CN111210877B - Method and device for deducing physical parameters - Google Patents

Method and device for deducing physical parameters Download PDF

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CN111210877B
CN111210877B CN202010006973.1A CN202010006973A CN111210877B CN 111210877 B CN111210877 B CN 111210877B CN 202010006973 A CN202010006973 A CN 202010006973A CN 111210877 B CN111210877 B CN 111210877B
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CN111210877A (en
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舒天宇
王雅儒
张红岩
王秀平
黄长航
周国顺
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Shandong Tianyue Advanced Technology Co Ltd
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Abstract

The application discloses a method and a device for deducing physical parameters, which are used for solving the problem that under certain specific conditions, the physical parameters of accurate materials are difficult to obtain, so that simulation results obtained by simulation through simulation software are affected. According to the method, a training data set is established through simulation software according to the physical parameters of a preset material to be inferred, and a neural network model is trained; determining actual result parameters corresponding to materials to be inferred under preset process conditions; and determining the actual physical parameters of the material to be inferred by adopting the neural network model and a preset numerical optimization algorithm according to the actual result parameters. The method is based on machine learning and combined with a numerical optimization algorithm, so that the physical property parameters of the material can be obtained as accurately as possible, and the physical property parameters can be accurately mastered, so that the consistency between the simulation result and the actual result is enhanced.

Description

Method and device for deducing physical parameters
Technical Field
The application relates to the technical field of simulated crystal growth, in particular to a method and a device for deducing physical parameters.
Background
In the industrial production process, physical parameters of materials often have great influence on the production process and the production result. Wherein, the physical property parameters of the material represent the parameter data of whether the material can meet the production requirements in the aspects of manufacturing, performance and the like.
In particular, in the process of simulating crystal growth, incorrect physical parameters of materials may cause inaccurate prediction of result parameters such as temperature distribution, crystal convexity, crystal shape and the like in the process of crystal growth, so that an error between a simulation result and an actual result is large.
Currently, the physical parameters of materials are determined and available from the material suppliers. However, the accuracy of the data given by the material suppliers may be low. In particular, for physical parameters of materials required in the crystal growth process, since the temperature in the crystal growth process is as high as thousands of degrees celsius, it is difficult to obtain accurate data of the physical parameters at high temperature, which is unfavorable for accurate simulation of the crystal growth process.
Disclosure of Invention
The embodiment of the application provides a method and a device for deducing physical parameters, which are used for solving the problem that under specific conditions such as high temperature, the physical parameters of accurate materials are difficult to obtain, so that simulation results obtained by simulation through simulation software are affected.
The method for deducing the physical parameters provided by the embodiment of the application comprises the following steps:
according to the physical parameters of the preset material to be inferred, a training data set is established through simulation software, and a neural network model is trained;
determining actual result parameters corresponding to the material to be inferred under preset process conditions;
and determining the actual physical parameters of the material to be inferred by adopting the neural network model and a preset numerical optimization algorithm according to the actual result parameters.
The device for deducing the physical parameters provided by the embodiment of the application comprises:
the training module is used for establishing a training data set through simulation software according to the physical parameters of the preset material to be inferred and training a neural network model;
the first determining module is used for determining actual result parameters corresponding to the material to be inferred under the preset process conditions;
and the second determining module is used for determining the actual physical parameters of the material to be inferred by adopting the neural network model and a preset numerical optimization algorithm according to the actual result parameters.
The embodiment of the application provides a method and a device for deducing physical parameters, which are characterized in that a neural network model is trained, a numerical value optimization algorithm is adopted for reverse thrust, a plurality of initial values are subjected to iterative optimization, and an optimal solution of the physical parameters of a material is determined from an optimization result and is used as the actual physical parameters of the material.
By the method, on the basis of machine learning, a numerical optimization algorithm is combined, and under the condition that the physical property parameters of the material are difficult to obtain, the actual physical property parameters of the material are obtained as accurately as possible through multiple iterations according to the actual result parameters.
In particular, the crucible used in crystal growth is not limited by the high temperature of the crystal growth environment, and there is no need to worry about the difficulty in obtaining the physical parameters of the crucible. Even under the high temperature condition, the physical property parameters of the most accurate materials can be determined by the result parameters of crystal growth in a back-pushing way, so that the simulation result parameters of the crystals obtained through simulation are further perfected.
The physical parameters obtained by the method can enable the simulation result parameters obtained by the simulation software according to the physical parameters to be consistent with the actual result parameters as much as possible, so as to reduce the error between the simulation result and the actual result and achieve the consistency of the simulation result and the actual result.
