Polycrystalline silicon growth weight calculation method based on machine learning

Abstract

The invention discloses a polycrystalline silicon growth weight calculation method based on machine learning, and the method comprises the steps: sorting heat data according to time, unifying the heat data into a time sequence format, filling missing values, and removing low-quality heat data; estimating the diameter and the initial weight of the silicon rod: calculating the estimated diameter of the silicon rod through a simplified model based on the preset parameters and the real-time resistance, and estimating the weight of the silicon rod preliminarily according to the estimated diameter; model training and preliminary prediction: dividing a data set, training a multiple linear regression model to carry out preliminary weight prediction, and evaluating a prediction effect; estimating a prediction residual error of the multiple linear regression model by using a Transform deep learning model; and in combination with the furnace starting weight and the operation time, residual error correction and time weighting processing are carried out on the predicted weight, and a final real-time weight estimation value is obtained. According to the method, a depth model with more parameters is used for extracting time sequence features to fit residual errors, and higher fitting precision is achieved; and in combination with a forward mechanism and time weighted calculation, calculation distortion of the tapping weight is prevented.

Description

Technical Field

[0001] The present invention relates to the technical field of polysilicon growth weight calculation, and in particular to a polysilicon growth weight calculation method based on machine learning. Background Art

[0002] The modified Siemens process is a widely used method in polysilicon production. This method utilizes the principles of chemical vapor deposition (CVD). A cylindrical silicon core is heated electrically in an atmosphere of hydrogen and trichlorosilane. The resulting silicon element is deposited on the core's surface, ultimately producing a sufficiently heavy silicon ingot. The weight of the silicon ingot out of the furnace is a key metric for calculating the power consumption of the ingot and evaluating the quality of each furnace. Therefore, being able to calculate the real-time weight of the ingot allows for more timely control of furnace conditions.

[0003] The shortcomings of the existing technology are that since the deposition reaction time for each furnace can be as long as dozens or even hundreds of hours, and the high-temperature environment inside the furnace is not easy to directly observe, it is difficult to directly obtain the real-time weight of the silicon rods during production. The situation inside the furnace can only be indirectly inferred through other real-time data. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the existing technology. To achieve the above purpose, a polysilicon growth weight calculation method based on machine learning is adopted to solve the problems raised in the above background technology.

[0005] A method for calculating polysilicon growth weight based on machine learning, comprising the following steps:

[0006] Step S1, data preprocessing and standardization: sort the heat data by time, unify them into a time series format, fill missing values ​​and remove low-quality heat data, perform data standardization, and form a data set;

[0007] Step S2, silicon rod diameter and preliminary weight estimation: Based on preset parameters and real-time resistance, the estimated silicon rod diameter is calculated using a simplified model, and the silicon rod weight is preliminarily estimated accordingly;

[0008] Step S3, model training and preliminary prediction: divide the data set, train a multivariate linear regression model for preliminary weight prediction, and evaluate the prediction effect;

[0009] Step S4: Introducing residual estimation and deep learning model: Using the Transformer deep learning model to estimate the prediction residuals of the multivariate linear regression model;

[0010] Step S5, residual correction and final weight estimation: Combined with the furnace start-up weight and operating time, residual correction and time weighting processing are performed on the predicted weight to obtain the final real-time weight estimation value.

[0011] As a further solution of the present invention: the specific steps in step S1 include:

[0012] Each furnace data is sorted in the order of running time to ensure the time sequence of the data;

[0013] All collected point data is converted into a time series format, with the recording interval of each data point set to a fixed time interval, so that each running time point corresponds to a real-time value. For individual missing values ​​in the data, linear interpolation is used to fill in the missing values ​​based on the previous and next data to restore data integrity.

[0014] If the proportion of missing values ​​in the heat data exceeds a preset proportion threshold, the heat data will be removed from the dataset; wherein the point data includes the current and voltage of each phase, the intake flow rate of hydrogen and raw gas, the flow rate of cooling water, the inlet and outlet temperature difference of cooling water, the exhaust gas temperature, and the operating time.

