CN112214006A

CN112214006A - Intermittent process fault detection method and system considering two-dimensional dynamic characteristics

Info

Publication number: CN112214006A
Application number: CN202011091463.5A
Authority: CN
Inventors: 张汉元; 梁泽宇; 孙雪莹
Original assignee: Shandong Jianzhu University
Current assignee: Shandong Jianzhu University
Priority date: 2020-10-13
Filing date: 2020-10-13
Publication date: 2021-01-12

Abstract

The invention provides an intermittent process fault detection method and system considering two-dimensional dynamic characteristics. Extracting low-dimensional characteristic information of test data by using a load matrix of a two-dimensional dynamic kernel slow characteristic analysis model, and calculating monitoring statistics of the test data in a principal component space and a residual error space; judging whether the intermittent process has a fault or not according to the comparison result of the monitoring statistic and the corresponding control limit; expanding each batch of data sets in the three-dimensional training data set by using an autoregressive moving average time sequence model to obtain corresponding expanded batch of data sets; the training data is normal operation condition data of an intermittent process; the method comprises the steps of mapping an augmented batch data set to a high-dimensional feature space in a nonlinear mode, establishing a time dynamic kernel slow feature analysis model, introducing a kernel function skill calculation kernel matrix and a time change kernel matrix, calculating a total average kernel matrix and a total time change kernel matrix based on a global modeling strategy, and establishing a two-dimensional dynamic kernel slow feature analysis model.

Description

Intermittent process fault detection method and system considering two-dimensional dynamic characteristics

Technical Field

The invention belongs to the technical field of dynamic nonlinear multivariable intermittent process fault detection, and particularly relates to an intermittent process fault detection method and system considering two-dimensional dynamic characteristics.

Background

The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.

As intermittent processes increasingly tend to be highly integrated, large-scale and complex, fault detection of intermittent processes has become a key technology for ensuring safe and stable operation thereof. With the development of modern computer control technology, abundant process operation data is collected and stored in the intermittent process. Therefore, data-driven fault detection technology is becoming a research hotspot in the field of intermittent process monitoring. Researchers have proposed a series of data-driven fault detection methods such as Principal Component Analysis (PCA), Partial Least Squares (PLS), and representative variable analysis (CVA). Whereas batch processes have essentially two-dimensional dynamics (batch-dimensional dynamics and time-dimensional dynamics) and significant non-linear characteristics, the above-mentioned monitoring methods have significant limitations in fault detection of batch processes. Therefore, with respect to the two-dimensional dynamic characteristics and non-linear characteristics of the intermittent process, how to extract useful characteristic information from the measurement data to monitor the operation state of the intermittent process is a challenging research topic.

To extract the dynamic time-varying features inherent in intermittent process data, Slow Feature Analysis (SFA) based methods are gradually being introduced into the field of intermittent process fault detection. In recent years, slow feature analysis has attracted extensive attention from researchers at home and abroad as an effective intermittent process fault detection technique. The method can extract slowly-changing low-dimensional characteristic information from the dynamic time-varying data of the intermittent process, represent the potential driving force causing the dynamic time-varying of the intermittent process, and solve the dynamic time-varying characteristic of the intermittent process data to a certain extent. Although the slow feature analysis technology has achieved certain application results in the field of fault detection in the intermittent process, the inventors found that the slow feature analysis technology has disadvantages in the field of fault detection in the intermittent process: (1) the batch process has essentially two-dimensional dynamics: although the slow feature analysis can handle the dynamic characteristics in the time dimension of the batch process, the dynamic characteristics in the batch dimension of the batch process cannot be eliminated, and the effect of fault detection is affected. (2) The slow feature analysis is actually a linear dimension reduction method, cannot process strong nonlinear features of an intermittent process, and reduces the performance of fault detection.

