A data completion method based on position encoding adaptive deep belief network

Abstract

The present invention belongs to the technical field of industrial data completion methods, and specifically discloses a data completion method based on a position coding adaptive deep belief network. The data of a training set and its position coding are combined into a position coding data layer and a position coding adaptive deep belief network is pre-trained, so that the position information of the actual data can be taken into account, thereby improving the prediction accuracy of the prediction model; and similar sample sets can be screened to perform rapid fine-tuning on a basic global model to obtain an optimal local industrial data completion model, so that a high data completion accuracy can be continuously maintained in an industrial system with strong time-varying properties.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial data completion methods, and specifically relates to a data completion method based on a position encoding adaptive deep belief network. Background Art

[0002] With the advent of the big data era, data-driven process monitoring, fault diagnosis, fault classification, and soft sensors have become research hotspots. However, the success of data-driven methods depends largely on the quality of process data. Due to problems such as data collection, transmission, and management, industrial data often have varying degrees of missing values. This not only increases the difficulty of data analysis, but may also lead to errors in data-driven models, making it impossible to provide effective guidance for industrial production.

[0003] In the prior art, in order to solve the problem of missing industrial data, data interpolation is generally used to complete the missing values. Due to its learning goal of reconstructing inputs, deep belief networks are particularly suitable for restoring incomplete samples, so they are often used to interpolate missing industrial data. However, current data completion methods based on deep belief networks usually use the average value of the non-missing values ​​of each variable to initialize the value of the missing position, resulting in the model being unable to obtain the missing position information. In addition, due to factors such as the complex process industry environment and equipment aging, the production process has a strong time-varying nature, which makes the globally trained model often face performance degradation problems when running online. Summary of the invention

[0004] The technical problem to be solved by the present invention is to overcome the defects of the data completion method based on deep belief network in the prior art that it cannot obtain missing position information and has performance degradation under data with strong time-varying characteristics, thereby providing a data completion method based on position encoding adaptive deep belief network.

[0005] A data completion method based on position encoding adaptive deep belief network includes the following method steps:

[0006] Step S1: obtaining a complete data set, randomly deleting values ​​in the data set, and normalizing the data set; dividing the complete data set into a training set and a test set;

[0007] Step S2: Position-encoding the data of the training set, and combining the data of the training set with the position coding to form a position coding input layer;

[0008] Step S3: Pre-train the first layer of the position coding adaptive deep belief network based on the position coding input layer to obtain the first layer hidden layer feature state, and use the first layer hidden layer feature state combined with the position coding as the second layer input data, and so on, train multiple layers in sequence to obtain a global model of industrial data completion based on the position coding adaptive deep belief network.

[0009] Step S4: For the test set samples, similar samples are screened from the training set and a similar sample set is formed to quickly fine-tune the global model, and the deep belief network global model is adaptively updated until convergence to obtain the optimal local industrial data completion model; Step S5: The data in the test set are input into the corresponding optimal local industrial data completion model in turn, and the completed complete test set data is output.

[0010] Step S6: Obtain the data set to be completed, select and form a similar sample set from the training set for the samples of the data set to be completed, quickly fine-tune the global model, and adaptively update the deep belief network global model until convergence to obtain the optimal local industrial data completion model;

[0011] Step S7: input the data in the data set to be completed into the corresponding optimal local industrial data completion model, and output the completed complete data set data.

[0012] Furthermore, the position code is:

[0013] ;

[0014] in, Indicates a The missing sample i Positional encoding of variables; Indicates a The missing sample i variables; Indicates the missing sample i variables with missing values;

[0015] The position encoding input layer is:

[0016] ;

[0017] in, Represents the original input t Missing samples at time instant; Indicates t The position code of the moment; Indicates missing samples With position encoding The concatenated input vector.

