An intermittent process online measurement data mode recognition method based on D-S evidence fusion

Abstract

The application discloses a kind of intermittent process online measurement data modal recognition method based on D-S evidence fusion, first standardization of intermittent process historical batch data, modal division is carried out using density peak clustering algorithm, obtain each modal data of intermittent process;Then modal membership, time sequence constraint and modal data variance are used to construct intermittent process modal evidence, the support of different evidence is calculated, evidence correction model is established, and evidence basic probability function value is redistributed;Finally, multiple evidences are fused using Dempster synthesis rule, obtain the trust value of all modes, realize intermittent process online measurement data modal recognition according to modal trust value.The application fully considers the similarity between intermittent process online measurement data and historical modal data and the time sequence characteristics of process data, constructs the evidence framework of online measurement data modal recognition, identifies the mode to which online measurement data belongs according to modal trust value, and improves the accuracy of intermittent process online measurement data modal recognition.

Description

Technical Field

[0001] This invention belongs to the field of intermittent process monitoring technology, and particularly relates to a method for modal identification of online measurement data of intermittent processes based on DS (Dempster Shafer) evidence fusion. Background Technology

[0002] Batch processes are an important production method in modern manufacturing, widely used in fields such as biopharmaceuticals and fine chemicals. The inherent characteristics of batch processes result in multiple operating stages or stable modes, with significant differences in process characteristics across these modes. Analyzing the process data characteristics of different modes of batch processes, and accurately identifying the mode to which online measurement data belongs based on mode classification, plays a crucial role in improving the performance of online monitoring and soft measurement for batch processes.

[0003] In existing methods for modal identification of online measurement data for intermittent processes, similarity-based methods rely on the similarity index used during modality segmentation to identify the modality to which the online measurement data belongs, ignoring the temporal characteristics of the intermittent process measurement data, leading to temporal discrepancies in the modal identification results. Time-label-based methods directly apply the results of offline modality segmentation to online measurement data modal identification, ignoring the differences between batches of intermittent process measurement data, thus reducing the accuracy of modal identification. Therefore, this paper proposes a modal identification method for online measurement data of intermittent processes based on DS evidence fusion. This method fully considers the similarity between online measurement data and historical modal data of intermittent processes, as well as the temporal characteristics of the process data. It introduces evidence theory to construct an online measurement data modal identification framework and identifies the modality to which the intermittent process online measurement data belongs based on the modal trust value obtained by the multi-evidence correction fusion model, effectively improving the accuracy of modal identification for online measurement data of intermittent processes. Summary of the Invention

[0004] This invention aims to improve the accuracy of modal identification in online measurement data of intermittent processes. It proposes a modal identification method based on DS evidence fusion for online measurement data of intermittent processes, comprising the following steps:

[0005] Step 1: Collect data from multiple batches of intermittent production processes, standardize the process data, and use the Density Peaks Clustering (DPC) algorithm to divide the intermittent process into multiple modes to obtain the mode center set;

[0006] Step 2: Introduce a time sliding window to construct multiple intermittent process modal evidences based on modal membership, temporal constraints, and variance of modal data. Calculate the support of different evidences, use the weighted average of multiple evidences as the modality switching judgment threshold, and establish an evidence correction model to recalculate and reassign the basic probability values ​​of the evidence.

[0007] Step 3: Use Dempster's synthesis rule to fuse the basic probability values ​​after correction of multiple pieces of evidence to obtain the confidence values ​​of all modes, and identify the mode to which the online measurement data of the intermittent process belongs based on the mode confidence values.

[0008] Step one specifically includes:

[0009] Collect P batches of intermittent process data X(P×K×J), where P is the number of batches, J is the number of variables in the intermittent process, and K is the number of sampling points in the intermittent process. Average the historical data of the P batches of intermittent process data along the batch direction, and standardize each variable by subtracting the mean and dividing by the standard deviation to obtain the intermittent process modal classification dataset.

[0010] Using DPC to partition the dataset of intermittent process modes To perform modality segmentation, the dataset is first calculated. Each data point x i Local density ρ i and relative distance δ i for

[0011]

[0012]

[0013] In the formula, e is the natural base; i and j represent the sampling point numbers of the intermittent process data; d ij For intermittent process data point x i and x j Euclidean distance; ρ j For intermittent process data point x j Local density; d c To truncate the distance, the values ​​of the first 1% to 2% of the distances between all data points are generally taken after sorting them from smallest to largest.

