A Method for Predicting Ethylene Content in Ethylene Fractionation Towers Based on Target-Related Laplace Autoencoders

Abstract

The application discloses an ethylene content prediction method for an ethylene fractionating tower based on a target-related Laplacian self-encoder, wherein a pre-training loss function with an additional target-related Laplacian constraint is designed, so that the model can use the constraint information brought by the unlabeled samples in the training stage, and the modeling problem under the condition that the unlabeled data without ethylene content measurement values are more and the labeled data with ethylene content measurement values are less in the ethylene fractionation process is solved. The method obtains the Laplacian constraint between samples through a near-neighbor adjacency graph of the samples, introduces a Laplacian constraint penalty term between the samples on the basis of a supervised loss function, and improves the generalization ability of the network model. The application can provide accurate real-time ethylene content prediction under the condition of partial labeled data.

Description

Technical Field

[0001] This invention belongs to the field of industrial process control, and specifically relates to a method for predicting the ethylene content in an ethylene fractionation tower based on a target-related Laplace autoencoder. Background Technology

[0002] In modern process industries, companies need to maintain competitive product prices and quality under various constraints such as raw material consumption, compliance with safety regulations, and environmental pollution issues. Therefore, it is necessary to monitor key quality indicators (KPIs) in the production process to control and improve product quality, maintain process safety, and reduce plant emissions. However, due to harsh environments and the expensive installation and maintenance costs of measurement networks, it is difficult to measure each KPI in real time. Soft measurement technology aims to estimate these difficult-to-measure KPIs by using mathematical models and data acquired from other available physical sensors. In today's production, most first-principles methods are difficult to implement due to the complexity of production processes. Meanwhile, with the widespread application of distributed control systems and the Internet of Things (IoT), industries have collected vast amounts of historical data records. Data-driven modeling methods, developed directly on the data without requiring complete knowledge of process mechanisms, have become an indispensable tool in the process industry. In the application of soft measurement modeling, partially labeled data is common because some process variables are sampled at high frequencies, such as flow rate and pressure, while key / quality variables (or key quality indicators) are sampled at low frequencies, for example, by laboratory analysis. Therefore, the number of unlabeled samples, which consist of variables from a fast sampling process, is much greater than the number of labeled samples, and soft measurement models that use only labeled data for modeling have poor generalization performance.

[0003] Ethylene is a fundamental raw material for the synthesis of polymers and other useful chemicals. To produce high-purity ethylene, purification is necessary. Ethylene purification is a process that separates ethylene from other impurities. This purification is typically carried out using ethylene fractionation towers. A key operation in the ethylene fractionation process is maintaining a high ethane concentration to reduce operating costs, while ensuring the ethane concentration does not exceed its upper limit; therefore, real-time monitoring of the ethylene concentration in the product is crucial. In industry, gas chromatography is used to detect ethylene content. However, this method has a long detection time and cannot achieve real-time detection of the product ethylene concentration. Furthermore, because gas chromatographs have a lower sampling frequency compared to temperature and pressure sensors, the number of process variable samples with corresponding ethylene content measurements is far fewer than those without. Therefore, there is an urgent need for a robust soft measurement modeling strategy that can provide accurate real-time ethylene content predictions even with partially labeled data. Summary of the Invention

[0004] The purpose of this invention is to address the problem of scarce labeled data in ethylene fractionation processes, characterized by a large number of unlabeled samples and a small number of labeled samples. This invention provides a method for predicting ethylene content in ethylene fractionation towers based on a target-related Laplace autoencoder. The method includes the following steps:

[0005] A method for predicting ethylene content in an ethylene fractionation tower based on a target-related Laplace autoencoder, the method comprising the following steps:

[0006] Step 1: Using a fixed sampling period T, continuously sample the temperature, gas pressure, and liquid flow rate at the outlet of the ethylene fractionation tower l+u times, obtaining l+u samples containing only process variables; within the same time period, using a fixed sampling period... The ethylene content of l emitted gases was measured, and a training dataset for modeling was constructed, including a labeled sample set. and unlabeled sample set Where x represents the process variable of the sample, y represents the ethylene content value to be measured, l represents the number of labeled samples, and u represents the number of unlabeled samples;

[0007] Step 2: Construct the K-nearest neighbor graph for all samples in the training dataset;

[0008] Step 3: Construct a stacked autoencoder model and pre-train it using the training dataset and the constructed K-nearest neighbor graph;

[0009] Step 4: Take the encoder part of the pre-trained stacked autoencoder, add a regression layer on it to build a regression network, and fine-tune the parameters of the regression network using labeled samples from the training dataset.