[0015] As a further solution of the present invention, the specific steps of estimating the silicon rod diameter and preliminary weight in step S2 include:

[0016] Step S21: Divide the silicon rods in the polysilicon reduction furnace into m groups, and connect the silicon cores in each group in series to form an electrical phase, and regard them as a uniform columnar conductor;

[0017] According to the preset silicon rod resistivity Silicon rod density And the real-time resistance R, calculate the estimated forward real-time diameter D of the silicon rod, the formula is:

[0018] i=1,…,m, where m is the number of silicon rod phases;

[0019] Step S22: Calculate the forward real-time weight VW based on the obtained diameter using the formula:

[0020]

[0021] in, is the simplified coefficient, V i represents the volume of the i-th phase silicon rod, L i represents the total length of the silicon rod of phase i, R i represents the resistance of the silicon rod of phase i;

[0022] Step S23: Evaluate the weight prediction effect based on the evaluation index on the data set. For each data in the test set, calculate the weight at the time of baking.

[0023] Among them, the evaluation indicators include mean deviation dev, mean absolute error MAE, mean percentage absolute error MAPE, and determination coefficient R 2 ;

[0024] The formula for the evaluation index is:

[0025]

[0026] In the formula, n represents the size of the dataset, represents the mean of the true weight;

[0027] Based on the calculated evaluation indicators, if any one of them is greater than or less than the benchmark value, the weight parameters required are calculated based on the machine learning method;

[0028] Step S24: Calculate the real abbreviation coefficient according to the real out-of-the-box weight W. The formula is:

[0029] Where m is the number of silicon rod phases, L i is the total length of the i-th phase silicon rod, R i is the resistance of the i-th phase silicon rod;

[0030] Step S25, the sensor point data is used to calculate the characteristic data X=[x1, x2…, x6] at the furnace moment;

[0031] Among them, features x1 to x6 are the real-time values ​​of current and voltage, the average value of the previous data of the molar ratio of hydrogen to feed gas, the real-time value of cooling water flow, the real-time value of exhaust gas temperature, and the total length of the silicon core;

[0032] Repeat steps S24 and S25 for the start-up and discharge weights of all heat data and combine them to obtain features X1, X2, ... X n , and the corresponding fitting targets ρ1,ρ2,…,ρ n , a total of n groups of data, that is, the characteristic data of n batches.

[0033] As a further solution of the present invention: the specific steps in step S3 include:

[0034] Step S31: Divide the data set into a preset proportion to obtain a training set X train ,P train , and the test set X test ,P test ;

[0035] Step S32: Construct and train a multiple linear regression model to estimate the true parameter ρ. The estimated value is recorded as

[0036] Set the linear parameters A=[a1,a2,…,ak ], for the parameter estimation equation

[0037] The model is adjusted on the training set using the minimized loss function. The minimized loss function is expected to be:

[0038]

[0039] Among them, p represents the test set size, and np represents the training set size;

[0040] Step S33: Estimate the parameters based on the obtained multiple linear regression model and calculate the parameter estimation weights The formula is:

[0041]

[0042] As a further solution of the present invention: the specific steps in step S4 include:

[0043] Step S41: Based on the transformer-based deep learning model, the residual between the linear model and the true value is calculated using the time series data of each heat. Make estimates;

[0044] Step S42: The trained depth model is used to calculate the residual estimate And calculate the residual correction weight

[0045] As a further solution of the present invention: the specific steps in step S5 include:

[0046] Step S51: Use the furnace starting weight W in Time-weighted correction Get the final weight estimate

[0047] Calculate the weight at furnace start-up based on silicon core specifications using the following formula:

[0048]

[0049] Among them, V in Indicates the total volume of silicon core at furnace start-up, S i Indicates the cross-sectional area of ​​the single-phase silicon core at furnace startup.

