and the other part of the raw sewage enters the secondary sedimentation tank for sedimentation. The biochemical pool is used for performing biochemical reactionThe most important place for sewage treatment is the process and the purification. The biochemical pool part comprises a biochemical pool l belonging to {1,2,3,4,5}, wherein the biochemical pool l belongs to 1 Belongs to {1,2} as an anoxic zone for mainly completing the denitrification reaction process, i.e. a biochemical pool 2 The epsilon {3,4,5} is an aerobic zone which mainly completes the nitration reaction process; in the step 1, as shown in the following Table 1, the m 1 The operation variables of the sewage treatment comprise inflow, inflow ammonia nitrogen, the biomass of active heterotrophic bacteria in a biochemical pond I E {1,2,3,4,5}, the biomass of easily biodegradable organic matters in the biochemical pond I E {1,2,3,4,5}, the alkalinity in the biochemical pond I E {1,2,3,4,5}, and the biochemical pond I 1 Amount of nitrol in E {1,2}, biochemical pool l 2 Active autotrophic bacteria biomass in epsilon {3,4,5}, biochemical pond l 2 Amount of ammonia nitrogen in E {3,4,5}, biochemical pool l 2 The dissolved oxygen content in the epsilon {3,4,5 }; m is said 2 The quality variables of the effluent comprise biochemical oxygen demand, chemical oxygen demand, suspended matters and ammonia nitrogen amount of the effluent.
The abnormal conditions are known to those skilled in the art as sludge bulking, foaming, scum, toxic shock, heavy rain, etc. In this embodiment, 100 sewage treatment process data samples under normal conditions and 1300 sewage treatment process data samples under abnormal conditions including rainstorm weather and toxic impact are collected to form a mixed data sample set including 1400 samples. Collecting m mixed data samples 1 Taking data of =28 sewage treatment operation variables as input data matrix X ∈ R 1400×28 Set m of mixed data samples 2 Taking the data of the =4 water outlet quality variables as an output data matrix Y ∈ R 1400×4 。
TABLE 1
Step 2: preprocessing an input data matrix X and an output data matrix Y; the preprocessing comprises the steps of calculating the mean value and the standard deviation of each variable in the input data matrix X and the output data matrix Y, and normalizing the input data matrix X and the output data matrix Y into data with zero mean value and unit standard deviation.
And 3, step 3: constructing a KPLS model for monitoring the sewage treatment process, and mapping an input sample X in an input data matrix X to a high-dimensional feature space F: x → phi (X) is in the middle of F, a Gaussian kernel function is introduced to obtain a Gram matrix K of the input data matrix X, and the Gram matrix K is subjected to centralization processing.
The step 3 comprises the following steps:
step 3.1: the KPLS model for monitoring the sewage treatment process is constructed as
Φ＝TP 1 '+Φ r
Y＝TQ'+Y r
Step 3.2: mapping input samples X in an input data matrix X to a high-dimensional feature space F: x → phi (X) belongs to F, a Gaussian kernel function is introduced to obtain a Gram matrix K of the input data matrix X, the Gram matrix K is subjected to centralization processing, and a KPLS model is converted into
K＝TP 2 '+E
Y＝TQ'+Y r
Wherein, the element of the ith row and the jth column of the Gram matrix K is K ij ＝k(x i ,x j )＝<Φ(x i ),Φ(x j )>，x i 、x j Respectively, the ith input sample X in the input data matrix X i J-th input sample x j ，k(x i ,x j ) Is a Gaussian kernel function, i, j belongs to {1, 2., n }, and n is the number of samples in the input data matrix X; t is high dimensional data phi = { phi (x) i ) I ∈ {1,2, ·, n } } score matrix, T = [ T ] } 1 ,...,t A ]A is the number of pivot elements, P 1 ＝[p 11 ,...,p 1A ]、P 2 ＝[p 21 ,...,p 2A ]、Q＝[q 1 ,...,q A ]Respectively a matrix phi, a Gram matrix K, a load matrix of an output data matrix Y, phi r 、E、Y r Respectively are the modeling residual errors of the matrix phi, the Gram matrix K and the output data matrix Y.