[0010] Step 5: Collect field work data. When the regression network is trained and the model is converted to online prediction, new samples are input into the regression network, and the predicted value of ethylene content is output.

[0011] Furthermore, step two includes the following sub-steps:

[0012] (2.1) Calculate the distance between samples and store it in the adjacency matrix G. Use a Gaussian kernel as the distance metric. The calculation formula is as follows:

[0013] w ij =exp(-||x i -x j || 2 / 2σ 2 (1)

[0014] Where x i x i This represents two samples, where σ represents the bandwidth coefficient;

[0015] (2.2) For each sample x i Find the N that is closest to it. neighbor 1 sample, retain these samples and x i The distance value, comparing other samples with x i Set the distance value to 0 and update the distance values ​​in the adjacency matrix G.

[0016] Furthermore, step three includes the following sub-steps:

[0017] (3.1) Construct the first layer of autoencoder, which includes an encoder and a decoder. The encoder is used to encode the sample quality variable x into a latent vector, and the decoder uses the latent vector to generate a reconstructed quality variable. and reconstructed quality variables The calculation formula is:

[0018] h 1 =f h (W 1 x+b 1 (2)

[0019]

[0020]

[0021] Where h 1 Represents the latent vector, {W 1 b 1} represents encoder weights and offsets. f represents the decoder weights and offsets. h Represents the nonlinear activation function of the encoder layer. Represents the non-linear activation function of the decoder layer;

[0022] (3.2) Using the dataset constructed in step one, the first-layer autoencoder model is pre-trained using the stochastic gradient descent algorithm. The training loss function is defined as the reconstruction error of the input process variable and ethylene content value, plus the nearest neighbor Laplace regularization term of the quality variable, and is expressed by the following formula:

[0023]

[0024] Where w ij Representative sample x i and x j The distance y in the K-nearest neighbor graph i λ1 and λ2 represent the measured ethylene content, and the weighting coefficients of each part of the loss function. This represents the estimated ethylene content obtained using rules in a subset of labeled samples. The calculation rules are as follows:

[0025]

[0026] After training is complete, collect the set of latent vectors generated from the training dataset samples.

[0027] (3.3) Based on the latent vectors generated by the first-layer encoder, a second-layer autoencoder is constructed, and its calculation formula is as follows:

[0028] h 2 =f h (W 2 x+b 2 (7)

[0029]

[0030]

[0031] Where h 2 Represents the latent vector, {W 2 b 2} represents encoder weights and offsets. Represents decoder weights and offsets;

[0032] (3.4) Using the latent vector set collected in step (3.2), the second-layer autoencoder model is pre-trained using the stochastic gradient descent algorithm. The training loss function is defined as the reconstruction error of the input process variable and the ethylene content value plus the nearest neighbor Laplace regularization term of the ethylene content value, expressed by the following formula:

[0033]

[0034] in The calculation rules are similar to those in formula (6), as follows:

[0035]

[0036] After training is complete, collect the set of latent vectors generated from the training dataset samples.

[0037] (3.5) Based on the latent vectors of the second-layer autoencoder collected in step (3.4), construct and pre-train the third-layer autoencoder in the same way as in steps (3.3) and (3.4), and so on, until the K-th layer autoencoder is constructed and pre-trained.