[0014] Then, using the local density ρ i and relative distance δ i Calculate the decision value γ for each data point i for

[0015] γ i =ρ i ×δ i (3)

[0016] The larger the decision value of a data point in an intermittent process, the higher the probability of it becoming a mode center. To obtain the optimal number of modes for an intermittent process, an optimal mode number evaluation index (MEI) is defined. f for

[0017]

[0018]

[0019]

[0020] In the formula, f = 1, 2, ..., K represents the decision value index after the decision values ​​of the intermittent process data are sorted in descending order; γ f F represents the f-th decision value after the decision values ​​of the intermittent process data are sorted in descending order; f The number of modal divisions representing an intermittent process; and γ f and F f The normalized value.

[0021] Will MEI f The number of modes f corresponding to the minimum value is obtained * As the optimal number of modes for an intermittent process, the first f is taken. * The intermittent process data points corresponding to each decision value are used as mode centers, and the remaining intermittent process data points are assigned to the modes with higher density and the closest points.

[0022] Finally, the intermittent process is divided into f * Given several modalities, obtain the modality center set {c} n}, n=1,2,…,f * .

[0023] Step two specifically includes:

[0024] Based on the modal segmentation results of historical batch data of the intermittent process, modal evidence is constructed using modal membership degrees, and the online measurement data x of the intermittent process at time t is calculated. t The modal membership degree is

[0025]

[0026] In the formula, u n For online measurement data of intermittent processes x t Membership degree of mode n; c n d(x) represents the nth mode center of the intermittent process; t ,c n () represents online measurement data of the intermittent process. t To the nth modal center c n Euclidean distance.

[0027] The basic probability allocation function m1 for each moment of the intermittent process's online measurement data is obtained by normalizing the membership degree.

[0028]

[0029] Modal evidence is constructed using time-series constraints to calculate the online measurement data point x of the intermittent process at time t. t The timing constraint values ​​with each mode center are

[0030]

[0031] In the formula, T n For the online measurement data point x of the intermittent process t The timing constraint value with respect to the nth mode center; τ n The sampling time corresponds to the nth modal center.

[0032] The basic probability allocation function m2 for the online measurement data at each moment of the intermittent process is obtained by using the normalized time series constraint values.

[0033]

[0034] Modal evidence is constructed using the variance of online measurement data of intermittent processes. A sliding window is introduced to calculate the x-point of the online measurement data of the intermittent process at time t. t The change in variance ΔS of the data within the window before and after adding the sliding window. t

[0035] ΔS t =sum(|S new -S old |) (11)

[0036] In the formula, sum(·) represents the summation operation; S new and S old These represent the variance within the window after adding the online measurement data of the intermittent process at time t and the variance within the window before adding the data at time t, respectively.

[0037] Based on the modality segmentation results of historical batch data of the intermittent process, let the sliding window size be L. Using L-1 time points before the right endpoint of each modality as the sliding window, calculate the variance change difference between the data after the right endpoint of the modality and the data before the window for all historical batches. Averaging these variance changes yields the set of variance change differences used as the modality switching threshold.

[0038] If the intermittent process online measurement data x t It belongs to mode n, when ΔS t If the current mode switching threshold is exceeded, then the online measurement data x of the intermittent process at time t is determined.t This caused a significant change in the statistical properties of the data within the window. By shifting the sliding window one time point to the right sequentially, the online measurement data x of the intermittent process at times t+1 and t+2 were calculated. t+1 and x t+2 The change in variance ΔS of the data within the window before and after adding the sliding window. t+1 and ΔS t+2 When the addition of online measurement data during the intervals of three consecutive sampling times significantly affects the statistical characteristics of the data within the sliding window, then the online measurement data x at time t+2 is considered to be... t+2 A mode switch has occurred, and its mode is n+1.

[0039] Therefore, the basic probability allocation function m3 for the online measurement data at each time point is obtained as follows:

[0040]

[0041]

[0042] In the formula, a n For online measurement data of intermittent processes x t The trust value belonging to modality n.

