A silicon carbide wafer production line performance prediction method based on theoretical model and data driving fusion
By combining theoretical models and data-driven methods on a silicon carbide wafer production line, and utilizing queuing theory and Bi-LSTM neural networks, the problems of long training time and low accuracy of prediction models were solved, achieving efficient and accurate performance prediction and providing a reference for production optimization and scheduling.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
- Filing Date
- 2023-03-20
- Publication Date
- 2026-06-09
AI Technical Summary
Existing technologies make it difficult to establish accurate performance prediction models on silicon carbide wafer production lines. Directly using raw data for prediction leads to excessively long training times and low accuracy. Traditional dimensionality reduction algorithms have poor interpretability.
We employ a method that combines theoretical models with data-driven approaches. We establish a theoretical model of a silicon carbide wafer production line using queuing theory, extract statistical parameters that affect performance, and transform directly collected data into these statistical data for dimensionality reduction. Then, we combine this data with a Bi-LSTM neural network for prediction.
It improves the accuracy and training efficiency of prediction models, provides highly interpretable performance metrics, and can scientifically guide production optimization and scheduling.
Smart Images
Figure CN116720599B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent manufacturing technology, and in particular to a production line performance prediction technology, specifically a method for predicting the performance of a silicon carbide wafer production line based on the fusion of theoretical models and data-driven approaches. Background Technology
[0002] Third-generation semiconductor materials such as silicon carbide are in high demand in aerospace, 5G communications, and automotive electronics. However, due to the high hardness and brittleness of silicon carbide, its production suffers from low efficiency and poor quality stability. Furthermore, the complex processes, mixed-product workflows, reflow processing, stringent quality control, and high levels of automation in semiconductor wafer production lines make production planning, scheduling, work-in-process control, and production optimization difficult, severely hindering capacity expansion. Performance prediction of the production line is fundamental to production line management; therefore, rapidly obtaining production line performance indicators is essential.
[0003] Currently, there are three main methods for modeling production line performance prediction: mathematical modeling, simulation modeling, and data-driven methods. Mathematical modeling-based methods require a deep understanding of the specific production line's processes and operating mechanisms, enabling the acquisition of accurate solutions for production line performance. However, the significantly increased complexity of silicon carbide wafer processing production lines makes it difficult to establish accurate mathematical models for production line performance prediction. Simulation modeling simplifies the actual production process, but many unknown factors cannot be considered during simulation. In large-scale, complex, and variable production lines like silicon carbide wafer lines, satisfactory models are almost impossible to obtain. Data-driven methods require a large amount of historical data as the basis for the prediction model, but they have strong nonlinear fitting capabilities and do not require attention to the system's internal mechanisms, making them widely used in various production variable prediction problems. However, the raw data collected directly from the production line has a huge dimensionality, and using it directly as input data for prediction leads to excessively long training times and affects prediction accuracy. Therefore, a method is needed to reduce the dimensionality of the input data. Traditional dimensionality reduction algorithms mostly use mathematical statistics to find correlations between variables. This method has poor interpretability and ignores the theoretical relationships between variables. Therefore, it is necessary to propose a prediction method that integrates theoretical models and data-driven models. Summary of the Invention
[0004] The purpose of this invention is to address the problem that raw data collected directly from the production line has a huge dimensionality, leading to excessively long training times and affecting prediction accuracy when used directly as input data for prediction. This invention provides a performance prediction model for silicon carbide wafer production lines based on a fusion of theoretical models and data-driven approaches. The production line performance prediction model provided by this invention extracts and summarizes statistical parameters affecting production line performance from the theoretical model, transforming the directly collected production line data into these statistical data to reduce the dimensionality of the input data, thereby improving the accuracy of the prediction model and reducing training time.
