Method for estimating molten silicon level based on hybrid adaptive resampling particle filter

Abstract

The application discloses a molten silicon liquid level estimation method based on a hybrid adaptive resampling particle filter, and comprises the following steps: firstly, processing laser spot images collected by a CCD sensor to obtain observation data of the liquid level; then, establishing a system state equation of the molten silicon liquid level according to a kinematic principle to describe the movement of the liquid level; performing state estimation on a laser centroid vertical coordinate by using a particle filter algorithm, and obtaining a new particle set by using a hybrid adaptive resampling method; after re-normalizing all particle weights, outputting an optimal estimation value; and finally, smoothing the filtered data by using a moving weighted average method, and the smoothed result is the estimation value of the molten silicon liquid level. The application solves the problem that in the prior art, the variance of Gaussian variation is too large, particles jump out of a sampling range, and it is difficult to accurately estimate a real liquid level.

Description

Technical Field

[0001] This invention belongs to the field of non-contact silicon molten liquid level detection technology, specifically relating to a method for estimating molten silicon liquid level based on hybrid adaptive resampling particle filtering. Background Technology

[0002] Single-crystal silicon, as a crucial semiconductor material in integrated circuits, is widely used in microelectronics, aerospace, and other fields. During the Czochralski (CZ) single-crystal silicon growth process, the molten silicon level is a critical parameter. As the crystal length increases, the amount of molten silicon in the crucible gradually decreases, resulting in a smaller measured diameter of the silicon single crystal, and even causing the diameter control system to diverge, thus affecting the production of high-quality single-crystal silicon. Therefore, to further meet the requirements of the single-crystal furnace molten silicon level control system, accurately detecting the liquid level position is a key issue in silicon single-crystal growth.

[0003] Molten silicon is contained within a single-crystal furnace. Due to the high temperature and sealed nature of this equipment, its liquid level cannot be directly measured. Therefore, it is indirectly obtained by installing a CCD camera on the furnace lid. This method calculates the liquid level position based on the positional changes of the laser spot in the camera. The liquid level data acquired by the CCD camera often contains complex noise influenced by the actual environment, severely affecting the accuracy of the measured liquid level and impacting the estimation results. Therefore, accurate estimation of the molten silicon liquid level is crucial for producing high-quality crystals. This paper proposes a molten silicon liquid level estimation method based on hybrid adaptive resampling particle filtering. By improving the particle distribution, the filtering accuracy and precision are enhanced, thereby improving the estimation accuracy of the molten silicon liquid level. Summary of the Invention

[0004] The purpose of this invention is to provide a method for estimating the level of molten silicon based on hybrid adaptive resampling particle filtering, which solves the problem in the prior art where the variance of Gaussian variation is too large and particles jump out of the sampling range, making it difficult to accurately estimate the true level.

[0005] The technical solution adopted in this invention is a molten silicon level estimation method based on hybrid adaptive resampling particle filtering, which is implemented according to the following steps:

[0006] Step 1: Process the acquired laser spot image using a CCD sensor to obtain liquid level observation data;

[0007] Step 2: Establish the system state equation of the molten silicon level based on the principles of kinematics to describe the motion of the level;

[0008] Step 3: Estimate the state of the laser centroid ordinate using the particle filter algorithm, and obtain a new particle set using the hybrid adaptive resampling method;

[0009] Step 4: After renormalizing all particle weights Output the optimal estimate;

[0010] Step 5: Finally, smooth the filtered data using the moving weighted average method. The smoothed result is the estimated value of the molten silicon level.

