A method for constructing a soft sensing model based on one-dimensional convolution-stacked autoencoder

Abstract

The present invention discloses a new soft measurement method based on one-dimensional convolution-stacked autoencoder, which aims to study and construct a soft measurement model for high-dimensional noisy data. The main core of the method of the present invention is to construct an autoencoder (AE) module that introduces one-dimensional convolution, remove the pooling layer and use a double-step convolution layer. Multiple modules are stacked to form a stacked autoencoder pre-training, minimize the reconstruction error of the module input and output and extract and save the parameters. The network is connected to the fully connected layer, and the model is initialized with the saved parameters and then fine-tuned to minimize the output and actual quality data errors, thereby completing the construction of the soft measurement model. In addition, the method of the present invention takes into account the local characteristics of the data while taking into account the data correlation. Compared with other traditional methods, this method can better process high-dimensional noisy data and obtain better results. It can be said that the method of the present invention is a more excellent method for building a soft measurement model.

Description

Technical Field

[0001] The present invention relates to a data-driven soft measurement method, and in particular to a soft measurement model construction method based on a one-dimensional convolution-stacked autoencoder (1D-SAE). Background Art

[0002] In industrial production, advanced and optimized control is widely used in the production process in exchange for the greatest economic benefits, and these methods widely rely on the real-time identification of key product qualities. However, these quality data are often difficult to detect in real time, and even if they can be obtained through experimental analysis, their acquisition has a considerable time delay. In order to solve these problems, methods for building soft sensor models have been developed, which indirectly estimate those difficult-to-measure quality data by building mathematical models with easy-to-measure process data. As more and more process data are collected and stored, data-driven soft sensor model construction methods have become mainstream, among which the most popular methods are principal component regression (PCR), partial least squares regression (PLSR), artificial neural networks (ANNs) and support vector regression (SVR).

[0003] In recent years, deep learning has been used for big data feature extraction in complex and large-scale systems to solve problems such as high dimensionality, irrelevant information, and high redundancy. Among them, the stacked autoencoder (SAE) is a deep network with multiple autoencoder (AE) units, which uses unsupervised layer-by-layer pre-training and supervised fine-tuning techniques to train the model. Pre-training simulates the multi-layer abstract function of the human brain, allowing the extraction of abstract data features layer by layer. The fine-tuning process uses the network parameters trained by the pre-training process to initialize and train with subsequent network fusion to build a more powerful and accurate soft measurement model.

[0004] One limitation of deep neural networks is that they are slow to train, and this limitation is more pronounced for high-dimensional data. One-dimensional convolution can extract effective features at a lower computational cost. Compared with two-dimensional convolution, its convolution kernel only moves in a single direction, performs dot product operations on one-dimensional data, and reduces the data dimension through the pooling layer. However, although the pooling layer can effectively extract significant features, in the process of building a soft measurement model, the pooling layer will miss some important information, resulting in unsatisfactory final results. Summary of the invention

[0005] The main technical problem to be solved by the present invention is: how to extract features more effectively and stably and construct a soft measurement model with higher accuracy for high-dimensional and noisy data. Specifically, the present invention first standardizes the noisy data collected by different sensors, and then introduces a one-dimensional convolutional autoencoder (AE) module. In order to ensure that important information is not omitted during the pooling process, the pooling layer is removed and the feature dimension is reduced using a double-step convolution layer. Multiple modules are stacked to form a stacked autoencoder with one-dimensional convolution for training. The pre-training process is completed by minimizing the reconstruction error of the input and output of each module, and the convolution kernel parameters of each module are extracted and saved. Finally, fine-tuning is performed, the pre-trained one-dimensional convolution stacked autoencoder network structure is connected to the fully connected layer, and the convolution kernel parameters of the saved pre-training process are used as the convolution kernel initialization parameters of the fine-tuning process for training, minimizing the error between the network output and the actual quality data of the industrial process, thereby completing the construction of a soft measurement model for industrial process quality data.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a new method for constructing a soft measurement model based on a one-dimensional convolution-stacked autoencoder, comprising the following steps:

[0007] Step (1): Collect m sensor variable noisy data at n sampling moments under normal operating conditions to form a data set matrix X = [x1, x2, ..., x m ]∈R n×m , where n is the number of data set samples, m is the number of sensor measurement variables, and R is a real number set;

[0008] Step (2): The sensor noisy data is normalized using the z-score normalization method. The specific calculation formula is as follows:

[0009]

[0010] Among them, μ i Represents all samples of a single sensor in the dataset matrix x i The mean value, σ i represents the standard deviation, and the mean value of all sensors is U=[μ1,μ2,…,μ m ] and standard deviation Φ=[σ1,σ2,…,σ m ] to store. After standardizing the data in each column, we finally get the standardized data set Z train =[z train1 ,z train2 ,…,z trainm ]∈R n×m ;

[0011] Step (3): Select the quality variable data T that needs to be fitted and predicted by the soft measurement modeltrain =[z trainj ]∈R n×1 and the characteristic variable X train =[z train1 ,z train2 ,…,z trainj-1 ,z trainj+1 …,z trainm ]∈R n×(m-1) ;

[0012] Step (4): Construct a one-dimensional convolutional autoencoder module, design a trainer and set network hyperparameters. The specific implementation process is as follows:

[0013] Step (4.1): For the encoder module of the one-dimensional convolutional autoencoder, a one-dimensional convolutional layer is used for construction. The settings of the one-dimensional convolutional layer are as follows: the kernel size kernel_size is set to 3, the padding size padding is set to 1, and the convolution step stride is set to 2. The formula for calculating the size of the convolutional layer is:

[0014]

[0015] W and N are the number of layers of the convolution layer input and output respectively. It can be seen that when the above one-dimensional convolution is set, the number of output layers W is always half of the number of input layers N. According to this convolution setting, the data dimension can be reduced without going through the pooling layer. Although the feature extraction capability is reduced to a certain extent, it enables the entire encoder to retain more useful information.

[0016] Step (4.2): For the decoder module of the one-dimensional convolutional autoencoder, a one-dimensional deconvolution layer is used for construction. The one-dimensional deconvolution layer is set as follows: the kernel size kernel_size is set to 2, the convolution step size stride is set to 2, and the deconvolution layer size is calculated according to the formula:

[0017] N = (W-1)*stride-2*padding+kernel_size (3)W and N are the number of layers of the deconvolution layer input and output respectively. It can be seen that when the above one-dimensional convolution setting is performed, the number of output layers W is always twice the number of input layers N. According to this convolution setting, the data dimension can be increased without going through the pooling layer to complete the decoder function;

[0018] Step (4.3): For the one-dimensional convolutional autoencoder module, the MSE loss function is used to minimize the reconstruction error between the input and output, and its formula is as follows:

[0019]

[0020] Where X represents the input data, h = f(X) represents the encoding process of the encoder, h represents the hidden data obtained after the input passes through the encoder, y = g(h) represents the decoding process of the decoder, and y represents the reconstructed data obtained after the hidden data passes through the decoder;

[0021] Step (4.4): Use the Adam trainer to train and optimize the entire one-dimensional convolutional autoencoder module, so that after the training is completed, the hidden layer data h and the convolution layer convolution kernel parameter weight weight and bias bias can be obtained;

[0022] Step (4.5): Set the network hyperparameters such as training cycle epoch, learning rate lr, one-dimensional convolutional autoencoder module layer number k through multiple tests;

