A machine learning-based multi-crystalline silicon growth weight calculation method

Abstract

This invention discloses a machine learning-based method for calculating the weight of polycrystalline silicon growth, including: sorting furnace data by time, unifying it into a time-series format, filling missing values, and removing low-quality furnace data; silicon rod diameter and preliminary weight estimation: based on preset parameters and real-time resistance, the estimated diameter of the silicon rod is calculated through a simplified model, and the weight of the silicon rod is initially estimated accordingly; model training and preliminary prediction: the dataset is divided, a multiple linear regression model is trained to perform preliminary weight prediction, and the prediction effect is evaluated; a Transformer deep learning model is used to estimate the prediction residuals of the multiple linear regression model; combining the furnace start-up weight and running time, the predicted weight is subjected to residual correction and time-weighted processing to obtain the final real-time weight estimate. This invention uses a deep model with more parameters to extract time-series features to fit the residuals, resulting in higher fitting accuracy; it also combines a forward mechanism and time-weighted calculation to prevent distortion in the calculation of the furnace output weight.

Description

Technical Field

[0001] This invention relates to the field of polycrystalline silicon growth weight calculation technology, and in particular to a polycrystalline silicon growth weight calculation method based on machine learning. Background Technology

[0002] The modified Siemens process is a widely used method in polysilicon production. This method utilizes the principle of chemical vapor deposition, where a cylindrical silicon core is electrically heated in a hydrogen and trichlorosilane atmosphere, causing elemental silicon produced by the chemical reaction to deposit on the core surface, ultimately yielding a silicon rod of sufficient weight. The furnace weight of the silicon rod is a core indicator for calculating the power consumption per rod and evaluating the quality of a furnace run; therefore, if the real-time weight of the silicon rod can be calculated, furnace conditions can be adjusted more promptly.

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

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

[0005] A machine learning-based method for calculating the weight of polycrystalline silicon growth includes the following steps:

[0006] Step S1, Data Preprocessing and Standardization: Sort the furnace data by time, unify it into a time series format, fill in missing values ​​and remove low-quality furnace data, perform data standardization, and form a dataset;

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

[0008] Step S3, Model Training and Preliminary Prediction: Divide the dataset, train the multiple linear regression model to make preliminary weight predictions, and evaluate the prediction results;

[0009] Step S4: Introduce residual estimation and deep learning model: Use the Transformer deep learning model to estimate the prediction residuals of the multiple linear regression model;

[0010] Step S5, Residual Correction and Final Weight Estimation: Combining the start-up weight and running time, the predicted weight is corrected for residuals and time-weighted to obtain the final real-time weight estimate.

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

[0012] For each furnace data entry, the data is sorted according to the order of its execution time to ensure the timeliness of the data.

[0013] All collected point data are converted into time series format, and the recording interval for 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, a linear interpolation method is used to fill in the missing values ​​based on the preceding and following data to restore the integrity of the data.

[0014] If the proportion of missing values ​​in the furnace data exceeds a preset threshold, the furnace data will be removed from the dataset. The data points include the current and voltage of each phase, the inlet flow rate of hydrogen and feed gas, the flow rate of cooling water, the temperature difference between the inlet and outlet of cooling water, the tail gas temperature, and the operating time.

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

[0016] Step S21: Divide the silicon rods in the polycrystalline silicon reduction furnace into m groups, and connect the silicon cores in the group in series to form an electrical phase, and regard it as a uniform cylindrical conductor.

[0017] Based on the preset silicon rod resistivity Silicon rod density And based on the real-time resistance R, the estimated forward real-time diameter D of the silicon rod is calculated using the following formula:

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

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

[0020]

[0021] in, For the simplified notation of coefficients, V i L represents the volume of the silicon rod in phase i. i R represents the total length of the silicon rod in phase i. i This represents the resistance of the silicon rod in phase i;

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

[0023] The evaluation metrics include mean deviation (dev), mean absolute error (MAE), mean percentage absolute error (MAPE), and coefficient of determination (R²). 2 ;

[0024] The formula for the evaluation metrics is:

[0025]

[0026] In the formula, n represents the size of the dataset. This represents the average of the actual weights.

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

[0028] Step S24: Calculate the true simplified coefficient based on the actual furnace weight W. The formula is:

[0029] Where m is the number of phases of the silicon rod, L i R is the total length of the silicon rod in phase i. i Let be the resistance of the silicon rod in phase i;

[0030] Step S25: Calculate the characteristic data X = [x1, x2, ..., x6] from the sensor location data at the furnace time;

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

[0032] Repeat steps S24 and S25 for the start-up and tapping weights of all furnaces and combine them to obtain features X1, X2, ... X n And the corresponding fitting targets ρ1, ρ2, ..., ρ n There are a total of n sets of data, which are the characteristic data of n furnace cycles.