In the step 3, the Gram matrix after the centralization processing
Where En is an n × n identity matrix, 1 n Is n-dimensional all 1-column vector, 1' n Is 1 n The transposed matrix of (2).
A KPLS model is constructed by adopting a nonlinear least square iterative algorithm, and KPLS is kernel projection to relative structure. In this embodiment, the Gaussian kernel function is
Wherein, c 1 Is a Gaussian kernel function width parameter, c 1 Is taken from 5m 1 Empirical determination, i.e. determination of c 1 ＝5*m 1 ＝140。
And 4, step 4: and determining the number of the principal elements by adopting a cross verification method, and solving a score matrix T.
In the step 4, determining the number of the principal elements A by adopting a cross verification method, and solving a scoring matrix T, wherein the method comprises the following steps:
step 4.1: let u be any column of the output data matrix Y;
step 4.2: calculating a score vector: t = Ku;
step 4.3: normalizing the score vector t: i t | → 1;
step 4.4: and (3) performing regression on each column in the output data matrix Y on the score vector t: q = Y't;
step 4.5: calculating a new score for the output data matrix Y: u = Yq;
step 4.6: and (3) carrying out normalization processing on the u vector: | | u | → 1;
step 4.7: judging whether u converges: if yes, jumping to step 4.8; if not, jumping to step 4.2;
step 4.8: updating the matrix: k = (I-tt ') K (I-tt '), Y = Y-tq ', repeat steps 4.2 through 4.7, and perform the calculation of the next score vector until a score vectors are all extracted; wherein I is an identity matrix.
In this embodiment, a cross-validation method is used to determine the number of pivot elements a =3.
And 5: clustering the score matrix T based on the RWFCM algorithm to obtain a membership matrix U, and monitoring abnormal working conditions of the sewage treatment process according to the membership matrix U: and if the membership degree of the sample to the clustering center of the normal working condition sample at a certain time is less than mu, the sewage treatment process generates an abnormality at the sample.
The step 5 comprises the following steps:
step 5.1: clustering the score matrix T based on the RWFCM algorithm, and constructing an RWFCM target function as
Wherein the content of the first and second substances,
is the ith row vector of the scoring matrix T,
is a new dimension-reduced A-dimension sample, u, corresponding to the input sample xi of m1 dimension ij Is a sample
For jth cluster center v j Degree of membership of s ij Is a sample
Likelihood of belonging to the j-th cluster, membership matrix U = (U) ij ) n×c Cluster center matrix V = (V) j ) c×A And c is the number of clusters; m is an element of [1, + ∞]Is a fuzzy index;
is a sample
With the jth cluster center v j Mahalanobis distance between them, S j To blur the covariance matrix, S j Is a positive definite matrix;
as a penalty term, η j P is a probability index as a penalty factor; c clustering centers obtained by clustering the score matrix T comprise clustering centers of normal working condition samples and clustering centers of c-1 abnormal working condition samples; step 5.2: solving a membership matrix U:
by introducing lagrange multipliers λ and γ, the following function is constructed:
separately relating s to function L ij 、u ij 、v j 、S j Partial derivatives of (A) to obtain
By
To obtain
Will be provided with
Brought into the above formula
S j -1 +(S j -1 ) T Reversible, get
Step 5.2.1: initializing RWFCM algorithm parameters: determining the clustering number c, setting a fuzzy index m and a probability index p, setting an algorithm termination limit epsilon and a maximum iteration count, initializing the iteration count k =1, and randomly initializing a membership matrix U (k) ＝(u ij (k) ) n×c Randomly initializing a cluster center matrix V (k) ＝(v j (k) ) c×A Randomly initializing a fuzzy covariance matrix set S (k) ＝(S j (k) ) n×n×c ；
Step 5.2.2: will u ij (k) 、v j (k) 、S j (k) Substitution formula
Computing a likelihood matrix B for the (k + 1) th iteration (k+1) ＝(s ij (k+1) ) n×c ；