[0011] The invention is further characterized in that,

[0012] Step 1 is as follows:

[0013] Linear laser emitters and CCD cameras are installed on both sides of the single-crystal furnace cover. A straight laser beam is emitted from the laser emitter, reflected by the surface of the molten silicon, and finally received and collected by the CCD camera to obtain the laser spot image. The laser spot image collected by the CCD is binarized to obtain several laser spot regions. The centroid of each laser spot is calculated, and finally, the ordinate of the centroid of each laser spot is obtained. The observed liquid level data is used as the ordinate y of the laser spot. k That is, the vertical coordinate of the line laser centroid of each frame of the spot image;

[0014] Step 2 is implemented in the following steps:

[0015] Step 2.1: Let the state variable x k Given the true value of the laser centroid's ordinate, the observed values ​​obtained from the CCD camera are filtered, and a mathematical model of the liquid level is established based on kinematic principles:

[0016]

[0017] In the formula, x k Let x be the true value of the ordinate of the laser centroid at time k. k-1 Let v be the true value of the ordinate of the laser centroid at time k-1. k Let a be the laser spot movement velocity at time k. k-1 Let v be the acceleration of the laser spot at time k-1. k and a k It is determined by the moving speed and acceleration of the liquid level, respectively, and Δt is the sampling time;

[0018] Step 2.2: Define the state variable x k =[x k ,ν k ] T The mathematical model for liquid level is written as:

[0019]

[0020] In the formula, w k and vk Let the process noise and measurement noise be respectively, and define the observation matrix of the observation equation as C = [1, 0].

[0021] Step 3 is implemented in the following steps:

[0022] Step 3.1: Perform initialization, i.e., at time k = 0, randomly draw state samples from the prior distribution p(x) to obtain the initial particles. Where k is the time series, k = 1, 2, ..., T, and T is the length of the time series. This represents a random estimate of the system state. The initial weights of the particles are represented by , where i represents the index of the i-th particle, i = 1, 2, ..., N, and N is the number of samples for the random estimate of the system state.

[0023] Step 3.2, from the importance probability density function q(x) k |x k-1 ,y k Particles are extracted from the sample, and the particle weights are calculated according to equation (3). The weights are then normalized according to equation (4) to obtain the particle set.

[0024]

[0025]

[0026] In formulas (3) and (4), For the i-th particle at time k Weights before normalization To observe the likelihood probability density, Let the state transition probability density be... Let be the importance probability density function. This represents the state of the i-th particle at time k. This represents the normalized weight of the i-th particle at time k;

[0027] Step 3.3: First, set the weight threshold W. T Then the particle set Based on the weight threshold W T Divided into a high-weight particle set X H and low-weight particle set X L If the particle's weight is greater than the weight threshold W T Then it is stored in X H If the particle's weight is less than the weight threshold W T Then it is stored in X L For the high-weight particle set X H To retain, particle set The specific division method is as follows:

[0028]

[0029] W T Defined as:

[0030]

[0031] N eff Defined as:

[0032]

[0033] In formulas (5), (6), and (7), X L For a set of low-weight particles, X H For a high-weighted particle set, W T For the weight threshold, Indicates rounding up, N eff The effective number of particles;

[0034] Step 3.4: The low-weight particle set X obtained in Step 3.3... L Resampling is performed, and the selection probability of the two strategies is controlled by adaptively adjusting the value of the selection probability λ. Specifically, the adaptive Gaussian mutation strategy of step 3.5 is selected with probability λ, or the crossover strategy of step 3.6 is selected with probability 1-λ, generating new particles. The formula for calculating λ is...

[0035]

[0036] Step 3.5: Use an adaptive Gaussian mutation strategy to generate new particles, employing a random walk strategy to select particles from the high-weight particle set X. H A particle is randomly selected from the sample and Gaussian mutation is performed according to equation (9). Then, an adaptive variance function is established using the minimum Euclidean distance between each pair of particles to ensure that the re-selected particle is located near the high-weight particle and in a high-probability region.

[0037]

[0038] In the formula, Let j be the particle after the crossover, where j∈{1,2,…N} L}, N L The number of particles in the low-weight particle set; For each particle before mutation, l∈{1,2,…N} H}, N H is the number of particles in the high-weight particle set; μ is the mean. For variance;

[0039] The adaptive variance function is:

[0040]

[0041] In the formula, m is the particle number extracted.