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The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1 is a flow chart of a method for estimating physical parameters according to an embodiment of the present application;
fig. 2 is a schematic diagram of an optimization principle of an L-BFGS algorithm provided in an embodiment of the present application;
FIGS. 3 (a) to 3 (c) are schematic diagrams showing the results of optimizing physical properties of the crucible according to the embodiment of the present application;
fig. 4 (a) -4 (b) are schematic diagrams illustrating the relationship between simulation result parameters and actual result parameters according to embodiments of the present application;
fig. 5 is a schematic view of the structure of the device for estimating physical parameters according to the embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be clearly and completely described below with reference to specific embodiments of the present application and corresponding drawings. It will be apparent that the described embodiments are only some, but not all, embodiments of the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
FIG. 1 is a flowchart of a method for estimating physical parameters according to an embodiment of the present application, specifically including the following steps:
s101: according to the physical parameters of the preset material to be inferred, a training data set is established through simulation software, and a neural network model is trained.
In the embodiment of the application, the relation between the physical property parameters of the material and the corresponding result parameters can be represented by training the neural network model.
Specifically, the training process of the neural network model includes:
the first step, corresponding simulation result parameters are determined through simulation software according to preset physical parameters.
The server can determine different value ranges corresponding to the physical parameters according to the preset physical parameters. And determining possible values of the physical parameters within the corresponding value ranges of the physical parameters. The different values of the physical parameters are combined to form a large amount of combined data.
And inputting each combination data into simulation software, and performing simulation through the simulation software to obtain corresponding simulation result parameters under preset process conditions for each combination data. The parameters of the simulation result of the crystal growth can be obtained through simulation software for simulating the crystal growth. For example, simulation software Virtual Reactor, etc.
Taking a crystal growth process as an example, determining different physical property parameters of the crucible, namely heat conductivity lambda, electric conductivity sigma and surface emissivity epsilon, and simulating by simulation software to determine simulation result parameters of crystal growth corresponding to the corresponding physical property parameters, wherein the simulation result parameters comprise temperatures T of preset monitoring points corresponding to a plurality of preset moments in a crystal growth stage, and the thickness H and the convex rate C of the crystal. Wherein the convexity of the crystal represents the difference between the thickness of the middle and the thickness of the edge of the crystal.
For convenience of description, a crucible used in the crystal growth process is exemplified below. However, this is not intended to limit the scope of application of the present application, and the present method is not limited to estimating physical parameters of a crucible, but is equally applicable to other production processes having the same principle.
Second, a training data set is established.
The server can establish a training data set according to the determined simulation result parameters and the corresponding values of all physical parameters.
Taking a crucible adopted in the crystal growth process as an example, the server can establish a training data set according to physical property parameters of the crucible, such as thermal conductivity lambda, electrical conductivity sigma, surface emissivity epsilon, and simulation result parameters of crystal growth, including temperatures T of preset monitoring points corresponding to a plurality of preset moments in the crystal growth stage, thickness H of crystal growth and convexity C of the crystal.
And thirdly, training a neural network model by adopting the established training data set.
Specifically, the server can use physical property parameters of the material as input data of the neural network model training, and use corresponding simulation result parameters as output data of the neural network model training to perform model training. Through machine learning, the neural network model can learn the functional relation between physical property parameters of materials and corresponding simulation result parameters under preset process conditions.
In one embodiment, the server may employ a BP neural network model for training of the neural network model. In the training process, the training data set may be divided into a training set and a test set, wherein if the training data set is 300 sets, the training set may include 200 sets of training data, and the test set may include 100 sets of training data. The server can train the BP neural network model by adopting the data of the training set, and verify the accuracy and the like of the trained BP neural network model by adopting the data of the testing set.
Specifically, the trained BP neural network model may include three fully connected layers, for a total of 33 neurons. Wherein the three fully-connected layers comprise 16, 16 and 5 neurons, respectively. Taking the crystal growth process as an example, the 5 neurons of the last layer can respectively correspond to the temperatures of three preset monitoring points in the result parameters of the crystal growth, the thickness of the crystal and the convexity of the crystal.
And, when training BP neural network model, the activation function can adopt Relu, the optimization mode can adopt Adam, and the loss function can adopt average absolute error.
S102: and determining the actual result parameters corresponding to the material to be inferred under the preset process conditions.
