CN111027645B

CN111027645B - Microbial fermentation process fault monitoring method based on high-order statistic construction in sub-stage

Info

Publication number: CN111027645B
Application number: CN201911388480.2A
Authority: CN
Inventors: 常鹏; 卢瑞炜; 张祥宇; 王普
Original assignee: Beijing University of Technology
Current assignee: Beijing University of Technology
Priority date: 2019-12-27
Filing date: 2019-12-27
Publication date: 2023-05-26
Anticipated expiration: 2039-12-27
Also published as: CN111027645A

Abstract

The invention discloses a novel method for realizing real-time fault monitoring of penicillin fermentation process. The method utilizes the high-order information of penicillin fermentation process data to establish an effective process monitoring scheme to timely detect abnormal phenomena. The invention comprises two stages of off-line modeling and on-line monitoring. "offline modeling" includes: dividing the original data into stages, and solving the nonlinearity of the data while adopting Kernel Entropy Component Analysis (KECA) processing; new sub-phase statistics are then constructed for process monitoring using HCA techniques in the high-dimensional kernel entropy space. "on-line monitoring" includes: preprocessing the newly acquired data, calculating statistics and comparing with a control limit to judge whether the fermentation process is normal. The invention can better reveal the change of the related relation of the process variable, objectively reflect the diversity of the characteristics of each stable stage and each transition stage, and effectively reduce the false alarm and the missing alarm rate of the system.

Description

Microbial fermentation process fault monitoring method based on high-order statistic construction in sub-stage

Technical Field

The invention relates to the technical field of fault diagnosis based on data driving, in particular to a fault diagnosis technology aiming at a sub-stage of an intermittent process. The data-driven method of the invention is a specific application in the aspect of fault monitoring of a typical batch process, namely penicillin fermentation process.

Background

Multistage, nonlinear, non-gaussian are inherent features of batch processes, common batch processes are microbiology, sewage treatment, beer preparation, yogurt preparation, etc. The batch production scale of the intermittent process is flexible, the process is easy to change, meanwhile, the intermittent process has certain compatibility for product switching, can carry out production of a small amount of different varieties, and can adapt to the change of raw materials or operation conditions relatively quickly. However, compared with the continuous process, the method has the advantages that the manual participation components are more, the operation control requirement is more complex, the problems of bacteria contamination, manual damage of a detection device and the like in the production process can exist, the process is easy to stop, and the cleaning and the disinfection can be performed regularly, but the problem can be found as early as possible, so that the unnecessary sinking cost is still needed to be considered. Therefore, it is important to establish a reasonable and efficient online monitoring and fault diagnosis mechanism.

In recent years, the KICA monitoring method has been widely used in the field of monitoring for non-gaussian, non-linear coexistence in batch processes. However, the method of KICA uses the kernel skill to maximize the data information in the high-dimensional feature space for data dimension reduction, and does not consider the cluster structure information of the data, so that the dimension-reduced data distribution has great difference from the original data distribution, and the process monitoring by using the model can lead to the phenomena of missing alarm and false alarm of a large number of faults.

In the field of batch process monitoring, KECA has achieved an effect superior to that of traditional KICA in terms of nonlinear batch production process fault monitoring, but the above monitoring strategy based on KECA does not consider the problem of nonlinear and non-Gaussian coexistence. If only KECA is used to monitor batch processes with both non-Gaussian and non-linear characteristics, a large number of false alarms and missed alarms will be caused, and some monitoring performance of the process is even lost.

The intermittent process is provided with a plurality of operation stabilization stages and a plurality of operation transition stages, when the production process runs in different stages, the characteristics such as the mean value, variance, correlation and the like of the normal production process data can be obviously changed, for example, the built monitoring model is built according to the thought of integral modeling, so that the built model cannot describe all the operation stages of the production process well, and the built integral model is often reflected in that only a certain production stage can be described well; or the constructed integral control limit is too wide, and the false alarm rate and the missing alarm rate of the faults are higher.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a method for monitoring faults in a microbial fermentation process, which is constructed based on high-order statistics in sub-stages. The method fully considers the characteristics of nonlinearity, non-Gaussian property, multiple phases and the like of intermittent process data. Firstly, dividing time periods, solving the multi-stage characteristic of an intermittent process, then utilizing KECA to map original data to a high-dimensional kernel entropy space to solve the nonlinear characteristic of the data, enabling the original data to be linearly separable, establishing an ICA monitoring model in each stage, decomposing data of Gao Weihe entropy space into an independent element space and a residual space, and then respectively constructing monitoring statistics HS and HE of high-order cumulative quantity in two subspaces for online monitoring.