Disclosure of Invention

In order to solve the problems, the invention provides a fault detection method and a system for an intermittent process considering two-dimensional dynamic characteristics, which firstly integrate an autoregressive moving average time sequence model and kernel function skills into a slow feature analysis method to construct a time dynamic kernel slow feature analysis technology and process strong nonlinearity of the intermittent process and dynamic characteristics on a time dimension; then, a two-dimensional dynamic kernel slow characteristic analysis technology is constructed by combining a global modeling strategy and time dynamic kernel slow characteristic analysis, dynamic change and random offset among different batches in the intermittent process are further eliminated, and the dynamic characteristic on the batch dimension is effectively solved; and finally, based on the extracted low-dimensional slow characteristic information, monitoring statistics are respectively constructed in a principal component space and a residual error space, the running state of the intermittent process is monitored in real time, and the performance of real-time fault detection of the intermittent process can be improved.

In order to achieve the purpose, the invention adopts the following technical scheme:

a first aspect of the invention provides a method of intermittent process fault detection that takes into account two-dimensional dynamics.

A method of intermittent process fault detection considering two-dimensional dynamics, comprising:

extracting low-dimensional characteristic information of the test data by using a load matrix of a two-dimensional dynamic kernel slow characteristic analysis model, and calculating monitoring statistics of the test data in a principal component space and a residual error space; the test data are different working condition data of an intermittent process;

judging whether the intermittent process has a fault or not according to the comparison result of the monitoring statistic and the corresponding control limit;

the load matrix is constructed by generalized eigenvectors corresponding to the optimization problem of the two-dimensional dynamic kernel slow characteristic analysis model; the construction process of the two-dimensional dynamic nuclear slow characteristic analysis model comprises the following steps:

expanding each batch of data sets in the three-dimensional training data set by using an autoregressive moving average time sequence model to obtain corresponding expanded batch of data sets; the training data is normal operation condition data of an intermittent process;

the method comprises the steps of mapping an augmented batch data set to a high-dimensional feature space in a nonlinear mode, establishing a time dynamic kernel slow feature analysis model, introducing a kernel function skill to calculate a kernel matrix and a time change kernel matrix, calculating a total average kernel matrix and a total time change kernel matrix based on a global modeling strategy, and finally establishing a two-dimensional dynamic kernel slow feature analysis model.

As a specific embodiment, before expanding each batch of data sets in the three-dimensional training data set, the method further includes:

the method comprises the steps of firstly expanding an original three-dimensional training data set in an intermittent process into a two-dimensional data matrix according to the batch direction, carrying out zero-mean and unit variance standardization operation on the two-dimensional data matrix, then rearranging the standardized two-dimensional data matrix into a new three-dimensional training data set, and expanding by using the new three-dimensional training data set.

The technical scheme has the advantages that the correlation among the intermittent process variables and the dynamic characteristics on the time dimension can be captured more fully, and the accuracy of fault detection is improved.

As a specific embodiment, the determination process of the control limit of the monitoring statistic is:

and extracting low-dimensional characteristic information from a standardized two-dimensional data matrix by using a load matrix of a two-dimensional dynamic kernel slow characteristic analysis model, respectively constructing monitoring statistics in a principal component space and a residual error space, and determining corresponding control limits.

As a specific embodiment, the calculation process of the total average kernel matrix and the total time variation kernel matrix is as follows:

calculating a corresponding kernel matrix by using the current batch data set and the rest other batch data sets;

calculating an average kernel matrix of the current batch of data sets based on all the kernel matrices, and carrying out mean centering operation on the average kernel matrix to obtain a centered average kernel matrix;

and calculating to obtain a total average kernel matrix and a total time change kernel matrix based on all the batch average kernel matrices with the mean values being centralized.

The technical scheme has the advantages that the global modeling strategy can be utilized, the dynamic change and random offset among different batches of data sets in the intermittent process can be eliminated, and the dynamic characteristic of batch dimensionality in the intermittent process is effectively solved; in addition, the strong non-linear characteristic of the intermittent process can be processed due to the application of kernel function skills.

As a specific implementation mode, low-dimensional feature information of the test data is extracted from the mean-centered average test kernel vector.

As a specific embodiment, the calculation process of the mean-centered average test kernel vector is as follows:

expanding the test data by using an autoregressive moving average time sequence model to obtain an augmentation vector;

calculating a kernel vector of the test data by using a kernel function skill based on the augmentation vector and the augmentation matrix of any batch of data sets;

and after the test kernel vectors relative to all batches of data sets are obtained through calculation, further calculating the average test kernel vector and carrying out mean centering on the average test kernel vector to obtain the centered average test kernel vector.