[0023] Step (5): Set the feature variable X train =[z train1 ,z train2 ,…,z trainj-1 ,z trainj+1 …,z trainm ]∈R n ×(m-1) Input into the first layer one-dimensional convolutional autoencoder module, and after training, obtain the first layer hidden data h1 and the convolutional kernel parameter weight weight1 and bias bias1 under the condition of minimum input and output reconstruction error. The first layer hidden data h1 is used as the input of the second layer one-dimensional convolutional autoencoder module for training to obtain the second layer hidden data h2 and the convolutional kernel parameter weight weight2 and bias bias2. And so on, until after k one-dimensional convolutional autoencoder modules, the high-dimensional training set input data is reduced to a suitable dimension. At this point, the pre-training process is completed and the following parameters are obtained:

[0024] Hidden layer data: h1,h2,…,h k , where for the hidden layer data at the i-th moment, h i The dimension is h i+1 Twice the dimension;

[0025] Convolution kernel weight: weight = [weight1, weight2, ..., weight k ]∈R 3×k ;

[0026] Convolution kernel bias: Bias = [bias1, bias2, ..., bias k ]∈R 1×k ;

[0027] Step (6): Build a fine-tuned network structure, design a trainer and set network hyperparameters. The specific implementation process is as follows:

[0028] Step (6.1): Construct k layers of one-dimensional convolutional layers. The settings of the one-dimensional convolutional layers are as follows: kernel size kernel_size is set to 3, padding size padding is set to 1, and stride is set to 2. The convolutional kernel weights obtained during the pre-training process: Weight = [Weight1, Weight2, ..., weight k ]∈R 3×k And convolution kernel bias: Bias = [bias1, bias2, ..., bias k ]∈R 1×k Set as the initialization parameter of the k-layer network;

[0029] Step (6.2): ​​Construct two fully connected layers. The input dimension of the first fully connected layer is the same as the kth hidden layer data h k The dimension of the second fully connected layer is the same as that of the first fully connected layer, and the output dimension is set to about half of the input dimension to reduce the dimension, so as to further extract data features. The input dimension of the second fully connected layer is the same as the output dimension of the first fully connected layer, and the output dimension is one-dimensional, which is used as the output of the soft measurement model;

[0030] Step (6.3): Connect k layers of one-dimensional convolutional layers with initialization parameters and two fully connected layers to build a complete fine-tuning network structure;

[0031] Step (6.4): For the fine-tuned network, the MSE loss function is used to minimize the error between the output fitting value and the actual quality data corresponding to the input. The formula is as follows:

[0032] Where X represents the input data, and Y represents the quality data corresponding to the input data. Represents the process of fine-tuning the network to fit the quality data from the input data;

[0033] Step (6.5): Use the Adam trainer to train and optimize the entire fine-tuning network so that The error with Y is minimal;

[0034] Step (7): Transform the data X train =[z train1 ,z train2 ,…,z trainj-1 ,z trainj+1 …,z trainm ]∈R n×(m-1) and Y train =[z trainj ]∈R n×1Input into the fine-tuning network for training, adjust the network hyperparameters such as training cycle epoch, learning rate lr, etc. Finally, the construction of the soft measurement model is completed.

[0035] The above steps (1) to (7) are the offline modeling stage of the method of the present invention, and the following steps (8) to (11) are the implementation process of the online analysis of the method of the present invention.

[0036] Step (8): Collect noisy sample data at the new sampling time Where m is the number of sensor measurement variables, and R is a set of real numbers;

[0037] Step (9): Apply the mean U = [μ1, μ2, …, μ m ]∈R 1×m and standard deviation Φ=[σ1,σ2,…,σ m ]∈R 1×m Processing is performed to obtain standardized test sample data

[0038] Step (10): Select the quality variable according to the selection method in step (3) and characteristic variables

[0039] Step (11): Set the feature variables The input is fed into the fine-tuned network and compared with the actual quality data. Conduct comparative testing.

[0040] Compared with the traditional method, the advantages of the method of the present invention are:

[0041] First, the method of the present invention not only considers the correlation between the data collected by different types of sensors and the quality data, but also considers the local characteristics of the data, and can better deal with noise interference; secondly, compared with other traditional training methods, the method of the present invention can better process high-dimensional data, and can more efficiently and stably fit and predict the quality data, and can obtain better results. It can be said that the method of the present invention is a more excellent method for building a soft sensor model. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The present invention is a flowchart for implementing the method. DETAILED DESCRIPTION

[0043] The method of the present invention is described in detail below with reference to the accompanying drawings and specific implementation cases.