In the embodiment of the application, the server can determine the corresponding actual result parameter according to the application of the material to be inferred in the actual production process with the preset process conditions, so as to infer the actual physical property parameter of the material to be inferred according to the actual result parameter. The material to be inferred refers to a material of which accurate physical parameters need to be determined, and preset process conditions represent operations such as pressurization, temperature rise and the like adopted in the production process and can be set according to requirements.
The server can determine a plurality of actual result parameters corresponding to the material to be inferred under different preset process conditions, so that the physical parameters of the material to be inferred are optimized through the actual result parameters, and the physical parameters of the material to be inferred are more accurate.
In one embodiment, if the material to be inferred is a crucible employed during crystal growth, the physical parameters of the crucible may include thermal conductivity, electrical conductivity, surface emissivity, etc., and the resulting parameters of the crystal produced by the crucible may include the temperature of the predetermined monitoring point of the crystal, the thickness of the crystal, the convexity of the crystal, etc.
It should be noted that, in the embodiment of the present application, there is no limitation on the sequence between the step 101 and the step 102, and the step 101 and the step 102 may be performed simultaneously.
S103: and determining the actual physical parameters of the material to be inferred by adopting a neural network model and a preset numerical optimization algorithm according to the actual result parameters.
In the embodiment of the application, the actual physical parameters of the material to be inferred can be determined by back-pushing through the trained neural network model according to the actual result parameters corresponding to the material to be inferred. The process of determining the physical property parameters of the material to be inferred in a back-pushing manner is realized through a preset numerical optimization algorithm.
Specifically, the server may determine a plurality of initial values of the physical property parameter of the material, and determine a predicted result parameter obtained by predicting each initial value through the neural network model. And the server can evaluate the correlation between the predicted result parameter and the actual result parameter corresponding to each initial value through the objective function so as to carry out iterative optimization on the initial value according to the evaluation result.
And then, the server can carry out iterative optimization on each initial value by adopting an optimizer in an L-BFGS-B algorithm according to the fitting result between the predicted result parameter and the actual result parameter until the iteration is completed.
And finally, according to an optimization result obtained after iterative optimization of each initial value, determining the optimal physical parameters as the actual physical parameters of the material to be inferred.
Further, the server may determine an initial value of the physical property parameter according to the preset range. Also, in order for the initial values to achieve full coverage of the preset range while minimizing the gap between the initial values, the number of initial values determined should be sufficient. For example, 10000 initial values may be determined.
The numerical optimization algorithm comprises a gradient algorithm and a Newton algorithm, wherein the gradient algorithm is low in convergence speed and low in calculation efficiency, and is easy to sink into local minimum points. Compared with the gradient algorithm, the Newton algorithm has the advantages of high precision, high convergence speed and the like, but the Newton algorithm needs more storage variables, and Hessian matrix and the inverse of the Hessian matrix are difficult to obtain.
Thus, in order to avoid direct computation of the Hessian matrix, the embodiment of the application adopts a quasi-Newton-like algorithm L-BFGS-B algorithm. In the L-BFGS-B algorithm, a positive definite matrix without second derivative can be constructedWherein H is k Is an approximation to a Hessian matrix. Thus, by the structure B k The inverse of the Hessian matrix can be directly obtained.
The optimization principle of the L-BFGS algorithm is schematically shown in FIG. 2. In fig. 2, three circles at the top of the curve represent initial values, two circles in the middle represent locally optimal solutions, and a large circle at the bottom represents globally optimal solutions. It can be known that, through iterative optimization, only the local optimal solution is found by two initial values, and the global optimal solution is found by one initial value.
Further, the server may be based on the objective function And determining the correlation between the predicted result parameter and the actual result parameter of the neural network model. Wherein, taking the crystal growth process as an example, F represents T i H, C and t i Correlation between h, c, T i The temperature of each preset monitoring point of the crystal predicted by the neural network model is represented, H represents the thickness of the crystal predicted by the neural network model, C represents the convex rate of the crystal predicted by the neural network model, and t i The actual temperature of each preset monitoring point of the crystal is represented, h represents the actual thickness of the crystal, and c is representedShowing the actual convexity of the crystal. Fitting between the two can be achieved by minimizing the square of the difference between the result parameter predicted by the neural network model and the actual result parameter, i.e., F.
Further, in the process of fitting the result parameters predicted by the neural network model and the actual result parameters, the adopted iterative update formula is m k+1 =m k +a k P k . Wherein m represents a physical property parameter, a k Representing the step size, P, of the iteration k Represents the iteration direction and k represents the number of iterations.
The selection of the search step length has an important influence on the process of deducing the physical parameters of the material. If the search step length is too small, the local optimization capacity is strong, but the local optimization solution is easy to fall into, the convergence speed is slow, and the solution precision is low. If the search step is too large, the stability of the iterative process may be compromised and the optimal value may be easily skipped.
