An air compressor quality related process monitoring method based on ASSA-KPLS

Abstract

The application discloses an air compressor quality related process monitoring method based on ASSA-KPLS, relates to the field of data-driven process monitoring, and comprises the following steps: offline modeling, an ASSA-KPLS model: obtaining sample data under a normal working state of an air compressor as training sample data, performing normalization processing on the training sample data, obtaining a stationary projection matrix through analytic stationary subspace analysis (ASSA) after the normalization processing, obtaining stationary sources from the stationary projection matrix and the normalized training set, then taking the stationary sources as input to establish a kernel partial least squares (KPLS) model, and constructing monitoring statistics and a control limit; online monitoring: collecting data under a fault state of the air compressor in real time as test data, obtaining stationary sources from the established ASSA model, obtaining monitoring statistics through the KPLS model, comparing the monitoring statistics with the control limit, and thus determining whether a quality related fault of the air compressor occurs. The non-stationarity and non-linear characteristics of the air compressor process data are considered simultaneously, and the efficiency of process monitoring and fault detection is effectively improved.

Description

TECHNICAL FIELD

[0001] The application relates to the field of process monitoring and fault diagnosis of air compressors, and in particular to an air compressor quality-related process monitoring method based on ASSA-KPLS. BACKGROUND

[0002] With the progress of science and technology and the rapid development of the national economy, air compressors are increasingly widely used in social production. An air compressor is an air compression preparation device mainly composed of a main machine, an oil-gas separator, a cooler, valves and the like. During the operation of the air compressor, faults such as insufficient exhaust capacity, over-temperature, over-pressure, overload and abnormal sound often occur, which affect the normal production of enterprises. Therefore, it is very important to detect faults of the air compressor and maintain the normal operation and safe operation of the air compressor.

[0003] In recent years, with the improvement of product quality requirements, quality-related process monitoring has been valued. During the operation of the air compressor, quality-related process monitoring can find quality-related faults, so as to timely adjust and improve work efficiency. Kernel Partial Least Squares (KPLS) is a method widely used in the field of nonlinear quality-related process monitoring. It projects low-dimensional features into high-dimensional space through a nonlinear mapping function to establish a Partial Least Squares (PLS) model, and realizes quality-related process monitoring. The operation process of the air compressor often presents non-stationary characteristics. In order to better process the non-stationary characteristics, the Analytic Stationary Subspace (ASSA) method is used to extract stationary components from non-stationary process variables, and the method has no restriction on the integral order. SUMMARY

[0004] In view of the quality-related faults and quality-unrelated faults that may occur during the operation of the air compressor, and the nonlinear and non-stationary characteristics of the operation process, an air compressor quality-related process monitoring method based on ASSA and KPLS is proposed. First, an ASSA model is established to obtain a stationary projection matrix, so as to obtain a stationary source. Then, the stationary source is taken as input to establish a KPLS model, construct a monitoring statistic and a control limit, so as to realize process monitoring. The proposed ASSA-KPLS method simultaneously considers the non-stationary and nonlinear characteristics of the operation process of the air compressor, and effectively improves the process monitoring and fault detection efficiency.

[0005] To solve the above technical problems, the application provides an air compressor quality-related process monitoring method based on ASSA-KPLS, comprising the following steps:

[0006] Offline training:

[0007] Obtaining sample data in normal working state of the air compressor as a training set, the sample data including process variable data and quality variable data;

[0008] Normalizing the sample data to obtain a training matrix X;

[0009] The training matrix X is analyzed by an ASSA model to obtain a stationary projection matrix, and a stationary source is obtained from the stationary projection matrix and the normalized training set;

[0010] The stationary source is taken as an input to establish a KPLS model, and a monitoring statistic and a control limit are constructed;

[0011] Online monitoring:

[0012] Real-time acquisition of data in a fault state of the air compressor as test data, obtaining a stationary source from the established ASSA model, and then obtaining a monitoring statistic from the KPLS model, comparing the statistic with the control limit, and determining whether a quality-related fault of the air compressor occurs.