[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0006] A performance prediction method for silicon carbide wafer production lines based on the fusion of theoretical models and data-driven approaches, comprising the following steps:
[0007] Step 1: Specify the production line performance indicators of the silicon carbide wafer processing production line and the state parameters that affect them, as the input and output of the feature parameters of the data model;
[0008] Step 2: Collect historical data on the production line performance indicators and influencing factors mentioned in Step 1 from the silicon carbide wafer processing production line; model the production line based on queuing theory to obtain a theoretical model, and perform dimensionality reduction processing on the characteristic parameters;
[0009] Step 3: Normalize the input and output data of the dimensionality-reduced feature parameters from Step 2; select appropriate memory step size and prediction step size to construct a time series dataset suitable for Bi-LSTM;
[0010] Step 4: Construct a performance prediction model for the silicon carbide wafer processing production line using the Bi-LSTM-based method. Train the Bi-LSTM using the dataset obtained in Step 3 and find the optimal hyperparameters through gridded search.
[0011] Furthermore, the production line performance indicators include the number of products, yield rate, and product processing cycle in the short, medium, and long term; the influencing factors include: the status of each machine, the processing progress of each machine, the downtime of each machine, the type of workpiece, the theoretical processing time of the workpiece, the logistics status, the logistics speed, and the length of each buffer zone.
[0012] Furthermore, the process of reducing the dimensionality of the data using a theoretical model in step 2 includes the following steps:
[0013] (1) Based on the characteristics of the silicon carbide wafer production line, considering parameters such as the number of parallel equipment, workstation utilization rate, buffer capacity, workpiece arrival time variability, processing time variability and output rate, a theoretical model of its production line performance index is established based on queuing theory.
[0014] In the M / M / m / b queuing model, the probability p0 of a workstation being in a starvation state is calculated using the following formula:
[0015]
[0016] In the formula, m is the number of parallel devices in the workstation, u is the workstation utilization rate, and b is the workstation front buffer capacity.
[0017] The formula for calculating the output of the workstation is:
[0018]
[0019] In the formula, r e The output rate of the workstation;
[0020] The formula for calculating the average processing cycle of a product is:
[0021]
[0022] In the formula, k is the batch size, c a For the variability of workpiece arrival time, c e For the variability of processing time, t e This represents the average processing time.
[0023] The variability of processing time can be obtained from the following formula:
[0024]
[0025] Where t e Indicates the effective processing time, σ e This represents the standard deviation of the effective processing time of the equipment, and c0 represents the natural variability coefficient. r The maintenance variability coefficient, m r t represents the average repair time, and t0 represents the natural processing time (t e =t0 / A), where A represents equipment availability, and we have:
[0026]
[0027] Where m f Indicates the mean time between failures (MTBF).
[0028] The variability in workpiece arrival intervals can be calculated using the following formula:
[0029]
[0030] Where σ a The standard deviation of the time interval between workpiece arrivals is represented by t. a This represents the average arrival time of the workpiece.
[0031] Then, by Liddell's law, the work-in-process (WIP) count of the workstation can be obtained, and its calculation formula is as follows:
[0032]
[0033] Based on the above formula, the cycle time CT of the entire production line can be obtained by summing the cycle time and work-in-process quantity of each station in the series-parallel production line. l Work in process (WIP) l Approximate estimate:
[0034]
[0035]
[0036] (2) Using inductive reasoning, parameters affecting production line performance are derived from the above production line performance theoretical model. The relationship between production line status data and parameters such as utilization rate and output rate of each workstation is obtained. The directly collected production line status data such as machine status, machine processing progress, and machine failure time are transformed into these features.
[0037] The statistical parameters summarized from the theoretical model include: station utilization rate and station output rate; the station utilization rate can be calculated using the following formula:
[0038]
[0039] In the formula, t a t is the interval between workpiece arrivals. e The average effective processing time is given by m, where m is the number of parallel devices.
[0040] Similarly, the utilization rate of the logistics system can also be calculated.
[0041] The station's productivity can be calculated using the following formula:
[0042]
[0043] In the formula, N2 represents the number of finished products processed by the workstation at time T2, and N1 represents the number of finished products processed by the workstation at time T1.
