CN111160811B

CN111160811B - Batch process fault monitoring method based on multi-stage FOM-SAE

Info

Publication number: CN111160811B
Application number: CN202010057396.9A
Authority: CN
Inventors: 金辰; 王普
Original assignee: Beijing University of Technology
Current assignee: Beijing University of Technology
Priority date: 2020-01-17
Filing date: 2020-01-17
Publication date: 2023-10-03
Anticipated expiration: 2040-01-17
Also published as: CN111160811A

Abstract

The invention relates to a batch industrial process fault monitoring method based on multi-stage FOM-SAE, which is necessary for ensuring the safety and stability of a production process and improving the quality of products. The specific method comprises two steps of off-line modeling and on-line monitoring. The off-line modeling is to process the normal data, divide the whole batch production process into stages, then build FOM-SAE monitoring model and monitor statistic in each stage, and determine the control limit of statistic by nuclear density estimation method. The step of 'online monitoring' selects a corresponding sub-model according to the current sampling time, calculates statistics and compares the statistics with a control limit, and judges whether the current system operates normally or not. The method provided by the invention can simultaneously process the multi-stage, non-Gaussian and nonlinear characteristics of batch data, effectively reduces the missing report rate of monitoring, greatly improves the accuracy of fault monitoring, and has higher practical application value.

Description

Batch process fault monitoring method based on multi-stage FOM-SAE

Technical Field

The invention relates to batch process fault diagnosis based on multi-stage FOM-SAE, belonging to the field of industrial process fault diagnosis and soft measurement.

Background

In recent decades, batch processes have been widely used in biopharmaceutical, semiconductor processing and other fields as they can meet the demand for the production of high-add-on products and as market demand rapidly adjusts production. And the industrial process has complex mechanism, high operation control difficulty, and easily influenced by uncertainty factors, and the product quality and the production efficiency. In order to ensure the safety and stability of industrial systems, it is necessary to establish an effective process monitoring means to discover abnormal conditions in time. Currently, multivariate statistical process monitoring (Multivariate Statistical Process Monitoring, MSPM) methods based on principal component analysis (Principal Component Analysis, PCA), partial least squares (Partial Least Squares, PLS), etc. are widely used in batch industrial processes. However, the application of the above method is limited by two: the data must conform to a gaussian distribution, and the different variables must be linearly related.

To address the non-gaussian nature of batch process data, independent component analysis (Independent Component Analysis, ICA) was introduced into the process monitoring field. While this approach can handle non-gaussian data, ICA is unstable in solving the unmixed matrix, resulting in reduced monitoring performance. The relevant literature demonstrates that the fourth-order distance (Fourth Order Moment, FOM) can effectively extract non-gaussian information of the data. Furthermore, for nonlinear relationships between batch process data variables, the introduction of Kernel tricks (Kernel tricks) was introduced into traditional MSPM algorithms, such as KPCA, KPLS, KICA. However, these nonlinear monitoring methods require manual setting of the values of the nuclear parameters, which affects the monitoring effect.

The batch process has multiple operation stages, and monitoring the whole batch with a single model tends to result in reduced monitoring effects in the different stages. For this feature, many scholars have made a lot of researches, and by reasonably dividing the batch data into stages and establishing a separate monitoring model at each sub-stage, the monitoring accuracy can be improved.

The process monitoring aims at extracting characteristic information from industrial data and separating normal data from fault data. The self-encoder (AE) algorithm is an unsupervised feature extraction method proposed by Hinton, and consists of an encoder and a decoder. The AE algorithm is used for projecting the normal sample to the low-dimensional nominal space through nonlinear transformation, so that the nonlinear problem of data can be effectively solved, and meanwhile, deep information of the data is extracted. While the stacked self-encoder (Stacked Autoencoder, SAE) has a stronger feature extraction capability than AE. SAE has been used in image processing, natural language processing, etc., and applications in the field of fault monitoring have begun to be appreciated.

A multi-stage batch process fault monitoring method based on a four-step distance and a stacked self-encoder can effectively improve the fault monitoring capability of a batch process. The method can simultaneously process the problems of non-Gaussian, non-linear and multi-stage of the process data, and has better fault monitoring performance.