[0050] Step S52: The weighted correction formula based on the running time is:

[0051]

[0052] Among them, t *Indicates the weight correction time limit;

[0053] The final calculation This is the final estimated real-time weight.

[0054] Compared with the prior art, the present invention has the following technical effects:

[0055] The above-mentioned technical solution uses sensor data related to weight to calculate the weight of silicon ingots in real time. For resistivity and density parameters that cannot be measured during the deposition process, this method uses multiple linear regression to fit the parameters and ensure model smoothness. A transformer model, capable of extracting time series features, is then used to correct residuals. Finally, the calculated weight is calculated by weighting the out-of-battery weight by time.

[0056] Compared to previous fixed-parameter forward calculation methods, this method uses real-world data to modify parameters, improving the accuracy of out-of-baked weight predictions. It also uses a deep model with more parameters to extract time series features to fit the residuals, resulting in higher fitting accuracy. Furthermore, it combines forward mechanics with time-weighted calculations to prevent distortion in out-of-baked weight calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The specific embodiments of the present invention are described in detail below with reference to the accompanying drawings:

[0058] Figure 1 This is a schematic diagram of the steps of the weight calculation method disclosed in the embodiment of this application. DETAILED DESCRIPTION

[0059] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0060] Please refer to Figure 1 In an embodiment of the present invention, a method for calculating the growth weight of polysilicon based on machine learning includes the following steps:

[0061] Step S1, data preprocessing and standardization: sort the heat data by time, unify them into a time series format, fill missing values, remove low-quality heat data, and perform data standardization to form a data set. The specific steps include:

[0062] Each furnace data is sorted in the order of running time to ensure the time sequence of the data;

[0063] All collected point data is converted into a time series format, with the recording interval of each data point set to a fixed time interval, so that each running time point corresponds to a real-time value. For individual missing values ​​in the data, linear interpolation is used to fill in the missing values ​​based on the previous and next data to restore data integrity.

[0064] If the proportion of missing values ​​in the heat data exceeds a preset proportion threshold, the heat data will be removed from the dataset; wherein the point data includes the current and voltage of each phase, the intake flow rate of hydrogen and raw gas, the flow rate of cooling water, the inlet and outlet temperature difference of cooling water, the exhaust gas temperature, and the operating time.

[0065] In the specific implementation steps, the acquired heat data is standardized. For each heat data entry, the data is sorted from smallest to largest by run time. All collected point data is in time series format, recorded at a step interval (set to 1 minute in this example), with each run time corresponding to a real-time value for the point data. If individual missing values ​​exist, linear interpolation is used based on the preceding and following data. Heats with missing data exceeding a certain percentage (20% in this example) are removed to ensure data quality.

[0066] Step S2, silicon rod diameter and preliminary weight estimation: Based on preset parameters and real-time resistance, the estimated silicon rod diameter is calculated using a simplified model, and the silicon rod weight is preliminarily estimated accordingly;

[0067] The specific steps for estimating the diameter and preliminary weight of silicon rods include:

[0068] Step S21: Divide the silicon rods in the polysilicon reduction furnace into m groups, and connect the silicon cores in each group in series to form an electrical phase, and regard them as a uniform columnar conductor;

[0069] According to the preset silicon rod resistivity Silicon rod density And the real-time resistance R, calculate the estimated forward real-time diameter D of the silicon rod, the formula is:

[0070]

[0071] In the specific implementation steps, since the silicon rods in the polysilicon reduction furnace are divided into m groups, the silicon cores in the group are connected in series to form an electrical phase through beams and electrodes, and the length and thickness specifications of the silicon cores and beams are relatively uniform, the combination of the silicon cores and beams of a single electrical phase can be regarded as a uniform columnar conductor, thereby simplifying the calculation.

[0072] In this embodiment, the reduction furnace is divided into 6 electrical phases, each of which contains 4-8 pairs of silicon cores and a corresponding number of beams. The silicon core lengths are available in two specifications: 3000mm or 3200mm, and the beam length is 270mm. Therefore, the calculated total lengths of the 6-phase silicon cores are different, which requires the weight of the 6-phase silicon cores to be calculated separately.

