A non - linear dynamic data anomaly detection method for multi - process stages of silicon single crystal growth

Abstract

The present application proposes a method for detecting anomalies of nonlinear dynamic data in multiple process stages of silicon single crystal growth, which belongs to the technical field of integrated circuit silicon single crystal preparation. The method includes: obtaining historical data sets and monitoring data sets during the growth of silicon single crystals, and constructing a reconstruction training set and a reconstruction test set; iteratively training the correlation vector machine model using the reconstruction training set to obtain a correlation vector machine training model; performing single-step prediction on the monitoring data set to obtain a prediction sequence, and using the prediction sequence to obtain a residual sequence; dividing the residual sequence into multiple segmented windows, and using all sliding windows to traverse each segmented window in turn to obtain multiple sliding window data sets; introducing a dynamic threshold strategy, performing anomaly detection on the corresponding sliding window according to the candidate threshold set generated for each sliding window data set, and fusing all anomaly detection results into the final anomaly detection result. The present application can effectively improve the accuracy and reliability of nonlinear data anomaly detection.

Description

Technical Field

[0001] The present application relates to the technical field of integrated circuit silicon single crystal preparation, and in particular to a method for detecting anomalies in nonlinear dynamic data during multiple process stages of silicon single crystal growth. Background Art

[0002] Silicon single crystals are the fundamental material for integrated circuit (IC) chip manufacturing. As IC manufacturing requirements continue to increase, so too do increasingly stringent standards for silicon single crystal quality. During the silicon single crystal production process, abnormal growth conditions often occur due to factors such as flexible shaft wobble and mechanical vibration in the Czochralski system. Promptly detecting these abnormalities during silicon single crystal growth and implementing appropriate adjustments are essential to ensuring high-quality silicon single crystal production.

[0003] At present, the process of the commonly used method for detecting abnormalities in silicon single crystal growth conditions mainly includes the following processes: defining normal behavior, selecting anomaly detection algorithms, training models, setting thresholds, detecting anomalies, and evaluating results. The specific process is: first, defining the scope of normal behavior through statistical analysis, business knowledge, or expert opinions; then, selecting a suitable anomaly detection algorithm based on data characteristics and business needs, such as statistical methods, machine learning models, or deep learning methods; then, using normal data to train the selected model so that it learns the characteristics of normal behavior; after that, setting a reasonable threshold to distinguish normal data points from abnormal data points; finally, after the model training is completed, predicting future data based on existing historical data, and judging whether anomalies occur by comparing the difference between the predicted value and the actual value with the reasonable threshold. However, this existing anomaly detection method has the following problems:

[0004] First, for the multiple process modes involved in the growth of silicon single crystals, the adopted model cannot simultaneously and effectively detect abnormalities in different modes;

[0005] Secondly, using a fixed reasonable threshold cannot adapt well to the situation where data changes over time. Especially in a dynamic environment, it often fails to correctly capture the data anomalies at a certain moment;

[0006] Finally, since this nonlinear data places higher demands on model training, simple models are difficult to adapt to complex patterns.

[0007] Therefore, it is necessary to propose a solution to improve one or more problems existing in the above-mentioned related technical solutions.

[0008] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to ordinary technicians in this field. Summary of the Invention

[0009] The present invention provides a method for detecting anomalies in nonlinear dynamic data during multiple process stages of silicon single crystal growth, the method comprising the following steps:

[0010] Obtaining a historical data set and a monitoring data set during the growth of a silicon single crystal, reconstructing the historical data set to obtain a reconstructed training set, reconstructing the monitoring data set to obtain a reconstructed test set, and performing Bayesian online jump point detection on the monitoring data set to obtain multiple segmentation points in the monitoring data set, wherein the reconstructed training set includes multiple training samples, and the reconstructed test set includes multiple test samples;

[0011] Constructing a relevance vector machine model, and iteratively training the relevance vector machine model using the reconstructed training set to obtain a relevance vector machine training model;

[0012] Using the reconstructed training set and the reconstructed test set in the relevance vector machine training model, single-step prediction is performed on the monitoring data set to obtain a prediction sequence, and the prediction sequence is subjected to corresponding difference processing with the output target of each test sample to obtain a residual sequence, wherein the residual sequence includes a plurality of residual values;

[0013] Dividing the residual sequence into a plurality of segmentation windows using all the segmentation points, and traversing each of the segmentation windows in sequence using all the sliding windows to obtain a plurality of sliding window data sets;

[0014] A dynamic threshold strategy is introduced to generate corresponding candidate threshold sets according to the statistical characteristics of all the sliding window data sets. All the candidate threshold sets are used to perform anomaly detection on the corresponding sliding windows respectively, and the anomaly detection results of all the sliding windows are fused to obtain the final anomaly detection result.

[0015] Furthermore, the steps of obtaining a historical data set and a monitoring data set during the growth of a silicon single crystal, reconstructing the historical data set to obtain a reconstructed training set, reconstructing the monitoring data set to obtain a reconstructed test set, and performing Bayesian online jump point detection on the monitoring data set to obtain multiple segmentation points in the monitoring data set include:

[0016] Acquiring all historical data during the growth of a silicon single crystal to form the historical data set, and forming all the historical data without abnormalities in the historical data set into the reconstruction training set;

[0017] The reconstructed training set is express, , Represents the total length of all historical data in the reconstructed training set, Indicates the The input vector of the training sample, The input vector of the training sample is to The historical data is composed of a continuous , Represents the reconstruction of the training set Historical data, Indicates the The output target of the training samples is , Represents the reconstruction of the training set Historical data, express dimensional real space, Indicates the training samples, Represents the multiplication sign, represents a one-dimensional real number space, Indicates the dimension;

[0018] Acquiring all monitoring data during the growth of the silicon single crystal to form the monitoring data set, and forming all the monitoring data without abnormalities in the monitoring data set into the reconstruction test set;

[0019] Performing the Bayesian online jump point detection on the monitoring data set to obtain a plurality of segmentation points;

[0020] The reconstructed test set is used express, , Represents the total length of all monitoring data in the reconstructed test set, Indicates the The input vector of the test sample, the The input vector of the test sample is composed of to The monitoring data is composed of a continuous , Reconstructs the test set Monitoring data, Indicates the The output target of the test sample is Indicates the test samples, Indicates the dimension;

[0021] The historical data set is used Indicates that the monitoring data set is express.