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

[0034] Step S31: Divide the dataset according to a preset ratio to obtain the training set X. train ,P train and test set X test ,P test ;

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

[0036] Set the linear parameter A = [a1, a2, ..., a...]k For parameter estimation equations

[0037] The model is tuned on the training set by minimizing the loss function, and the expected value of the minimized loss function is:

[0038]

[0039] Where p represents the size of the test set and np represents the size of the training set;

[0040] Step S33: Estimate the parameters based on the obtained multiple linear regression model. And calculate parameters to estimate weight The formula is:

[0041]

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

[0043] Step S41: Based on the transformer-based deep learning model, use the time series data of each batch to compare the residuals between the linear model and the true values. Make an estimate;

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

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

[0046] Step S51, use the furnace start-up weight W in Time-weighted adjustment To obtain the final weight estimate

[0047] The formula for calculating the furnace start-up weight based on silicon core specifications is as follows:

[0048]

[0049] Among them, V in S represents the total volume of the silicon core at the time of furnace startup. i This indicates the cross-sectional area of ​​the single-phase silicon core when the furnace is started.

[0050] Step S52: The time-weighted correction formula is as follows:

[0051]

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

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

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

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

[0056] Compared to previous fixed-parameter forward calculation methods, this method uses real furnace output data to correct parameters, improving the prediction accuracy of furnace output weight. Furthermore, it uses a deep model with more parameters to extract time-series features to fit the residuals, resulting in higher fitting accuracy. Additionally, it combines forward mechanism and time-weighted calculation to prevent distortion in the calculation of furnace output weight. Attached Figure Description

[0057] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings:

[0058] Figure 1 This is a schematic diagram illustrating the steps of a weight calculation method according to an embodiment of this application. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

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

[0061] Step S1, Data Preprocessing and Standardization: Sort the furnace data by time, unify it into a time-series format, fill in missing values ​​and remove low-quality furnace data, perform data standardization, and form a dataset. Specific steps include:

[0062] For each furnace data entry, the data is sorted according to the order of its execution time to ensure the timeliness of the data.

[0063] All collected point data are converted into time series format, and the recording interval for 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, a linear interpolation method is used to fill in the missing values ​​based on the preceding and following data to restore the integrity of the data.

[0064] If the proportion of missing values ​​in the furnace data exceeds a preset threshold, the furnace data will be removed from the dataset. The data points include the current and voltage of each phase, the inlet flow rate of hydrogen and feed gas, the flow rate of cooling water, the temperature difference between the inlet and outlet of cooling water, the tail gas temperature, and the operating time.

[0065] In the specific implementation steps, the format of the acquired furnace data is standardized. For each furnace data entry, the data is arranged in ascending order of runtime. All data from the collection points are in time-series format, with a recording interval of steps (set to 1 minute in this embodiment). Each runtime corresponds to a real-time value for a data point. If there are any missing values, linear interpolation is used to fill them in using the preceding and following data. For furnaces where the proportion of missing data exceeds a certain percentage (20% in this embodiment), the data for that furnace is removed to ensure dataset quality.

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

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

[0068] Step S21: Divide the silicon rods in the polycrystalline silicon reduction furnace into m groups, and connect the silicon cores in the group in series to form an electrical phase, and regard it as a uniform cylindrical conductor.

[0069] Based on the preset silicon rod resistivity Silicon rod density And based on the real-time resistance R, the estimated forward real-time diameter D of the silicon rod is calculated using the following formula:

[0070]

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

[0072] In this embodiment, the reduction furnace is divided into 6 electrical phases. Each electrical phase contains 4-8 pairs of silicon cores and a corresponding number of crossbeams. The silicon cores have two specifications: 3000mm or 3200mm in length, and the crossbeams are 270mm long. Therefore, the total length of the 6-phase silicon cores is different for each phase, which means that the weight of the 6-phase silicon cores needs to be calculated separately.

[0073] For data from a single furnace cycle, let the total length of the silicon rod in the i-th phase be L. i The real-time resistance is R i , i = 1, 2, ..., m, where m is the number of phases of the silicon rod.

[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 phases of the silicon rod.

[0075] In this embodiment, the furnace temperature is assumed to be 1050℃, so the silicon rod density is preset to be 2.33 g / cm³. 3 The preset resistivity of the silicon rod is 0.0973 Ω·mm.