[0038] Furthermore, step four includes the following sub-steps:

[0039] (4.1) Based on the encoder part of the stacked autoencoder pre-trained in step three, a regression network is constructed. Its function is to determine the process variable x of the input sample.i At that time, the corresponding predicted ethylene content value is generated. The calculation formula is as follows:

[0040]

[0041]

[0042] in x represents i The latent vector output by the Kth layer, {W o b o} represents the weights and biases of the regression layer, f o () represents the activation function of the regression layer;

[0043] (4.2) Using the labeled dataset constructed in step one, and based on the regression network constructed in step (4.1), the regression network model is trained using the stochastic gradient descent algorithm. The training loss function is defined as the error between the measured ethylene content of the labeled samples and the model estimate, expressed by the following formula:

[0044]

[0045] The beneficial effects of this invention are as follows:

[0046] This invention designs a modeling strategy based on a target-related Laplace autoencoder. By introducing ethylene content prediction error and manifold regularization terms into the loss function, the model utilizes both labeled sample values ​​and unlabeled sample manifold constraint information during pre-training. Then, the pre-trained model undergoes parameter fine-tuning using a supervised loss function to obtain an ethylene content prediction model for forecasting ethylene content. Compared to existing modeling techniques, this invention solves the problem of poor prediction accuracy in ethylene fractionation processes where there is abundant unlabeled data without ethylene content measurements but scarce labeled data with ethylene content measurements. It improves the prediction accuracy under these conditions, enhances the operator's understanding of the process status, and is more conducive to the automated implementation of ethylene fractionation processes. Attached Figure Description

[0047] Figure 1 A schematic diagram of a target-dependent Laplace stacked autoencoder;

[0048] Figure 2 Flowchart for modeling a target-dependent Laplace stacked autoencoder;

[0049] Figure 3 This is a flow chart of the ethylene fractionation process.

[0050] Figure 4 A schematic diagram showing the tracking accuracy and error of ethylene content using different algorithms. Detailed Implementation

[0051] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0052] This invention discloses a method for predicting ethylene content in an ethylene fractionation tower based on a target-related Laplace autoencoder. The method first generates a K-nearest neighbor graph for all samples, where the distance between sample points is used as the edges of the graph. Labeled samples are then used to pre-train the stacked autoencoder layer by layer with target-related reconstructions. Next, based on the calculated adjacency graph, the neighboring samples of each sample are identified, and the stacked autoencoder is pre-trained layer by layer with target-related Laplace constraints using labeled and unlabeled samples and their neighboring samples. Further, the pre-trained stacked autoencoder is fine-tuned using a set of labeled samples to construct a regression model. The target-related Laplace autoencoder regression model incorporates a pre-training loss function with additional target-related Laplace constraints, allowing the model to utilize constraint information from unlabeled samples during pre-training. This not only enables in-depth data mining but also improves the generalization ability of the network model.

[0053] The method for predicting ethylene content in an ethylene fractionation tower based on a target-related Laplace autoencoder provided in this embodiment includes the following steps:

[0054] Step 1: At a fixed sampling period T, continuously sample the temperature, pressure, and liquid flow rate at the sensors of the top, bottom, 29th, 37th, 90th, and 129th trays, and outlets 2 and 3 of the ethylene fractionation column, obtaining 1+u samples containing only process variables. Within the same time period, the gas chromatograph operates at a fixed sampling period... The ethylene content of l emitted gases was measured to obtain the training dataset for modeling: a labeled sample set. and unlabeled sample set in, The process variables representing the samples include 18 observed process variables such as the temperature and pressure at the top of the ethylene fractionation tower and the temperature of the intermediate tray (details are shown in Table 1). y represents the ethylene content value to be measured, l represents the number of labeled samples, and u represents the number of unlabeled samples.

[0055] Step 2: Construct the K-nearest neighbor graph for all samples in the training dataset, which is divided into the following sub-steps:

[0056] (2.1) Calculate the distance between samples and store it in the adjacency matrix G. Use a Gaussian kernel as the distance metric. The calculation formula is as follows:

[0057] w ij =exp(-||x i -x j || 2 / 2σ 2 (1)

[0058] Where x i x i This represents two samples, where σ represents the bandwidth coefficient;

[0059] (2.2) For each sample x i Find the N that is closest to it. neighbor 1 sample, retain these samples and x i The distance value, comparing other samples with x i Set the distance value to 0 and update the distance values ​​in the adjacency matrix G.