[0044] Furthermore, in step 3, normalization is performed according to the following formula:
[0045]
[0046] Where X represents the data before normalization, X std X is the normalized standard value. min It is the minimum value in the data, X max It is the maximum value in the data;
[0047] Through comparative experiments, a suitable short-term prediction step size was selected within the range of [20, 30, 40, 50, 60], a suitable medium-term prediction step size within the range of [300, 360, 420, 480, 540], a suitable long-term prediction step size within the range of [1440, 2160, 2880, 3600, 4320], and a suitable memory step size within the range of [1000, 1500, 2000, 2500, 3000]. This determines how long of historical data to use to predict performance indicators at what point in time. Next, operational data from the silicon carbide wafer production line was collected. Since the production line was still in the preheating stage during initial operation, data from 20,000 minutes later was selected for prediction. The processed data was then divided into training and testing sets in a 7:3 ratio for subsequent training and testing of the prediction model.
[0048] In the Bi-LSTM model constructed in step 4, the LSTM unit includes a forget gate, an input gate, and an output gate. Its corresponding governing equations are as follows:
[0049] Forgotten Gate: f n =σ f (x n W xf +h n-1 W hf +C n-1 W cf +b f )
[0050] Input gate: i n =σ i (x n W xi +h n-1 W hi +b i )
[0051] Unit state update: C n =f n ·C n-1 +i n ·t c (x n W xc +h n-1 W hc +b c )
[0052] Output gate: O n =σ o (x n W xo +h n-1 W ho +b o )
[0053] Hidden layer update: h n =O n ·t o (C n )
[0054] Among them W xf W xi W xc W xo These are the input data weight matrices W for the forgetting gate, input gate, cell state update, and output gate corresponding to long short-term memory cells. hf W hi W hc and W ho These are the hidden layer information weight matrices for the forget gate, input gate, state update gate, and output gate from the previous time step; W cf It is a weight matrix that measures the weight of the state update information of the previous unit; b f b i b c and b o These are the bias matrices used in the operations of the forget gate, input gate, cell state update, and output gate, respectively. n f is the input value at time n. n and i n Let the forget gate and input gate values be at time n, O(n). n Let C be the output value at time n. n and C n-1 h represents the cell state at time n and time n-1, respectively. n and h n-1 σ represents the hidden layer values at time n and time n-1. f σ i and σ o The sigmoid functions for the forget gate, input gate, and output gate, respectively. c and t o These are the tanh functions for state updates and hidden layers, respectively.
[0055] The Bi-LSTM neural network architecture consists of two independent LSTMs. The input sequence is fed into the two LSTM neural networks in both forward and reverse order for computation. Finally, the two output vectors are combined to obtain the final output. The design philosophy of the Bi-LSTM model is to simultaneously obtain information from both the past and the future.
[0056] The Bi-LSTM neural network used in this invention requires the determination of the following parameters: number of network layers, number of neurons in each network layer, learning rate, number of mini-batches, and number of iterations. Its accuracy requirement uses mean squared error as a benchmark, and its calculation formula is as follows:
[0057]
[0058] Compared with the prior art, the present invention has the following advantages:
[0059] The performance prediction method for silicon carbide wafer production lines provided by this invention, which integrates theoretical and data-driven models, constructs a theoretical model of silicon carbide wafer processing production lines based on queuing theory. It extracts features from the theoretical model that affect the prediction results and then transforms multiple features from the existing input data into features extracted from the theoretical model. This allows the prediction method to combine the interpretability of the theoretical model with the accuracy of the data-driven model. The accurately predicted performance indicators can be used to optimize production scheduling and provide reference indicators for scheduling schemes, thereby scientifically guiding production and having practical application value. Attached Figure Description
[0060] Figure 1 This is a flowchart of the prediction method involved in the present invention.
[0061] Figure 2 This is a structural diagram of a silicon carbide wafer production line in an embodiment of the present invention.
[0062] Figure 3 This is a structural diagram of the neural network unit involved in this invention.
[0063] Figure 4 This is a diagram of the neural network architecture involved in this invention.
[0064] Figure 5 This is a comparison chart of the predicted and actual number of work-in-process items in the silicon carbide wafer production line in an embodiment of the present invention.