[0013] As an optimization, obtaining the stationary source includes the following steps: normalizing the training set to be a matrix X = [x1 x2 L xn] ∈ Rm×n containing m-dimensional process variables and n samples, m n×m taking it as input data of the ASSA model, using a moving window strategy to divide the input data into N epochs, and obtaining the following stationary projection matrix:

[0014]

[0015] Constraint condition:

[0016] Specifically,

[0017]

[0018]

[0019]

[0020] wherein μ i is a mean value of each epoch, ∑ i is a variance of each epoch; and stationary variables are extracted from the sample data, and are specifically as shown in the following formula:

[0021]

[0022] wherein X s ∈ R n×d is the stationary source.

[0023] ​As preferred, the KPLS model is established by the following steps: setting a quality variable matrix Y = [y1 y2 Ly p ]∈R n×p , containing n samples with p-dimensional quality variables collected under normal working state of the air compressor, introducing a kernel matrix:

[0024] K ij = k(x i , x j ) = <φ(x i ), φ(x j )>(i, j = 1, 2, L, n)

[0025] Wherein, k is a kernel function, and <·> represents an inner product operator;

[0026] A Gaussian kernel function is selected, and the specific expression is as follows:

[0027]

[0028] Wherein, c is the width of the kernel function;

[0029] Centralized processing, specifically as follows:

[0030]

[0031] Wherein, E is an n-dimensional unit matrix, and 1 n is an n-dimensional column vector with all elements being 1;

[0032] Through the KPLS model, X s is projected to a high-dimensional space through a nonlinear mapping function Φ, and the KPLS is specifically expressed as follows:

[0033]

[0034] Wherein, T = [t1 t2 L t A ], U = [u1 u2 L u A ] are score matrices of , P and Q are load matrices of Y, and A is the number of latent variables; T is derived according to the following formula:

[0035]

[0036]

[0037] Wherein, R is a matrix calculated by the KPLS iterative process, is obtained by centralized processing of Φ.

[0038] As preferred, the monitoring statistics and control limits are constructed by the following steps: for an input sample xnew According to the KPLS model thereof, a monitoring statistic T is calculated 2 and a control limit thereof The specific process is as follows:

[0039]

[0040]

[0041] Covariance matrix of scores:

[0042] Where t new is the score vector of a certain test sample, F A,n-A,α is the F-distribution threshold with degrees of freedom A and n-A and confidence level α, A and n-A are degrees of freedom, and α is the confidence level;

[0043] According to the KPLS model, a monitoring statistic SPE and a control limit SPE lim are calculated, and the specific process is as follows:

[0044] SPE = || φ r (x new ) || 2

[0045]

[0046] Where, is the chi-square distribution with degrees of freedom h, if the mean and variance of the SPE index are represented by μ and S, then g = S / 2μ, h = 2μ 2 / S, where g represents the weight coefficient; regarding the statistic SPE, for an input sample x new , the score vector is calculated by the following formula, and the specific formula is as follows:

[0047]

[0048]

[0049] Where, is the characteristic vector of the input sample projected into the high-dimensional space.

[0050] Therefore, the SPE statistic of x new is calculated as follows:

[0051]

[0052] Where x j and x j' are data of the training set.

[0053] As preferred, in the process of online monitoring, for a newly collected sample data H new , the monitoring statistics new of H and SPE new are calculated by the ASSA and KPLS models, and then compared with the corresponding control limits and SPE lim , respectively, and the process monitoring result is obtained according to the following logic: if , a quality-related fault is detected; and SPE new <SPE lim , no quality-related fault occurs.