Disclosure of Invention

Aiming at the problems of multi-stage, non-Gaussian and non-linearity of batch process data, the invention provides a batch industrial process fault monitoring method based on multi-stage FOM-SAE, and a model overall flow chart is shown in figure 1.

The invention adopts the following technical scheme and implementation steps:

A. offline modeling stage:

1) Collecting multi-batch historical data under normal working conditions to form a three-dimensional array X, wherein three dimensions respectively produce batch times i=1, …, I, process variables j=1, …, J, and sampling moments k=1, …, K;

2) Performing optimal phase division on the historical data X of multiple batches by adopting a Fisher algorithm;

3) Splitting the three-dimensional data X into I lot matrix along the lot direction, wherein the matrix T of the ith lot _i The rows represent sampling instants k=1, …, K, and the columns represent process variables j=1, …, J, as shown in fig. 3;

4) For each batch of chip matrices T _i Calculating FOM, i=1, …, I for all elements in (I) to obtain I FOM matrices, wherein the I-th batch of FOM matrices T _FOMi The form is as follows:

wherein, the element t of the kth row and the jth column in the ith batch of slices _j (k) Fourth order distance f of (2) _j (k) Calculated by the following formula:

f _j (k)＝t _j (k)t _j (k-1)t _j (k-2)t _j (k-3)

for the data at the previous 3 time, the 4 th time data is used for filling, namely f _j (1)＝f _j (2)＝f _j (3)＝f _j (4)；

5) Combining the data of the s-th stage in all batches of FOM matrixes into a new two-dimensional data matrix T according to the optimal stage division obtained in the step 2 _Stage _s S=1, …, S, the rows of which represent the sampling instants, together with i× (p _s+1 -p _s ) The rows and columns represent process variables j=1, …, J, as shown in fig. 4;

6) For each stage data matrix T _Stage _s All elements in s=1, … are normalized to obtainWherein, the kth row in the data matrix of the s-th stageElement f of the j-th column _j (k) The normalized formula of (2) is as follows:

wherein f _j ^max And f _j ^min Respectively represent the current s-th stage data matrix T _Stage _s The maximum and minimum values of the j-th column,represents f _j (k) Normalized values;

7) SAE of set stage s _s Super-parameters of sub-model are utilizedLayer-by-layer training SAE as input _s A sub-model that minimizes the reconstruction error function for each layer:

wherein θ _En And theta _De Is SAE (SAE) _s Parameters of submodel, x ⁽ⁱ⁾ Sum s ⁽ⁱ⁾ Is SAE (SAE) _s Input and output of the ith layer of the submodel, M is the total sample amount; SAE is carried out _s The output of the previous layer of the submodel is used as the input of the next layer to train layer by layer until the last layer completes SAE _s Training a model;

8) SAE is carried out _s The reconstruction error function of the last layer of the model is used as RE statistic, RE statistic of all data in each stage is calculated, and the control limit of RE statistic in the sub-stage s is determined by using a kernel density estimation method and is used for online monitoring of the stage s;

9) And 5-8, respectively training the monitoring models of the S sub-phases, and respectively calculating the control limit of each sub-phase.

B. On-line monitoring:

1) Acquiring sampling data at the current momentSelecting a corresponding stage monitoring model according to the stage to which the sampling value at the current k moment belongs;

2) Calculating the current timeFOM matrix x of (2) _f ＝[f ₁ (k),f ₂ (k),…,f _J (k)]Where the j variable sample value x at time k _j (k) FOM value f of (F) _j (k) The method is obtained by adopting the following formula:

f _j (k)＝x _j (k)x _j (k-1)x _j (k-2)x _j (k-3)

for the data at the previous 3 time, the 4 th time data is used for filling, namely f _j (1)＝f _j (2)＝f _j (3)＝f _j (4)。

3) The x obtained in the previous step is calculated according to the maximum value and the minimum value obtained in the offline modeling step 6) _f Standardized to obtainWherein the j variable k is the FOM value f _j (k) The normalized formula of (2) is as follows:

wherein f _j ^max And f _j ^min Respectively represent the s-th stage offline data T _Stage _s The maximum and minimum values of the j-th column,represents f _j (k) Normalized values;

4) The obtained in the previous stepInputting corresponding stage submodel SAE _s And calculates a statistic RE;

5) And comparing the monitoring statistic RE obtained in the previous step with the control limit of the corresponding stage obtained in the offline modeling step 8), if the control limit exceeds the limit, considering that the fault occurs, otherwise, considering that the control limit is normal, and ending the batch process.