The technical scheme has the advantages that the autoregressive moving average time series model is used for expanding the model, and the correlation among intermittent process variables and the dynamic characteristic on the time dimension can be fully captured. In order to process the strong nonlinear characteristics of the intermittent process, a kernel function skill is introduced to calculate a kernel matrix and a time change kernel matrix, so that the problem of definitely solving the nonlinear transformation function can be avoided.

As a specific implementation mode, the monitoring statistic of the pivot space is T²For monitoring the main slow-changing trend of intermittent processes; the monitoring statistic of the residual space is SPE, which is used for monitoring random fluctuation and noise interference in a short time of an intermittent process.

A second aspect of the invention provides an intermittent process fault detection system that takes into account two-dimensional dynamics.

An intermittent process fault detection system that accounts for two-dimensional dynamics, comprising:

the monitoring statistic calculation module extracts low-dimensional characteristic information of the test data by utilizing a load matrix of the two-dimensional dynamic kernel slow characteristic analysis model and calculates monitoring statistics of the test data in a principal component space and a residual error space; the test data are different working condition data of an intermittent process;

the intermittent process fault judgment module is used for judging whether the intermittent process has faults or not according to the comparison result of the monitoring statistic and the corresponding control limit;

A third aspect of the invention provides a computer-readable storage medium.

A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the intermittent process fault detection method taking into account two-dimensional dynamics as described above.

A fourth aspect of the invention provides a computer apparatus.

A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor when executing the program implementing the steps in the intermittent process fault detection method taking into account two-dimensional dynamics as described above.

Compared with the prior art, the invention has the beneficial effects that:

(1) according to the invention, an autoregressive moving average time sequence model and kernel function skills are integrated into a slow feature analysis method to construct a time dynamic kernel slow feature analysis technology, so that not only can the strong nonlinear features of the intermittent process be processed, but also the dynamic characteristics of the intermittent process in the time dimension can be more fully extracted, and the fault detection effect of the intermittent process is improved;

(2) according to the invention, a two-dimensional dynamic kernel slow characteristic analysis technology is constructed by combining a global modeling strategy and time dynamic kernel slow characteristic analysis, so that dynamic change and random offset among different batch data sets in an intermittent process can be eliminated, the dynamic characteristic in batch dimensions in the intermittent process is effectively solved, finally, based on extracted low-dimensional slow characteristic information, monitoring statistics are respectively constructed in a principal component space and a residual error space, the running state of the intermittent process is monitored in real time, and the performance of fault real-time detection in the intermittent process is improved.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.

Fig. 1 is a flow chart of intermittent process fault detection considering two-dimensional dynamic characteristics according to an embodiment of the present invention.

FIG. 2 is a block diagram of a two-dimensional dynamic kernel slow profile analysis according to an embodiment of the present invention.

FIG. 3 is a schematic diagram of the penicillin fermentation process in the example of the present invention.

FIG. 4 is a schematic diagram of the standardization and rearrangement of three-dimensional training data in penicillin fermentation process according to the embodiment of the present invention.

FIG. 5 is a flow chart of the calculation of the total average kernel matrix for the penicillin fermentation process according to the embodiment of the present invention.

FIG. 6(a) is a diagram showing the T of the BDKPCA method for penicillin fermentation process failure F3 in accordance with an embodiment of the present invention²And monitoring the statistic fault detection result.

Fig. 6(b) is the SPE monitoring statistic fault detection result of the BDKPCA method for penicillin fermentation process fault F3 according to the embodiment of the present invention.

FIG. 6(c) is the T of TKSFA method for penicillin fermentation process failure F3 in the example of the present invention²And monitoring the statistic fault detection result.

FIG. 6(d) is the SPE monitoring statistic fault detection result of TKSFA method for penicillin fermentation process fault F3 in accordance with the present invention.

FIG. 6(e) is a diagram showing T of TDKSFA method for F3 failure in penicillin fermentation process in accordance with an embodiment of the present invention²And monitoring the statistic fault detection result.

FIG. 6(F) is the SPE monitoring statistic fault detection result of TDKSFA method for penicillin fermentation process fault F3 according to the embodiment of the present invention.