[0073] For the data of one heat, the total length of the silicon rod of phase i is L i , the real-time resistance is R i , i=1,2,…,m, m is the number of silicon rod phases.

[0074] Preset silicon rod density and silicon rod resistivity Calculate the forward real-time diameter of the silicon rod: i=1,…,m, where m is the number of silicon rod phases.

[0075] In this embodiment, it is assumed that the furnace temperature is 1050°C, so the preset silicon rod density is 2.33g / cm 3 , the preset silicon rod resistivity is 0.0973Ω·mm.

[0076] Step S22: Calculate the forward real-time weight based on the obtained diameter The formula is:

[0077]

[0078] in, is the simplified coefficient, V i represents the volume of the i-th phase silicon rod, L i represents the total length of the silicon rod of phase i, R i represents the resistance of the silicon rod of phase i;

[0079] Step S23: Evaluate the weight prediction effect based on the evaluation index on the data set. For each data in the test set, calculate the weight at the time of baking.

[0080] Among them, the evaluation indicators include mean deviation dev, mean absolute error MAE, mean percentage absolute error MAPE, and determination coefficient R 2 ;

[0081] The formula for the evaluation index is:

[0082]

[0083] In the formula, n represents the size of the dataset, represents the mean of the true weight;

[0084] Based on the calculated evaluation indicators, if any one of them is greater than or less than the benchmark value, the weight parameters required are calculated based on the machine learning method;

[0085] In this embodiment, the dev reference value is 20, the MAE reference value is 750, the MAPE reference value is 7%, and the R 2 The baseline value is 0.5.

[0086] Step S24: Calculate the real abbreviation coefficient according to the real out-of-the-box weight W. The formula is:

[0087] Where m is the number of silicon rod phases, L i is the total length of the silicon rod of phase i, R i is the resistance of the silicon rod of phase i;

[0088] Step S25, the sensor point data is used to calculate the characteristic data X=[x1, x2…, x6] at the furnace moment;

[0089] Among them, features x1 to x6 are the real-time values ​​of current and voltage, the average value of the previous data of the molar ratio of hydrogen to feed gas, the real-time value of cooling water flow, the real-time value of exhaust gas temperature, and the total length of the silicon core;

[0090] Repeat steps S24 and S25 for the start-up and discharge weights of all heat data and combine them to obtain features X1, X2, ... X n , and the corresponding fitting targets ρ1,ρ2,…,ρ n , a total of n groups of data, that is, the characteristic data of n batches.

[0091] Step S3, model training and preliminary prediction: divide the data set, train a multivariate linear regression model for preliminary weight prediction, and evaluate the prediction effect. The specific steps include:

[0092] Step S31: Divide the data set into a preset proportion to obtain a training set X train ,P train , and the test set X test ,P test ;

[0093] In this embodiment, the proportion of the training set is 70%, and the proportion of the test set is 30%;

[0094] Step S32: Construct and train a multiple linear regression model to estimate the true parameter ρ. The estimated value is recorded as

[0095] Set the linear parameters A=[a1,a2,…,a k ], for the parameter estimation equation

[0096] The model is adjusted on the training set using the minimized loss function. The minimized loss function is expected to be:

[0097]

[0098] Among them, p represents the test set size, and np represents the training set size;

[0099] Step S33: Estimate the parameters based on the obtained multiple linear regression model and calculate the parameter estimation weights The formula is:

[0100]

[0101] Step S4: Introducing residual estimation and deep learning model: Use the Transformer deep learning model to estimate the prediction residuals of the multivariate linear regression model. The specific steps include:

[0102] Step S41: Based on the transformer-based deep learning model, the residual between the linear model and the true value is calculated using the time series data of each heat. Make estimates;

[0103] Step S42: The depth model trained in the subsequent steps is used to calculate the residual estimate And calculate the residual correction weight

[0104] In the specific implementation steps, due to the model's restrictions on the input format, the length of the time series data of each heat needs to be limited to max_len. In this embodiment, it is 512.