[0054] The application has the following beneficial effects: the application proposes an air compressor quality-related process monitoring method based on ASSA-KPLS, the ASSA model is used to extract stationary sources, and the non-stationarity of the air compressor operation process is considered; the KPLS model is established to realize quality-related feature extraction, and the nonlinearity of the air compressor operation process is considered; and the efficiency of process monitoring and fault detection is effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0055] The drawings constituting a part of the application are used to provide further understanding of the application, the illustrative embodiments of the application and the description thereof are used to explain the application, and do not constitute improper limitation on the application.

[0056] In order to more clearly illustrate the technical solutions in the embodiments of the application, the drawings needed to be used in the embodiment description will be briefly introduced below, and obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor on the premise of the drawings.

[0057] Figure 1 is a flowchart of an air compressor quality-related process monitoring method based on ASSA-KPLS according to an embodiment of the application. DETAILED DESCRIPTION

[0058] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application; obviously, the described embodiments are only some of the embodiments of the application, but not all the embodiments of the application, and all other embodiments obtained by those skilled in the art without creative labor on the basis of the embodiments in the application belong to the protection scope of the application.

[0059] Please refer to Figure 1A preferred embodiment of the present application is an air compressor quality-related process monitoring method based on ASSA-KPLS, comprising the following steps:

[0060] Offline training:

[0061] Obtain sample data under normal working state of the air compressor as a training set, and the sample data includes process variable data and quality variable data;

[0062] Normalize the sample data to obtain a training matrix X;

[0063] The training matrix X is analyzed by the ASSA model to obtain a stationary projection matrix, and a stationary source is obtained from the stationary projection matrix and the normalized training set; specifically, the training set is normalized and recorded as a matrix X=[x1 x2 L xn]∈R m n×m , which is used as input data of the ASSA model, and the input data is divided into N epochs by using a moving window strategy to obtain the following stationary projection matrix:

[0064]

[0065] Constraint condition:

[0066] Specifically,

[0067]

[0068]

[0069]

[0070] wherein μ i is the mean of each epoch, and ∑ i is the variance of each epoch; then the stationary variables are extracted from the sample data, and the specific formula is as follows:

[0071]

[0072] wherein X s ∈R n×d is the stationary source.

[0073] The stationary source is used as input to establish a KPLS model, i.e., a kernel least squares model; specifically, a quality variable matrix Y=[y1 y2 L yp]∈R p n×p is set, which contains n samples with p-dimensional quality variables collected under the normal working state of the air compressor, and a kernel matrix K is introduced:

[0074] K ij ​​= k(x i , x j ) = <φ(x i ), φ(x j )> (i, j = 1, 2, L, n)

[0075] where k is the kernel function, and <·> denotes the inner product operator;

[0076] The Gaussian kernel function is selected, and the specific expression is as follows:

[0077]

[0078] where c is the width of the kernel function;

[0079] The centering process is as follows:

[0080]

[0081] where E is an n-dimensional unit matrix, and 1 n is an n-dimensional column vector with all elements being 1.

[0082] Using the KPLS algorithm, the algorithm steps are as follows:

[0083] Step 1: Let i = 1, K1 = K, Y1 = Y;

[0084] Step 2: Randomly initialize u i ;

[0085] Step 3: Calculate the input score vector t i = K i u i ;

[0086] Step 3: Normalize the input score vector t i = t i / ||t i ||;

[0087] Step 4: Calculate the output load vector q i = Y T t i ;

[0088] Step 5: Calculate the output score vector u i = Yq i ;

[0089] Step 6: Normalize the output score vector u i = u i / ||u i ||;

[0090] Step 7: Determine t iConvergence status: If converged, proceed to step 8; otherwise, return to step 3.

[0091] Step 8: Update the Gram matrix

[0092] Step 9: Update the output matrix

[0093] Step 10: Determine the value of i: If i > A, the loop terminates; otherwise, return to step 2.