FIG. 7(a) is a diagram showing the T of the BDKPCA method for penicillin fermentation process failure F6 in accordance with an embodiment of the present invention²And monitoring the statistic fault detection result.

Fig. 7(b) is the SPE monitoring statistic fault detection result of the BDKPCA method for penicillin fermentation process fault F6 according to the embodiment of the present invention.

FIG. 7(c) is the T of TKSFA method for penicillin fermentation process failure F6 in accordance with the present invention²And monitoring the statistic fault detection result.

FIG. 7(d) is the SPE monitoring statistic fault detection result of TKSFA method for penicillin fermentation process fault F6 in accordance with the present invention.

FIG. 7(e) is a diagram showing T of TDKSFA method for F6 failure in penicillin fermentation process in accordance with an embodiment of the present invention²And monitoring the statistic fault detection result.

FIG. 7(F) is the SPE monitoring statistic fault detection result of TDKSFA method for penicillin fermentation process fault F6 according to the embodiment of the present invention.

Detailed Description

The invention is further described with reference to the following figures and examples.

It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.

The fault detection method and the fault detection system are realized based on two-dimensional dynamic kernel slow characteristic analysis and are suitable for fault detection in an intermittent process. Wherein the intermittent process comprises a penicillin fermentation process, an injection molding process, a sewage treatment process, a beer brewing process, a semiconductor manufacturing process and the like.

The principle of the intermittent process fault detection method of the invention is as follows:

Taking the penicillin fermentation process as an example below, the penicillin fermentation process is a well-known benchmark simulation process widely used to evaluate batch process fault detection methods.

Example one

The principle diagram of the penicillin fermentation process is shown in fig. 3, and the fermentation process comprises two operation stages: a pre-culture phase and a fed-batch phase. During the initial pre-culture phase, a large number of nutrients essential for the cells begin to be produced and penicillin cells appear during the exponential growth of the cells. In the fed-batch phase, in order to maintain a high penicillin yield, a continuous glucose supply to the fermentation process is required to keep the biomass growth rate constant. In order to provide the best conditions for penicillin production, closed loop control of the temperature and pH of the fermentor is used.

In the simulation experiment, a simulator Pensim V2.0 was used to generate simulation data for the penicillin fermentation process. The 10 variables listed in table 1 were selected as the monitored variables and gaussian noise was added during variable sampling. The training data set was collected from 40 batches under normal conditions, each of 400 hours in length, with the first 45 hours being the pre-incubation phase and the last 355 hours being the fed-batch phase. Considering the dynamic variation and offset between the normal working condition data sets of different batches, the normal operating conditions of the penicillin fermentation process fluctuate within a certain allowable range, and the specific fluctuation range is shown in table 2. In addition, we also simulated that 6 batches of fault data were generated, each batch also being 400 hours in length. The types of faults added included step changes and ramping of the three variables aeration rate, agitation power and substrate feed rate, and detailed information about the failure modes added in the simulation is shown in table 3.

TABLE 1 Process variables used for monitoring the penicillin fermentation Process

TABLE 2 Normal operating conditions variation Range for penicillin fermentation Process

TABLE 3 six failure mode information for penicillin fermentation process

The fault detection method for the penicillin fermentation process, as shown in figure 1, comprises the following steps:

an off-line modeling stage:

collecting normal operation data X of 40 batches in penicillin fermentation process_iI-1, 2, …,40 form a three-dimensional training data set

First, a three-dimensional training data set is formed

Expanding the two-dimensional training data matrix according to the batch direction

And the zero mean and unit variance normalization is performed. The normalized two-dimensional data matrix X (I × JK) is then rearranged into a new three-dimensional training data matrix X (I × J × K). The data in the training data set are all normal operation condition data of an intermittent process;

computing a two-dimensional training data set

Mean value of

And the standard deviation std (X (I × KJ)), the training data set X (I × KJ) is normalized to obtain a normalized two-dimensional training data set X (I × KJ).