Advantageous effects

Compared with the prior art, the method divides the whole production batch into a plurality of operation stages, fully considers the stage characteristics of the batch process, establishes the FOM-SAE model for each stage, and constructs monitoring statistics for fault monitoring. Because the traditional FOM can effectively extract non-Gaussian information in the data, unstable solving of an ICA model is avoided. SAE can efficiently extract deep information of batch process while solving the nonlinearity of batch data. The method can reduce the missing report in the monitoring process and improve the accuracy of fault monitoring.

Drawings

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

FIG. 2 is three-dimensional data X _30×10×400 Expanded into a two-dimensional time slice matrix x _k Schematic of (2);

FIG. 3 is three-dimensional data X _30×10×400 Spread into a two-dimensional batch sheet matrix X _I Schematic of (2);

FIG. 4 shows a two-dimensional data matrix T at each stage reconstructed by data processing _Stage _s Schematic of (2);

FIG. 5 is a block diagram of a stacked self-encoder monitoring model

FIG. 6 is a graph showing the relationship between the number of partitions and α in the fermentation process of penicillin batches;

FIG. 7 is a stage division result of penicillin batch fermentation process;

FIG. 8 (a) is a diagram showing the effect of SAE method on fault No. 5

FIG. 8 (b) is a graph showing the effect of the FOM-SAE method on monitoring fault No. 5

FIG. 8 (c) is a graph showing the effect of the multi-stage SAE method on fault No. 5

FIG. 8 (d) is a graph showing the effect of the multistage FOM-SAE method on the monitoring of fault No. 5

FIG. 9 (a) is a diagram showing the effect of SAE method on monitoring fault No. 7

FIG. 9 (b) is a graph showing the effect of the FOM-SAE method on monitoring the fault No. 7

FIG. 9 (c) is a graph showing the effect of the multi-stage SAE method on the monitoring of fault No. 7

FIG. 9 (d) is a graph showing the effect of the multi-stage FOM-SAE method on the monitoring of fault No. 7

Detailed Description

Penicillin fed-batch fermentation is a typical batch industrial process, the production process of which has obvious non-gaussian, non-linear, multi-stage characteristics. Based on Birol model improved by Bajpai mechanism model, pensim2.0 software developed by Yirino science and technology institute has become a standard test platform for monitoring, fault diagnosis and control of penicillin fermentation process. Related studies have demonstrated the effectiveness and practicality of this simulation platform.

In the experiment, pensim2.0 simulation data are adopted as a research object, the sampling time is set to be 1 hour, the fermentation time of each batch is 400 hours, and 10 main process variables are selected to monitor the running condition of the process, as shown in table 1. Three-dimensional matrix X for generating 30 batches of normal data by adopting platform _30×10×400 For modeling, and additionally generating 10 batches of fault data to test the validity of the monitoring model. The set fault type, amplitude and start-stop time are shown in table 2.

Table 1 modeling process variables

Table 2 faulty batch data

The application process of the penicillin fermentation production simulation platform is specifically stated as follows:

A. offline modeling stage:

1) The historical data X collected by the batch collecting process under the normal working condition is a three-dimensional array, and three dimensions respectively comprise batch production times i=1, …,30, process variables j=1, …,10 and sampling points k=1, …,400.