Step 5.2.3: will s ij (k+1) 、v j (k) 、S j (k) Substitution formula
Calculating membership matrix U of the (k + 1) th iteration (k+1) ＝(u ij (k+1) ) n×c ；
Step 5.2.4: will u ij (k+1) 、s ij (k+1) Substitution formula
Calculating the clustering center matrix of the (k + 1) th iteration as V (k+1) ＝(v j (k+1) ) c×A ；
Step 5.2.5: will u ij (k+1) 、s ij (k+1) 、v j (k+1) Substitution formula
Calculating the fuzzification covariance matrix set S of the (k + 1) th iteration (k+1) ＝(S j (k+1) ) n×n×c (ii) a Wherein, γ j Is a lagrange multiplier;
step 5.2.6: if | | | U (k+1) -U (k) If | | < epsilon or the iteration times k > count, stopping iteration to obtain a final membership matrix U, and entering the step 5.3; otherwise, let k = k +1, return to step 5.2.2;
step 5.3: according to the membership matrixU carries out abnormal condition monitoring to sewage treatment process: if the ith sample
If the membership degree of the clustering center of the normal working condition sample is less than mu, the sewage treatment process is abnormal at the ith sample; if the sewage treatment process is abnormal, entering the step 6; and if no abnormity occurs in the sewage treatment process, ending the KPLS and RWFCM-based sewage treatment process monitoring method.
In the step 5.2.1, determining the cluster number c includes:
computing input samples X in an input data matrix X i Point density value D of i Is composed of
Wherein the content of the first and second substances,
r d is the effective radius of the neighborhood density,
calculating a constructor S (j) of
The image of the structural function S (j) is drawn, and the number of slopes of the image of the structural function S (j) is set as the cluster number c.
Wherein the slope of the constructor S (j) reflects the point density value of the sample data, which has the practical significance that the slopes of the constructor S (j) at the homogeneous data are the same. In this embodiment, the number of slopes of the image of the constructor S (j) is 3, and according to the analysis, it can be determined that the mixed data sample set is classified into 3 types: class1 is class1 abnormal condition sample class, class2 is class2 abnormal condition sample class, and class3 is normal condition sample class, thereby determining cluster number c =3.
Wherein the fuzzy index m influences the fuzzy degree of the membership matrix. In this embodiment, the fuzzy index m =2.4 is set, so that the algorithm effect is optimal. RWFCM is robust weighted fuzzy c-means clustering.
In this example, the sample was monitored
For the clustering center v of the normal working condition sample 3 1 st type abnormal working condition sample clustering center v 1 And the clustering center v of the 2 nd abnormal working condition sample 2 Degree of membership u of i3 、u i1 、u i2 As shown in fig. 2,3, and 4, the clustering effect of the score matrix T is shown in fig. 5.μ =0.5 was set. As can be seen from fig. 2,3,4, at the 200 th and 800 th samples, samples
And the membership degrees of the clustering centers of the normal working condition samples are all less than 0.5, so that the wastewater treatment process is judged to be abnormal at the 200 th and 800 th samples. Therefore, the monitoring method can timely monitor the occurrence of abnormal working conditions in the sewage treatment process.
And 6: establishing a linear regression model of variables in the membership matrix U and the input data matrix X, solving a variable contribution matrix N by adopting a Lagrange multiplier method, and identifying abnormal working conditions of the sewage treatment process according to the variable contribution matrix N: if the contribution of the a-th variable to all clusters { η } a1 ,...,η ac Maximum of η ag If the variable a is a fault variable related to the g abnormal working condition, judging that the variable a is a fault variable related to the g abnormal working condition; wherein c is the number of clusters, g belongs to { 1., c-1}, and the c-th cluster is the cluster of the normal working condition sample.