[0065] Figure 6 This is a comparison chart of the predicted and actual cycle time of the silicon carbide wafer production line in an embodiment of the present invention.
[0066] Figure 7 This is a comparison chart of the predicted and measured yield of the silicon carbide wafer production line in an embodiment of the present invention. Detailed Implementation
[0067] The technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0068] like Figure 1 As shown.
[0069] This embodiment uses a 6-inch silicon carbide wafer processing production line as the research object to test the performance prediction method for silicon carbide wafer processing production lines based on the fusion of theoretical models and data-driven models proposed in this embodiment of the invention. The specific structure of the production line is as follows: Figure 2 As shown.
[0070] Using this 6-inch silicon carbide wafer processing production line as an example, the workflow of the above-mentioned performance prediction method for silicon carbide wafer processing production line based on the fusion of theoretical models and data-driven models is as follows:
[0071] Step 1: Specify the production line performance indicators of the silicon carbide wafer processing production line and the state parameters that affect them, as the input and output of the feature parameters of the data model, and define the sample information as X = {M}. t B t ,T t W t}, in Describe information about each machine on the production line at different times. Describe information about each buffer zone on the production line at different times. Describe information about the logistics on the production line at different times. Describes information about the workpieces being processed on the production line at different times; Describe the short-term work-in-process inventory, cycle time, and yield respectively; Describe the work-in-process inventory, cycle time, and yield during the intermediate period; WIP l t CT l t YP l t Describe the long-term work-in-process inventory, cycle time, and yield rate; machine information M in the sample information. t Buffer information B t Logistics Information T t Workpiece Information W t Detailed definitions are shown in Tables 1, 2, 3 and 4.
[0072] Table 1. Machine Information M from a Sample Information of a 6-inch Silicon Carbide Wafer Processing Production Line t definition
[0073]
[0074] Table 2 shows the buffer information (B) in the sample information of a certain 6-inch silicon carbide wafer processing production line. t definition
[0075] Feature name describe Data types Number of workpieces A in the buffer Number of workpieces A in the buffer Plastic Surgery Number of B workpieces in the buffer Number of B workpieces in the buffer Plastic Surgery
[0076] Table 3 shows the logistics information (T) from a sample information of a 6-inch silicon carbide wafer processing production line. t definition
[0077]
[0078] Table 3 shows the workpiece information (W) from a sample information sheet of a 6-inch silicon carbide wafer processing production line.t definition
[0079] Feature name describe Data types Workpiece type Type of workpiece Plastic Surgery Planned processing time The planned processing time for this workpiece Plastic Surgery Thickness before processing The thickness of the workpiece before processing floating point Parallelism before processing Parallelism of the workpiece before machining floating point
[0080] In this embodiment, a total of 180 days of production line data were sampled, and the production line processed two types of products.
[0081] Step 2: Collect historical data on the performance indicators and influencing factors of the silicon carbide wafer processing production line as described in Step 1. Model the production line using queuing theory to obtain a theoretical model, and then perform dimensionality reduction on the characteristic parameters. First, a theoretical model of the silicon carbide wafer processing production line needs to be established based on queuing theory.
[0082] In the M / M / m / b queuing theory model, the probability p0 of a workstation being in a starvation state is calculated using the following formula:
[0083]
[0084] In the formula, m is the number of parallel devices in the workstation, u is the workstation utilization rate, and b is the workstation front buffer capacity; the formula for calculating workstation output is:
[0085]
[0086] In the formula, r e The output rate of the workstation;
[0087] The formula for calculating the average processing cycle of a product is:
[0088]
[0089] In the formula, k is the batch size, c a For the variability of workpiece arrival time, c e For the variability of processing time, t e This represents the average processing time.
[0090] The variability of processing time can be obtained from the following formula:
[0091]
[0092] Where t e Indicates the effective processing time, σ e This represents the standard deviation of the effective processing time of the equipment, and c0 represents the natural variability coefficient. r The maintenance variability coefficient, m r t represents the average repair time, and t0 represents the natural processing time (t e =t0 / A), where A represents equipment availability, and we have:
[0093]
[0094] Where m f Indicates the mean time between failures (MTBF).