[0018] Furthermore, in step S3, the position encoding adaptive deep belief network includes a multi-layer restricted Boltzmann machine, and in every two adjacent layers of restricted Boltzmann machines, the hidden layer neuron state of the bottom layer restricted Boltzmann machine is input into the upper layer restricted Boltzmann machine as the newly extracted feature data, and the upper layer restricted Boltzmann machine is trained;

[0019] The energy function of each restricted Boltzmann machine is:

[0020] ;

[0021] in, Represents the state vector of the visible layer, which is also the position encoding input layer; Represents the state vector of the hidden layer; Indicates Visible layer units; Indicates The state of each visible layer unit; Indicates The bias of the visible layer unit; Indicates hidden layer units; Indicates The state of the hidden layer units; Indicates The bias of the hidden layer units; Represents the connection weight between two layers; Indicates the number of nodes in the visible layer; Represents the number of nodes in the hidden layer.

[0022] Furthermore, the training process of the restricted Boltzmann machine includes:

[0023] Step S3.1: Forward propagate the input data and calculate the activation state of the hidden layer :

[0024] ;

[0025] ;

[0026] The starting value of the summation is Represents the first hidden layer unit Start calculation; Indicates the number of nodes in the hidden layer;

[0027] Step S3.2: Use the activation state of the hidden unit to reconstruct the visible layer, reconstruct and sample each visible unit to obtain the visible layer :

[0028] ;

[0029] ;

[0030] The starting value of the summation is Indicates that the first visible layer unit Start calculation; is the number of nodes in the visible layer, is the sigmoid function.

[0031] Furthermore, the unsupervised pre-training objective function of the restricted Boltzmann machine is:

[0032] ;

[0033] in, T represents the number of samples in the training data set, Indicates t training samples;

[0034] Further, the reverse fine-tuning method includes:

[0035] ;

[0036] ;

[0037] in, represents the learning rate, Indicates the value of the hidden layer or visible layer; Represents the value of reconstructing the hidden layer or visible layer; represents the initial weight; represents the updated weight; represents the initial hidden layer bias; represents the updated hidden layer bias; represents the initial visible layer bias; Represents the updated visible layer bias.

[0038] Furthermore, the method steps of updating the position encoding deep belief network model through online adaptive updating include:

[0039] Step S4.1: Filter out samples to be completed based on feature similarity in the industrial dataset Similar s samples, forming a similar sample set ;

[0040] Step S4.2: Using similar sample sets The global model is quickly fine-tuned by adjusting model parameters until the model converges on the validation set. The fine-tuned model is determined to be the optimal local industrial data completion model.

[0041] Step S4.3: Input the sample to be completed into the optimal local industrial data completion model to obtain the completion value.

[0042] Furthermore, the method further includes step S4.4: evaluating the data completion performance using the root mean square error:

[0043] The formula for calculating the root mean square error is:

[0044] ;

[0045] Among them, RMSE means root mean square error; K Indicates the number of missing values; Indicates k actual missing values; Indicates k estimated missing values;

[0046] Furthermore, the similar sample set The generation method is:

[0047] Step S4.1.1: Calculate the samples to be completed Concentrate with historical data The Euclidean distance between each sample :

[0048] ;

[0049] Step S4.1.2: Calculate the weight coefficient based on the Euclidean distance :

[0050] ;

[0051] Step S4.1.3: sort the weight coefficients in ascending order Arrange from small to large and select the one with the largest weight. s A complete sample of Similar sample sets .

[0052] Furthermore, the method steps of the rapid fine-tuning include:

[0053] Step S4.2.1: Similar sample set It is input into the pre-trained global model and the relevant data set is obtained by performing forward propagation from the input layer to the output layer. The completion value of The error loss is calculated and the network parameters are updated using the back propagation algorithm.

[0054] Step S4.2.2: When the subsequent samples to be completed When you arrive, follow the steps above for The relevant sample selection, online update and completion steps are performed sequentially.

[0055] Beneficial effects: The present invention discloses a data completion method based on a position coding adaptive deep belief network. The data of the training set and its position coding are combined into a position coding data layer and a position coding adaptive deep belief network is pre-trained, so that the position information of the actual data can be taken into account, thereby improving the prediction accuracy of the prediction model; and similar sample sets can be screened to perform rapid fine-tuning on the basic global model to obtain the optimal local industrial data completion model, thereby continuously maintaining a high data completion accuracy in an industrial system with strong time-varying properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0057] Figure 1 It is a schematic block diagram of the overall method flow of the present invention;

[0058] Figure 2 Schematic diagram of the position encoding adaptive deep belief network of the present invention. DETAILED DESCRIPTION

[0059] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present application, so the present application is not limited by the specific embodiments disclosed below.