The invention adopts the following technical scheme and implementation steps:

A. offline modeling stage:

1) For the acquired data matrix X, each row corresponds to each sampling instant and each column corresponds to each sensor.

2) And (3) carrying out phase division on all operation moments by using a clustering method to obtain K classes, wherein each class is a subperiod. Decomposing the matrix X according to the dividing result to obtain a data matrix X of each stage _k ，k＝1，2，...，K。

3) Each X is taken _k Mapping to a kernel space to obtain a subinterval kernel matrix K _k ，k＝1，2，...，K。K _k The ith row and the jth column element k _kij The calculation method comprises the following steps:

k _kij ＝φ(x _i ，x _j )

wherein phi is a kernel mapping function, which can be selected according to specific conditions, wherein a Gaussian kernel function, x _i 、x _j Respectively X _k I, j row vectors of (c).

4) Calculating normalized whitening score matrices for K stages, respectively

k=1, 2,..k, the specific steps are as follows:

i. calculating a whitening score matrix Z based on a KECA method _k ：

Wherein H is _k ＝[a ₁ ，...，a _K ]，a _k Is K _k Is a k-th feature vector of (c). Λ type _k ＝diag(ξ ₁ ，...，ξ _K )，ξ _k Is K _k Diag (·) represents generating a diagonal matrix.

Whitening score matrix Z _k Normalizing to obtain matrix

Thus, the data conversion of all sub-phase data into the core space is completed. Each sub-phase is mapped into a core space unit

5) Nuclear space unit for each period using ICA algorithm

Calculating a separation matrix W _k Mixing matrix A _k Thereby to an independent element matrix S _k Residual matrix e _k ：

6) The monitoring statistics and control limits based on the higher order cumulative amounts are constructed, and at the ith sampling instant,

the mth independent component s _m The third-order cumulative amounts of samples of (2) are:

hs _m (i)＝s _m (i)s _m (i-1)s _m (i-2)

wherein s is _m (i) Is an independent element matrix S _k M row and i column values, 1 < m < S _k Number of lines of (3) i < S _k Is a column number of columns.

The first monitoring statistic HS of the higher-order cumulative quantity at the time i is:

7) At the ith sample time, the qth residual e _q The third-order cumulative amounts of samples of (2) are:

he _q (i)＝e _q (i)e _q (i-1)e _q (i-2)

wherein e _q (i) Is the residual matrix e _k The value of the ith row and ith column of the q-th row is 1 < q < e _k Number of lines of (3) i < e _k Is a column number of columns.

The second monitoring statistic HE of the higher order cumulative amount at time i is:

8) The slices S (i) at all times in the sub-period are formed into a time sequence [ HS (1), HS (2), …, HS (i), … ]]Using a kernel density method for this time series, the output value is used as the monitoring control limit HS of the kth period _klimit . Similarly, a time series [ HE (1), HE (2), …, HE (i), … ] was constructed]Control limit HE is obtained using a nuclear density method _klimit 。

B. On-line monitoring:

9) On-line acquisition of data vector x at ith moment _new And judging whether the sampling time belongs to the kth subperiod according to the sampling time. Performing kernel function mapping to obtain a vector K _knew ：

k _knewi ＝φ(x _new ，x _j )

Wherein k is _knewj Is the vector K _knew Is the j-th element, x _j Offline data matrix X for this period _k Phi is the kernel mapping function selected during offline modeling.

10 Calculating X _knew Normalized whitening score matrix of (a)

i. First calculate the whitening score vector Z _knew

Calculating normalized whitening score vectors

Wherein H is _k 、Λ _k All are matrices obtained in the offline modeling process.