[0105] For approximately 100 hours of minute-level heat data, we first convert the time interval to 12 minutes by taking the average of the equal intervals, so that the total number of data points is around 500. If the heat data length exceeds max_len, the leading data is truncated. If the length is less than max_len, the end is padded with zeros to ensure the input sequence length is fixed.

[0106] Since the model needs to perform positional encoding on the runtime, the model input needs to be added with the relative position corresponding to the runtime, starting from 0 and with a length of max_len, in the form of [0, 1, ..., 511].

[0107] If there is truncation, start from the relative position corresponding to the initial running time.

[0108] The final model input format:

[0109] Matrix Z of dimension (c+1)×max_len i,i=1,2,…,np, and fitting target E=[∈1,∈2,…,∈ n-p ]. For the input matrix Z, the first row is the relative position, and the remaining c rows are the features in time series form.

[0110] Configure model hyperparameters and train to obtain the deep model D(·), and estimate the residual Set hyperparameters such as the number of attention heads head_num, the hidden vector dimension hidden_dim, and the number of hidden layers hidden_layers, and select the optimizer to train the depth model D(·) to minimize the expected loss function.

[0111] In this implementation, head_num=8, hidden_dim=64, hidden_layers=8, AdamW is selected as the optimizer, and other settings are set according to the model default options.

[0112] Calculate residual corrected weight

[0113] Step S5, residual correction and final weight estimation: Combined with the furnace start-up weight and operating time, residual correction and time weighting are performed on the predicted weight to obtain the final real-time weight estimate. The specific steps include:

[0114] Step S51: Use the furnace starting weight W in Time-weighted correction Get the final weight estimate

[0115] In this embodiment, since the training data are all the weights out of the furnace, it is bound to cause underfitting of the previous weights, so the weight at the time of furnace startup is used to correct the real-time calculated weight.

[0116] Calculate the weight at furnace start-up based on silicon core specifications using the following formula:

[0117]

[0118] Among them, V in Indicates the total volume of silicon core at furnace start-up, S i Indicates the cross-sectional area of ​​the single-phase silicon core at furnace startup.

[0119] Step S52: The weighted correction formula based on the running time is:

[0120]

[0121] Among them, t * Indicates the weight correction time limit;

[0122] The final calculation This is the final estimated real-time weight.

[0123] Although the embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations may be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents, and all should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the growth weight of polysilicon based on machine learning, characterized in that: The following steps are involved: Step S1, data preprocessing and standardization: sort the heat data by time, unify them into a time series format, fill in missing values ​​and remove low-quality heat data, perform data standardization, and form a data set; Step S2, silicon rod diameter and preliminary weight estimation: based on preset parameters and real-time resistance, the estimated silicon rod diameter is calculated by a simplified model, and the weight of the silicon rod is preliminarily estimated accordingly; Step S3, model training and preliminary prediction: divide the data set, train the multivariate linear regression model for preliminary weight prediction, and evaluate the prediction effect; Step S4, introducing residual estimation and deep learning model: using the Transformer deep learning model to estimate the prediction residual of the multivariate linear regression model; Step S5, residual correction and final weight estimation: Combined with the furnace start-up weight and operating time, residual correction and time-weighted processing are performed on the predicted weight to obtain the final real-time weight estimate.

2. The method for calculating the growth weight of polysilicon based on machine learning according to claim 1, characterized in that: The specific steps in step S1 include: Each furnace data is sorted in the order of running time to ensure the time sequence of the data; All collected point data are converted into time series form, and the recording interval of each data point is set to a fixed time interval, so that each running time point corresponds to a real-time value; for individual missing values ​​in the data, linear interpolation method is used to fill in based on the previous and next data to restore the integrity of the data; If the proportion of missing values ​​in the furnace data exceeds the preset ratio threshold, the furnace data will be removed from the data set; wherein the point data includes the current and voltage of each phase, the intake flow rate of hydrogen and raw gas, the flow rate of cooling water, the inlet and outlet temperature difference of cooling water, the exhaust gas temperature, and the operating time.