[0022] Furthermore, the steps of constructing a RVM model and iteratively training the RVM model using the reconstructed training set to obtain a RVM training model include:

[0023] In the process of iteratively training the RVM model using the reconstructed training set, the input vectors of all the training samples are used as the input of the RVM model, the output targets of all the corresponding training samples are used as the output of the RVM model, and a likelihood function of the reconstructed training set is constructed to obtain the RVM training model;

[0024] The likelihood function of the reconstructed training set is processed to prevent parameter overfitting, multiple hyperparameters are found, and all the hyperparameters are updated alternately and iteratively until the change amplitude of all the hyperparameters is less than the preset amplitude threshold, thereby completing the joint optimization of all the hyperparameters.

[0025] Furthermore, the expression of the RVM training model is:

[0026] (1)

[0027] in, represents the predicted output of the RVM training model, , represents the number of all training samples in the reconstructed training set, , represents the weight vector of the RVM training model, The weight vector of the RVM training model is represented by elements, Indicates the The input vector of training samples, , represents the kernel function for reconstructing the training set, , represents the weight of the Gaussian kernel in the kernel function of the reconstructed training set, Represents the width of the Gaussian kernel in the kernel function of the reconstructed training set, represents transpose, represents the bias term of the polynomial kernel in the kernel function of the reconstructed training set, represents the power of the polynomial kernel in the kernel function for reconstructing the training set, Indicates the The Gaussian white noise corresponding to the training samples, the Gaussian distribution of the Gaussian white noise is , represents the variance of Gaussian white noise, represents the exponential function, represents the norm of the vector, the number of all the elements of the weight vector is the same as the number of all the training samples in the reconstructed training set, and for the first The training samples, there is the The elements correspond thereto;

[0028] Utilizing the Gaussian white noise corresponding to all the training samples, respectively calculating the likelihood function of each of the training samples, and utilizing the mutual independence between all the training samples in the reconstructed training set, multiplying the likelihood functions of all the training samples to obtain the likelihood function of the reconstructed training set;

[0029] The expression of the likelihood function of the training sample is:

[0030] P sample y h i w, σ 2 = 1 2π σ 2 exp { - [y h i -Y x h i ,w ] 2 2 σ 2 } (2)

[0031] in, Indicates the The likelihood function of the training samples;

[0032] The expression of the likelihood function of the reconstructed training set is:

[0033] (3)

[0034] in, represents the likelihood function of reconstructing the training set, represents the output target of all training samples, represents the kernel matrix, , express dimensional real number space;

[0035] To prevent the weight vector Overfitting, the weight vector Assume a Gaussian distribution with zero mean , and As a prior distribution, ,in, represents the first hyperparameter, represents a Gaussian distribution, Indicates the first hyperparameter The reciprocal of a value;

[0036] According to the Bayesian formula, the expression of the posterior distribution is:

[0037] (4)

[0038] in, Represents the weight vector The posterior distribution of Represents the weight vector The conditional probability of , , represents the second hyperparameter, represents the covariance matrix, , , represents the mean vector of the posterior distribution, , Represents the weight vector The marginal posterior probability of

[0039] The expression of the first hyperparameter is:

[0040] (5)

[0041] in, Indicates that after The first hyperparameter after the iteration update A value, The effective degree of freedom A value, , Indicates that after The first hyperparameter after the iteration update A value, represents the covariance matrix Rank Elements of the column, The first vector representing the mean of the posterior distribution A value;

[0042] The expression of the second hyperparameter is:

[0043] (6)

[0044] in, express The transpose of the all-one column vector, express dimensional real space, represents the effective degrees of freedom;

[0045] Using (5) and formula (6), the first hyperparameter and the second hyperparameter are subjected to the alternating iterative update. When the change amplitudes of the first hyperparameter and the second hyperparameter are both less than the preset amplitude threshold, the joint optimization process ends.

[0046] Furthermore, the step of using the reconstructed training set and the reconstructed test set in the relevance vector machine training model to perform single-step prediction on the monitoring data set to obtain a prediction sequence, and performing corresponding difference processing on the prediction sequence and the output target of each test sample to obtain a residual sequence includes:

[0047] The reconstructed training set and the reconstructed test set are input into the RVM training model, and the mean vector of the posterior distribution is As the weight vector , performing the single-step prediction on the monitoring data set to obtain a prediction sequence;

[0048] All prediction data in the prediction sequence are respectively subjected to the corresponding difference processing with the output targets of the corresponding test samples in the reconstructed test set, and all the obtained residual values are combined into the residual sequence.