The training data set X (I × KJ) is normalized by equation (1), and the expression is as follows:

X(I×KJ)＝(X(I×KJ)-mean(X(I×KJ)))/std(X(I×KJ)) (1)

the penicillin fermentation process comprises the steps of firstly expanding and standardizing an original three-dimensional training data set according to the batch direction, then rearranging the original three-dimensional training data set into a new three-dimensional training data set, wherein the data preprocessing process is as shown in figure 4

It should be noted that the method for normalizing the training data set can also be implemented by other existing methods, and those skilled in the art can specifically select the method according to the actual situation.

Secondly, in order to more fully capture the correlation among the intermittent process variables and the dynamic characteristics on the time dimension, each batch of data sets X in a newly-formed three-dimensional training matrix X (I multiplied by J multiplied by K)_iExpanding the time series model by using the autoregressive moving average time series model to obtain a corresponding augmentation batch data set

Ith batch dataset X_iOf the augmented batch dataset X_i ^dThe model was constructed from an autoregressive moving average time series as follows:

where d represents the order of the time lag.

And (III) the construction process of the time dynamic kernel slow characteristic analysis model comprises the following steps: expanding each batch of data sets in the standardized three-dimensional training matrix to obtain an expanded batch of data sets, then mapping the data sets to a high-dimensional feature space by adopting a nonlinear transformation function to obtain a corresponding data set, and then establishing a time dynamic kernel slow feature analysis model by a kernel function technique.

Specifically, each augmented batch dataset is transformed using a non-linear transformation function

Nonlinear mapping to high-dimensional feature space to obtain corresponding data set

Based on data sets

Establishing a time dynamic kernel slow characteristic analysis model, and introducing kernel function skill to calculate a kernel matrix K_iiAnd time varying kernel matrix Δ K_iiTo avoid the troublesome problem of explicitly solving the nonlinear transformation function.

Given data set

Representing an augmented batch dataset in a high-dimensional feature space

Wherein the vector

Representing a non-linear transformation function. Based on data sets

Establishing an objective function of time dynamic nonlinear slow feature analysis:

wherein the content of the first and second substances,

w_jrepresenting the jth load vector.

First derivative with respect to time

The approximate calculation is:

substituting equation (4) into equation (3), the objective function of the time-dynamic nonlinear slow feature analysis is rewritten as:

taking into account the load vector w_jCan be expressed as the ith augmentation batch data set in a high-dimensional feature space

Linear combination of all samples in (1):

wherein alpha is_j,kK is 1,2, …, K denotes the coefficient present, α_j＝[α_j,1,α_j,2,…,α_j,K]^TRepresenting a coefficient vector.

Substituting equation (6) into equation (5), the objective function of the time-dynamic nonlinear slow feature analysis is further expressed as:

to avoid explicitly solving nonlinear transformation functions

The kernel function techniqueSmart toy

Combined with a time-dynamic nonlinear slow feature analysis method. Using kernel function techniques, kernel vectors can be computed

And kernel matrix of ith batch dataset

In this embodiment, a polynomial core ker (x, y) ═ is selected<x,y>^hAs a kernel function, where h represents the order of the polynomial kernel function. Constructing an objective function of a time dynamic kernel slow characteristic analysis method:

wherein the content of the first and second substances,

matrix Δ K_iiA time-varying kernel matrix representing the ith batch dataset calculated as:

ΔK_ii＝[Δk_i,1,Δk_i,2,…,Δk_i,K]，

(IV) continuously calculating the rest I-1 kernel matrixes K by using the ith batch data set and the rest I-1 batch data sets_ijJ ≠ 1,2, …, I, j ≠ I. I kernel matrixes K obtained based on calculation_ijJ 1,2, …, I, and further calculating an average kernel matrix for the ith batch dataset

And carrying out mean value centering operation on the mean value to obtain a centered average kernel matrix

Average kernel matrix for ith batch dataset

The calculation is as follows:

wherein, the matrix K_ijJ ≠ 1,2, …, I, j ≠ I denotes the remaining I-1 kernel matrices computed using the ith batch dataset and the remaining I-1 batch datasets.

Average kernel matrix over batches

Carrying out mean centering:

wherein, I_KA K-dimensional matrix is represented, which contains all elements 1/K.