[0042] Step 3.6: Use an adaptive crossover strategy to generate intermediate-weight particles between the high-weight particle set and the low-weight particle set. Specifically, randomly select particles from the high-weight particle set X. H Extracting a particle from the sample and crossing it with the currently sampled low-weight particle is essentially sampling in the region between the high-weight particle region and the low-weight particle region, which helps to increase the number of effective particles. The particles after the adaptive cross-resampling strategy are calculated according to equation (11).

[0043]

[0044] In the formula, For the crossed particles, For particles in the low-weight particle set, where j∈{1,2,…N} L}, N L This represents the number of particles in the low-weight particle set. For particles in the high-weight particle set, where l∈{1,2,…N} H}, N H The number of particles in the high-weight particle set, a random number. The crossover rate is calculated using the following formula:

[0045]

[0046] Step 3.7: Based on the improved accept-rejection criterion function, directly compare the weights of the two particles and deterministically accept or reject the new particle to obtain the particle. The improved acceptance / rejection function is shown in equation (13):

[0047]

[0048] In the formula, These are particles that have undergone acceptance / rejection operations after resampling;

[0049] Step 3.8: Add new particles Place it into the high-weight particle set X H A new set of particles is obtained.

[0050] Step 4 is implemented in the following steps:

[0051] Step 4.1: Weight the resampled particles to obtain the state estimate at time k:

[0052]

[0053] Step 4.2, Output as the optimal estimate of the vertical coordinate of the laser spot.

[0054] Step 5 is implemented in the following steps:

[0055] Step 5.1: Based on the principle of laser triangulation, the change in liquid level and the vertical coordinate of the laser spot are... The relationship between the changes is approximately linear, that is:

[0056]

[0057] In the formula, L k Let x be the molten silicon level at time k. zero Let M be the estimated value of the initial position, which is the zero point of the laser spot's ordinate. M is a scaling factor, which can be obtained from the absolute position of the crucible and... relative to x zero The changes were derived from;

[0058] Step 5.2: Analyze the filtered liquid level output L... k Smoothing is performed using a moving weighted average method. The smoothing formula is as follows:

[0059]

[0060] In the formula, This is the final estimated silicon melt level, where m is the set smoothing interval value, and L... i Let be the level of the molten silicon at time i.

[0061] The beneficial effects of this invention are as follows: The molten silicon level estimation method based on hybrid adaptive resampling particle filtering filters the centroid ordinate obtained by laser triangulation. An adaptive selection strategy is designed using the adaptive MH sampling method. Depending on the particle distribution, low-weight particle sets are resampled using either Gaussian mutation or crossover, causing particles to move towards higher probability regions. Specifically, Gaussian mutation involves randomly selecting a particle from the high-weight particle set and performing Gaussian mutation. The variance in Gaussian mutation is based on the minimum Euclidean distance between any two particles in the high-weight particle set, avoiding particle deviation from the high-probability region in multi-peak distribution scenarios. Crossover involves generating intermediate-weight particles between the high-weight and low-weight particle sets through crossover between them. Then, a receive-reject criterion function is used to decide whether to accept new particles or retain existing ones, and the high-weight particle set is updated in real time. This ensures that better particles are accepted and worse particles are eliminated, overcoming the problem of concentrated new particle distribution when there are few high-weight particles. Finally, the system is filtered to obtain the optimal molten silicon level estimate. This invention uses a hybrid adaptive resampling operation to keep newly extracted particles in a high-probability region, optimizing the quality of particles after resampling. After new particles are generated, they are added to the high-weight particle set in real time, avoiding the situation where individual particles are repeatedly extracted when the number of high-weight particles is small, which would cause the distribution of new particles to be too concentrated in a narrow high-probability region. This improves the precision and accuracy of filtering, resulting in better filtering performance of the system. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the detection principle of the estimation method of the present invention;

[0063] Figure 2 This is a sequence of original data on the centroid ordinate of the line laser when the liquid surface is stationary in the estimation method of this invention;

[0064] Figure 3 This is the estimation result of the centroid ordinate of the line laser when the liquid surface is stationary, using the estimation method of this invention;

[0065] Figure 4 This is the liquid level detection result when the liquid surface is stationary, as estimated by the method of the present invention;

[0066] Figure 5 This is a sequence of original data on the centroid ordinate of the linear laser beam when the liquid level rises by 2.5 mm in the estimation method of this invention.