[0060] Step 3: Construct a stacked autoencoder model and pre-train it using the training dataset and the constructed K-nearest neighbor graph. This is divided into the following sub-steps:

[0061] (3.1) Construct the first layer of autoencoder, which includes an encoder and a decoder. The encoder is used to encode the sample quality variable x into a latent vector, and the decoder uses the latent vector to generate a reconstructed quality variable. and reconstructed quality variables The calculation formula is:

[0062] h 1 =f h (W 1 x+b 1 (2)

[0063]

[0064]

[0065] Where h 1 Represents the latent vector, {W 1 b 1} represents encoder weights and offsets. f represents the decoder weights and offsets. h Represents the nonlinear activation function of the encoder layer. This represents the non-linear activation function of the decoder layer.

[0066] (3.2) Using the dataset constructed in step one, the first-layer autoencoder model is pre-trained using the stochastic gradient descent algorithm. The training loss function is defined as the reconstruction error of the input process variable and ethylene content value, plus the nearest neighbor Laplace regularization term of the quality variable, and is expressed by the following formula:

[0067]

[0068] Where w ij Representative sample x i and x j The distance y in the K-nearest neighbor graph i λ1 and λ2 represent the measured ethylene content, and the weighting coefficients of each part of the loss function. This represents the estimated ethylene content obtained using rules in a subset of labeled samples. The calculation rules are as follows:

[0069]

[0070] After training is complete, collect the set of latent vectors generated from the training dataset samples.

[0071] (3.3) Based on the latent vectors generated by the first-layer encoder, a second-layer autoencoder is constructed, and its calculation formula is as follows:

[0072] h 2 =f h (W 2 x+b 2 (7)

[0073]

[0074]

[0075] Where h 2 Represents the latent vector, {W 2 b 2} represents encoder weights and offsets. This represents the decoder weights and offsets.

[0076] (3.4) Using the latent vector set collected in step (3.2), the second-layer autoencoder model is pre-trained using the stochastic gradient descent algorithm. The training loss function is defined as the reconstruction error of the input process variable and the ethylene content value plus the nearest neighbor Laplace regularization term of the ethylene content value, expressed by the following formula:

[0077]

[0078] in The calculation rules are similar to those in formula (6), as follows:

[0079]

[0080] After training is complete, collect the set of latent vectors generated from the training dataset samples.

[0081] (3.5) Based on the latent vectors of the second-layer autoencoder collected in step (3.4), construct and pre-train the third-layer autoencoder in the same way as in steps (3.3) and (3.4), and so on, until the K-th layer autoencoder is constructed and pre-trained.

[0082] Step 4: Take the encoder portion of the pre-trained stacked autoencoder, add a regression layer on top to construct a regression network, and fine-tune the parameters of the regression network using labeled samples from the training dataset. This is specifically divided into the following sub-steps:

[0083] (4.1) Based on the encoder part of the stacked autoencoder pre-trained in step three, a regression network is constructed. Its function is to determine the process variable x of the input sample. i At that time, the corresponding predicted ethylene content value is generated. The calculation formula is as follows:

[0084]

[0085]

[0086] in x represents i The latent vector output by the Kth layer, {W o b o} represents the weights and biases of the regression layer, f o () represents the activation function of the regression layer;

[0087] (4.2) Using the labeled dataset constructed in step one, and based on the regression network constructed in step (4.1), the regression network model is trained using the stochastic gradient descent algorithm. The training loss function is defined as the error between the measured ethylene content of the labeled samples and the model estimate, expressed by the following formula:

[0088]

[0089] Step 5: Collect on-site work data. When the regression network is trained and the model is switched to online prediction, the new sample x... infer The input is fed into a regression network, which outputs a predicted value for ethylene content.