The step 6 comprises the following steps:
step 6.1: establishing a linear regression model of the variables in the membership matrix U and the input data matrix X as
Wherein, N 0 ＝(η 0j ) 1×c Is a constant term of ∈ ij For the error term, it is assumed that: e (ε) ij )＝0，Var(ε ij )＝δ 2 Delta is a constant; x is a radical of a fluorine atom ia For the ith input sample X in the input data matrix X i The value of the a variable of (a);
contribution matrix, η, for variables aj Is a regression coefficient, η aj Is the contribution of the a-th variable to the j-th cluster.
Step 6.2: solving a variable contribution matrix N by adopting a Lagrange multiplier method:
wherein, to solve eta aj 、η 0j Introducing a loss function of
η aj Representing the degree of interpretation of the jth cluster by the a variable, introducing a constraint on the loss function as
Solving a variable contribution matrix N by adopting a Lagrange multiplier method, introducing a Lagrange multiplier Zeta and constructing an objective function of
Separately solving the objective function L about eta 0j 、η aj Partial derivatives of (A) to obtain
By
General formula
Brought into the above formula
Step 6.2.1: initializing each parameter: setting an algorithm termination limit tau and a maximum iteration number T, initializing the iteration number k =1, and randomly initializing a variable contribution matrix
Step 6.2.2: will eta aj (k) Substitution formula
Calculate N for the k +1 th iteration 0 (k+1) ＝(η 0j (k+1) ) 1×c ；
Step 6.2.3: will eta 0j (k+1) Substituting into formula
Calculating the variable contribution matrix of the (k + 1) th iteration
Step 6.2.4: if N (k+1) -N (k) If | is less than tau or the iteration times k is more than T, stopping iteration and entering the step 6.3; otherwise, letting k = k +1, and returning to step 6.2.2;
step 6.3: and (3) identifying abnormal working conditions in the sewage treatment process according to the variable contribution matrix N: if the contribution of the a-th variable to all clusters { η } a1 ,...,η ac Maximum of η ag If the variable a is a fault variable related to the g abnormal working condition, judging that the variable a is a fault variable related to the g abnormal working condition; wherein g belongs to { 1., c-1}, and the c-th cluster is a cluster of normal working condition samples.
In this embodiment, the contribution values of the 28 sample variables to the 3 clusters are shown in fig. 6. From fig. 6 it can be recognized that: the fault variables related to the 1 st abnormal working condition are the biomass of active heterotrophic bacteria in the biochemical pools 1-5, the biomass of organic bottom products easy to biodegrade, the biomass of active autotrophic bacteria in the biochemical pools 3-5 and the amount of nitrate nitrogen in the biochemical pool 1; the fault variables related to the 2 nd abnormal working condition are the inflow water flow, the inflow ammonia nitrogen amount, the alkalinity in the biochemical tanks 1-5, the nitrate nitrogen amount in the biochemical tank 2, the dissolved oxygen amount in the biochemical tanks 3-5 and the ammonia nitrogen amount in the biochemical tanks 3-5. Therefore, the method can identify the fault variable of each abnormal working condition in time.
It is to be understood that the above-described embodiments are only some of the embodiments of the present invention, and not all of the embodiments. The above examples are only for explaining the present invention and do not constitute a limitation to the scope of protection of the present invention. All other embodiments, which can be derived by those skilled in the art from the above-described embodiments without any creative effort, namely all modifications, equivalents, improvements and the like made within the spirit and principle of the present application, fall within the scope of the present invention as claimed.