[0060] Reference Figure 1 As shown, this embodiment provides a data completion method based on a position encoding adaptive deep belief network, including the following method steps:

[0061] Step S1: obtaining a complete data set, randomly deleting values ​​in the data set, and normalizing the data set; dividing the complete data set into a training set and a test set;

[0062] In this embodiment, 10%-50% of the values ​​of the samples in the data set are randomly deleted to simulate data missing in a real environment.

[0063] Step S2: Position-encoding the data of the training set, and combining the data of the training set with the position coding to form a position coding input layer;

[0064] Step S3: Pre-train the first layer of the position coding adaptive deep belief network based on the position coding input layer to obtain the first layer hidden layer feature state, and use the first layer hidden layer feature state combined with the position coding as the second layer input data, and so on, train multiple layers in sequence to obtain a global model of industrial data completion based on the position coding adaptive deep belief network.

[0065] Step S4: For the test set samples, similar samples are selected from the training set and a similar sample set is formed to quickly fine-tune the global model, and the deep belief network global model is adaptively updated until convergence to obtain the optimal local industrial data completion model;

[0066] Step S5: input the data in the test set into the corresponding optimal local industrial data completion model in sequence, and output the completed complete test set data.

[0067] Step S6: Obtain the data set to be completed, select and form a similar sample set from the training set for the samples of the data set to be completed, quickly fine-tune the global model, and adaptively update the deep belief network global model until convergence to obtain the optimal local industrial data completion model;

[0068] In this embodiment, the specific operation method algorithm of step S6 is the same as that of step S4;

[0069] Step S7: input the data in the data set to be completed into the corresponding optimal local industrial data completion model, and output the completed complete data set data.

[0070] This embodiment discloses a data completion method based on a position coding adaptive deep belief network. The data of the training set and its position coding are combined into a position coding data layer and a position coding adaptive deep belief network is pre-trained, so that the position information of the actual data can be taken into account, thereby improving the prediction accuracy of the prediction model; and similar sample sets can be screened to perform rapid fine-tuning on the basic global model to obtain the optimal local industrial data completion model, so that a high data completion accuracy can be continuously maintained in industrial systems with strong time-varying properties.

[0071] Specifically, the position code is:

[0072] ;

[0073] in, Indicates a The missing sample iPositional encoding of variables; Indicates a The missing sample i variables; Indicates the missing sample i variables with missing values;

[0074] The position encoding input layer is:

[0075] ;

[0076] in, Represents the original input t Missing samples at time instant; Indicates t The position code of the moment; Indicates missing samples With position encoding The concatenated input vector.

[0077] Reference Figure 2 As shown, in step S3, the position encoding adaptive deep belief network includes a multi-layer restricted Boltzmann machine, Figure 2 It is a position-encoded adaptive deep belief network composed of three restricted Boltzmann machines. Based on a given training data set, it first undergoes position encoding to form a position encoding input layer. , and then train the first restricted Boltzmann machine RBM1 based on the given data set to obtain the first hidden layer feature state Then, the first layer of hidden feature data with position-encoded quality data Combined as the visible layer input variable of the second restricted Boltzmann machine RBM2 , similarly, complete the second hidden layer feature state Then the second layer hidden feature data with position-encoded quality data Combined as the visible layer input variable of the third restricted Boltzmann machine RBM3 , complete the training of RBM3 and obtain high-level features In every two adjacent layers of restricted Boltzmann machines, the hidden layer neuron states of the bottom layer restricted Boltzmann machine are input into the upper layer restricted Boltzmann machine as newly extracted feature data to train the upper layer restricted Boltzmann machine;

[0078] The energy function of each restricted Boltzmann machine is:

[0079] ;

[0080] in, Represents the state vector of the visible layer, which is also the position encoding input layer; Represents the state vector of the hidden layer; Indicates Visible layer units; Indicates The state of each visible layer unit; Indicates The bias of the visible layer unit; Indicates hidden layer units; Indicates The activation states of the hidden layer units; Indicates The bias of the hidden layer units; Represents the connection weight between two layers; Indicates the number of nodes in the visible layer; Represents the number of nodes in the hidden layer.