[0049] Furthermore, the expression of the single-step prediction is:

[0050] (7)

[0051] in, Indicates the The forecast data of the step, Indicates the training samples, represents the kernel function of the reconstructed test set, , represents the weight of the Gaussian kernel in the kernel function of the reconstructed test set, represents the width of the Gaussian kernel in the kernel function of the reconstructed test set, represents the bias term of the polynomial kernel in the kernel function of the reconstructed test set, represents the power of the polynomial kernel in the kernel function used to reconstruct the test set, Indicates that after The mean vector of the posterior distribution after the iteration update A value;

[0052] The predicted sequence is expressed as: ,in, represents the prediction sequence, express dimensional real number space;

[0053] The residual sequence is expressed as: , represents the residual sequence, Represents the output target of all test samples.

[0054] Furthermore, the step of dividing the residual sequence into a plurality of segmentation windows using all the segmentation points, and traversing each of the segmentation windows in sequence using all the sliding windows to obtain a plurality of sliding window data sets includes:

[0055] The set of all the segmentation points is expressed as: ,in, Indicates the segmentation points;

[0056] Using all the segmentation points, the residual sequence is divided into The segmentation windows; the set of all the segmentation windows is expressed as: ,in, represents the first All residual values within the segmented window, , represents the first The last residual value in the segmented window;

[0057] All the sliding windows are respectively subjected to preset processing, and all the sliding windows after the preset processing are used to traverse each of the segmented windows in sequence to obtain a plurality of sliding window data sets.

[0058] Furthermore, the step of introducing a dynamic threshold strategy, generating corresponding candidate threshold sets according to the statistical characteristics of all the sliding window data sets, performing anomaly detection on the corresponding sliding windows using all the candidate threshold sets, and fusing the anomaly detection results of all the sliding windows to obtain the final anomaly detection result includes:

[0059] Calculate the mean and standard deviation of all window data in each sliding window data set respectively, and make each sliding window data set The values are equally spaced within the preset interval;

[0060] According to the mean and standard deviation of all the window data in each sliding window data set and the results of all the corresponding equidistant values, a plurality of candidate thresholds of the corresponding sliding window are calculated respectively to form the candidate threshold set;

[0061] Calculate the corresponding values of each candidate threshold of all sliding windows respectively Value rating;

[0062] Traverse all the sliding windows separately Value score, get the corresponding maximum value of the sliding window The value score corresponds to the value;

[0063] Take advantage of all the maximum The value score corresponds to the value, respectively calculating the optimal threshold value of the corresponding sliding window;

[0064] Using all the optimal thresholds, perform anomaly detection on the corresponding sliding windows respectively, and mark all the window data in all the sliding windows that are greater than or equal to the corresponding optimal threshold as anomalies, and mark all the remaining window data as normal points;

[0065] Introducing a sliding window false alarm point, setting a lower limit on the number of abnormal points, and comparing the number of all abnormal points in each sliding window with the lower limit on the number of abnormal points;

[0066] If the number of all abnormal points in the sliding window is greater than or equal to the lower limit of the number of abnormal points, it is considered that an abnormality exists in the sliding window, and the abnormality detection results of all the sliding windows are integrated to obtain the final abnormality detection result;

[0067] If the number of all the outliers in the sliding window is less than the lower limit of the number of outliers, all the outliers are pruned, and the outlier detection results of all the sliding windows after the pruning process are fused to obtain the final outlier detection result.

[0068] Furthermore, the candidate threshold is expressed as:

[0069] (8)

[0070] in, represents the candidate threshold of the sliding window, Represents the mean of all window data in the sliding window dataset, express value, which is the quantile in the standard normal distribution, Represents the standard deviation of all window data in the sliding window dataset, Represents the number of all window data in the sliding window dataset;

[0071] described The expression for the value score is:

[0072] (9)

[0073] in, express Value rating, Indicates the offset of the mean of all abnormal points in the sliding window dataset, , represents the mean of all normal points in the sliding window dataset, represents the number of all abnormal points in the sliding window dataset, , represents the number of all normal points in the sliding window dataset, , represents the offset of the standard deviation of all abnormal points in the sliding window dataset, , represents the standard deviation of all normal points in the sliding window dataset, Represents the number of all abnormal points in the sliding window dataset after pruning, Represents the number of all consecutive outliers in the sliding window dataset.

[0074] Furthermore, the expression of the optimal threshold is:

[0075] (10)

[0076] in, represents the optimal threshold of the sliding window, Indicates the maximum sliding window The value score corresponds to value

[0077] The present application provides a method for detecting anomalies in nonlinear dynamic data during multiple process stages of silicon single crystal growth, which has at least the following beneficial effects:

[0078] (1) This application breaks away from the limitations of manual segmentation and fixed window length by automatically segmenting the silicon single crystal growth process and using independent dynamic thresholds in each segment, thus avoiding false positives and false negatives caused by differences in process stages and improving the accuracy and sensitivity of anomaly detection.

[0079] (2) This application uses a relevance vector machine training model to perform single-step prediction on the monitoring data set to obtain a prediction sequence, and uses the prediction sequence to obtain a residual sequence. Since the relevance vector machine training model can effectively process complex nonlinear data, it can more accurately predict the data changes during the silicon single crystal growth process, effectively improving the accuracy of data prediction during the silicon single crystal growth process;

[0080] (3) This application introduces a dynamic threshold strategy, uses all candidate threshold sets to perform anomaly detection on the corresponding sliding windows respectively, and merges all anomaly detection results into the final anomaly detection result, so as to adapt to data fluctuations in the anomaly detection process, effectively reduce false detections caused by factors such as noise, and improve the accuracy of anomaly detection; and the use of a dynamic threshold strategy can automatically adjust the window data of the sliding window in real time, so as to better cope with data changes and ensure the accuracy and reliability of nonlinear data anomaly detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] The accompanying drawings are incorporated into and constitute a part of the specification, illustrate embodiments consistent with the present application, and together with the specification, are used to explain the principles of the present application. Obviously, the drawings described below are only some embodiments of the present application, and those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0082] Figure 1 A schematic diagram showing the steps of a method for detecting anomalies in nonlinear dynamic data of multi-process stages of silicon single crystal growth in an exemplary embodiment of the present application is shown;