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

[0077]

[0078] in, For the simplified notation of coefficients, V i L represents the volume of the silicon rod in phase i. i R represents the total length of the silicon rod in phase i. i This represents the resistance of the silicon rod in phase i;

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

[0080] The evaluation metrics include mean deviation (dev), mean absolute error (MAE), mean percentage absolute error (MAPE), and coefficient of determination (R²). 2 ;

[0081] The formula for the evaluation metrics is:

[0082]

[0083] In the formula, n represents the size of the dataset. This represents the average of the actual weights.

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

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

[0086] Step S24: Calculate the true simplified coefficient based on the actual furnace weight W. The formula is:

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

[0088] Step S25: Calculate the characteristic data X = [x1, x2, ..., x6] from the sensor location data at the furnace time;

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

[0090] Repeat steps S24 and S25 for the start-up and tapping weights of all furnaces and combine them to obtain features X1, X2, ... X n And the corresponding fitting targets ρ1, ρ2, ..., ρ n There are a total of n sets of data, which are the characteristic data of n furnace cycles.

[0091] Step S3, Model Training and Preliminary Prediction: Divide the dataset, train the multiple linear regression model to perform preliminary weight prediction, and evaluate the prediction performance. Specific steps include:

[0092] Step S31: Divide the dataset according to a preset ratio to obtain the training set X. train ,P train and 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, and denote the estimated value as ρ.

[0095] Set the linear parameter A = [a1, a2, ..., a...] k For parameter estimation equations

[0096] The model is tuned on the training set by minimizing the loss function, and the expected value of the minimized loss function is:

[0097]

[0098] Where p represents the size of the test set and np represents the size of the training set;

[0099] Step S33: Estimate the parameters based on the obtained multiple linear regression model. And calculate parameters to estimate weight The formula is:

[0100]

[0101] Step S4: Introducing Residual Estimation and Deep Learning Model: The Transformer deep learning model is used to estimate the prediction residuals of the multiple linear regression model. Specific steps include:

[0102] Step S41: Based on the transformer-based deep learning model, use the time series data of each batch to compare the residuals between the linear model and the true values. Make an estimate;

[0103] Step S42: The deep model trained in 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 limitations on the input format, the length of the time series data for each batch needs to be limited to max_len. In this embodiment, it is set to 512.

[0105] For approximately 100 hours of minute-level furnace data, the time intervals are first averaged to convert them to 12 minutes, resulting in a total of around 500 data points. If the furnace data length exceeds `max_len`, the first few data points are truncated; if the length is less than `max_len`, zeros are added to the end to ensure a fixed input sequence length.

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

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

[0108] Final model input format:

[0109] A matrix Z of dimension (c+1)×max_len iLet i = 1, 2, ..., np, and the fitting objective E = [∈1, ∈2, ..., ∈ n-p For the input matrix Z, the first row represents the relative positions, and the remaining c rows represent the features in temporal form.

[0110] Configure the model hyperparameters and train the deep model D(·), then estimate the residuals. 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 an optimizer to train the deep model D(·), minimizing the expected loss function.

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

[0112] Calculate the corrected weight of the residual

[0113] Step S5, Residual Correction and Final Weight Estimation: Combining the start-up weight and running time, the predicted weight is corrected for residuals and time-weighted to obtain the final real-time weight estimate. Specific steps include:

[0114] Step S51, use the furnace start-up weight W in Time-weighted adjustment To obtain the final weight estimate

[0115] In this embodiment, since the training data are all the weights produced after the furnace, it will inevitably lead to underfitting of the previous weights. Therefore, the weight at the time of furnace start-up is used to correct the calculated weight in real time.

[0116] The formula for calculating the furnace start-up weight based on silicon core specifications is as follows:

[0117]

[0118] Among them, V in S represents the total volume of the silicon core at the time of furnace startup. i This indicates the cross-sectional area of ​​the single-phase silicon core when the furnace is started.