Fifthly, in order to eliminate the dynamic characteristics of batch dimensions of the batch process, a batch average kernel matrix based on I mean centralization is utilized by utilizing a global modeling strategy

Calculating an overall average kernel matrix

And total time variation kernel matrix

And establishing a two-dimensional dynamic kernel slow characteristic analysis model.

The two-dimensional dynamic kernel slow characteristic analysis model is constructed according to a total average kernel matrix and a total time change kernel matrix on the basis of the time dynamic kernel slow characteristic analysis model, wherein the total average kernel matrix is composed of total average kernel vectors, and the total time change kernel matrix is composed of variation of adjacent total average kernel vectors.

According to the kernel matrix

And

and constructing a two-dimensional dynamic nuclear slow characteristic analysis model.

Total average kernel matrix

The calculation is as follows:

wherein, the matrix

Represents the ith mean-centered batch-averaged kernel matrix. Total average kernel matrix

The calculation flow of (2) is shown in fig. 5.

Based on the total average kernel matrix

Constructing a total time variation kernel matrix

Wherein the content of the first and second substances,

from the total average kernel matrix

And total time variation kernel matrix

Constructing an objective function of two-dimensional dynamic kernel slow characteristic analysis:

wherein the content of the first and second substances,

and

to represent

And (VI) converting the optimization problem of the two-dimensional dynamic kernel slow characteristic analysis into a generalized eigenvalue decomposition problem, and constructing a load matrix A by solving the generalized eigenvector.

The optimization problem of the two-dimensional dynamic kernel slow feature analysis in equation (14) can be further transformed into a generalized eigenvalue decomposition problem as shown in equation (15).

By solving the formula (15), a series of generalized eigenvalues can be obtained

Corresponding generalized eigenvector

Selecting generalized eigenvectors corresponding to the first p minimum generalized eigenvalues

Constructing a load matrix

Wherein the value of the parameter p is determined according to the retained slow characteristic information, and the accumulated slow contribution rate can be at least 95%.

Wherein, mu_jIs defined as

For j ═ 1,2, …, K.

And (seventhly) extracting slowly-changing low-dimensional feature information from the standardized two-dimensional training data set according to the load matrix A, and then respectively constructing monitoring statistics on the principal component space and the residual error space and determining respective control limits of the principal component space and the residual error space.

Such as: constructing T in principal component space²Statistics monitor the main slow-changing trend of the batch process:

constructing SPE statistics in a residual space to monitor random fluctuation and noise interference in a short time of an intermittent process:

wherein the vector

Representing the total average kernel matrix

One sample point in (1), matrix A_totalIs constructed as

To determine if an intermittent process has failed, T²And the respective control limits of the SPE monitoring statistics are determined using a kernel density estimation algorithm based on the normal training data set.

It should be noted here that in other embodiments, other monitoring statistics and their corresponding control limits may be constructed to determine whether the intermittent process has failed.

The purpose of the off-line modeling step is to construct a two-dimensional dynamic kernel slow characteristic analysis model and determine corresponding control limit values of monitoring statistics in principal component space and residual error space based on normal operating condition data of an intermittent process.

And (3) an online monitoring stage:

the stage is to detect different working condition data of the intermittent process, and T is used below²And the SPE monitoring statistics are taken as an example to give the steps of intermittent process fault detection in detail:

a pair of test data x_t(k) Expanding the time sequence by using an autoregressive moving average time sequence model to obtain an augmentation vector of the time sequence

Wherein the test data are different working condition data of the intermittent process;

wherein the vector

Representing test data x_t(k) The previous d observations.

(II) based on augmented vector

And an augmentation matrix for the ith batch dataset

Kernel vector k of test data calculated by kernel function technique_t,i(ii) a Where I is 1,2, …, I.

Test kernel vector k_t,iThe calculation is as follows:

wherein the content of the first and second substances,

and

respectively, I is 1,2, …, and I and K are 1,2, …, K.

(III) calculating to obtain a test kernel vector k relative to all the I batch data sets_t,iI1, 2, …, after I, an average test kernel vector is further calculated

And mean centering is carried out on the test kernel vector to obtain a centered average test kernel vector

Average test kernel vector

The calculation is as follows:

wherein k is_t,iRepresenting the test kernel vector relative to the ith batch dataset.