[0081] The training process of the restricted Boltzmann machine includes:

[0082] Step S3.1: Forward propagate the input data and calculate the activation state of the hidden layer :

[0083] ;

[0084] ;

[0085] The starting value of the summation is Represents the first hidden layer unit Start calculation; Indicates the number of nodes in the hidden layer;

[0086] Step S3.2: Use the activation state of the hidden unit to reconstruct the visible layer, reconstruct and sample each visible unit to obtain the visible layer :

[0087] ;

[0088] ;

[0089] The starting value of the summation is Indicates that the first visible layer unit Start calculation; is the number of nodes in the visible layer, is the sigmoid function.

[0090] Combined with given The state of each visible unit , first calculate the activation value, convert the activation value into probability through the sigmoid function; then perform Bernoulli sampling on each hidden unit, which means that for each :if =1, then sampling is performed through P (i.e., randomly generated as 1); if =0, then 0 is generated with probability 1-P.

[0091] The unsupervised pre-training objective function of the restricted Boltzmann machine is:

[0092] ;

[0093] in, T represents the number of samples in the training data set, Indicates t training samples;

[0094] In this embodiment, the reverse fine-tuning method of the restricted Boltzmann machine includes:

[0095] ;

[0096] ;

[0097] in, represents the learning rate, Indicates the value of the hidden layer or visible layer; Represents the value of reconstructing the hidden layer or visible layer; represents the initial weight; represents the updated weight; represents the initial hidden layer bias; represents the updated hidden layer bias; represents the initial visible layer bias; Represents the updated visible layer bias.

[0098] The method steps of updating the position encoding deep belief network model by online adaptive updating include:

[0099] Step S4.1: Filter out samples to be completed based on feature similarity in the industrial dataset Similar s samples, forming a similar sample set ;

[0100] Step S4.2: Using similar sample sets The global model is quickly fine-tuned by adjusting model parameters until the model converges on the validation set. The fine-tuned model is determined to be the optimal local industrial data completion model.

[0101] Step S4.3: Input the sample to be completed into the optimal local industrial data completion model to obtain the completion value.

[0102] Step S4.4: Use the root mean square error to evaluate the data completion performance:

[0103] The formula for calculating the root mean square error is:

[0104] ;

[0105] Among them, RMSE means root mean square error; K Indicates the number of missing values; Indicates k actual missing values; Indicates k estimated missing values;

[0106] The similar sample set The generation method is:

[0107] Step S4.1.1: Calculate the samples to be completed Concentrate with historical data The Euclidean distance between each sample :

[0108] ;

[0109] Step S4.1.2: Calculate the weight coefficient based on the Euclidean distance :

[0110] ;

[0111] Step S4.1.3: sort the weight coefficients in ascending order Arrange from small to large and select the one with the largest weight. s A complete sample of Similar sample sets .

[0112] The method steps of the rapid fine-tuning include:

[0113] Step S4.2.1: Similar sample set It is input into the pre-trained global model and the relevant data set is obtained by performing forward propagation from the input layer to the output layer. The completion value of The error loss is calculated and the network parameters are updated using the back propagation algorithm.

[0114] Step S4.2.2: When the subsequent samples to be completed When you arrive, follow the steps above for The relevant sample selection, online update and completion steps are performed sequentially.

[0115] In this embodiment, all input variables that are not explicitly specified are preset values.

[0116] In this embodiment, the input data includes process data in the hydrocracking process, as shown in the following table.