In one possible implementation, the size of the step size may be determined using a line search algorithm. The algorithm can simply select smaller and smaller step sizes until iteration of the initial value is completed. The problem of too large or too small step size can be solved by the dynamic step size in the algorithm, and the determination of the optimal value is facilitated.
In each iteration process, each initial value is updated and is subjected to corresponding optimization adjustment. In the iterative optimization process, the conditions for the termination of the iteration may include: objective functionLess than a preset value, or the iteration has reached a maximum number of iterations. Then, until all iterations are completed, all optimized initial values can be obtained.
Further, when determining the optimal physical parameters, each different value in the optimized result can be counted according to the optimized result obtained by iterative optimization of the initial values. Then, the optimal result with the largest count can be determined as the optimal physical property parameter.
Fig. 3 (a) to 3 (c) are schematic diagrams showing results of optimizing physical properties parameters of the crucible according to the embodiment of the present application.
Fig. 3 (a) shows the result of optimizing the thermal conductivity of the crucible, wherein the abscissa shows the value of the thermal conductivity and the ordinate shows the count. FIG. 3 (b) shows the result of optimizing the conductivity of the crucible, wherein the abscissa represents the value of the conductivity and the ordinate represents the count. FIG. 3 (c) shows the result of optimizing the surface emissivity of the crucible, wherein the abscissa represents the value of the surface emissivity and the ordinate represents the count.
According to the ordinate of the three bar charts, the abscissa corresponding to the column with the largest ordinate in each chart, namely the abscissa with the highest column distribution frequency, can be determined to be the optimal thermal conductivity, the optimal electrical conductivity and the optimal surface emissivity of the crucible respectively.
Fig. 4 (a) to fig. 4 (b) are schematic diagrams showing the relationship between simulation results and actual results provided by the embodiments of the present application. In fig. 4 (a) and 4 (b), the abscissa represents the distance from the center of the crystal in millimeters, and the ordinate represents the crystal growth rate in micrometers per hour.
In fig. 4 (a), the solid line represents the actual result of crystal growth, and the broken line represents the simulation result corresponding to the non-optimized physical property parameter obtained by the simulation software. In fig. 4 (b), the solid line represents the actual result of crystal growth, and the broken line represents the simulation result corresponding to the optimized physical property parameter obtained by the simulation software.
It is known that under inaccurate physical parameters, the error between the simulation result obtained by the simulation software and the actual result is large, and the simulation result cannot truly reflect the actual result. After the physical parameters are optimized, the error between the simulation result and the actual result can be reduced, so that the simulation result is basically consistent with the actual result.
In the embodiment of the application, the optimal solution of the physical property parameters of the material can be determined as the actual physical property parameters of the material by training the neural network model and adopting a numerical optimization algorithm for back-pushing. In this way, the physical parameters of the material can be obtained as accurately as possible when the physical parameters of the material are difficult to be known, and thus, the error between the simulation result and the actual result can be advantageously reduced.
The above method for estimating the physical parameters provided in the embodiment of the present application is based on the same inventive concept, and the embodiment of the present application further provides a corresponding device for estimating the physical parameters, as shown in fig. 5.
Fig. 5 is a schematic structural diagram of an apparatus for estimating physical parameters according to an embodiment of the present application, specifically including:
the training module 401 establishes a training data set through simulation software according to the physical parameters of the preset material to be inferred, and trains a neural network model;
a second determining module 402, configured to determine an actual result parameter corresponding to the material to be inferred under a preset process condition;
and a third determining module 403, configured to determine, according to the actual result parameter, an actual physical parameter of the material to be inferred by using the neural network model and a preset numerical optimization algorithm.
The foregoing is merely exemplary of the present application and is not intended to limit the present application. Various modifications and variations of the present application will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the application are to be included in the scope of the claims of the present application.