Further averaging the test kernel vectors

Carrying out mean value centering treatment:

wherein, I_tRepresents a vector of dimension K x 1, which contains 1/K of elements.

(IV) mean test kernel vector from centralization according to two-dimensional dynamic kernel slow feature analysis algorithm

Extracting low-dimensional slow characteristic information of the test data, and respectively calculating T of the test data²And SPE monitoring statistics.

Establishing T²Monitoring statistics:

wherein matrix A represents a load matrix

Establishing SPE monitoring statistics:

wherein, the matrix A_totalIs constructed as

(V) T according to test data²And SPE monitors whether the statistics exceed their respective control limits to determine whether the non-intermittent process has failed.

If T is²And at least one of the values of the SPE monitoring statistics exceeds the corresponding control limit, indicating that the intermittent process has failed in the operation process; if T is²And the numerical value of the SPE monitoring statistic does not exceed the respective control limit, indicating that the intermittent process is operated in a normal state.

In specific implementation, in order to evaluate the fault detection effects of different monitoring methods, the fault detection effects of different methods are compared through two performance indexes, namely Fault Detection Time (FDT) and Fault Detection Rate (FDR).

The fault detection time instant (FDT) is defined as the sampling time instant at which the first sample considered as fault data is located, and the Fault Detection Rate (FDR) is defined as the ratio of the number of samples detected as fault data to the actual total number of fault samples.

Obviously, the smaller the value of the FDT, the larger the value of the FDR, which means the better the fault detection effect of the process monitoring method; the larger the value of the FDT is, the smaller the value of the FDR is, which indicates that the fault detection effect of the process monitoring method is worse.

In the simulation example, three methods, namely two-dimensional dynamic nuclear slow characteristic analysis (TDKSFA), two-dimensional nuclear slow characteristic analysis (TKSFA) and batch dynamic nuclear principal component analysis (BDKPCA), are used for comparing and analyzing the fault detection effect of the penicillin fermentation process. When the TDKSFA is modeled, a polynomial kernel is selected as a kernel function. And determining the value of the polynomial kernel function order h in the TDKSFA as 5 according to a grid search algorithm. The value of the time lag d in the TDKSFA is empirically chosen to be 2. For a fair comparison, polynomial kernels are also used as kernel functions in the BDKPCA and TKSFA methods. For BDKPCA, the values of the polynomial kernel order h and the time lag d are set to 5 and 2, respectively. For TKSFA, the polynomial kernel order h is determined to be 4 according to the grid search algorithm. In the BDKPCA, TKPCA and TDKSFA methods, the number of principal elements to be retained is selected according to the 95% cumulative information contribution rate. For the three monitoring methods, a 99% confidence limit for normal operating condition data is set as a fault detection threshold for each monitoring statistic. In all the monitoring graphs, if five consecutive sample points exceed the control limit, we consider that a fault is detected.

The three methods of BDKPCA, TKSFA and TDKSFA are comprehensively compared, and the failure detection effect of the penicillin fermentation process is illustrated by taking the failure F3 and F6 as examples.

Failure F3 is a step change in substrate feed flow rate at 100 h. The effects of fault detection of BDKPCA, TKSFA, and TDKSFA are shown in fig. 6(a) -6 (f). As can be seen from FIGS. 6(a) and 6(b), T of BDKPCA²And the SPE monitoring statistics detect failures at 139h and 121h, respectively. In FIGS. 6(c) and 6(d), T of TKSFA²The monitoring statistic detects a failure at 122h, giving a better detection result. But the SPE monitoring statistic for TKSFA does not detect a fault occurrence at 124h and results in a lower fault detection rate because some fault samples fall back below the control limit after 124 h. Compared with the monitoring graphs of BDKPCA and TKSFA, the TDKSFA obtains the best fault detection effect. In FIGS. 6(e) and 6(f), T of TDKSFA²And the SPE monitoring statistics both detect a fault at 109h, and after the fault is detected, almost no fault samples fall back below the corresponding control line. Thus the TDKSFA has the best fault detection effect because it gives the earliest moment of fault detection and the highest fault detection rate.