3. The method for calculating the growth weight of polysilicon based on machine learning according to claim 1, characterized in that: The specific steps of estimating the diameter and preliminary weight of the silicon rod in step S2 include: Step S21, dividing the silicon rods in the polysilicon reduction furnace into m groups, wherein the silicon cores in the groups are connected in series to form an electrical phase and regarded as a uniform columnar conductor; According to the preset silicon rod resistivity Silicon rod density And the real-time resistance r, calculate the estimated real-time forward diameter D of the silicon rod, the formula is: Step S22: Calculate the forward real-time weight based on the obtained diameter The formula is: in, is the simplified coefficient, V i represents the volume of the i-th phase silicon rod, L i represents the total length of the i-th phase silicon rod, R i represents the resistance of the i-th phase silicon rod; Step S23: Evaluate the weight prediction effect based on the evaluation index on the data set, and calculate the weight at the time of baking for each data in the test set. The evaluation indicators include mean deviation dev, mean absolute error MAE, mean percentage absolute error MAPE, and determination coefficient R 2 ; The formula for the evaluation index is: In the formula, n represents the size of the data set, represents the mean of the true weight; According to the calculated evaluation indicators, if one of them is greater than or less than the benchmark value, the parameters required for weight are calculated based on the machine learning method; Step S24, calculate the real simplified coefficient according to the real out-of-the-box weight W, the formula is: Where m is the number of silicon rod phases, L i is the total length of the i-th phase silicon rod, R i is the resistance of the i-th phase silicon rod; Step S25, the sensor point data calculates the characteristic data X=[x1, x2…, x6] at the furnace time; Among them, features x1 to x6 are the real-time values ​​of current and voltage, the average value of the previous data of the molar ratio of hydrogen and raw gas, the real-time value of cooling water flow, the real-time value of tail gas temperature, and the total length of the silicon core; Repeat steps S24 and S25 for the start-up and discharge weights of all heat data and combine them to obtain features X1, X2, ... X n , and the corresponding fitting targets ρ1,ρ2,…,ρ n , a total of n groups of data, that is, the characteristic data of n furnaces.

4. The method for calculating the growth weight of polysilicon based on machine learning according to claim 3, characterized in that: The specific steps in step S3 include: Step S31: Divide the data set according to a preset ratio to obtain a training set X train ,P train , and the test set X test ,P test ; Step S32: construct and train a multivariate linear regression model to estimate the true parameters. The estimated values ​​are recorded as Set the linear parameters A = [a1, a2, ..., a k ], for the parameter estimation equation The model is adjusted on the training set using the minimized loss function, and the minimized loss function is expected to be: Among them, p represents the test set size, and np represents the training set size; Step S33: Estimate the parameters based on the obtained multivariate linear regression model And calculate the parameter estimation weight The formula is:

5. The method for calculating the growth weight of polysilicon based on machine learning according to claim 1, characterized in that: The specific steps in step S4 include: Step S41: Based on the transformer-based deep learning model, the residual between the linear model and the true value is calculated using the time series data of each furnace. Make estimates; Step S42: The trained deep model is used to calculate the residual estimate And calculate the residual correction weight 6. The method for calculating the growth weight of polysilicon based on machine learning according to claim 1, characterized in that: The specific steps in step S5 include: Step S51: Use the furnace start-up weight W in Time-weighted correction Get the final weight estimate Calculate the weight at furnace start-up according to silicon core specifications, the formula is: Among them, V in Indicates the total volume of silicon core at furnace start-up, S i Indicates the cross-sectional area of ​​the single-phase silicon core at furnace startup. Step S52: The weighted correction formula according to the running time is: Among them, t * Indicates the weight correction time limit; The final calculated This is the final estimated real-time weight.

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