Claims (8)
1. A KPLS and RWFCM based sewage treatment process monitoring method is characterized by comprising the following steps:
step 1: respectively collecting data samples of a normal working condition and a sewage treatment process containing an abnormal working condition, wherein the data samples of the sewage treatment process comprise m 1 Operation variable m of sewage treatment 2 A water outlet quality variable; adding the sewage treatment process data sample under the normal working condition before the sewage treatment process data sample under the abnormal working condition from the time angle to form a mixed data sample set; collecting m mixed data samples 1 Taking the data of the running variable of the sewage treatment as an input data matrix X, and concentrating the mixed data sample into m 2 Taking the data of the effluent quality variable as an output data matrix Y;
and 2, step: preprocessing an input data matrix X and an output data matrix Y; the preprocessing comprises the steps of calculating the mean value and the standard deviation of all variables in an input data matrix X and an output data matrix Y, and normalizing the input data matrix X and the output data matrix Y into data with zero mean value and unit standard deviation;
and step 3: constructing a KPLS (kernel principal component analysis) model for monitoring the sewage treatment process, and mapping an input sample X in an input data matrix X to a high-dimensional feature space F: x → phi (X) belongs to F, a Gaussian kernel function is introduced to obtain a Gram matrix K of the input data matrix X, and the Gram matrix K is subjected to centralization processing;
and 4, step 4: determining the number of pivot elements by adopting a cross verification method, and solving a score matrix T;
and 5: clustering the scoring matrix T based on the RWFCM algorithm to obtain a membership matrix U, and monitoring abnormal working conditions in the sewage treatment process according to the membership matrix U: if the membership degree of the sample to the clustering center of the normal working condition sample at a certain time is less than mu, abnormality occurs in the sample in the sewage treatment process;
and 6: establishing a linear regression model of variables in the membership matrix U and the input data matrix X, solving a variable contribution matrix N by adopting a Lagrange multiplier method, and identifying abnormal working conditions of the sewage treatment process according to the variable contribution matrix N: if the contribution of the a-th variable to all clusters { η } a1 ,...,η ac The maximum value in (j) is η ag If the variable a is a fault variable related to the g abnormal working condition; wherein c is the number of clusters, g belongs to { 1., c-1}, and the c-th cluster is the cluster of the normal working condition sample.
2. The KPLS and RWFCM based sewage treatment process monitoring method according to claim 1, wherein the sewage treatment process adopts an activated sludge process, the raw sewage is subjected to primary treatment and then enters a biochemical tank part, after biological denitrification, one part of the raw sewage enters a secondary sedimentation tank for sedimentation after denitrification again through internal circulation reflux; the biochemical pond part comprises a biochemical pond I epsilon {1,2,3,4,5}, wherein the biochemical pond I epsilon 1 Belongs to {1,2} as an anoxic zone mainly completing the denitrification reaction process, a biochemical pool 2 The epsilon {3,4,5} is an aerobic zone which mainly completes the nitration reaction process; in the step 1, m is 1 The operation variables of the sewage treatment comprise inflow, inflow ammonia nitrogen, the biomass of active heterotrophic bacteria in a biochemical pond I E {1,2,3,4,5}, the biomass of easily biodegradable organic matters in the biochemical pond I E {1,2,3,4,5}, the alkalinity in the biochemical pond I E {1,2,3,4,5}, and the biochemical pond I 1 Amount of nitrol in E {1,2}, biochemical pool l 2 Activity autotrophic bacteria biomass in epsilon {3,4,5}, biochemical pool l 2 Amount of ammonia nitrogen in E {3,4,5}, biochemical pool l 2 The dissolved oxygen content in the epsilon {3,4,5 }; m is 2 The quality variables of the effluent comprise biochemical oxygen demand, chemical oxygen demand, suspended matters and ammonia nitrogen amount of the effluent.