[0067] Figure 6 This is the estimation result of the linear laser centroid ordinate when the liquid level rises by 2.5 mm using the estimation method of this invention;

[0068] Figure 7 This is the liquid level detection result when the liquid level rises by 2.5 mm using the estimation method of this invention;

[0069] Figure 8 This is a sequence of original data on the linear laser centroid ordinate when the liquid level drops by 2.5 mm in the estimation method of this invention;

[0070] Figure 9 This is the estimation result of the linear laser centroid ordinate when the liquid level drops by 2.5 mm using the estimation method of this invention;

[0071] Figure 10 This is the liquid level detection result when the liquid level drops by 2.5 mm using the estimation method of this invention. Detailed Implementation

[0072] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0073] This invention discloses a method for estimating molten silicon level based on hybrid adaptive resampling particle filtering. Due to the characteristics of a single-crystal furnace, laser triangulation is used to measure the level. A linear laser emitter is installed at a certain angle on one side of the furnace cover as the laser emitting device, and a CCD camera is installed symmetrically at the emitter as the receiving device. The angles of the laser emitter and the CCD camera are adjusted so that the linear laser emitted by the laser emitter is reflected by the molten silicon surface and received by the CCD camera, displaying the image of the laser spot. The centroid ordinate of the laser spot is thus obtained, and the transformation of the centroid's vertical coordinate reflects the change in the molten silicon level. First, a system state equation for the molten silicon level is established based on kinematic principles to describe the movement of the level. Then, state estimation is performed using particle filtering theory. A certain number of particles are extracted from the importance density function, and particle weights are calculated. The particles are arranged in descending order according to the weight threshold. Next, an adaptive MH resampling method is used to re-extract low-weight particles to optimize the particle distribution. Finally, the filtered data is smoothed using a moving weighted average method, and the position information of the level is obtained by calibration using the absolute displacement of the crucible.

[0074] This invention relates to a method for estimating the level of molten silicon based on hybrid adaptive resampling particle filtering. The detection principle is as follows: Figure 1 As shown, please follow these steps:

[0075] Step 1: Process the acquired laser spot image using a CCD sensor to obtain liquid level observation data;

[0076] Step 1 is as follows:

[0077] like Figure 1As shown, linear laser emitters and CCD cameras are installed on both sides of the single-crystal furnace cover. A straight laser beam is emitted by the laser emitter and reflected by the surface of the molten silicon, ultimately being received and collected by the CCD camera to obtain the laser spot image. The laser spot image collected by the CCD is binarized to obtain several laser spot regions. The centroid of each laser spot is calculated, and finally, the ordinate of the centroid of each laser spot is obtained. The observed liquid level data is used as the ordinate y of the laser spot. k That is, the vertical coordinate of the line laser centroid of each frame of the spot image;

[0078] Step 2: Establish the system state equation of the molten silicon level based on the principles of kinematics to describe the motion of the level;

[0079] Step 2 is implemented in the following steps:

[0080] Step 2.1: In the Czochralski method for growing single-crystal silicon, the movement of the centroid's ordinate in the linear laser is a disturbed, randomly accelerated linear motion, determined by the drop in liquid level and the control system. Let the state variable be x. k Given the true value of the laser centroid's ordinate, the observed values ​​obtained from the CCD camera are filtered, and a mathematical model of the liquid level is established based on kinematic principles:

[0081]

[0082] In the formula, x k Let x be the true value of the ordinate of the laser centroid at time k. k-1 Let v be the true value of the ordinate of the laser centroid at time k-1. k Let a be the laser spot movement velocity at time k. k-1 Let v be the acceleration of the laser spot at time k-1. k and a k It is determined by the moving speed and acceleration of the liquid level, respectively, and Δt is the sampling time;

[0083] Step 2.2: Define the state variable x k =[x k ,ν k ] T The mathematical model for liquid level is written as:

[0084]

[0085] In the formula, w k and v k Let the process noise and measurement noise be respectively, and define the observation matrix of the observation equation as C = [1, 0].