11 Using a separation matrix W obtained in an off-line stage _k Mixing matrix A _k So that the independent meta-vector s to the i-th moment _knew (i) Residual vector e _knew (i)：

12 High-order cumulative amount online statistics are constructed, and the specific form is shown as follows:

hs _knew (i)＝s _knew (i)s _knew (i-1)s _knew (i-2)

he _knew (i)＝e _knew (i)e _knew (i-1)e _knew (i-2)

will HS _knew (i)、HE _knew (i) And a kth period control line HS obtained in an off-line process _klimit 、HE _klimit And comparing, if the current time is not greater than the control line, indicating that the current time is normal, and if the current time is greater than the control line, indicating that the current time is abnormal, and generating an alarm.

Advantageous effects

According to the method, firstly, the data are divided into stages, kernel mapping and whitening processing are respectively carried out on the data in each stage by using the KECA, and the data after the KECA processing are mapped to a high-dimensional kernel entropy space so as to become linearly separable, so that the linear ICA method can be expanded to the nonlinear field. And (3) decomposing the processed stage data by using ICA to obtain independent elements and residual errors, respectively constructing third-order cumulative monitoring statistics HS and HE, and obtaining monitoring control limits of the three-order cumulative monitoring statistics HS and HE by using nuclear density estimation for online monitoring of the process.

Aiming at the defect that the monitoring statistic constructed by the traditional MKICA monitoring method is a second-order statistic, the monitoring statistic of a third-order cumulative quantity is provided for process monitoring, and the method aims to solve the problems of high false alarm and omission in the traditional statistic monitoring and improve the reliability and sensitivity of fault monitoring.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 (a) is a graph of the effect of MKICA method monitoring 1 st failure;

FIG. 2 (b) is a graph of the effect of HCA method monitoring 1 st failure;

FIG. 2 (c) is a graph of the effect of monitoring the 1 st failure of the multi-stage HCA process herein;

FIG. 3 (a) is a graph of the effect of MKICA method monitoring 2 nd failure;

FIG. 3 (b) is a graph of the effect of HCA method monitoring 2 nd failure;

FIG. 3 (c) is a graph of the effect of monitoring the 2 nd failure of the multi-stage HCA process herein;

Detailed Description

Penicillin fermentation simulation platform PenSim2.0 is used as an algorithm test platform to comprehensively test the monitoring strategy proposed in the chapter. The method is characterized in that the concept of the chapter is derived from the consideration of the characteristic coexistence of data in intermittent production process in stages, non-Gaussian and nonlinearity, the concept of sub-stage local modeling is introduced, a sub-stage HCA monitoring model is built, and high-order accumulated monitoring statistics are introduced for monitoring process faults.

For this purpose, a method of phase division is used to obtain multi-phase data. The process variables for modeling are shown in table 1, and the description of the fault settings in this chapter of experiments is shown in table 2.

The non-gaussian nature of all 17 sampling variables of the penicillin production process was verified. The non-gaussian nature of the variables in the penicillin production process was demonstrated using the jbtest function in matlab. jbtest has two return values h, p, respectively. h represents the result of the test, if h=0, it means that the variable follows a gaussian distribution, and if h=1, it means that the variable does not follow a gaussian distribution. p is a probability value of accepting the hypothesis, and the closer p is to 0, the more can indicate that the data does not obey the gaussian distribution. The results of the verification are shown in Table 3, and it is basically difficult for the variables to satisfy the above-described feature of normal distribution, so that the process has a non-Gaussian characteristic. In summary, penicillin production process data have strong non-gaussian properties.

TABLE 1 Process variable

Table 2 types of faults used in simulations

TABLE 3 jbtest result value of variable

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A. Offline modeling stage:

1) For the historical data X, the historical data X is firstly divided into K phases in total to obtain a data matrix X of a single phase _k ，k＝1，2，...，K。

2) Each X is taken _k Mapping to nuclear space to obtain K _k ，k＝1，2，...，K，K _k The method for calculating the middle elements comprises the following steps:

k _kij ＝φ(x _i ，x _j )

3) Based on K _k Calculating a normalized whitening score matrix

k＝1，2，...，K：

i.

ii.