[0117] serial number Process variable description serial number Process variable description 1 Total flow 2 Total inlet temperature of hydrogen furnace 3 Total hydrogen furnace exports 4 Hydrogenation reactor inlet temperature 5 Hydrogenation reactor bed top temperature 6 Hydrogenation reactor - middle bed temperature 7 Hydrogenation reactor bed bottom temperature 8 The top temperature of the second bed of hydrogenation reactor 9 The middle temperature of the second bed of hydrogenation reactor 10 The bottom temperature of the second bed of hydrogenation reactor 11 Top temperature of three-bed hydrogenation reactor 12 Temperature in the middle of the three beds of hydrogenation reactor 13 The bottom temperature of the three-bed hydrogenation reactor 14 Bottom temperature indication of hydrogenation reactor 15 Hydrogenation reactor pressure difference 16 Inlet temperature of the fracturing reactor 17 The top temperature of the second bed of the fracturing reactor 18 Top temperature of three beds in the fracturing reactor 19 Top temperature of the fourth bed of the fracturing reactor 20 Fracturing reactor pressure difference 21 Hot low oil flow 22 Top pressure of hot low separation tank 23 Total water volume 24 Cold low oil flow 25 New hydrogen flow rate of hydrogen compressor 26 Desulfurization stripper reflux 27 Bottom liquid flow rate of desulfurization stripper 28 Top gas flow rate of desulfurization stripper 29 Top pressure of main fractionator 30 Top reflux of main fractionator 31 Steam flow rate of main fractionation stripper 32 Main fractionator bottom temperature 33 Intermediate output flow of the main fractionator 34 Intermediate reflux temperature of the main fractionator

[0118] For the process data in the hydrocracking process, the completed data set was selected and the values ​​in the data set were randomly deleted. Three mainstream missing data completion methods were selected for comparison, namely, improved k-nearest neighbor-based input (KNN), denoising autoencoder (DAE) and generative adversarial network (GAN). The optimal hyperparameters of each method are selected from the set range. The nearest neighbors of KNN are selected from 1 to 5. For DAE, the number of hidden layers is selected from 1 to 5. The number of neurons in each hidden layer is selected in the range of [50,100]. For GAN, the network structure of the generator and the discriminator is the same, both with three layers. The activation function is sigmoid. For the gradient descent algorithm, the batch size is selected in the range of [32,64], the epoch is selected in the range of [800,1200], and the learning rate is selected in the range of [0.01,0.1]. In this experiment, the number of samples s adopted by the online adaptive update of ODBN in this method is set to 10.

[0119] ;

[0120] The experimental results are shown in the table above, where RMSE is the average of 5 repeated experiments. From the results, it can be seen that for different missing rates, the RMSE of ODBN of this method is the smallest, indicating that this method has better performance in processing missing data. The experiment shows that the estimated value provided by this method is very close to the true value, and only a small proportion of the estimated value has deviation.

[0121] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0122] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be construed as limiting the scope of the patent application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent application shall be subject to the attached claims.

Claims

1. A data completion method based on position encoding adaptive deep belief network, characterized in that: The following steps are included Step S1: obtaining a complete data set, the data set being process data of industrial production, randomly deleting values ​​in the data set, and normalizing the data set; dividing the complete data set into a training set and a test set; Step S2: Position-encoding the data of the training set, and combining the data of the training set with the position coding to form a position coding input layer; Step S3: pre-training the position coding adaptive deep belief network based on the position coding input layer to obtain an industrial data completion global model based on the position coding adaptive deep belief network; Step S4: For the test set samples, similar samples are selected from the training set and a similar sample set is formed to quickly fine-tune the global model, and the deep belief network global model is adaptively updated until convergence to obtain the optimal local industrial data completion model; Step S5: sequentially inputting the data in the test set into the optimal local industrial data completion model, and outputting the completed complete test set data; Step S6: Obtain the data set to be completed, select and form a similar sample set from the training set for the samples of the data set to be completed, quickly fine-tune the global model, and adaptively update the deep belief network global model until convergence to obtain the optimal local industrial data completion model; Step S7: inputting the data in the data set to be completed into the optimal local industrial data completion model, and outputting the completed complete data set data; The position code is: ； in, Indicates a The missing sample i Positional encoding of variables; Indicates a The missing sample i variables; Indicates the missing sample i variables with missing values; The position encoding input layer is: ； in, Represents the original input t Missing samples at time instant; Indicates t The position code of the moment; Indicates missing samples With position encoding The concatenated input vector; In step S3, the position-encoded adaptive deep belief network includes a multi-layer restricted Boltzmann machine, and in every two adjacent layers of restricted Boltzmann machines, the hidden layer neuron state of the bottom layer restricted Boltzmann machine is input into the upper layer restricted Boltzmann machine as the newly extracted feature data, and the upper layer restricted Boltzmann machine is trained; The energy function of each restricted Boltzmann machine is: ； in, Represents the state vector of the visible layer, which is also the position encoding input layer; represents the state vector of the hidden layer; Indicates Visible layer units; Indicates The state of each visible layer unit; Indicates The bias of the visible layer unit; Indicates hidden layer units; Indicates The activation states of the hidden layer units; Indicates The bias of the hidden layer units; Represents the connection weight between two layers; Indicates the number of nodes in the visible layer; Represents the number of nodes in the hidden layer.