[0086] Step 3: Estimate the state of the molten silicon level using a particle filter algorithm, and obtain a new particle set using a hybrid adaptive resampling method;

[0087] Step 3 is implemented in the following steps:

[0088] In the particle filter algorithm, a set of random sampling points (i.e., particles) is used to approximate the posterior probability density of the state variable. The actual meaning represented by the particle is the molten silicon level value.

[0089] Step 3.1: Perform initialization, i.e., at time k = 0, randomly draw state samples from the prior distribution p(x) to obtain the initial particles. Where k is the time series, k = 1, 2, ..., T, and T is the length of the time series. This represents a random estimate of the system state. The initial weights of the particles are represented by , where i represents the index of the i-th particle, i = 1, 2, ..., N, and N is the number of samples for the random estimate of the system state.

[0090] Step 3.2, from the importance probability density function q(x) k |x k-1 ,y k Particles are extracted from the sample, and the particle weights are calculated according to equation (3). The weights are then normalized according to equation (4) to obtain the particle set.

[0091]

[0092]

[0093] In formulas (3) and (4), For the i-th particle at time k Weights before normalization To observe the likelihood probability density, Let the state transition probability density be... Let be the importance probability density function. This represents the state of the i-th particle at time k. This represents the normalized weight of the i-th particle at time k;

[0094] Step 3.3: First, set the weight threshold W. T Then the particle set Based on the weight threshold W T Divided into a high-weight particle set X H and low-weight particle set X L If the particle's weight is greater than the weight threshold W T Then it is stored in X H If the particle's weight is less than the weight threshold WT Then it is stored in X L For the high-weight particle set X H To retain, particle set The specific division method is as follows:

[0095]

[0096] W T Defined as:

[0097]

[0098] N eff Defined as:

[0099]

[0100] In formulas (5), (6), and (7), X L For a set of low-weight particles, X H For a high-weighted particle set, W T For the weight threshold, Indicates rounding up, N eff The effective number of particles;

[0101] Step 3.4: The low-weight particle set X obtained in Step 3.3... L Resampling is performed, and the selection probability of the two strategies is controlled by adaptively adjusting the value of the selection probability λ. Specifically, the adaptive Gaussian mutation strategy of step 3.5 is selected with probability λ, or the crossover strategy of step 3.6 is selected with probability 1-λ, generating new particles. The formula for calculating λ is...

[0102]

[0103] Step 3.5: Use the adaptive Gaussian mutation strategy to generate new particles. Its main idea is to employ a random walk strategy to generate new particles from the high-weight particle set X. H A particle is randomly selected from the sample and Gaussian mutation is performed according to equation (9). Then, an adaptive variance function is established using the minimum Euclidean distance between each pair of particles to ensure that the re-selected particle is located near the high-weight particle and in a high-probability region.

[0104]

[0105] In the formula, Let j be the particle after the crossover, where j∈{1,2,N} L}, N L The number of particles in the low-weight particle set; For each particle before mutation, l∈{1,2,N} H}, N His the number of particles in the high-weight particle set; μ is the mean. For variance;

[0106] The adaptive variance function is:

[0107]

[0108] In the formula, m is the particle number extracted.

[0109] Step 3.6: Use an adaptive crossover strategy to generate intermediate-weight particles between the high-weight particle set and the low-weight particle set. Specifically, randomly select particles from the high-weight particle set X. H Extracting a particle from the sample and crossing it with the currently sampled low-weight particle is essentially sampling in the region between the high-weight particle region and the low-weight particle region, which helps to increase the number of effective particles. The particles after the adaptive cross-resampling strategy are calculated according to equation (11).