[0090] In this embodiment, experimental data was collected during the ethylene fractionation process, which is a process of separating ethylene from other impurities, such as... Figure 3As shown, the goal is to maintain a high ethane concentration to reduce operating costs while ensuring the ethane concentration does not exceed its upper limit. Therefore, it is necessary to measure the real-time ethylene content of the process product. In practice, the ethylene content is measured using gas chromatography, which requires a long measurement time, resulting in a significant lag in ethylene content measurement. To obtain the real-time ethylene content of the product, a soft measurement method can be used, which constructs a functional relationship between the ethylene content and 18 other observed process variables, as shown in Table 1.

[0091] Table 1 18 Observed Process Variables

[0092]

[0093]

[0094] Considering the dynamic nature of the ethylene fractionation process, the selection of input variables includes not only the current sample but also past samples measured 5, 10, 15, and 20 minutes prior. This is due to the shared experience among engineers and operators that the ethylene fractionation column typically reaches a new steady state within one hour. Furthermore, the ethane concentrations measured over the past 10, 15, and 20 minutes are considered as supplementary process variables.

[0095] 1500 labeled samples and 1800 unlabeled samples were collected during the ethylene fractionation process. To build and evaluate the proposed soft sensor model, the collected data was divided into a training set (first 600 samples), a validation set (next 200 samples), and a test set (remaining 700 samples). The training and validation sets each contained 800 labeled samples and 1800 unlabeled samples. Furthermore, training datasets with varying proportions of labeled and unlabeled data were used to demonstrate that additional unlabeled samples affect the model's predictive performance. Different numbers of unlabeled data were selected from the training set to achieve different proportions of labeled and unlabeled data.

[0096] To comprehensively evaluate the generalization performance of the proposed methods, four benchmarks are used for comparison. The first benchmark uses only labeled data for model training. Stacked Target-Related Autoencoders (STAE) are selected as the representative method for this benchmark. The other three benchmarks use both labeled and unlabeled samples for model training. Semi-supervised Stacked Autoencoders (SS-SAE) are selected as the comparison method, representing label-assisted pre-trained deep neural network models. Neighborhood Preserving Autoencoders (NPAE) and Deep Laplacian Autoencoders (DLapAE) are selected as comparison methods, representing geometry-assisted pre-trained deep neural network models. Furthermore, deep network models not based on stacked autoencoders are selected as the fourth benchmark. Semi-supervised Parallel Deep Factorization Machines (SS-PDeepFM) uses Deep Factorization Machines (DeepFM) as the base model and a graph-based pseudo-labeling method. Semi-supervised Hierarchical Extreme Learning Machines (SS-HELM) uses Hierarchical Extreme Learning Machines (HELM) as the base model and employs a manifold regularization method. The prediction accuracy of the method of this invention (STLapAE) and these four benchmarks is shown in Table 2. As can be seen from Table 2, the method of this invention achieves lower root mean square error and higher coefficient of determination across all proportions of labeled and unlabeled samples.

[0097] Table 2. Prediction accuracy of the method of this invention (STLapAE) and four benchmarks.

[0098]

[0099]

[0100] The tracking performance and error of the method of this invention and the other three benchmarks, when modeled using 800 labeled samples and 1200 unlabeled samples, are as follows: Figure 4 As shown.