[0119] Step S52: The time-weighted correction formula is as follows:

[0120]

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

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

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

Claims

1. A method for calculating the weight of polycrystalline silicon growth based on machine learning, characterized in that, Includes the following steps: Step S1, Data Preprocessing and Standardization: Sort the furnace data by time, unify it into a time series format, fill in missing values ​​and remove low-quality furnace data, perform data standardization, and form a dataset; Step S2, Silicon rod diameter and preliminary weight estimation: Based on preset parameters and real-time resistance, the estimated diameter of the silicon rod is calculated by a simplified model, and the weight of the silicon rod is estimated accordingly. The specific steps for estimating the diameter and preliminary weight of the silicon rod in step S2 include: Step S21: Divide the silicon rods in the polycrystalline silicon reduction furnace into... The silicon cores within the group are connected in series to form an electrical phase and are considered as a uniform cylindrical conductor. Based on the preset silicon rod resistivity Silicon rod density And real-time resistance, to calculate the estimated forward real-time diameter of the silicon rod. The formula is: , This represents the number of phases of the silicon rod. Step S22: Calculate the forward real-time weight based on the obtained diameter. The formula is: in, To simplify the notation of coefficients, Indicates the first The volume of the silicon rod, Indicates the first The total length of the silicon rod, Indicates the first The resistance of the silicon rod; Step S23: Evaluate the weight prediction effect on the dataset based on evaluation metrics. For each data point in the dataset, calculate the weight at the time of baking. ; The evaluation indicators include average deviation. Mean absolute error Mean percentage absolute error and the coefficient of determination ; The formula for the evaluation metrics is: ； ； ； ； In the formula, Indicates the size of the dataset. This represents the average of the actual weights. Indicates the actual weight value; Based on the calculated evaluation indicators, if any one of them is greater than or less than the benchmark value, the parameters required for weight are calculated based on machine learning methods. Step S24: Based on the actual weight after baking The formula for calculating the true simplified coefficient is as follows: ; in, For the number of phases of a silicon rod, For the first The total length of the silicon rod, For the first The resistance of the silicon rod; Step S25: Calculate the characteristic data of the furnace exit time from the sensor location data. ; Among them, features arrive These are the real-time values ​​of current and voltage, the average value of the preceding data for the molar ratio of hydrogen and feed gas, the real-time value of cooling water flow rate, the real-time value of exhaust gas temperature, and the total length of the silicon core. Repeat steps S24 and S25 and combine them for the start-up and tapping weights of all furnaces to obtain the characteristic. and the corresponding fitting target ,total Group data, i.e. Characteristic data of each furnace batch; Step S3, Model Training and Preliminary Prediction: Divide the dataset, train the multiple linear regression model to make preliminary weight predictions, and evaluate the prediction results; Step S4: Introduce residual estimation and deep learning model: Use the Transformer deep learning model to estimate the prediction residuals of the multiple linear regression model; Step S5, Residual Correction and Final Weight Estimation: Combining the start-up weight and running time, the predicted weight is corrected for residuals and time-weighted to obtain the final real-time weight estimate.

2. The method for calculating the weight of polycrystalline silicon growth based on machine learning according to claim 1, characterized in that, The specific steps in step S1 include: For each furnace data entry, the data is sorted according to the order of its execution time to ensure the timeliness of the data. All collected point data are converted into time series format, and the recording interval for 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, a linear interpolation method is used to fill in the missing values ​​based on the preceding and following data to restore the integrity of the data. If the proportion of missing values ​​in the furnace data exceeds a preset threshold, the furnace data will be removed from the dataset. The data points include the current and voltage of each phase, the inlet flow rate of hydrogen and feed gas, the flow rate of cooling water, the temperature difference between the inlet and outlet of cooling water, the tail gas temperature, and the operating time.

3. The method for calculating the weight of polycrystalline silicon growth based on machine learning according to claim 1, characterized in that, The specific steps in step S3 include: Step S31: Divide the dataset according to a preset ratio to obtain the training set. and test set ; Step S32: Construct and train a multiple linear regression model to estimate the true parameters. The estimated value is denoted as ; Set linear parameters For parameter estimation equations ; The model is tuned on the training set by minimizing the loss function, which is: ； in, Indicates the size of the test set. Indicates the size of the training set; Step S33: Estimate the parameters based on the obtained multiple linear regression model. And calculate parameters to estimate weight The formula is: 。 4. The method for calculating the weight of polycrystalline silicon growth 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, use the time series data of each batch to compare the residuals between the linear model and the true values. Make an estimate; Step S42: The trained deep model is used to calculate the residual estimate. And calculate the residual correction weight. .

5. The method for calculating the weight of polycrystalline silicon growth 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 Time-weighted adjustment This yields the final weight estimate. ; The formula for calculating the furnace start-up weight based on silicon core specifications is as follows: ； in, This indicates the total volume of the silicon core at the time of furnace startup. This indicates the cross-sectional area of ​​the single-phase silicon core at the time of furnace startup. Step S52: The time-weighted correction formula is as follows: ； in, Indicates the weight correction time limit; Final calculation This is the final estimated real-time weight.

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