3. A KPLS and RWFCM based sewage treatment process monitoring method according to claim 1 or 2, characterised in that said step 3 comprises the steps of:
step 3.1: the KPLS model for monitoring the sewage treatment process is constructed as
Φ＝TP 1 '+Φ r
Y＝TQ'+Y r
Step 3.2: mapping input samples X in an input data matrix X to a high-dimensional feature space F: x → phi (X) belongs to F, a Gaussian kernel function is introduced to obtain a Gram matrix K of the input data matrix X, the Gram matrix K is subjected to centralization processing, and a KPLS model is converted into
K＝TP 2 '+E
Y＝TQ'+Y r
Wherein, the element of the ith row and the jth column of the Gram matrix K is K ij ＝k(x i ,x j )＝<Φ(x i ),Φ(x j )>，x i 、x j Respectively, the ith input sample X in the input data matrix X i Jth input sample x j ，k(x i ,x j ) Is a Gaussian kernel function, i, j belongs to {1, 2., n }, and n is the number of samples in the input data matrix X; t is high dimensional data phi = { phi (x) i ) I ∈ {1,2, ·, n } } score matrix, T = [ T ] } 1 ,...,t A ]A is the number of pivot elements, P 1 ＝[p 11 ,...,p 1A ]、P 2 ＝[p 21 ,...,p 2A ]、Q＝[q 1 ,...,q A ]A load matrix phi, a Gram matrix K, and an output data matrix Y r 、E、Y r Respectively are the modeling residual errors of the matrix phi, the Gram matrix K and the output data matrix Y.
4. The KPLS and RWFCM based sewage treatment process monitoring method according to claim 3, wherein in step 4, the cross validation method is adopted to determine the number of principal elements A and solve the score matrix T, comprising the following steps:
step 4.1: let u be any column of the output data matrix Y;
and 4.2: calculating a score vector: t = Ku;
step 4.3: normalizing the score vector t: l t | → 1;
step 4.4: and (3) performing regression on each column in the output data matrix Y on the score vector t: q = Y't;
step 4.5: calculating a new score for the output data matrix Y: u = Yq;
step 4.6: and (3) normalizing the u vector: | | u | → 1;
step 4.7: judging whether u converges: if yes, jumping to step 4.8; if not, jumping to step 4.2;
step 4.8: updating the matrix: k = (I-tt ') K (I-tt '), Y = Y-tq ', repeat steps 4.2 through 4.7, and perform the calculation of the next score vector until a score vectors are all extracted; wherein I is an identity matrix.
5. The KPLS and RWFCM-based sewage treatment process monitoring method according to claim 3, wherein in step 3, the processed Gram matrix is centralized
Wherein, E n Is an n × n identity matrix, 1 n Is n-dimensional all 1-column vector, 1' n Is 1 n The transposed matrix of (2).
6. The KPLS and RWFCM based sewage treatment process monitoring method according to claim 4, wherein said step 5 comprises the steps of:
step 5.1: clustering the score matrix T based on the RWFCM algorithm, and constructing an RWFCM target function as
Wherein the content of the first and second substances,
is the ith row vector of the scoring matrix T,
is m 1 Input sample x of dimension i Corresponding reduced A-dimensional new sample, u ij Is a sample
For the jth clustering center v j Degree of membership of s ij Is a sample
Likelihood of belonging to the j-th cluster, membership matrix U = (U) ij ) n×c Cluster center matrix V = (V) j ) c×A And c is the number of clusters; m is in the range of [1, + ∞]Is a fuzzy index;
is a sample
With the jth cluster center v j Mahalanobis distance between them, S j Is a fuzzified covariance matrix, S j Is a positive definite matrix;
as a penalty term, η j P is a probability index as a penalty factor; c clustering centers obtained by clustering the score matrix T comprise clustering centers of normal working condition samples and clustering centers of c-1 abnormal working condition samples;
step 5.2: solving a membership matrix U:
step 5.2.1: initializing RWFCM algorithm parameters: determining the clustering number c, setting a fuzzy index m and a probability index p, setting an algorithm termination limit epsilon and a maximum iteration count, initializing the iteration count k =1, and randomly initializing a membership matrix U (k) ＝(u ij (k) ) n×c Randomly initializing a cluster center matrix V (k) ＝(v j (k) ) c×A Random initialization fuzzification covariance matrix set S (k) ＝(S j (k) ) n×n×c ；