[0095] The variability in workpiece arrival intervals can be calculated using the following formula:
[0096]
[0097] Where σ a The standard deviation of the time interval between workpiece arrivals is represented by t. a This represents the average arrival time of the workpiece.
[0098] Then, by Liddell's law, the work-in-process (WIP) count of the workstation can be obtained, and its calculation formula is as follows:
[0099]
[0100] Based on the above formula, the cycle time CT of the entire production line can be obtained by summing the cycle time and work-in-process quantity of each station in the series-parallel production line. l Work in process (WIP) l Approximate estimate:
[0101]
[0102]
[0103] Then, statistical parameters affecting production line performance indicators are summarized from the theoretical model, and data directly collected from the production line are converted into this type of statistical data.
[0104] From the theoretical model above, we can obtain statistical parameters, including: station utilization rate and station output rate. Station utilization rate is calculated using the following formula:
[0105]
[0106] In the formula, t a t is the interval between workpiece arrivals. e The average effective processing time is denoted by m, and the number of parallel workstations is denoted by m.
[0107] Similarly, we can also obtain the logistics utilization rate u. t The calculation formula is as follows:
[0108]
[0109] in The interval between workpiece arrivals. This represents the average working time.
[0110] The station's productivity can be calculated using the following formula:
[0111]
[0112] In the formula, N2 represents the number of finished products processed by the workstation at time T2, and N1 represents the number of finished products processed by the workstation at time T1.
[0113] By transforming the collected data into the aforementioned statistical data, data dimensionality reduction is achieved, reducing the original 246-dimensional input data to 188 dimensions, thereby improving the model's prediction accuracy and shortening the model's training time.
[0114] Step 3: Normalize the data samples obtained above. The normalization formula is as follows:
[0115]
[0116] Where X represents the data before normalization, X std X is the normalized standard value. min It is the minimum value in the data, X max It is the maximum value in the data;
[0117] Then, appropriate memory step size and prediction step size are selected to construct a time series dataset suitable for Bi-LSTM.
[0118] Through comparative experiments, a suitable short-term prediction step size was selected within the range of [20, 30, 40, 50, 60], a suitable medium-term prediction step size within the range of [300, 360, 420, 480, 540], a suitable long-term prediction step size within the range of [1440, 2160, 2880, 3600, 4320], and a suitable memory step size within the range of [1000, 1500, 2000, 2500, 3000]. This determined how long of historical data to use to predict performance indicators at what point in time. Next, operational data from the silicon carbide wafer production line was collected. Since the production line was still in the preheating stage during initial operation, data from 20,000 minutes later was selected for prediction. The processed data was then divided into training and testing sets in a 7:3 ratio for subsequent training and testing of the prediction model.
[0119] Through comparative experiments, suitable short-term prediction step sizes were selected within the range of [20, 30, 40, 50, 60], suitable medium-term prediction step sizes within the range of [300, 360, 420, 480, 540], suitable long-term prediction step sizes within the range of [1440, 2160, 2880, 3600, 4320], and suitable memory step sizes within the range of [1000, 1500, 2000, 2500, 3000]. Finally, after comparative experiments, a short-term prediction step size of 20 was chosen. The intermediate prediction step size was set to 420, the long-term prediction step size to 2160, and the memory step size to 2000. A total of 200,000 minutes of silicon carbide wafer production line operation data were collected. Since the production line was still in the preheating stage for the first 20,000 minutes, data after 20,000 minutes was selected for prediction. The final dataset was constructed with an input dimension of [178,000, 2000, 188] and an output dimension of [178,000, 3]. The data was then divided into training and test sets in a 7:3 ratio.
[0120] Step 4: Establish a performance prediction model for a silicon carbide wafer production line based on Bi-LSTM.