[0083] Figure 2 A schematic flow chart showing a method for detecting anomalies in nonlinear dynamic data during multiple process stages of silicon single crystal growth in an exemplary embodiment of the present application is shown;

[0084] Figure 3 A schematic diagram showing multiple segmentation points detected in a method for detecting anomalies in nonlinear dynamic data of multi-process stages of silicon single crystal growth in an exemplary embodiment of the present application;

[0085] Figure 4 A schematic diagram showing the actual value, predicted value, and abnormal situation of heater power in a simulation experiment of an exemplary embodiment of the present application;

[0086] Figure 5 A schematic diagram showing anomaly detection results obtained by using a dynamic threshold strategy in a simulation experiment of an exemplary embodiment of the present application. DETAILED DESCRIPTION

[0087] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0088] In addition, the accompanying drawings are merely schematic illustrations of the present application and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the blocks shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0089] The following describes in more detail a method for detecting anomalies in nonlinear dynamic data during multiple process stages of silicon single crystal growth proposed in this exemplary embodiment.

[0090] This exemplary embodiment provides a method for detecting abnormalities in nonlinear dynamic data during multi-process stages of silicon single crystal growth. Figure 1 and Figure 2 As shown, the method may include the following steps:

[0091] Step S101: Obtain a historical data set and a monitoring data set during the growth process of a silicon single crystal, reconstruct the historical data set to obtain a reconstructed training set, reconstruct the monitoring data set to obtain a reconstructed test set, and perform Bayesian online jump point detection on the monitoring data set to obtain multiple segmentation points in the monitoring data set.

[0092] In step S101 of this embodiment, the reconstructed training set includes multiple training samples, and the reconstructed test set includes multiple test samples.

[0093] In step S101 of this embodiment, the historical data set is used Indicates that the monitoring dataset is express.

[0094] In this embodiment, step S101 may include the following sub-steps:

[0095] Sub-step S1011: Acquire all historical data during the growth of the silicon single crystal to form a historical data set, and form all historical data without abnormalities in the historical data set into a reconstruction training set.

[0096] In sub-step S1011, the training set is reconstructed express, , Represents the total length of all historical data in the reconstructed training set, Indicates the The input vector of the training sample, The input vector of the training sample is to Consisting of continuous historical data, , Represents the reconstruction of the training set Historical data, Indicates the The output target of the training samples is , Represents the reconstruction of the training set Historical data, express dimensional real space, Indicates the training samples, Represents the multiplication sign, represents a one-dimensional real number space, Indicates the dimension.

[0097] Sub-step S1012: Acquire all monitoring data during the growth of the silicon single crystal to form a monitoring data set, and form all monitoring data without abnormalities in the monitoring data set into the reconstructed test set.

[0098] In sub-step S1012, the test set is reconstructed using express, , Represents the total length of all monitoring data in the reconstructed test set, Indicates the The input vector of the test sample, The input vector of the test sample is composed of to Continuous monitoring data, , Reconstructs the test set Monitoring data, Indicates the The output target of the test sample is Indicates the test samples, Indicates the dimension.

[0099] Sub-step S1013: performing Bayesian online jump point detection on the monitoring data set to obtain multiple segmentation points.

[0100] Step S102: Construct a RVM model and iteratively train the RVM model using the reconstructed training set to obtain a RVM training model. In this embodiment, step S102 may include the following sub-steps:

[0101] Sub-step S1021: In the process of iteratively training the relevant vector machine model using the reconstructed training set, the input vectors of all training samples are used as the input of the relevant vector machine model, the output targets of all corresponding training samples are used as the output of the relevant vector machine model, and the likelihood function of the reconstructed training set is constructed to obtain the relevant vector machine training model.

[0102] In sub-step S1021, the RVM model is preferably a hybrid kernel RVM model.

[0103] In sub-step S1021, the expression of the RVM training model is:

[0104] (1)

[0105] in, represents the predicted output of the RVM training model, , represents the number of all training samples in the reconstructed training set, , represents the weight vector of the RVM training model, The weight vector of the RVM training model is represented by elements, Indicates the The input vector of training samples, , represents the kernel function for reconstructing the training set, , represents the weight of the Gaussian kernel in the kernel function of the reconstructed training set, Represents the width of the Gaussian kernel in the kernel function of the reconstructed training set, represents transpose, represents the bias term of the polynomial kernel in the kernel function of the reconstructed training set, represents the power of the polynomial kernel in the kernel function for reconstructing the training set, Indicates the The Gaussian white noise corresponding to the training samples, the Gaussian distribution of the Gaussian white noise is , represents the variance of Gaussian white noise, represents the exponential function, Represents the norm of the vector, the number of all elements of the weight vector is the same as the number of all training samples in the reconstructed training set, and for the first training samples, there is the first elements corresponding to it.

[0106] In sub-step S1021, the Gaussian white noise corresponding to all training samples is used to calculate the likelihood function of each training sample respectively, and the mutual independence between all training samples in the reconstructed training set is used to multiply the likelihood functions of all training samples to obtain the likelihood function of the reconstructed training set.

[0107] Furthermore, the likelihood function of the training sample is expressed as:

[0108] P sample y h i w, σ 2 = 1 2π σ 2 exp { - [y h i -Y x h i ,w ] 2 2 σ 2 } (2)

[0109] in, Indicates the The likelihood function of the training samples.