[0101] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. An ethylene fractionator ethylene content prediction method based on target-dependent Laplacian autoencoder, characterized in that, The method comprises the following steps: Step one: sampling the sensors of temperature, gas pressure and liquid flow rate of the ethylene fractionating column outlet continuously l+u times with fixed sampling period T, obtaining l+u samples containing only process variables; in the same period, sampling the sensors of temperature, gas pressure and liquid flow rate of the ethylene fractionating column outlet continuously l+u times with fixed sampling period T Measuring l ethylene content values of the exhaust gas, and constructing training data set for modeling, including labeled sample set and unlabeled sample set Wherein, x represents the process variables of the sample, y represents the ethylene content value to be measured, l represents the number of labeled samples, and u represents the number of unlabeled samples; Step two: constructing a K-neighbor graph of all samples in the training data set; Step three: constructing a stacked auto-encoder model, and pre-training the stacked auto-encoder model by using the training data set and the constructed K-neighbor graph; Step four: taking the encoder part in the pre-trained stacked auto-encoder, adding a regression layer to construct a regression network, and fine-tuning the parameters of the regression network by using the labeled samples in the training data set; Step five: collecting field work data, when the regression network is trained and the model is converted into online prediction, the new sample is input into the regression network, and the predicted value of the ethylene content is output; The step two comprises the following sub-steps: (2.1) calculating the distance between samples and storing it in the adjacency matrix G, using Gaussian kernel as the distance measurement method, and the calculation formula is: w ij = exp(-||x i -x j || 2 / 2σ 2 ) (1) where x i ,x i denotes two samples, and σ denotes the bandwidth coefficient; (2.2) For each sample x i Find the N that is closest to it. neighbor 1 sample, retain these samples and x i The distance value, comparing other samples with x i Set the distance value to 0 and update the distance values ​​in the adjacency matrix G.

2. The target-dependent Laplacian autoencoder-based ethylene fractionator ethylene content prediction method of claim 1, wherein, The step three comprises the following sub-steps: (3.1) constructing a first layer auto-encoder comprising an encoder for encoding a sample quality variable x into a latent vector and a decoder for generating a reconstructed quality variable from the latent vector and the reconstructed quality variable The calculation formula is: h 1 = f h (W 1 x + b 1 ) (2) where h 1 represents the hidden vector, {W 1 ,b 1} represents the encoder weights and biases, represents the decoder weights and biases, f h represents the encoder layer nonlinear activation function, represents the decoder layer nonlinear activation function; (3.2) using the data set constructed in step one, using the stochastic gradient descent algorithm to pre-train the first layer auto-encoder model, and the training loss function is defined as the reconstruction error of the input process variable and the ethylene content value and the adjacent Laplace regularization term of the quality variable, which is represented by the following formula: where w ij represents the distance of sample x i and x j in the K- nearest neighbor graph, y i represents the measured value of ethylene content, and λ1and λ2represent the weight coefficients of the loss function parts, represents the estimated value of ethylene content obtained by using the rule under the condition of part of the labeled samples, and the calculation rule is as follows: After the training is completed, the set of latent vectors produced by the training dataset samples is collected (3.3) based on the hidden vector generated by the first layer encoder, constructing a second layer auto-encoder, and the calculation formula is: h 2 = f h (W 2 x + b 2 ) (7) where h 2 represents the hidden vector, {W 2 ,b 2} represents the encoder weights and bias, represents the decoder weights and bias; (3.4) using the hidden vector set collected in step (3.2), using the stochastic gradient descent algorithm to pre-train the second layer auto-encoder model, and the training loss function is defined as the reconstruction error of the input process variable and the ethylene content value and the adjacent Laplace regularization term of the ethylene content value, which is represented by the following formula: wherein The calculation rule is similar to equation (6) and is as follows: After the training is completed, the set of latent vectors produced by the training dataset samples is collected (3.5) based on the hidden vector of the second layer auto-encoder collected in step (3.4), using the same method as steps (3.3) and (3.4), constructing and pre-training the third layer auto-encoder, and so on until the Kth layer auto-encoder is constructed and pre-trained.

3. The target-dependent Laplacian autoencoder-based ethylene fractionator ethylene content prediction method of claim 2, wherein, The step four comprises the following sub-steps: (4.1) Based on the encoder part of the pre-trained stacked autoencoder in step three, build a regression network, whose role is to produce the corresponding ethylene content prediction value when the input sample process variable x i The calculation formula is as follows:​ wherein represents x i the hidden vector output by the Kth layer, {W o ,b o represents the weights and biases of the regression layer, f o () represents the activation function of the regression layer; (4.2) using the labeled data set constructed in step one, based on the regression network constructed in step (4.1), using the stochastic gradient descent algorithm to train the regression network model, and the training loss function is defined as the error between the measured value of the labeled sample ethylene content and the estimated value of the model, which is represented by the following formula:

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