Step 5.2.2: will u ij (k) 、v j (k) 、S j (k) Substitution formula
Computing a likelihood matrix B for the (k + 1) th iteration (k+1) ＝(s ij (k+1) ) n×c ；
Step 5.2.3: will s ij (k+1) 、v j (k) 、S j (k) Substitution formula
Calculating membership degree matrix U of k +1 iteration (k+1) ＝(u ij (k+1) ) n×c ；
Step 5.2.4: will u ij (k+1) 、s ij (k+1) Substitution formula
Calculating the clustering center matrix of the (k + 1) th iteration as V (k+1) ＝(v j (k+1) ) c×A ；
Step 5.2.5: will u ij (k+1) 、s ij (k+1) 、v j (k+1) Substitution formula
Calculating the fuzzification covariance matrix set S of the (k + 1) th iteration (k+1) ＝(S j (k+1) ) n×n×c (ii) a Wherein, γ j Is a lagrange multiplier;
step 5.2.6: if | | | U (k+1) -U (k) If | | < epsilon or the iteration times k > count, stopping iteration to obtain a final membership matrix U, and entering the step 5.3; otherwise, letting k = k +1, and returning to step 5.2.2;
step 5.3: monitoring abnormal working conditions in the sewage treatment process according to the membership matrix U: if the ith sample
If the membership degree of the clustering center of the normal working condition sample is less than mu, the sewage treatment process is abnormal at the ith sample; if the sewage treatment process is abnormal, entering the step 6; if no abnormity occurs in the sewage treatment process, ending the KPLS and RWFCM based sewage treatmentA water treatment process monitoring method.
7. A KPLS and RWFCM based sewage treatment process monitoring method according to claim 6, wherein said step 5.2.1, determining the cluster number c comprises:
computing input samples X in an input data matrix X i Point density value D of i Is composed of
Wherein the content of the first and second substances,
r d is the effective radius of the neighborhood density,
computing the constructor S (j) as
The image of the structural function S (j) is drawn, and the number of slopes of the image of the structural function S (j) is set as the cluster number c.
8. The KPLS and RWFCM-based sewage treatment process monitoring method according to claim 6, wherein the step 6 comprises the steps of:
step 6.1: a linear regression model of the variables in the membership matrix U and the input data matrix X is established as
Wherein N is 0 ＝(η 0j ) 1×c Is a constant term of ∈ ij For the error term, it is assumed that: e (ε) ij )＝0，Var(ε ij )＝δ 2 δ is a constant; x is the number of ia For the ith input sample X in the input data matrix X i The value of the a variable of (a);
is a variable contribution matrix, η aj Is a regression coefficient, η aj The contribution of the a variable to the j cluster;
step 6.2: solving a variable contribution matrix N by adopting a Lagrange multiplier method:
step 6.2.1: initializing each parameter: setting an algorithm termination limit tau and a maximum iteration number T, initializing the iteration number k =1, and randomly initializing a variable contribution matrix
Step 6.2.2: will eta aj (k) Substituting into formula
Calculate N for the k +1 th iteration 0 (k+1) ＝(η 0j (k+1) ) 1×c ；
Step 6.2.3: will eta 0j (k+1) Substituting into formula
Computing the variable contribution matrix for the (k + 1) th iteration
Step 6.2.4: if N (k+1) -N (k) If | is less than tau or the iteration times k is more than T, stopping iteration and entering the step 6.3; otherwise, letting k = k +1, and returning to step 6.2.2;
step 6.3: and (3) identifying abnormal working conditions in the sewage treatment process according to the variable contribution matrix N: if the contribution of the a-th variable to all clusters { η } a1 ,...,η ac Maximum of η ag Then the a is changedThe quantity is a fault variable related to the g abnormal working condition; wherein g belongs to { 1.,. C-1}, and the c-th cluster is the cluster of the normal working condition samples.
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| CN116092078B (en) * | 2023-04-11 | 2023-06-09 | 深圳市信远环保水务有限公司 | Intelligent control system for sewage treatment |
| CN116110516B (en) * | 2023-04-14 | 2023-07-21 | 青岛山青华通环境科技有限公司 | Method and device for identifying abnormal working conditions in sewage treatment process |
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