[0110] Furthermore, the expression of the likelihood function of the reconstructed training set is:

[0111] (2)

[0112] in, represents the likelihood function of reconstructing the training set, represents the output target of all training samples, represents the kernel matrix, , express dimensional real number space.

[0113] Sub-step S1022: Prevent parameter overfitting on the likelihood function of the reconstructed training set, find multiple hyperparameters, and iteratively update all hyperparameters alternately until the change amplitude of all hyperparameters is less than the preset amplitude threshold, completing the joint optimization of all hyperparameters. The specific process of sub-step S1022 includes:

[0114] To prevent the weight vector Overfitting, the weight vector Assume a Gaussian distribution with zero mean , and As a prior distribution, ,in, represents the first hyperparameter, represents a Gaussian distribution, Indicates the first hyperparameter The reciprocal of a value.

[0115] According to the Bayesian formula, the expression of the posterior distribution is:

[0116] (4)

[0117] in, Represents the weight vector The posterior distribution of Represents the weight vector The conditional probability of , , represents the second hyperparameter, represents the covariance matrix, , , represents the mean vector of the posterior distribution, , Represents the weight vector The marginal posterior probability of . It is a commonly used construct in mathematics to construct diagonal matrices.

[0118] The expression of the first hyperparameter is:

[0119] (5)

[0120] in, Indicates that after The first hyperparameter after the iteration update A value, The effective degree of freedom A value, , Indicates that after The first hyperparameter after the iteration update A value, represents the covariance matrix Rank Elements of the column, The first vector representing the mean of the posterior distribution A value.

[0121] The expression for the second hyperparameter is:

[0122] (6)

[0123] in, express The transpose of the all-one column vector, express dimensional real space, represents the effective degrees of freedom.

[0124] Using formula (5) and formula (6), the first hyperparameter and the second hyperparameter are alternately iterated and updated. When the change amplitudes of the first hyperparameter and the second hyperparameter are both less than the preset amplitude threshold, the joint optimization process ends.

[0125] It should be noted here that the preset amplitude threshold is a parameter result that is continuously updated according to experiments. After multiple rounds of iterations, it is basically maintained below 0.01. Therefore, in this embodiment, the preset amplitude threshold is set to 0.01.

[0126] Step S103: Using the reconstructed training set and the reconstructed test set, a single-step prediction is performed on the monitoring data set in the relevance vector machine training model to obtain a prediction sequence. The prediction sequence is then subtracted from the output target of each test sample to obtain a residual sequence. In this embodiment, step S103 may include the following sub-steps:

[0127] Sub-step S1031: Input the reconstructed training set and the reconstructed test set into the RVM training model, and convert the mean vector of the posterior distribution into As a weight vector The effective estimated value of is used to make a single-step forecast on the monitoring data set to obtain the forecast sequence.

[0128] Sub-step S1032: Figure 3 As shown in Figure 1, all predicted data in the prediction sequence are subjected to corresponding difference processing with the output targets of the corresponding test samples in the reconstructed test set, and all the residual values obtained are combined into a residual sequence. The residual value here refers to the absolute value of the corresponding difference obtained after the corresponding difference processing.

[0129] Depend on Figure 3 It can be seen that in step S103 of this embodiment, the expression for single-step prediction is:

[0130] (7)

[0131] in, Indicates the The forecast data of the step, Indicates the training samples, represents the kernel function of the reconstructed test set, , represents the weight of the Gaussian kernel in the kernel function of the reconstructed test set, represents the width of the Gaussian kernel in the kernel function of the reconstructed test set, represents the bias term of the polynomial kernel in the kernel function of the reconstructed test set, represents the power of the polynomial kernel in the kernel function used to reconstruct the test set, Indicates that after The mean vector of the posterior distribution after the iteration update A value.

[0132] The predicted sequence is expressed as: ,in, represents the prediction sequence, express dimensional real number space;

[0133] The residual sequence is expressed as: , represents the residual sequence, Represents the output target of all test samples.

[0134] Step S104: Divide the residual sequence into multiple segmentation windows using all segmentation points, and use all sliding windows to traverse each segmentation window in turn to obtain multiple sliding window data sets. In this embodiment, step S104 may include the following sub-steps:

[0135] Sub-step S1041: Express the set of all segmentation points as: ,in, Indicates the Segment points.

[0136] Sub-step S1042: Divide the residual sequence into segmentation windows; the set of all segmentation windows is expressed as: ,in, represents the first All residual values within the segmented window, , represents the first The last residual value in the segmented window.

[0137] Sub-step S1043: performing preset processing on all sliding windows respectively, and using all sliding windows after the preset processing to traverse each segmented window in turn, to obtain multiple sliding window data sets.

[0138] Here, the preset processing refers to setting the sizes of all sliding windows to 150 and the step sizes of all sliding windows to 1.

[0139] Step S105: Introduce a dynamic threshold strategy to generate corresponding candidate threshold sets based on the statistical characteristics of all sliding window data sets. Use all candidate threshold sets to perform anomaly detection on the corresponding sliding windows, and fuse the anomaly detection results of all sliding windows to obtain the final anomaly detection result. In this embodiment, step S105 may include the following sub-steps:

[0140] Sub-step S1051: Calculate the mean and standard deviation of all window data in each sliding window data set, and make each sliding window data set The values are taken at equal intervals within the preset interval; in this embodiment, the range of the preset interval is [2.0,5.0] .

[0141] Sub-step S1052: Based on the mean and standard deviation of all window data in each sliding window data set and the results of all corresponding equidistant values, multiple candidate thresholds of the corresponding sliding window are calculated to form a candidate threshold set.