[0043] The distance between different pieces of evidence was calculated using the Jousselme distance formula.

[0044]

[0045] In the formula, m z and m v Let z and v represent the evidence respectively; Q is... is a positive definite matrix; T is the matrix transpose symbol.

[0046] Then, the correlation matrix among all the evidence is calculated as follows:

[0047]

[0048] In the formula, A zv =1-J(m) z ,m v ) indicates evidence m z and m v The correlation between them; further calculate the support of evidence z. z for

[0049]

[0050] In the formula, sum(A) represents the summation of all elements in A; z and v represent the evidence numbers for intermittent process modality identification.

[0051] Multiply the support and basic probability distributions, and then perform average normalization to obtain the final decision threshold σ.

[0052]

[0053] In the formula, sum(·) is the summation operation; mean(·) is the average operation.

[0054] Furthermore, an evidence revision model is established for

[0055]

[0056] In the formula, e represents the natural base; x is the online measurement data of the intermittent process at time t. t The updated value of the basic probability assignment function for the z-th piece of evidence belonging to modality n; σ n The threshold for correcting the trust value of modality n for each piece of evidence.

[0057] Finally, Normalization yields the final basic probability assignment function value.

[0058]

[0059] The multi-evidence basic probability allocation function value of the online measurement data of the intermittent process is calculated according to equations (7) to (13), and the corrected basic probability allocation value is calculated and obtained according to equations (14) to (19).

[0060] Step three specifically includes:

[0061] According to Dempster's synthesis rules, the basic probability values ​​of the evidence obtained in step two are fused together to construct a system containing f. * The modality recognition framework for each subset is as follows For the basic probability assignment function m1,m2,…,m of multiple pieces of evidence, Z The final modal trust value M(θ) after fusion is

[0062]

[0063]

[0064] In the formula, θ is a proposition in the modality recognition framework Θ; H represents the empty set; H is the conflict coefficient between propositions of intermittent process modality recognition.

[0065] The final modal confidence value M(θ) is obtained according to equation (20), and the modal recognition result of the intermittent process online measurement data is obtained according to the value of the proposition probability in M(θ).

[0066] Advantages of this invention: It proposes a modality identification method for intermittent process online measurement data based on Dempster evidence fusion. This method fully considers the similarity between intermittent process online data and historical modality data, as well as the temporal characteristics of process data. It constructs three types of modality evidence based on modality membership, temporal constraints, and data variance. By establishing a multi-evidence correction model, it redistributes the basic probability function values ​​of multiple evidences. It then uses the Dempster synthesis rule to fuse multiple pieces of evidence to obtain the final modality confidence value to identify the modality to which the intermittent process online measurement data belongs. This method can effectively improve the accuracy of modality identification for intermittent process online measurement data. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of a method for modal identification of intermittent process online measurement data based on DS evidence fusion, as described in this invention.

[0068] Figure 2 This is a graph showing the optimal number of modes for DPC mode division of 15 historical batches of the intermittent process;

[0069] Figure 3 This is a diagram showing the modal identification results of online measurement data for batch 1 of the penicillin fermentation process tested using the method described in this invention; Detailed Implementation

[0070] The present invention will be further described below with reference to examples and accompanying drawings. It should be noted that the embodiments do not limit the scope of protection claimed by the present invention.

[0071] Example

[0072] The penicillin fermentation process is a typical multimodal batch process. Using the Pensim V2.0 simulation platform, 20 batches of data were generated under different initial conditions and Gaussian noise. 15 batches were used as the training set, and the remaining 5 batches were used as the test set. The sampling time for each batch was 400 hours, and the sampling interval was 1 hour. The process variables used for modal division of the penicillin fermentation process are shown in Table 1.

[0073] Table 1. Process variables used for modal classification of penicillin fermentation process.

[0074]

[0075] The specific steps of applying this invention to the penicillin fermentation process are as follows:

[0076] Step 1: Average and standardize the 15 batches of historical data from the intermittent process along the batch direction to obtain the modality partitioning dataset. Using DPC for mode segmentation, the MEI value of the intermittent process historical data is calculated according to equation (4), such as Figure 2As shown, the optimal number of modes was 4. Then, the penicillin fermentation process was divided into four modes, and the mode center set {c1,c2,c3,c4} of historical batch data of 15 intermittent processes was obtained, with the corresponding sampling times being 4h, 74h, 145h and 249h, respectively.