[0121] The Bi-LSTM constructed in this invention using gridded search comprises 5 layers: 3 LSTM layers, 1 fully connected layer, and 1 regression layer. The LSTM layers have 60 neurons, and the fully connected layer has 50 neurons. To prevent overfitting, a dropout layer is added after each layer. The learner is the Adam optimizer, with an initial learning rate of 0.01, a maximum of 200 iterations, a mini-batch size of 64, and the mean squared error loss function. The loss calculation formula is shown below:
[0122]
[0123] Input the dataset processed in step 3 into the constructed model. In this example, mean squared error (MSE), mean absolute error (MAE), mean absolute percentage error (MAPE), coefficient of determination (R²), and training time (TT) are used to measure the model's performance. The comparison between the predicted results and the actual values is shown below. Figure 5 , Figure 6 , Figure 7 As shown in Tables 5, 6, and 7, the prediction results were compared with the model constructed in this example using a dataset that had not undergone dimensionality reduction based on the theoretical model.
[0124] Table 5 Comparison of WIP prediction results between the two models
[0125]
[0126] Table 6 Comparison of CT prediction results between the two models
[0127]
[0128]
[0129] Table 7 Comparison of YP prediction results between the two models
[0130]
[0131] As can be seen from the table above, the prediction model based on the fusion of theoretical model and data-driven model has smaller prediction error and lower training time compared to the prediction model based solely on data-driven model. Therefore, the prediction method based on the fusion of theoretical model and data-driven model proposed in this invention has a better effect on the performance prediction of silicon carbide wafer production line.
[0132] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
[0133] The parts not covered in this invention are the same as or can be implemented using existing technologies.
Claims
1. A method for predicting the performance of a silicon carbide wafer processing production line based on the fusion of theoretical models and data-driven approaches, characterized in that... Includes the following steps: Step 1: Specify the production line performance indicators of the silicon carbide wafer processing production line and the state parameters that affect them, as the input and output of the feature parameters of the data model; The production line performance indicators include: the number of products, yield rate, and product processing cycle of the production line in the short, medium, and long term; the status parameters include: the status of each machine, the processing progress of each machine, the downtime of each machine, the type of workpiece, the theoretical processing time of the workpiece, the logistics status, the logistics speed, and the length of each buffer zone. Step 2: Collect historical data on the production line performance indicators and influencing state parameters mentioned in Step 1 from the silicon carbide wafer processing production line; based on the characteristics of the silicon carbide wafer production line, considering the number of parallel devices, station utilization rate, buffer capacity, workpiece arrival time variability, processing time variability, and output rate, establish a theoretical model of its production line performance indicators based on queuing theory; use inductive reasoning to deduce the statistical parameters affecting the production line performance from the above production line performance theoretical model, including station utilization rate and station output rate, obtain the relationship between the production line state parameter data and each statistical parameter, and convert the directly collected production line state parameter data into statistical parameters; Step 3: Normalize the data samples obtained in the above steps; select appropriate memory step size and prediction step size to construct a time series dataset suitable for bidirectional long short-term memory neural networks; through comparative experiments, select appropriate short-term prediction step size in the range of [20-60], appropriate medium-term prediction step size in the range of [300-540], appropriate long-term prediction step size in the range of [1440-4320], and appropriate memory step size in the range of [1000-3000], that is, select how long of historical data to use to predict performance indicators at how long later; then collect the operation process data of the silicon carbide wafer production line. Since the production line is still in the preheating stage in the initial operation stage, data after 20,000 minutes is selected for prediction; divide the processed data into training set and test set in a 7:3 ratio for subsequent training and testing of the prediction model; Step 4: Construct a performance prediction model for the silicon carbide wafer processing production line using the Bi-LSTM-based method. Train the Bi-LSTM using the dataset obtained in Step 3 and find the optimal hyperparameters through gridded search.
2. The performance prediction method for silicon carbide wafer processing production line based on the fusion of theoretical model and data-driven approach as described in claim 1, characterized in that, In the Bi-LSTM model constructed in step 4, the parameters that need to be determined are the number of network layers, the number of neurons in each network layer, the learning rate, the number of mini-batches, and the number of iterations. Its accuracy requirement uses the mean square error as the benchmark.