[0142] In sub-step S1052, the expression of the candidate threshold is:

[0143] (8)

[0144] in, represents the candidate threshold of the sliding window, Represents the mean of all window data in the sliding window dataset, express value, quantile in the standard normal distribution, Represents the standard deviation of all window data in the sliding window dataset, Indicates the number of all window data in the sliding window dataset.

[0145] Sub-step S1053: Calculate the Z-value score corresponding to each candidate threshold of all sliding windows respectively.

[0146] In sub-step S1053, The expression for the value score is:

[0147] (9)

[0148] in, express Value rating, Indicates the offset of the mean of all abnormal points in the sliding window dataset, , represents the mean of all normal points in the sliding window dataset, represents the number of all abnormal points in the sliding window dataset, , represents the number of all normal points in the sliding window dataset, , represents the offset of the standard deviation of all abnormal points in the sliding window dataset, , represents the standard deviation of all normal points in the sliding window dataset, Represents the number of all abnormal points in the sliding window dataset after pruning, Represents the number of all consecutive outliers in the sliding window dataset.

[0149] Sub-step S1054: traverse all the Value score, get the maximum value of the corresponding sliding window The value score corresponds to value.

[0150] Sub-step S1055: Utilize all maximum The value score corresponds to value, and calculate the optimal threshold of the corresponding sliding window respectively.

[0151] In sub-step S1055, the expression of the optimal threshold is:

[0152] (10)

[0153] in, represents the optimal threshold of the sliding window, Indicates the maximum sliding window The value score corresponds to value.

[0154] Sub-step S1056: using all optimal thresholds, perform anomaly detection on the corresponding sliding windows respectively, and mark all window data greater than or equal to the corresponding optimal threshold in all sliding windows as anomalies, and mark all other window data as normal points.

[0155] Sub-step S1056: Introduce sliding window false alarm points, set a lower limit for the number of outliers, and compare the number of all outliers in each sliding window with the lower limit, including the following two cases:

[0156] The first case: If the number of all abnormal points in the sliding window is greater than or equal to the lower limit of the number of abnormal points, it is considered that there is an abnormality in the sliding window, and the abnormality detection results of all sliding windows are fused to obtain the final abnormality detection result.

[0157] The second case: If the number of all outliers in the sliding window is less than the lower limit of the number of outliers, all outliers are pruned, and the anomaly detection results of all sliding windows after pruning are fused to obtain the final anomaly detection result.

[0158] In sub-step S1056 of this embodiment, the lower limit of the number of abnormal points is set to 2.

[0159] It is important to note that the sliding window false alarm points mentioned here refer to those points that are mistakenly marked as abnormal points but are actually normal points.

[0160] In order to verify the excellent effect of the nonlinear dynamic data anomaly detection method for multi-process stages of silicon single crystal growth proposed in this application, the following simulation experiments were carried out.

[0161] The data for this simulation experiment comes from the National and Local Joint Engineering Research Center for Crystal Growth Equipment and System Integration (abbreviated as the Crystal Center). The simulation data was collected from the operation of a TDR135 silicon single crystal growth device at the Crystal Center.

[0162] The heater power data selected from the simulation experiment data are analyzed, such as Figure 4 As shown in the figure, the sampling frequency of the data is 0.2Hz, the data length includes 4800 sampling points, and the sampling data set is the heater power data of the normal CZ silicon single crystal growth process. The sampling data set has an abnormality in the interval of 1500~1600 sampling points, and the process stage switching occurs at the 3649th sampling point. Figure 4 It can be seen that the hybrid kernel relevance vector machine model can well predict future changes in data.

[0163] like Figure 5 As shown, the dynamic threshold strategy adapts well to data changes and automatically adjusts based on real-time data. However, false detections and missed detections occur at very few sampling points. For example, false detections occur at sampling points 3794 and 4392, and a missed detection occurs at sampling point 1542. However, overall, the dynamic threshold strategy maintains good and stable performance throughout the anomaly detection process.

[0164] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of this application, the meaning of "plurality" is two or more, unless otherwise clearly specified.

[0165] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification.

[0166] The above is only a specific implementation method of the present application, but the scope of protection of the present application is not limited thereto. Any technician familiar with this technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in this application, and these modifications or replacements should be included in the scope of protection of the present application.

[0167] Those skilled in the art will readily appreciate other embodiments of the present invention after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of this application and include common knowledge or customary techniques in the art that are not disclosed herein.

Claims

1. A method for detecting anomalies in nonlinear dynamic data during multi-process stages of silicon single crystal growth, characterized in that: The method comprises the following steps: Obtaining a historical data set and a monitoring data set during the growth of a silicon single crystal, reconstructing the historical data set to obtain a reconstructed training set, reconstructing the monitoring data set to obtain a reconstructed test set, and performing Bayesian online jump point detection on the monitoring data set to obtain multiple segmentation points in the monitoring data set, wherein the reconstructed training set includes multiple training samples, and the reconstructed test set includes multiple test samples; Constructing a relevance vector machine model, and iteratively training the relevance vector machine model using the reconstructed training set to obtain a relevance vector machine training model; Using the reconstructed training set and the reconstructed test set in the relevance vector machine training model, single-step prediction is performed on the monitoring data set to obtain a prediction sequence, and the prediction sequence is subjected to corresponding difference processing with the output target of each test sample to obtain a residual sequence, wherein the residual sequence includes a plurality of residual values; Dividing the residual sequence into a plurality of segmentation windows using all the segmentation points, and traversing each of the segmentation windows in sequence using all the sliding windows to obtain a plurality of sliding window data sets; A dynamic threshold strategy is introduced to generate corresponding candidate threshold sets according to the statistical characteristics of all the sliding window data sets. All the candidate threshold sets are used to perform anomaly detection on the corresponding sliding windows respectively, and the anomaly detection results of all the sliding windows are fused to obtain the final anomaly detection result.