[0077] Step 2: Set the sliding window length to 4, and calculate and obtain the variance difference of each mode switching as {2.06, 0.45, 0.47}. Use equations (7) to (13) to calculate the basic probability allocation function for all intermittent process data in test batch 1, where the three basic probability allocation functions for the data at sampling time 128h are:

[0078]

[0079] Step 3: Construct a modal identification framework for online measurement data of intermittent processes.

[0080] Θ = {θ1, θ2, θ3, θ4}

[0081] Using the basic probability allocation correction model established in this paper, the confidence levels of each piece of evidence to the mode to which the data belongs are redistributed. The result obtained after evidence fusion is:

[0082]

[0083] Based on the value of M, the intermittent online measurement data at the sampling time of the 128th hour is determined to belong to the third mode. The mode identification results of the online measurement data of test batch 1 are as follows: Figure 3 As shown.

[0084] Modal identification was performed on online measurement data from five test batches of the intermittent process using the method described in this invention. The results are shown in Table 2.

[0085] Table 2. Modal identification results of online measurement data of intermittent processes from 5 test batches.

[0086]

[0087] As can be seen from the modal identification results of the online measurement data of the intermittent process, the method of the present invention fully considers the similarity between the online measurement data and the historical modal data, as well as the temporal characteristics of the process data, and effectively improves the accuracy of modal identification of the online measurement data of the intermittent process.

Claims

1. A method for modal identification of online measurement data of intermittent processes based on DS evidence fusion, characterized in that: The method comprises the following steps: Step 1: Collect data from multiple batches of intermittent production processes, standardize the process data, and use the Density Peak Clustering (DPC) algorithm to divide the intermittent process into multiple modes, obtaining the set of mode centers; Step 2: Introduce a time sliding window to construct multiple intermittent process modal evidences based on modal membership, temporal constraints, and variance of modal data. Calculate the support of different evidences, use the weighted average of multiple evidences as the modality switching judgment threshold, and establish an evidence correction model to recalculate and reassign the basic probability values ​​of the evidence. Step 3: Use Dempster's synthesis rule to fuse the basic probability values ​​after correction of multiple pieces of evidence to obtain the confidence values ​​of all modes, and identify the mode to which the online measurement data of the intermittent process belongs based on the mode confidence values; Step two specifically includes: According to the mode division result of the batch data of the intermittent process history, the mode membership is used to construct the mode evidence, and the mode membership is calculated The mode membership of the online measurement data of the intermittent process at the moment is （7） wherein on-line measurement data for batch processes to the mode of membership; represents the n-th mode center of a batch process on-line measurement data for batch processes to the n-th mode center Euclidean distance The basic probability assignment function for the online measurement data at each moment of the intermittent process is obtained by normalizing the membership degree. for （8） Modal evidence is constructed using time-series constraints, and calculations are performed. Online measurement data points of time interval process The timing constraint values ​​with each mode center are （9） In the formula, For online measurement data points of intermittent processes The timing constraint value with respect to the nth mode center; For the first The sampling time corresponding to each modal center; It is the number of modes; The basic probability allocation function of the online measurement data at each moment of the intermittent process is obtained by using normalized time series constraint values. for （10） Modal evidence is constructed using the variance of online measurement data of intermittent processes. A sliding window is introduced to calculate the online measurement data points of the intermittent process at time t. Changes in variance of data within the window before and after adding a sliding window （11） In the formula, This represents the summation operation; and Let Vt represent the in-window variance after adding the online measurement data of the intermittent process at time t and the in-window variance before adding the data at time t, respectively. Based on the modal segmentation results of historical batch data of the intermittent process, let the sliding window size be... Before the right endpoint of each mode Using a time point as a sliding window, the variance change difference between the data after the right endpoint of the modality is added to the window and before the data is added to the window is calculated for all historical batches. The average of these variance change differences is used as the set of variance change differences to serve as the modality switching threshold. ; If the intermittent process online measurement data It belongs to mode n, when If the current mode switching threshold is exceeded, then the online measurement data of the intermittent process at time t is determined. This caused a significant change in the statistical properties of the data within the window. Shifting the sliding window one time step to the right sequentially, the calculation... and Online measurement data of time interval process and Changes in variance of data within the window before and after adding a sliding window and When the addition of online measurement data during the intermittent process at three consecutive sampling times significantly affects the statistical characteristics of the data within the sliding window, it is considered that... Online measurement data at time A mode switch occurred, and the mode it belongs to is ; Thus, the basic probability allocation function for online measurement data at each time point is obtained. for （12） （13） In the formula, For online measurement data of intermittent processes The trust value belonging to modality n; The distance between different pieces of evidence was calculated using the Jousselme distance formula. （14） In the formula, and They represent the first Article 1 and Article 2 One piece of evidence; for A positive definite matrix; T is the matrix transpose symbol; Then, the correlation matrix among all the evidence is calculated as follows: （15） In the formula, Present evidence and The correlation between them; further calculate the support of evidence z. for （16） In the formula, This represents the summation of all elements in A; z and v represent the evidence numbers for the intermittent process mode identification. The support score and the basic probability distribution are multiplied together and then averaged to obtain the final decision threshold. for （17） In the formula, For the summation operation; mean To achieve the average operation; and further establish the evidence correction model as follows: （18） In the formula, Represents the natural base; Online measurement data of the intermittent process at time t Belongs to modality The Updated values ​​of the basic probability assignment function for each piece of evidence; For each piece of evidence, modality The threshold for adjusting the trust value; Finally, Normalization yields the final basic probability assignment function value. （19） The multi-evidence basic probability allocation function value of the online measurement data of the intermittent process is calculated according to Equations (7) to (13), and the corrected basic probability allocation value is calculated and obtained according to Equations (14) to (19).