4) Decomposition using ICA algorithm

Obtaining each sub-stage separation matrix W _k And mixing matrix A _k Thereby obtaining the independent element matrix S _k Residual matrix e _k ：

5) And constructing a high-order monitoring statistic at the ith moment.

i. The mth independent component s _m The third-order cumulative amounts of samples of (2) are:

hs _m (i)＝s _m (i)s _m (i-1)s _m (i-2)

the q-th residual e _q The third-order cumulative amounts of samples of (2) are:

he _q (i)＝e _q (i)e _q (i-1)e _q (i-2)

6) Constructing a time series [ HS (1), HS (2), …, HS (i), … ]]、[HE(1)，HE(2)，…，HE(i)，…]Obtaining the monitoring control limit HS by a nuclear density method _klimit 、HE _klimit k＝1，2，...，K。

B. On-line monitoring:

7) On-line acquisition of data vector x at ith moment _new Judging the time period attribution, and performing nuclear mapping to obtain K _knew 。

8) Calculation of K _knew Normalized whitening score matrix of (a)

Using separation matrices W obtained in an off-line stage _k Mixing matrix A _k Obtaining the independent element vector s _knew (i) Residual vector e _knew (i)。

9) The higher order cumulative amount at this time is calculated:

hs _knew (i)＝s _knew (i)s _knew (i-1)s _knew (i-2)

he _knew (i)＝e _knew (i)e _knew (i-1)e _knew (i-2)

The first fault in table 2 was first introduced and the stirring power was ramped at 200h with a slope of 0.002 until the end of the reaction.

I in MKICA method ² And SPE monitor graph (FIG. 2 a), monitors the I of the independent metaspace ² The SPE statistics of the statistics and the monitoring residual space have false alarm phenomenon exceeding 99% control limit at the beginning stage of fermentation, and the false alarm rate is higher.

Although the high-order cumulative monitoring statistic HS of the HCA method (fig. 2 b) and the high-order cumulative monitoring statistic HE of the residual space both have false alarm phenomenon exceeding the control limit at the fermentation start stage, the failure false alarm rate of the HCA method is lower than that of the MKICA method in terms of the false alarm rate of the previous 200h normal stage.

The sub-HCA method (fig. 2 c) provided by the invention does not exceed the monitoring control limit under the normal working condition before 200h, meanwhile, the HS monitoring graph exceeds the monitoring control limit near 206h, and the HE monitoring graph exceeds the monitoring control limit near 203h, so that faults can be found in time.

The second fault in Table 2 was introduced, which was a substrate feed rate of 200h to 250h, and a step disturbance occurred to decrease the feed rate by 15% until the reaction was completed.

The sub-HCA method (FIG. 3 c) and HCA method (FIG. 3 b) herein detected a fault at 200h, 2h earlier than the traditional MKICA method (FIG. 3 a). However, during the beginning of fermentation, the MKICA and HCA methods still have more false alarms, while the methods presented herein do not generate any alarms during the start-up phase.

The two simulation examples show that the multi-stage monitoring model based on the sub-HCA is superior to the traditional MKICA and HCA based methods in terms of accuracy and robustness.

Compared with MKICA, HCA has two advantages, namely HCA utilizes KECA to whiten the original data, and the feature extraction is carried out according to the size of a kernel entropy value after the data is considered to be mapped to a high-dimensional space, so that the converted data maintains the clustering structure of the original data. In the traditional MKICA method, KPCA is utilized to perform original data whitening treatment, and feature extraction is performed according to the feature value, so that the clustering characteristic of data is ignored. And secondly, the monitoring statistic used by the HCA is a high order accumulated statistic which is superior to the second order statistic used by the traditional MKICA.

However, the MKICA and HCA methods are all used for overall modeling, and all process data of a complete batch process are taken as an overall statistical model, so that the multi-stage local process behavior characteristics in batch production are ignored, the change of the correlation relationship between batch process variables is difficult to reveal, and a large amount of missing alarms can occur when the method is applied to monitoring of process faults, and some of the methods even lose monitoring performance.

Analysis shows that the MKICA monitoring method and the HCA based monitoring method have obvious characteristics due to the mechanism characteristics in the beginning stage of microbial fermentation, have poor monitoring performance in the beginning stage of microbial fermentation and have larger false alarm phenomenon, the multistage based monitoring model fully considers the stage characteristics of the production process, and constructs corresponding monitoring statistics and monitoring control limits in each stage, so that the local characteristics of the intermittent production process can be better described, the phenomenon that the model is not clearly described for the process can not occur, the result of excessively loosening the whole monitoring control limits can not be caused, the monitoring precision of the model can be improved, and the false alarm rate and the missing alarm rate of the model can be effectively reduced.