[0110]

[0111] In the formula, For the crossed particles, For particles in the low-weight particle set, where j∈{1,2,N} L}, N L This represents the number of particles in the low-weight particle set. For particles in the high-weight particle set, where l∈{1,2,…N} H}, N H The number of particles in the high-weight particle set, a random number. The crossover rate is calculated using the following formula:

[0112]

[0113] Step 3.7: Based on the improved accept-rejection criterion function, directly compare the weights of the two particles and deterministically accept or reject the new particle to obtain the particle. The improved acceptance / rejection function is shown in equation (13):

[0114]

[0115] In the formula, These are particles that have undergone acceptance / rejection operations after resampling;

[0116] Step 3.8: Add new particles Place it into the high-weight particle set X H A new set of particles is obtained.

[0117] Step 4: After renormalizing all particle weights Output the optimal estimate;

[0118] Step 4 is implemented in the following steps:

[0119] Step 4.1: Weight the resampled particles to obtain the state estimate at time k:

[0120]

[0121] Step 4.2, Output as the optimal estimate of the vertical coordinate of the laser spot.

[0122] Step 5: Finally, smooth the filtered data using the moving weighted average method. The smoothed result is the estimated value of the molten silicon level.

[0123] Step 5 is implemented in the following steps:

[0124] Step 5.1: Based on the principle of laser triangulation, the change in liquid level and the vertical coordinate of the laser spot are... The relationship between the changes is approximately linear, that is:

[0125]

[0126] In the formula, L k Let x be the molten silicon level at time k. zero Let M be the estimated value of the initial position, which is the zero point of the laser spot's ordinate. M is a scaling factor, which can be obtained from the absolute position of the crucible and... relative to x zero The changes were derived from;

[0127] Step 5.2: Analyze the filtered liquid level output L... k Smoothing is performed using a moving weighted average method. The smoothing formula is as follows:

[0128]

[0129] In the formula, This is the final estimated silicon melt level, where m is the set smoothing interval value, and L... i Let be the level of the molten silicon at time i.

[0130] Example 1

[0131] This embodiment estimates the liquid level in a TDR-150 single-crystal furnace. A 650nm linear semiconductor laser is located on one side of the furnace, and a CCD camera is located on the other side. The linear laser emitted by the laser emitter is reflected from the liquid surface and received by the CCD camera. The acquisition principle is as follows: Figure 1 As shown.

[0132] Adjusting the crucible changes the liquid level. As the liquid level moves up and down, the position of the laser spot received by the CCD camera also changes. The change in the vertical position of the laser spot can reflect the change in the silicon melt level relative to the reference position, thereby calculating the change in the silicon melt level.

[0133] The liquid level is calibrated by positioning the crucible. Let M be the calibration proportionality coefficient. The specific method is as follows: Let the initial observed liquid level value be X. zero The value is 400.4. The position of the crucible is adjusted so that the liquid level drops by 1 mm. The observed value after the liquid level drops is 408.6. According to the formula (15), the proportionality coefficient is calculated to be M-0.122.

[0134] After calibration, the liquid level was first kept constant, then increased by 2.5 mm, and finally decreased by 2.5 mm. Data was collected and image processed. The original data sequences of the linear laser centroid ordinates for the liquid level at constant level, 2.5 mm increase, and 2.5 mm decrease are shown below. Figure 2 , Figure 5 and Figure 8 As shown; Figure 3 , Figure 6 and Figure 9 The results are the estimated ordinates of the line laser centroid estimated by this invention when the liquid level remains constant, the liquid level rises by 2.5 mm, and the liquid level falls by 2.5 mm, respectively.