Claims (8)

1. A method of inferring a physical property parameter, comprising:
according to the physical parameters of the preset material to be inferred, a training data set is established through simulation software, and a neural network model is trained; the material to be inferred is a crucible;
determining actual result parameters corresponding to the material to be inferred under preset process conditions; the actual result parameters at least comprise any one of the following: the temperature of a preset monitoring point of the crystal, the thickness of the crystal and the convexity of the crystal;
according to the actual result parameters, determining actual physical parameters of the material to be inferred by adopting the neural network model and a preset numerical optimization algorithm; the actual physical parameters of the material to be inferred are obtained through the neural network model in a back-pushing manner, and the process of determining the physical parameters of the material to be inferred through the numerical optimization algorithm in the back-pushing manner is realized; the actual physical parameters at least comprise any one of the following: thermal conductivity, electrical conductivity, surface emissivity;
according to the actual result parameters, determining the actual physical parameters of the material to be inferred by adopting the neural network model and a preset numerical optimization algorithm, wherein the determining comprises the following steps:
determining a plurality of initial values of physical parameters;
determining prediction result parameters corresponding to the initial values by adopting the neural network model;
according to a preset objective function, evaluating the correlation between the predicted result parameter and the actual result parameter corresponding to each initial value to obtain a corresponding evaluation result;
adopting an L-BFGS-B algorithm, and performing iterative optimization on the initial values according to the evaluation result;
and determining the optimal physical parameters according to the optimization results obtained after the iterative optimization of the initial values, and taking the optimal physical parameters as the actual physical parameters of the material to be inferred.
2. The method of claim 1, wherein building a training data set by simulation software and training a neural network model according to predetermined physical parameters of the material to be inferred, comprises:
according to a plurality of preset physical parameters, determining the values of the physical parameters from a preset value range, and determining the values of corresponding simulation result parameters under preset process conditions by adopting simulation software;
according to the determined simulation result parameters and the corresponding values of all preset physical parameters, a training data set is established;
and training the neural network model by adopting the established training data set.
3. The method of claim 2, wherein the neural network model is a BP neural network model, the BP neural network model comprising 3 fully connected layers, the 3 fully connected layers comprising 16, 5 neurons, respectively.
4. A method according to claim 3, wherein the neural network model uses an activation function of Relu, an optimization method of Adam, and a loss function of mean absolute error.
5. The method of claim 1, wherein evaluating the predicted outcome parameter according to a predetermined objective function comprises:
according toDetermining a correlation between the predicted outcome parameters obtained by the neural network model and the actual outcome parameters, wherein F represents T i H, C and t i Correlation between h, c, T i The temperature of each preset monitoring point of the crystal predicted by the neural network model is represented, H represents the thickness of the crystal predicted by the neural network model, C represents the convex rate of the crystal predicted by the neural network model, and t i The actual temperature of each preset monitoring point of the crystal is represented, h represents the actual thickness of the crystal, and c represents the actual convexity of the crystal.
6. The method of claim 5, wherein in iteratively optimizing the plurality of initial values, an iteratively updated formula of m is used k+1 =m k +a k P k Wherein m represents a physical property parameter, a k Representing the step size, P, of the iteration k Represents the iteration direction and k represents the number of iterations.
7. The method of claim 1, wherein determining the optimal physical parameters based on the optimization results obtained by iteratively optimizing the plurality of initial values comprises:
determining an optimization result obtained after iterating the initial values;
respectively counting the optimization results with different values;
and determining the optimal result with the maximum count as the optimal physical property parameter.
8. An apparatus for estimating a physical property parameter, comprising:
the training module is used for establishing a training data set through simulation software according to the physical parameters of the preset material to be inferred and training a neural network model; the material to be inferred is a crucible;
the first determining module is used for determining actual result parameters corresponding to the material to be inferred under the preset process conditions; the actual result parameters at least comprise any one of the following: the temperature of a preset monitoring point of the crystal, the thickness of the crystal and the convexity of the crystal;
the second determining module is used for determining the actual physical parameters of the material to be inferred by adopting the neural network model and a preset numerical optimization algorithm according to the actual result parameters; the actual physical parameters of the material to be inferred are obtained through the neural network model in a back-pushing manner, and the process of determining the physical parameters of the material to be inferred through the numerical optimization algorithm in the back-pushing manner is realized; the actual physical parameters at least comprise any one of the following: thermal conductivity, electrical conductivity, surface emissivity;
according to the actual result parameters, determining the actual physical parameters of the material to be inferred by adopting the neural network model and a preset numerical optimization algorithm, wherein the determining comprises the following steps:
determining a plurality of initial values of physical parameters;
determining prediction result parameters corresponding to the initial values by adopting the neural network model;
according to a preset objective function, evaluating the correlation between the predicted result parameter and the actual result parameter corresponding to each initial value to obtain a corresponding evaluation result;
adopting an L-BFGS-B algorithm, and performing iterative optimization on the initial values according to the evaluation result;
and determining the optimal physical parameters according to the optimization results obtained after the iterative optimization of the initial values, and taking the optimal physical parameters as the actual physical parameters of the material to be inferred.
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