2. The method for modal identification of online measurement data of intermittent processes based on DS evidence fusion according to claim 1, characterized in that: Step one specifically includes: collection Intermittent process data for each batch ), Let J be the number of batches in the intermittent process, J be the number of variables in the intermittent process, and K be the number of sampling points in the intermittent process. The historical data of the intermittent process from each of the P batches are averaged along the batch direction, and each variable is standardized by subtracting the mean and dividing by the standard deviation to obtain the intermittent process modal classification dataset. ); Using the DPC method to partition the dataset of intermittent process modes To perform modality segmentation, first calculate the dataset. Each data point in ) Local density and relative distance for （1） （2） In the formula, The base is the natural number; i and j represent the sampling point numbers of the intermittent process data; Data points for intermittent processes and The Euclidean distance; Data points for intermittent processes Local density; To truncate the distance, the values ​​of the first 1% to 2% after sorting all data points from smallest to largest are generally taken; Then utilize local density and relative distance Calculate the decision value for each data point for （3） To obtain the optimal number of modes for an intermittent process, an evaluation index for the optimal number of modes is defined. for （4） （5） （6） In the formula, This represents the sequence number of the decision values ​​after the decision values ​​of the intermittent process data are sorted in descending order; This represents the f-th decision value after the decision values ​​of the intermittent process data are sorted in descending order; The number of modal divisions representing an intermittent process; and They are respectively and The normalized value; Will The number of modes corresponding to the minimum value As the optimal number of modes for an intermittent process, take the first... The intermittent process data points corresponding to each decision value are used as mode centers, and the remaining intermittent process data points are assigned to the modes with higher density and the closest points, ultimately dividing the intermittent process into... Given a modality, obtain the set of modality centers. , .

3. The method for modal identification of intermittent process online measurement data based on DS evidence fusion according to claim 1, characterized in that: Step three specifically includes: According to Dempster's rules of synthesis, the basic probability values ​​of the evidence obtained in step two are fused together to construct a composite data set containing... The modality recognition framework for each subset is as follows For the basic probability assignment function of multiple pieces of evidence The final modal trust value after fusion for （20） （21） In the formula, For modality recognition framework The proposition in; H represents the empty set; H is the conflict coefficient between propositions in the intermittent process modality recognition. The final modal trust value is obtained according to equation (20). and according to The modality recognition results of the intermittent process online measurement data are obtained by taking the value of the proposition probability.

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