[0044] like Figure 1As shown, the present invention discloses a novel soft sensor model construction method based on one-dimensional convolution-stacked autoencoder. The specific implementation process of the method of the present invention and its superiority over the existing methods are explained below in conjunction with a specific industrial process case.

[0045] By analyzing the historical information collected from the energy storage power station in Zhenjiang, China, the stack voltage is an important parameter, and it is often difficult to obtain in real time, with a long delay. Therefore, the stack voltage is selected as the key quality parameter of the energy storage power station to be predicted. The historical data set of the energy storage power station is divided into two categories: battery cell data and non-battery data. The battery cell data includes the voltage of 228 battery cells, the temperature of 228 battery cells and the SOC of 228 battery cells. The monitoring variables of non-battery data are listed in Table 1. In order to predict the stack voltage, the voltage of 226 battery cells, the temperature of 76 battery cells, the SOC of 226 battery cells, the SOH of 226 battery cells, the maximum voltage of the stack cell, the minimum voltage of the stack cell, the maximum temperature of the stack cell, the minimum temperature of the stack cell, the chargeable amount of the stack, the dischargeable amount of the stack, the cumulative charge amount of the stack, the cumulative discharge amount of the stack, the total voltage of the cluster, the pre-charge voltage of the cluster, the SOC of the cluster, the average voltage of the cluster, the maximum voltage of the cluster, and the minimum voltage of the cluster are selected. A total of 768 characteristic variables are described in detail in conjunction with this process.

[0046] Table 1 Non-battery data monitoring variables

[0047]

[0048]

[0049] First, the implementation process of the method of the present invention is as follows Figure 1 As shown, a soft sensor model is established using sample data sampled under normal operating conditions of an energy storage power station, including the following steps:

[0050] Step (1): Collect noisy sample data under the operation state of the industrial process to form a data set matrix X = [x1, x2, ..., x 769 ]∈R 5760×769 ;

[0051] Step (2): Standardize the data using the z-score method to obtain data Z train =[z train1 ,z train2 ,…,z train769 ]∈R 5760×769 , and get the mean U=[μ1,μ2,…,μ 769 ]∈R 1×769 and standard deviation Φ=[σ1,σ2,…,σ 769 ]∈R 1×769 ;

[0052] Step (3): Select the quality variable Y that needs to be fitted by the soft sensor train =[z trainj ]∈R 5760×1 and the characteristic variable X train =[z train1 ,z train2 ,…,z trainj-1 ,z trainj+1 …,z trainm ]∈R 5760×768 ;

[0053] Step (4): Construct a one-dimensional convolutional autoencoder module, design a trainer and set network hyperparameters. In this experiment, the training cycle epoch is set to 6, the learning rate lr is set to 0.005, and the number of layers of the one-dimensional convolutional autoencoder module is set to 6;

[0054] Step (5): Set the feature variable X train =[z train1 ,z train2 ,…,z trainj-1 ,z trainj+1 …,z trainm ]∈R 5760 ×768 Input into the first layer one-dimensional convolutional autoencoder module, and after training, obtain the first layer hidden data h1 and the convolutional kernel parameter weight weight1 and bias bias1 under the condition of minimum input and output reconstruction error. The first layer hidden data h1 is used as the input of the second layer one-dimensional convolutional autoencoder module for training to obtain the second layer hidden data h2 and the convolutional kernel parameter weight weight2 and bias bias2. After passing through 6 one-dimensional convolutional autoencoder modules, the high-dimensional training set input data is reduced to a suitable dimension. At this point, the pre-training process is completed and the following parameters are obtained:

[0055] Hidden layer data: h1, h2, …, h6, where the feature dimension of h1 is 384, the feature dimension of h2 is 192, and so on, the feature dimension of h6 is 12;

[0056] Convolution kernel weight: Weight = [weight1, weight2, ..., weight6] ∈ R 3×6 ;

[0057] Convolution kernel bias: Bias = [bias1, bias2, ..., bias6] ∈ R 1×6 ;

[0058] Step (6): Construct a fine-tuned network structure, design a trainer and set network hyperparameters. In this experiment, the training cycle epoch is set to 6 and the learning rate lr is set to 0.005. The convolution kernel weights obtained during the pre-training process are: weight = [weight1, weight2, ..., weight k ]∈R 3×k And convolution kernel bias: Bias = [bias1, bias2, ..., bias k ]∈R 1×k Set as the initialization parameter of the k-layer network. The two fully connected layers are constructed, and the input dimension of the first fully connected layer is set to 12 and the output dimension is set to 6. The input dimension of the second fully connected layer is set to 6 and the output dimension is set to 1 as the output of the soft measurement model;

[0059] Step (7): X train =[z train1 ,z train2 ,…,z trainj-1 ,z trainj+1 …,z trainm ]∈R 5760×768 and Y train =[z trainj ]∈R 5760×1 Input into the fine-tuning network for training, adjust the network hyperparameters such as training cycle epoch, learning rate lr, etc. Finally, the construction of the soft measurement model is completed.

[0060] The offline modeling phase is now complete, and the next step is to analyze the online data. 1440 sets of sample data collected under normal operating conditions of the energy storage power station were used for testing.

[0061] Step (8): Collect noisy sample data at the new sampling time There are 1440 test data in total, m is the number of sensor measurement variables, and R is the real number set;

[0062] Step (9): Apply the mean U = [μ1, μ2, …, μ 769 ]∈R 1×769 and standard deviation Φ=[σ1,σ2,…,σ 769 ]∈R 1×769 Processing is performed to obtain standardized test sample data

[0063] Step (10): Select the quality variable according to the selection method in step (3) and characteristic variables

[0064] Step (11): Set the feature variables Input to the fine-tuned network and quality variables A comparative test was performed, and then the same operation was performed on the remaining 1439 test data in the test data set.

[0065] Finally, the experiment was tested using 50 initialized random number seeds. The mean square error comparison between the traditional soft measurement model construction method based on one-dimensional convolutional neural network (1D-CNN) and stacked autoencoder (SAE) and the method of the present invention is shown in Table 2, and the mean square error comparison between the soft measurement model construction method using pooled one-dimensional convolution-stacked autoencoder and the method of the present invention is shown in Table 3. It can be found that the method of the present invention is better than traditional 1D-CNN and SAE and is not easy to fall into the local minimum problem, while the traditional 1D-CNN method is very easy to fall into the local minimum. Compared with the soft measurement model construction method of one-dimensional convolution-stacked autoencoder with added pooling layer, the method of the present invention has shorter training time, is less likely to fall into the local minimum problem, and has better effect.

[0066] The above implementation cases are only used to explain the specific implementation of the present invention, rather than to limit the present invention. Within the protection scope of the claims of the present invention, any modification made to the present invention falls within the protection scope of the present invention.

[0067] Table 2 Comparison of results of three methods

[0068]