2. The method for detecting anomalies in nonlinear dynamic data during multi-process stages of silicon single crystal growth according to claim 1, characterized in that: The steps of obtaining a historical data set and a monitoring data set during the growth of a silicon single crystal, reconstructing the historical data set to obtain a reconstructed training set, reconstructing the monitoring data set to obtain a reconstructed test set, and performing Bayesian online jump point detection on the monitoring data set to obtain multiple segmentation points in the monitoring data set include: Acquiring all historical data during the growth of a silicon single crystal to form the historical data set, and forming all the historical data without abnormalities in the historical data set into the reconstruction training set; The reconstructed training set is express, , Represents the total length of all historical data in the reconstructed training set, Indicates the The input vector of the training sample, the The input vector of the training sample is to The historical data is composed of a continuous , Represents the reconstruction of the training set Historical data, Indicates the The output target of the training samples is , Represents the reconstruction of the training set Historical data, express dimensional real space, Indicates the training samples, Represents the multiplication sign, represents a one-dimensional real number space, Indicates the dimension; Acquiring all monitoring data during the growth of the silicon single crystal to form the monitoring data set, and forming all the monitoring data without abnormalities in the monitoring data set into the reconstruction test set; Performing the Bayesian online jump point detection on the monitoring data set to obtain a plurality of segmentation points; The reconstructed test set is used express, , Represents the total length of all monitoring data in the reconstructed test set, Indicates the The input vector of the test sample, the The input vector of the test sample is composed of to The monitoring data is composed of a continuous , Reconstructs the test set Monitoring data, Indicates the The output target of the test sample is Indicates the test samples, Indicates the dimension; The historical data set is used Indicates that the monitoring data set is express.

3. The method for detecting anomalies in nonlinear dynamic data during multi-process stages of silicon single crystal growth according to claim 2, characterized in that: The steps of constructing a RVM model and iteratively training the RVM model using the reconstructed training set to obtain a RVM training model include: In the process of iteratively training the RVM model using the reconstructed training set, the input vectors of all the training samples are used as the input of the RVM model, the output targets of all the corresponding training samples are used as the output of the RVM model, and a likelihood function of the reconstructed training set is constructed to obtain the RVM training model; The likelihood function of the reconstructed training set is processed to prevent parameter overfitting, multiple hyperparameters are found, and all the hyperparameters are updated alternately and iteratively until the change amplitude of all the hyperparameters is less than the preset amplitude threshold, thereby completing the joint optimization of all the hyperparameters.

4. The method for detecting anomalies in nonlinear dynamic data during multi-process stages of silicon single crystal growth according to claim 3, characterized in that: The expression of the RVM training model is: (1) in, represents the predicted output of the RVM training model, , represents the number of all training samples in the reconstructed training set, , represents the weight vector of the RVM training model, The weight vector of the RVM training model is represented by elements, Indicates the The input vector of training samples, , represents the kernel function for reconstructing the training set, , represents the weight of the Gaussian kernel in the kernel function of the reconstructed training set, Represents the width of the Gaussian kernel in the kernel function of the reconstructed training set, represents transpose, represents the bias term of the polynomial kernel in the kernel function of the reconstructed training set, represents the power of the polynomial kernel in the kernel function for reconstructing the training set, Indicates the The Gaussian white noise corresponding to the training samples, the Gaussian distribution of the Gaussian white noise is , represents the variance of Gaussian white noise, represents the exponential function, represents the norm of the vector, the number of all the elements of the weight vector is the same as the number of all the training samples in the reconstructed training set, and for the first The training samples, there is the The elements correspond thereto; Utilizing the Gaussian white noise corresponding to all the training samples, respectively calculating the likelihood function of each of the training samples, and utilizing the mutual independence between all the training samples in the reconstructed training set, multiplying the likelihood functions of all the training samples to obtain the likelihood function of the reconstructed training set; The expression of the likelihood function of the training sample is: (2) in, Indicates the The likelihood function of the training samples; The expression of the likelihood function of the reconstructed training set is: (3) in, represents the likelihood function of reconstructing the training set, represents the output target of all training samples, represents the kernel matrix, , express dimensional real number space; To prevent the weight vector Overfitting, the weight vector Assume a Gaussian distribution with zero mean , and As a prior distribution, ,in, represents the first hyperparameter, represents a Gaussian distribution, Indicates the first hyperparameter The reciprocal of a value; According to the Bayesian formula, the expression of the posterior distribution is: (4) in, Represents the weight vector The posterior distribution of Represents the weight vector The conditional probability of , , represents the second hyperparameter, represents the covariance matrix, , , represents the mean vector of the posterior distribution, , Represents the weight vector The marginal posterior probability of The expression of the first hyperparameter is: (5) in, Indicates that after The first hyperparameter after the iteration update A value, The effective degree of freedom A value, , Indicates that after The first hyperparameter after the iteration update A value, represents the covariance matrix Rank Elements of the column, The first vector representing the mean of the posterior distribution A value; The expression of the second hyperparameter is: (6) in, express The transpose of the all-one column vector, express dimensional real space, represents the effective degrees of freedom; Using formula (5) and formula (6), the first hyperparameter and the second hyperparameter are alternately iteratively updated. When the change amplitudes of the first hyperparameter and the second hyperparameter are both less than the preset amplitude threshold, the joint optimization process ends.