[0094] Using the KPLS model, X s After being projected onto a high-dimensional space via a nonlinear mapping function Φ, KPLS is specifically represented as follows:

[0095]

[0096] Where, T=[t1 t2 L t A ],U=[u1 u2 L u A ]yes The score matrix is ​​given by P and Q, which are the loading matrices of Y, and A is the number of latent variables; T is derived from the following formula:

[0097]

[0098]

[0099] Where R is a matrix calculated by the KPLS iterative process. It is obtained by centralizing Φ.

[0100] Construct monitoring statistics and control limits; in this step, for an input sample x new Based on its KPLS model, the monitoring statistic T is calculated. 2 and its control limits Specifically as follows:

[0101]

[0102]

[0103] Covariance matrix of scores:

[0104] Among them, t new Let F be the score vector of a certain test sample. A,n-A,α It is the threshold of the F-distribution with degrees of freedom A and nA and a confidence level of α, where A and nA are the degrees of freedom and α is the confidence level;

[0105] According to the KPLS model, the monitoring statistics SPE and the control limit SPE are calculated lim , as follows:

[0106] SPE = || φ r (x new ) || 2

[0107]

[0108] wherein, is a chi-square distribution with degree of freedom h, if the mean and variance of the SPE index are represented by μ and S, then g = S / 2 μ, h = 2 μ 2 / S, wherein g represents a weight coefficient.

[0109] For an input sample x new , the score vector is calculated by the following formula, and the specific formula is as follows:

[0110]

[0111]

[0112] wherein, is the characteristic vector of the input sample projected into the high-dimensional space.

[0113] Therefore, the SPE statistics of x new is calculated as follows:

[0114]

[0115] wherein x j and x j' are data of the training set.

[0116] Online monitoring:

[0117] The data in the fault state of the air compressor are collected in real time as test data, the stationary source is obtained by the established ASSA model, the monitoring statistics are obtained through the KPLS model, the statistics are compared with the control limit, and it is judged whether the air compressor has a quality-related fault; in this step, for a newly collected sample data H new , the monitoring statistics and SPE new of H new are calculated through the ASSA and KPLS models, and then compared with the corresponding control limits and SPE lim , respectively, and the process monitoring result is obtained according to the following logic: if , a quality-related fault is detected; and SPE new<SPE lim , no quality related fault occurs.

[0118] Specific examples of data substitution:

[0119] The method is based on a public model Tennessee Eastman (TE) process simulation experiment, and verifies the effectiveness of the quality related process monitoring method based on ASSA-KPLS. The TE process is an industrial simulator developed according to a real industrial process, which mainly includes five operating units: reactor, condenser, compressor, separator and stripper. Five gaseous reactants (A, B, C, D, E), in which B is an inert gas, generate liquid products (G, H) and reaction by-products F. The TE process includes a total of 21 preset faults, 12 operating variables and 41 measured variables.

[0120] In this embodiment, 22 process variables XMEAS(1)-XMEAS(22) and 11 operating variables XMV(1)-XMV(11) are selected as input variables, and XMEAS(35) and XMEAS(36) are selected as output variables. Take the first 15 faults of the TE process as an example, in which faults 3, 4, 9, 11, 14 and 15 are quality related faults, and faults 1, 2, 5-8, 10, 12 and 13 are quality independent faults. PCA, KPCA, PLS, KPLS, ASSA-PLS and the method of the present application are compared, and since T 2 can effectively monitor quality related faults, therefore, the fault detection rates of various methods on the quality related faults of T 2 are shown in Table 1.

[0121] Table 1 Fault detection rate of quality related faults of various methods (%)

[0122]

[0123]

[0124] As can be seen from the above table, the method of the present application can effectively detect quality related faults compared with other process monitoring methods.