2) The Fisher algorithm is adopted to divide the time slice matrix in stages, and the steps are as follows:

2.1 Splitting three-dimensional data into 400 time slice matrices along a time direction, wherein a time slice matrix x at a kth time instant _k The rows represent the production lot numbers i=1, …,30, and the columns represent the process variables j=1, …,10;

2.2 Dividing the time slice matrix into S phases according to time sequence, and arbitrarily setting the starting time of each phase as p _s Where s=1, …, S, p at this time ₁ ＝1<p ₂ <…<p _S K is less than or equal to K. The class inner diameter of each stage is calculated, wherein for stage S its class inner diameter is calculated using the following formula (when s=s, p _s+1 -1＝K)：

Wherein the method comprises the steps ofRepresenting the average of all time slice matrices during this phase. The time slice matrix is divided into S phases of error functions by the following formula:

2.3 In order to obtain the optimal division result quickly, the optimal division result divided into S stages can be obtained at this time by calculating the minimum value of the error function by a recursive formula preferably:

when divided into two phases, the two phases are divided,

when the division stage is greater than 2,

the error function minima at s=1, 2, …, K are calculated by the above equation, respectively.

2.4 When a recursive formula is adopted, the discriminant function can be calculatedThe more the value of alpha approaches 1, the more accurate the staged result, the more the process of determining the value of alpha is divided into 5 stages by combining the stage characteristics of penicillin fermentation, and the value change of alpha and the division result are shown in fig. 6 and 7.

3) Splitting the three-dimensional data X into 30 lot chip matrices by lot, wherein the matrix T of the ith lot _i The rows thereof represent sampling instants k=1, …,400, and the columns represent process variables j=1, …,10;

4) For each batch of chip matrices T _i Calculating FOM for all elements in (i=1, …, 30) to obtain I FOM matrices, wherein the I-th batch of FOM matrices T _FOMi The form is as follows:

f _j (k)＝t _j (k)t _j (k-1)t _j (k-2)t _j (k-3)

5) Optimal phase division according to step 2Combining the data of the s-th stage in all batches of FOM matrix into a new two-dimensional data matrix T _Stage _s S=1, …, S, the rows of which represent the sampling instants, together 30× (p _s+1 -p _s ) The rows and columns represent process variables j=1, …, J;

6) For s-stage data matrix T _Stage _s All elements in s=1, …,5 are normalized to obtainWherein, the element f of the kth row and the jth column in the s-th stage data matrix _j (k) The normalized formula of (2) is as follows:

wherein θ _En And theta _De Is SAE (SAE) _s Parameters of submodel, x ⁽ⁱ⁾ Sum s ⁽ⁱ⁾ Is SAE (SAE) _s Input and output of the ith layer of the submodel, M is the total sample amount; SAE is carried out _s The output of the previous layer of the submodel is used as the input of the next layer to train layer by layer until the last layer completes SAE _s Model training the SAE model is a well-known structure as shown in FIG. 5.

9) Repeating the steps 5-8, respectively training the monitoring models of 5 sub-phases, and respectively calculating the control limit of each sub-phase.

B. On-line monitoring:

1) Acquiring sampling data at the current momentSelecting a corresponding stage monitoring sub-model according to the stage to which the sampling value at the current k moment belongs;

f _j (k)＝x _j (k)x _j (k-1)x _j (k-2)x _j (k-3)

The steps are the specific application of the invention on a penicillin fermentation simulation platform. To verify the effectiveness of the monitoring algorithms herein, two faults selected for fault numbers 5 and 7 are shown in detail as compared to the SAE, FOM-SAE, multi-stage FOM-SAE algorithms, respectively, see FIGS. 8 and 9. Each graph comprises 5 straight lines parallel to the abscissa, namely a control limit obtained through nuclear density estimation, and an up-down fluctuation curve is a value of monitoring statistics. If the curve value is greater than the control limit, this indicates that a fault has occurred. For more visual comparison of the monitoring performance of the method, the Missing Alert Rate (MAR) and the accuracy rate (ACC) of the model for 10 faults are respectively calculated as monitoring indexes:

fig. 8 shows a graph of the monitoring results for the fault No. 5, the fault type being a slope type fault with an increase of 2W/h for the stirring rate fault, the fault being introduced from the time 70, and ending at the time 150. For a sloped fault, the fault magnitude increases cumulatively over time, and it is more difficult to detect the fault at an early time when the fault occurs. As can be seen from FIG. 8 (a), the single-stage SAE model has a higher false alarm rate 86.42%, while the multi-stage SAE model of FIG. 8 (c) captures the stage characteristics better, the false alarm rate is reduced to 67.9%, and meanwhile, the two models have obvious alarm lag. Fig. 8 (b) shows that the accuracy is significantly improved up to 95% after FOM is added, and the model is proved to effectively improve the monitoring accuracy by extracting non-gaussian information. The monitoring result of the invention is shown in fig. 8 (d), and the highest accuracy is 95.25%.