2. According to claim 1, a data completion method based on position encoding adaptive deep belief network is characterized in that: The training process of the restricted Boltzmann machine includes: Step S3.1: Forward propagate the input data and calculate the activation state of the hidden layer : ； ； The starting value of the summation is Represents the first hidden layer unit Start calculation; Indicates the number of nodes in the hidden layer; Step S3.2: Use the activation state of the hidden unit to reconstruct the visible layer, reconstruct and sample each visible unit to obtain the visible layer : ； ； The starting value of the summation is Indicates that the first visible layer unit Start calculation; Indicates the number of nodes in the visible layer, is the sigmoid function.

3. The data completion method based on position encoding adaptive deep belief network according to claim 2 is characterized in that: The unsupervised pre-training objective function of the restricted Boltzmann machine is: ； in, T represents the number of samples in the training data set, Indicates t training samples.

4. The data completion method based on position encoding adaptive deep belief network according to claim 3 is characterized in that: Reverse fine-tuning methods include: ； ； in, represents the learning rate, Indicates the value of the hidden layer or visible layer; Represents the value of reconstructing the hidden layer or visible layer; represents the initial weight; represents the updated weight; represents the initial hidden layer bias; represents the updated hidden layer bias; represents the initial visible layer bias; Represents the updated visible layer bias.

5. The data completion method based on position encoding adaptive deep belief network according to claim 1, characterized in that: The method steps of updating the position encoding deep belief network model by online adaptive updating include: Step S4.1: Filter out samples to be completed based on feature similarity in the industrial dataset Similar s samples, forming a similar sample set ; Step S4.2: Using similar sample sets The global model is quickly fine-tuned by adjusting model parameters until the model converges on the validation set. The fine-tuned model is determined to be the optimal local industrial data completion model. Step S4.3: Input the sample to be completed into the optimal local industrial data completion model to obtain the completion value.

6. The data completion method based on position encoding adaptive deep belief network according to claim 5, characterized in that: It also includes step S4.4: using the root mean square error to evaluate the data completion performance: The formula for calculating the root mean square error is: ； Among them, RMSE means root mean square error; K Indicates the number of missing values; Indicates k actual missing values; Indicates k estimated missing values.

7. The data completion method based on position encoding adaptive deep belief network according to claim 5, characterized in that: The similar sample set The generation method is: Step S4.1.1: Calculate the samples to be completed Concentrate with historical data The Euclidean distance between each sample : ； Step S4.1.2: Calculate the weight coefficient based on the Euclidean distance : ； Step S4.1.3: sort the weight coefficients in ascending order Arrange from small to large and select the one with the largest weight. s A complete sample of Similar sample sets .

8. The data completion method based on position encoding adaptive deep belief network according to claim 5, characterized in that: The method steps of the rapid fine-tuning include: Step S4.2.1: Similar sample set It is input into the pre-trained global model and the relevant data set is obtained by performing forward propagation from the input layer to the output layer. The completion value of The error loss is calculated and the network parameters are updated using the back propagation algorithm. Step S4.2.2: When the subsequent samples to be completed When you arrive, follow the steps above for The relevant sample selection, online update and completion steps are performed sequentially.

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