Failure F6 is a ramp of substrate feed flow rate at 100 h. The effects of fault detection of BDKPCA, TKSFA, and TDKSFA are shown in fig. 7(a) -7 (f). In FIGS. 7(e) and 7(f), T of TDKSFA²And the SPE monitoring statistic detected the failure occurrence at 106h and 105h, respectively, the fastest and most accurate response to failure F6 was made in these three methods. However, BDKPCA gives the worst fault detection results in fig. 7(a) and 7 (b). T of BDKPCA²The monitoring statistic detects a failure at 136h, while its SPE monitoring statistic detects a failure at 127 h. Compared with BDKPCA, TKSFA has some improvement in the failure detection results in fig. 7(c) and fig. 7 (d). T of TKSFA²And SPE monitoring statistics alarm for faults at 107 h. In summary, fig. 7(a) -7 (F) show that the TDKSFA has the best detection effect on the fault F6.

TABLE 4 FAIL DETECTION TIME (FDT) COMPARATIVE TABLE FOR THREE METHODS

TABLE 5 comparison of Fault Detection Rate (FDR) for three methods

Table 4 and table 5 show the failure detection time and failure detection rate for the failures F1 to F6 by the three methods BDKPCA, TKSFA, and TDKSFA, respectively. As can be seen from table 4, for step faults F1 and F2, the three methods can detect the fault occurrence at 100h, and the fault detection rate is 100%. Since the true fault variable in step fault F3 slowly affects the remaining normal variables, these three methods cannot be detected immediately after fault F3 is added. But the TDKSFA has the smallest fault detection delay time for the fault F3 among the three methods. For the slope faults F4, F5 and F6, which are difficult to detect, the TDKSFA obtained faster monitoring results than the BDKPCA and TKSFA. This is because the TDKSFA gives the smallest fault detection delay time for each of the faults F4, F5, and F6. As can be seen from table 5, although DKPCA, TKSFA, and TDKSFA obtained 100% failure detection rate for both failures F1 and F2. However, for the more difficult faults F3, F4, F5, and F6, the TDKSFA achieved the highest fault detection rate in all of the three methods. By combining the above analysis, the monitoring results of the faults F1 to F6 show that the fault detection effect of the TDKSFA in this embodiment is significantly better than that of the BDKPCA and TKSFA methods.

Example two

The present embodiment provides an intermittent process fault detection system considering two-dimensional dynamic characteristics, which includes:

Each module in the intermittent process fault detection system of this embodiment corresponds to a step in the intermittent process fault detection method described in the first embodiment one by one, and will not be described here in a repeated manner.

EXAMPLE III

The present embodiment provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps in the intermittent process fault detection method considering two-dimensional dynamics as described in the first embodiment above.

Example four

This embodiment provides a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the intermittent process fault detection method considering two-dimensional dynamics as described in the first embodiment above when executing the program.

As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method of intermittent process fault detection considering two-dimensional dynamics, comprising:

2. The method of intermittent process fault detection accounting for two-dimensional dynamics of claim 1, wherein before expanding each batch of data sets in the three-dimensional training data set, further comprising:

3. A method of intermittent process fault detection considering two-dimensional dynamics as in claim 2, characterized in that the control limit of the monitoring statistics is determined by:

4. An intermittent process fault detection method considering two-dimensional dynamics as claimed in claim 1, characterized in that the calculation process of the total average kernel matrix and the total time variation kernel matrix is:

5. The intermittent process fault detection method taking into account two-dimensional dynamics of claim 1, wherein low-dimensional feature information of the test data is extracted from the mean-centered average test kernel vector.

6. An intermittent process fault detection method considering two-dimensional dynamics as in claim 5, wherein the mean-centered mean test kernel vector is calculated by:

7. The method of claim 1, wherein the monitoring statistic of the principal component space is T²For monitoring the main slow-changing trend of intermittent processes; the monitoring statistic of the residual space is SPE, which is used for monitoring random fluctuation and noise interference in a short time of an intermittent process.

8. An intermittent process fault detection system that accounts for two-dimensional dynamics, comprising:

9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method for intermittent process fault detection taking into account two-dimensional dynamics as claimed in any one of claims 1 to 7.

10. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor, when executing the program, implements the steps in the intermittent process fault detection method taking into account two-dimensional dynamics as claimed in any one of claims 1 to 7.