[0135] When the liquid level remains constant, the observed data remains at 400.6. Substituting this into formula (15) yields the change in liquid level position as follows:

[0136] L=-0.122×(400.6-400.6)≈0mm

[0137] After smoothing the data, a measurement curve with the liquid level remaining unchanged is obtained, such as... Figure 4 As shown.

[0138] Example 2

[0139] When the liquid level rises by 2.5 mm, the observed data moves from 400.6 to 420.9. Substituting this into formula (15), the change in liquid level is:

[0140] L=-0.122×(400.6-420.9)≈2.5mm

[0141] After smoothing the data, a measurement curve showing the liquid level rising 2.5 mm from 0 is obtained, as shown below. Figure 7 As shown.

[0142] Example 3

[0143] When the liquid level drops by 2.5 mm, the observed data moves from 420.9 to 400.4. Substituting this into formula (15), the change in liquid level is:

[0144] L=-0.122×(420.9-400.4)≈-2.5mm

[0145] After smoothing the data, a measurement curve showing the liquid level dropping 2.5 mm from 0 is obtained, as shown below. Figure 10 As shown.

[0146] pass Figure 4 , Figure 7 and Figure 10 Based on the raw data and actual silicon molten liquid level movement data, the average and maximum absolute measurement errors for all data points were calculated. Figure 4 The calculated results are 0.013 mm and 0.008 mm, respectively. Figure 7 The calculated results are 0.017 mm and 0.011 mm, respectively. Figure 10 The calculated results are 0.012 mm and 0.009 mm, respectively, which meet the requirements of the large-scale electronic-grade integrated circuit silicon melt level control system (within ±0.1 mm).