In summary, the method provided by the invention can better reveal the change of the related relation of the process variable, objectively reflect the diversity of the characteristics of each stable stage and each transition stage, and effectively reduce the false alarm and the false alarm rate of the system.

Claims

1. A method for monitoring faults of a microbial fermentation process based on high-order statistics in sub-stages is characterized by comprising two stages of off-line modeling and on-line monitoring, and specifically comprises the following steps:

A. offline modeling stage:

1) For the acquired data matrix X, each row corresponds to each sampling time and each column corresponds to each sensor;

2) Dividing all operation moments by a clustering method to obtain K classes, wherein each class corresponds to K production stages, each class is a subperiod, and the matrix X is decomposed according to the dividing result to obtain a data matrix X of each stage _k ，k＝1,2,…,K；

3) Each X is taken _k Mapping to a kernel space to obtain a subinterval kernel matrix K _k ，k＝1,2,…,K，K _k The ith row and the jth column element k _kij The calculation method comprises the following steps:

k _kij ＝φ(x _i ,x _j )

wherein phi is a kernel mapping function, selectGaussian kernel function, x _i 、x _j Respectively X _k I, j row vectors of (a);

4) Calculating normalized whitening score matrices for K stages, respectively

The method comprises the following specific steps:

i. calculating a whitening score matrix Z based on a KECA method _k ：

Wherein H is _k ＝[a ₁ ,…,a _K ]，a _k Is K _k Is the kth eigenvector, Λ _k ＝diag(ξ ₁ ,…,ξ _K ),ξ _k Is K _k Is used for generating a diagonal matrix;

whitening score matrix Z _k Normalizing to obtain matrix

Each sub-phase is mapped into a core space unit

I represents an identity matrix;

5) Nuclear space unit for each period using ICA algorithm

Calculating a separation matrix W _k Mixing matrix A _k Thereby obtaining the independent element matrix S _k Residual matrix e _k ：

6) Constructing monitoring statistics and control limits based on high-order cumulants, and at the ith sampling moment, the mth independent component s _m The third-order cumulative amounts of samples of (2) are:

hs _m (i)＝s _m (i)s _m (i-1)s _m (i-2)

wherein s is _m (i) Is an independent element matrix S _k M row i column value, 1<m<S _k Number of lines 3<i<S _k The number of columns of (a);

he _q (i)＝e _q (i)e _q (i-1)e _q (i-2)

wherein e _q (i) Is the residual matrix e _k The value of the ith column of the q-th row, 1<q<e _k Number of lines 3<i<e _k The number of columns of (a);

8) The HS (i) at all times in the subinterval is formed into a time series [ HS (1), HS (2), …, HS (i), … ]]Using a kernel density method for this time series, the output value is used as a monitoring control for the corresponding periodA limit, wherein the monitoring control limit of the kth period is denoted as HS _klimit The method comprises the steps of carrying out a first treatment on the surface of the Construction of a time sequence [ HE (1), HE (2), …, HE (i), … ]]Control limit HE is obtained using a nuclear density method _klimit ；

B. On-line monitoring:

9) On-line acquisition of data vector x at ith moment _new Judging whether the sampling time belongs to the kth subperiod according to the sampling time, and performing kernel function mapping on the sampling time to obtain a vector K _knew ：

k _knewj ＝φ(x _new ,x _j )

Wherein k is _knewj Is the vector K _knew Is the j-th element, x _j Offline data matrix X for this period _k Phi is a nuclear mapping function selected during offline modeling;

10 Calculating K) _knew Normalized whitening score matrix of (a)

i. First calculate the whitening score vector z _knew

Calculating normalized whitening score vectors

Wherein H is _k 、Λ _k All are matrixes obtained in the offline modeling process;

11 Using a separation matrix W obtained in an off-line stage _k Mixing matrix A _k Obtaining independent element vector s at the ith moment _knew (i) Residual vector e _knew (i)：

hs _knew (i)＝s _knew (i)s _knew (i-1)s _knew (i-2)

he _knew (i)＝e _knew (i)e _knew (i-1)e _knew (i-2)

will HS _knew (i)、HS _knew (i) And a kth period control line HS obtained in an off-line process _klimit 、HE _klimit And comparing, if the current time is not greater than the control line, indicating that the current time is normal, and if one of the current time is greater than the control line, indicating that the current time is abnormal, and generating an alarm.