[0069] Table 2 Comparison of 1D-SAEpool and 1D-SAE results

[0070] Serial number 1D-SAEpool 1D-SAE Serial number 1D-SAEpool 1D-SAE Serial number 1D-SAEpool 1D-SAE 1 1.0067 0.0965 17 0.1160 0.0915 33 0.1117 0.1135 2 0.1022 0.0888 18 0.1110 1.0069 34 0.1101 0.1000 3 1.0070 0.1017 19 1.0069 0.1099 35 0.1128 0.0989 4 0.1084 0.1029 20 0.1069 1.0067 36 0.1067 0.0972 5 0.1031 0.0925 21 0.1092 0.0993 37 0.1067 0.1064 6 1.0069 0.1093 22 0.1053 0.0970 38 0.1097 0.0990 7 0.1065 0.0991 23 0.1045 0.0956 39 0.1073 0.1114 8 0.1126 0.0994 24 0.1121 0.1050 40 0.1183 0.0972 9 0.1153 0.1070 25 0.1018 0.0949 41 0.1176 0.0954 10 0.1004 0.0988 26 0.1307 0.1019 42 0.1042 0.0927 11 0.1406 0.1007 27 0.1148 0.1068 43 0.1150 0.1073 12 0.1214 0.0944 28 0.1205 0.1009 44 0.1124 0.0984 13 0.1069 0.0987 29 1.0066 0.0924 45 0.1038 0.1282 14 0.1068 0.0956 30 0.9910 0.0987 46 0.1098 0.1032 15 0.1021 0.0904 31 0.1214 0.0886 47 0.1233 0.0918 16 0.1220 0.0970 32 0.1089 0.0956 48 0.1031 0.1008 49 0.1088 0.0956 50 0.1006 0.0967