Claims

1. A method for estimating molten silicon level based on hybrid adaptive resampling particle filtering, characterized in that, The specific steps are as follows: Step 1: Process the acquired laser spot image using a CCD sensor to obtain liquid level observation data; Step 1 is described in detail as follows: Linear laser emitters and CCD cameras are installed on both sides of the single-crystal furnace cover. A straight laser beam is emitted from the laser emitter, reflected by the surface of the molten silicon, and finally received and collected by the CCD camera to obtain the laser spot image. The laser spot image collected by the CCD is binarized to obtain several laser spot regions. The centroid of each laser spot is calculated, and finally, the ordinate of the centroid of each laser spot is obtained. The observed liquid level data is used as the ordinate of the laser spot. That is, the vertical coordinate of the line laser centroid of each frame of the spot image; Step 2: Establish the system state equation of the molten silicon level based on the principles of kinematics to describe the motion of the level; Step 2 is implemented in the following steps: Step 2.1: Define the state variables. Given the true value of the laser centroid's ordinate, the observed values ​​obtained from the CCD camera are filtered, and a mathematical model of the liquid level is established based on kinematic principles: （1） In the formula, for The true value of the ordinate of the laser centroid at time [time]. for The true value of the ordinate of the laser centroid at time [time]. for The speed at which the laser spot moves at any given moment. for The acceleration of the laser spot movement at any given moment. and It is determined by the speed and acceleration of the liquid level movement, respectively. Sampling time; Step 2.2: Define state variables The mathematical model for liquid level is written as: （2） In the formula, , , and Let process noise and measurement noise be respectively, and the observation matrix of the observation equation be defined as follows: ; Step 3: Estimate the state of the laser centroid ordinate using the particle filter algorithm, and obtain a new particle set using the hybrid adaptive resampling method; Step 3 is implemented in the following steps: Step 3.1: Perform initialization operations, i.e., at time... From the prior distribution Initial particles are obtained by randomly sampling state samples. ,in, It is a time series. , The length of the time series. This represents a random estimate of the system state. This represents the initial particle weights. Indicates the first The index of each particle. , The number of samples for the random estimate of the system state; Step 3.2, from the importance probability density function Particles are extracted from the sample, and their weights are calculated according to equation (3). The weights are then normalized according to equation (4) to obtain the particle set. ; （3） （4） In formulas (3) and (4), for Time of the first Particles Weights before normalization To observe the likelihood probability density, Let the state transition probability density be... Let be the importance probability density function. express Time of the first The state of each particle express Time of the first Normalized weights of each particle; Step 3.3: First, set the weight threshold. Then the particle set Based on weight threshold Divided into high-weight particle sets and low-weight particle set If the particle's weight is greater than the weight threshold Then stored in If the particle's weight is less than the weight threshold Then stored in For high-weight particle sets To retain, particle set The specific division method is as follows: （5） Defined as: （6） Defined as: （7） In formulas (5), (6), and (7), For a low-weight particle set, For a high-weight particle set, For the weight threshold, Indicates rounding up. The effective number of particles; Step 3.4: The low-weight particle set obtained in Step 3.3... Resampling is performed, and the selection probability is adaptively adjusted. The value controls the probability of choosing between the two strategies, that is, using probability... Choose the adaptive Gaussian mutation strategy from step 3.5, or... The probability selection step 3.6 uses the crossover strategy to generate new particles. The calculation formula is （8） Step 3.5: Use an adaptive Gaussian mutation strategy to generate new particles, employing a random walk strategy to select from the high-weight particle set. A particle is randomly selected from the sample and Gaussian mutation is performed according to equation (9). Then, an adaptive variance function is established using the minimum Euclidean distance between the two particles to ensure that the re-selected particle is located near the high-weight particle and in a high-probability region. （9） In the formula, For the crossed particles, where, , The number of particles in the low-weight particle set; For the particles before mutation, among which, , The number of particles in the high-weight particle set; The mean, For variance; The adaptive variance function is: （10） In the formula, The extracted particle number. ; Step 3.6: Use an adaptive crossover strategy to generate intermediate-weight particles between the high-weight particle set and the low-weight particle set. Specifically, randomly select particles from the high-weight particle set... Extracting a particle from the sample and crossing it with the currently sampled low-weight particle is essentially sampling in the region between the high-weight particle region and the low-weight particle region, which helps to increase the number of effective particles. The particles after the adaptive cross-resampling strategy are calculated according to equation (11). （11） In the formula, For the crossed particles, For particles in the low-weight particle set, among which, , This represents the number of particles in the low-weight particle set. For particles in the high-weight particle set, among which, , The number of particles in the high-weight particle set, a random number. The crossover rate is calculated using the following formula: （12） Step 3.7: Based on the improved accept-rejection criterion function, directly compare the weights of the two particles and deterministically accept or reject the new particle to obtain the particle. The improved acceptance / rejection function is shown in equation (13): （13） In the formula, These are particles that have undergone acceptance / rejection operations after resampling; Step 3.8: Add new particles Place into a high-weight particle set A new set of particles is obtained. . Step 4: After renormalizing all particle weights Output the optimal estimate; Step 5: Finally, smooth the filtered data using the moving weighted average method. The smoothed result is the estimated value of the molten silicon level.

2. The method for estimating molten silicon level based on hybrid adaptive resampling particle filtering according to claim 1, characterized in that, Step 4 is implemented in the following steps: Step 4.1: Weight the resampled particles to obtain... State estimate at time: （14） Step 4.2, Output as the optimal estimate of the vertical coordinate of the laser spot.

3. The method for estimating molten silicon level based on hybrid adaptive resampling particle filtering according to claim 2, characterized in that, Step 5 is implemented in the following steps: Step 5.1: Based on the principle of laser triangulation, the change in liquid level and the vertical coordinate of the laser spot are... The relationship between the changes is approximately linear, that is: （15） In the formula, for The level of the molten silicon at any given time. This is an estimated value for the initial position of the laser spot's ordinate zero. This is the proportionality coefficient. It can be determined by the absolute position of the crucible and relatively The changes were derived from; Step 5.2: Analyze the filtered liquid level output. Smoothing is performed using a moving weighted average method. The smoothing formula is as follows: （16） In the formula, This represents the final estimated molten silicon level, where m is the set smoothing interval value. for The level of the molten silicon at any given time.

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