Fig. 9 shows a graph of the monitoring results for the fault No. 7, the fault type is a step type fault in which the substrate flow rate increases by 3%, and the fault is introduced from the time 58 and continues to the end of the time 130. As can be seen from fig. 9 (a) and 9 (b), the phase model has a high rate of missing report, and the monitoring effect is lost. FIG. 9 (c) Multi-stage SAE, there is a slight improvement over single-stage SAE, but there is still a false-negative rate of 87.67%. The method disclosed by the invention is shown in fig. 9 (d), and can keep lower missing report rate and false report rate at the same time, and the accuracy rate reaches 97.75%.

The monitoring performance indexes of ten faults are shown in Table 3, and the multi-stage FOM-SAE provided herein has higher accuracy rate for various faults, and improves the fault monitoring effect of the penicillin fermentation process.

TABLE 3 monitoring Performance indicators

Claims

1. A complex industrial process fault monitoring method based on multistage FOM-SAE, FOM is Fourth Order Moment abbreviation, namely four-step distance; SAE is an abbreviation of Stacked Autoencoder, i.e. stacked self-encoder; the implementation method comprises two steps of off-line modeling and on-line monitoring, and the specific scheme is as follows: the method comprises the following implementation steps:

A. offline modeling stage:

3) Splitting the three-dimensional data X into I lot matrix along the lot direction, wherein the matrix T of the ith lot _i The rows represent sampling instants k=1, …, K, and the columns represent process variables j=1, …, J;

f _j (k)＝t _j (k)t _j (k-1)t _j (k-2)t _j (k-3)

5) Combining the data of the s-th stage in all batches of FOM matrixes into a new two-dimensional data matrix T according to the optimal stage division obtained in the step 2 _Stages S=1, …, S, the rows of which represent the sampling instants, together with i× (p _s+1 -p _s ) The rows and columns represent process variables j=1, …, J;

6) For each stage data matrix T _Stages All elements in s=1, … are normalized to obtainWherein, the elements of the kth row and the jth column in the s-th phase data matrixf _j (k) The normalized formula of (2) is as follows:

wherein f _j ^max And f _j ^min Respectively represent the current s-th stage data matrix T _Stages The maximum and minimum values of the j-th column,represents f _j (k) Normalized values;

9) Repeating the steps 5-8, respectively training the monitoring models of the S sub-phases, and respectively calculating the control limit of each sub-phase;

B. on-line monitoring:

1) Acquiring the current timeIs a sampling data of (a)Selecting a corresponding stage monitoring sub-model according to the stage to which the sampling value at the current k moment belongs;

f _j (k)＝x _j (k)x _j (k-1)x _j (k-2)x _j (k-3)

wherein f _j ^max And f _j ^min Respectively represent the s-th stage offline data T _stages The maximum and minimum values of the j-th column,represents f _j (k) Normalized values;

2. The complex industrial process fault monitoring method based on multi-stage FOM-SAE of claim 1, wherein: the specific steps of the optimal phase division in the offline modeling phase are as follows:

2.1 Splitting three-dimensional data X into K time slice matrices along a time direction, where X _k A time slice matrix representing the time of k samples, the rows representing the number of production lots i=1, …, I, and the columns representing the process variables j=1, …, J;

2.2 Randomly dividing the multi-batch historical data X into S stages, calculating the class inner diameter of each stage, and calculating the error function of the stage division according to the obtained class inner diameter, wherein the class inner diameter calculation formula of the stage S is as follows:

wherein p is _s Represents the start time of the s-th phase, p _s+1 Represents the start time, p, of the s+1 stage _s+1 -1 represents the end time of the s-th phase, i.e. p _s+1 Is used for the time period of the previous sample,representing the average of all time slice matrices within phase s,

the error function of dividing the multi-batch historical data X into S stages is as follows:

2.3 The division mode with the smallest error function is the optimal division mode.