Claims

1. A method for constructing a soft sensor model based on one-dimensional convolution-stacked autoencoder (1D-SAE), characterized in that: The following steps are involved: The implementation process of the offline modeling phase is as follows: Step (1): Collect m sensor variable noisy data at n sampling moments under normal operating conditions to form a data set matrix X = [x1, x2, ..., x m ]∈R n×m , where n is the number of data set samples, m is the number of sensor measurement variables, and R is a real number set; Step (2): Standardize the data using the z-score method to obtain data z train =[z train1 ,z train2 ,…,z trainm ]∈R n×m , and get the mean U=[μ1,μ2,…,μ m ]∈R 1×m and standard deviation Φ=[σ1,σ2,…,σ m ]∈R 1×m ; Step (3): Select the quality variable data Y that needs to be fitted and predicted by the soft measurement model train =[z trainj ]∈R n×1 and the characteristic variable X train =[z train1 ,z train2 ,…,z trainj-1 ,z trainj+1 …,z trainm ]∈R n×(m-1) ; Step (4): Construct a one-dimensional convolutional autoencoder module, design a trainer and set the training cycle, learning rate, and one-dimensional convolutional autoencoder module layer network hyperparameters; Step (4.1): For the encoder module of the one-dimensional convolutional autoencoder, a one-dimensional convolutional layer is used for construction. The settings of the one-dimensional convolutional layer are as follows: the kernel size kernel_size is set to 3, the padding size padding is set to 1, and the convolution step stride is set to 2. According to this convolution setting, the data dimension is reduced without going through the pooling layer; Step (4.2): For the decoder module of the one-dimensional convolutional autoencoder, a one-dimensional deconvolution layer is used for construction. The one-dimensional deconvolution layer is set as follows: the kernel size kernel_size is set to 2, and the convolution step length stride is set to 2. According to this convolution setting, the data dimension is increased without going through the pooling layer to complete the decoder function. Step (4.3): For the one-dimensional convolutional autoencoder module, the MSE loss function is used to minimize the reconstruction error between the input and output, and its formula is as follows: Where X represents the input data, h = f(X) represents the encoding process of the encoder, h represents the hidden data obtained after the input passes through the encoder, y = g(h) represents the decoding process of the decoder, and y represents the reconstructed data obtained after the hidden data passes through the decoder; Step (4.4): Use the Adam trainer to train and optimize the entire one-dimensional convolutional autoencoder module, and after the training is completed, obtain the hidden layer data h, the convolution layer convolution kernel parameter weight weight, and the bias bias; Step (4.5): Set the training cycle epoch, learning rate lr, one-dimensional convolutional autoencoder module layer number k network hyperparameters through multiple tests; Step (5): Set the feature variable X train =[z train1 ,z train2 ,…,z trainj-1 ,z trainh+1 …,z trainm ]∈R n×(m-1) Input into the first-layer one-dimensional convolutional autoencoder module, and after training, obtain the first-layer hidden data h1, convolutional kernel parameter weight weight1, and bias bias1 under the condition of minimum input and output reconstruction error; use the first-layer hidden data h1 as the input of the second-layer one-dimensional convolutional autoencoder module for training to obtain the second-layer hidden data h2, convolutional kernel parameter weight weight2, and bias bias2; and so on, until after k one-dimensional convolutional autoencoder modules, the high-dimensional training set input data is reduced to a suitable dimension, the influence of process variable noise is reduced through the convolution layer, and the deep features of the process variables are extracted through the hidden layer; At this point the pre-training process is complete and the following parameters are obtained: Hidden layer data: h1,h2,…,h k , where for the hidden layer data at the i-th moment, h i The dimension is h i+1 Twice the dimension; Convolution kernel weight: Weight = [weight1, weight2, ..., weight k ]∈R 3×k ; Convolution kernel bias: Bias = [bias1, bias2, ..., bias k ]∈R 1×k ; Step (6): Construct a fine-tuned network structure, design a trainer and set the training cycle, learning rate and network hyperparameters; the convolution kernel weights obtained during the pre-training process: weight = [weight1, weight2, ..., weight k ]∈R 3×k And convolution kernel bias: Bias = [bias1, bias2, ..., bias k ]∈R 1×k Set as the initialization parameter of the k-layer network; construct two fully connected layers as the output of the soft measurement model; Step (6.1): Construct k layers of one-dimensional convolutional layers. The settings of the one-dimensional convolutional layers are as follows: the convolution kernel size kernel_size is set to 3, the padding size padding is set to 1, and the convolution step stride is set to 2; the convolution kernel weights obtained in the pre-training process are: Weight = [Weight1, Weight2, ..., Weight k ]∈R 3×k And convolution kernel bias: Bias = [bias1, bias2, ..., bias k ]∈R 1×k Set as the initialization parameter of the k-layer network; Step (6.2): ​​Construct two fully connected layers. The input dimension of the first fully connected layer is the same as the kth hidden layer data h k The dimension of the second fully connected layer is the same as that of the first fully connected layer, and the output dimension is set to half of the input dimension to reduce the dimension, so as to further extract data features; the input dimension of the second fully connected layer is the same as the output dimension of the first fully connected layer, and the output dimension is one-dimensional as the output of the soft sensor; Step (6.3): Connect k layers of one-dimensional convolutional layers with initialization parameters and two fully connected layers to build a complete fine-tuning network structure; Step (6.4): For the fine-tuned network, the error between the output fitting value and the quality variable corresponding to the input is minimized according to the MSE loss function, and the formula is as follows: Where X represents the input data, and Y represents the quality variable corresponding to the input data. represents the process of fine-tuning the network to fit the quality variables from the input data; Step (6.5): Use the Adam trainer to train and optimize the entire fine-tuning network so that The error with Y is minimal; Step (7): Transform the data X train =[z train1 ,z train2 ,…,z trainj-1 ,z trainj+1 …,z trainm ]∈R n×(m-1) and Y train =[z trainj ]∈R n×1 Input into the fine-tuning network for training, adjust the training cycle epoch, learning rate lr network hyperparameters; finally complete the construction of the soft measurement model; The implementation process of online prediction is as follows: Step (8): Collect noisy sample data at the new sampling time Where m is the number of sensor measurement variables, and R is a set of real numbers; Step (9): Apply the mean U = [μ1, μ2, …, μ m ]∈R 1×m and standard deviation Φ=[σ1,σ2,…,σ m ]∈R 1×m Processing is performed to obtain standardized test sample data Step (10): Select the quality variable according to the selection method in step (3) and characteristic variables Step (11): Set the feature variables The soft measurement prediction results are input into the one-dimensional convolution-stacked autoencoder network constructed in the offline modeling stage.

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