[0125] The above is only a preferred specific embodiment of the present application; however, the protection scope of the present application is not limited thereto. Any skilled person in the art can make equivalent substitutions or changes to the technical solutions and improvement concepts of the present application within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for monitoring air compressor quality-related processes based on ASSA-KPLS, characterized in that, Includes the following steps: Offline training: Obtain sample data of the air compressor under normal operating conditions as a training set; the sample data includes process variable data and quality variable data. The sample data is normalized to obtain the training matrix X; The training matrix X is analyzed by the ASSA model to obtain the stationary projection matrix, and the stationary source is obtained by the stationary projection matrix and the normalized training set. A KPLS model is built using a stationary source as input, including selecting a Gaussian kernel function and centering it, and constructing the monitoring statistic T. 2 and SPE and control limits; Online monitoring: Real-time data of the air compressor under fault conditions is collected as test data. The stable source is obtained by the established ASSA model, and then the monitoring statistics are obtained by the KPLS model. The statistics are compared with the control limits to determine whether the air compressor has a quality-related fault. The process of obtaining the stationary source includes the following steps: normalizing the training set and denoting it as a matrix X = [x1x2…x] containing m-dimensional process variables and n samples. m ]∈R n×m Using this as input data for the ASSA model, a moving window strategy is employed to divide the input data into N epochs, resulting in the following stationary projection matrix: Constraints: Specifically, Where, μ i It is the mean of each epoch, ∑ i This represents the variance for each epoch; then, a stationary variable is extracted from the sample data, as shown in the following formula: Among them, X s ∈R n×d It is a stable source.

2. The method for monitoring air compressor quality-related processes based on ASSA-KPLS according to claim 1, characterized in that, Building a KPLS model includes the following steps: Define a mass variable matrix Y = [y1y2…y p ]∈R n×p It contains n samples with p-dimensional quality variables collected under normal operating conditions of the air compressor, and introduces a kernel matrix: K ij =k(x i ,x j )=<φ(x i ),φ(x j )>(i,j=1,2,…,n) Where k is the kernel function, and <·> represents the inner product operator; The Gaussian kernel function is selected, and its specific expression is as follows: Where c is the width of the kernel function; Centralized processing, as detailed below: Where E is an n-dimensional identity matrix, 1 n It is an n-dimensional column vector with all elements being 1; Using the KPLS model, X s After being projected onto a high-dimensional space via a nonlinear mapping function Φ, KPLS is specifically represented as follows: Where, T = [t1t2…t] A ], U=[u1u2…u A ]yes The score matrix is ​​given by P and Q, which are the loading matrices of Y, and A is the number of latent variables; T is derived from the following formula: Where R is a matrix calculated by the KPLS iterative process. It is obtained by centralizing Φ.

3. The method for monitoring air compressor quality-related processes based on ASSA-KPLS according to claim 1, characterized in that, Constructing monitoring statistics and control limits includes the following steps: For an input sample x new Based on its KPLS model, the monitoring statistic T is calculated. 2 and its control limits Specifically as follows: Covariance matrix of scores: Among them, t new Let F be the score vector of a certain test sample. A,n-A,α It is the threshold of the F-distribution with degrees of freedom A and nA and a confidence level of α, where A and nA are the degrees of freedom and α is the confidence level; Then, based on the KPLS model, calculate the monitoring statistic SPE and its control limit SPE. lim The details are as follows: SPE=||φ r (x new )|| 2 in, If the SPE index is a chi-square distribution with h degrees of freedom, and the mean and variance are represented by μ and S, then g = S / 2μ, h = 2μ 2 / S, where g represents the weighting coefficient; regarding the statistic SPE, for an input sample x new The score vector is calculated using the following formula: in, The feature vector projected from the input sample into a high-dimensional space; Therefore, x new The SPE statistic is calculated as follows: Where, x j and x j' This is the data for the training set.

4. The method for monitoring air compressor quality-related processes based on ASSA-KPLS according to claim 3, characterized in that, During online monitoring, for a newly collected sample data H new H is then calculated using the ASSA and KPLS models. new Monitoring statistics and SPE new Then compare them with the corresponding control limits. and SPE lim The process monitoring results are obtained through comparison based on the following logic: If Then a quality-related fault was detected; And SPE new <SPE lim If so, no quality-related faults will occur.

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