5. The method for detecting anomalies in nonlinear dynamic data during multi-process stages of silicon single crystal growth according to claim 4, characterized in that: The step of using the reconstructed training set and the reconstructed test set in the relevance vector machine training model to perform single-step prediction on the monitoring data set to obtain a prediction sequence, and performing corresponding difference processing on the prediction sequence and the output target of each test sample to obtain a residual sequence includes: The reconstructed training set and the reconstructed test set are input into the RVM training model, and the mean vector of the posterior distribution is As the weight vector , performing the single-step prediction on the monitoring data set to obtain the prediction sequence; All prediction data in the prediction sequence are respectively subjected to the corresponding difference processing with the output targets of the corresponding test samples in the reconstructed test set, and all the obtained residual values are combined into the residual sequence.

6. The method for detecting anomalies in nonlinear dynamic data during multi-process stages of silicon single crystal growth according to claim 5, characterized in that: The expression of the single-step prediction is: (7) in, Indicates the The forecast data of the step, Indicates the training samples, represents the kernel function for reconstructing the test set, , represents the weight of the Gaussian kernel in the kernel function of the reconstructed test set, represents the width of the Gaussian kernel in the kernel function of the reconstructed test set, represents the bias term of the polynomial kernel in the kernel function of the reconstructed test set, represents the power of the polynomial kernel in the kernel function used to reconstruct the test set, Indicates that after The mean vector of the posterior distribution after the iteration update A value; The predicted sequence is expressed as: ,in, represents the prediction sequence, express dimensional real number space; The residual sequence is expressed as: , represents the residual sequence, Represents the output target of all test samples.

7. The method for detecting anomalies in nonlinear dynamic data during multi-process stages of silicon single crystal growth according to claim 1, characterized in that: The step of dividing the residual sequence into a plurality of segmentation windows by using all the segmentation points, and traversing each of the segmentation windows in sequence by using all the sliding windows to obtain a plurality of sliding window data sets includes: The set of all the segmentation points is expressed as: ,in, Indicates the segmentation points; Using all the segmentation points, the residual sequence is divided into The segmentation windows; the set of all the segmentation windows is expressed as: ,in, represents the first All residual values within the segmented window, , represents the first The last residual value in the segmented window; All the sliding windows are respectively subjected to preset processing, and all the sliding windows after the preset processing are used to traverse each of the segmented windows in sequence to obtain a plurality of sliding window data sets.

8. The method for detecting anomalies in nonlinear dynamic data during multi-process stages of silicon single crystal growth according to claim 7, characterized in that: The steps of introducing a dynamic threshold strategy, generating corresponding candidate threshold sets according to the statistical characteristics of all the sliding window data sets, performing anomaly detection on the corresponding sliding windows using all the candidate threshold sets, and fusing the anomaly detection results of all the sliding windows to obtain the final anomaly detection result include: Calculate the mean and standard deviation of all window data in each sliding window data set respectively, and make each sliding window data set The values are equally spaced within the preset interval; According to the mean and standard deviation of all the window data in each sliding window data set and the results of all the corresponding equidistant values, a plurality of candidate thresholds of the corresponding sliding window are calculated respectively to form the candidate threshold set; Calculate the corresponding values of each candidate threshold of all sliding windows respectively Value rating; Traverse all the sliding windows separately The value score is obtained to obtain the maximum value of the corresponding sliding window The value score corresponds to the value; Utilize all the maximum The value score corresponds to the value, respectively calculating the optimal threshold value of the corresponding sliding window; Using all the optimal thresholds, perform anomaly detection on the corresponding sliding windows respectively, and mark all the window data in all the sliding windows that are greater than or equal to the corresponding optimal threshold as anomalies, and mark all the remaining window data as normal points; Introducing a sliding window false alarm point, setting a lower limit on the number of abnormal points, and comparing the number of all abnormal points in each sliding window with the lower limit on the number of abnormal points; If the number of all abnormal points in the sliding window is greater than or equal to the lower limit of the number of abnormal points, it is considered that an abnormality exists in the sliding window, and the abnormality detection results of all the sliding windows are integrated to obtain the final abnormality detection result; If the number of all the outliers in the sliding window is less than the lower limit of the number of outliers, all the outliers are pruned, and the outlier detection results of all the sliding windows after the pruning process are fused to obtain the final outlier detection result.

9. The method for detecting anomalies in nonlinear dynamic data during multi-process stages of silicon single crystal growth according to claim 8, characterized in that: The expression of the candidate threshold is: (8) in, represents the candidate threshold of the sliding window, Represents the mean of all window data in the sliding window dataset, express value, which is the quantile in the standard normal distribution, Represents the standard deviation of all window data in the sliding window dataset, Represents the number of all window data in the sliding window dataset; described The expression for the value score is: (9) in, express Value rating, Indicates the offset of the mean of all abnormal points in the sliding window dataset, , represents the mean of all normal points in the sliding window dataset, represents the number of all abnormal points in the sliding window dataset, , represents the number of all normal points in the sliding window dataset, , represents the offset of the standard deviation of all abnormal points in the sliding window dataset, , represents the standard deviation of all normal points in the sliding window dataset, Represents the number of all abnormal points in the sliding window dataset after pruning, Represents the number of all consecutive outliers in the sliding window dataset.

10. The method for detecting anomalies in nonlinear dynamic data during multi-process stages of silicon single crystal growth according to claim 8, characterized in that: The expression of the optimal threshold is: (10) in, represents the optimal threshold of the sliding window, Indicates the maximum sliding window The value score corresponds to value.

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