CN115392138B - Optical-mechanical-thermal coupling analysis model based on machine learning - Google Patents

Optical-mechanical-thermal coupling analysis model based on machine learning Download PDF

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CN115392138B
CN115392138B CN202211322033.9A CN202211322033A CN115392138B CN 115392138 B CN115392138 B CN 115392138B CN 202211322033 A CN202211322033 A CN 202211322033A CN 115392138 B CN115392138 B CN 115392138B
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李强
高政旺
武春风
姜永亮
胡黎明
韩西萌
刘利民
朱梦楠
王旭锋
胡金萌
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Abstract

The invention provides an optical-mechanical-thermal coupling analysis model based on machine learning, which is characterized in that a feedforward neural network model is constructed by acquiring an optical-mechanical-thermal coupling analysis related data set of an optical system and forming an input-output matrix by using the data set, and then training, evaluating and testing the feedforward neural network model; by the method, machine learning and optics can be combined, the purpose of predicting the optical-mechanical-thermal coupling analysis of the optical system by using data driving is achieved, the establishment of a complex optical system optical-mechanical-thermal coupling simulation mathematical equation is avoided, the difficulty of the optical-mechanical-thermal coupling analysis is reduced, and the accuracy of coupling simulation is improved.

Description

Optical-mechanical-thermal coupling analysis model based on machine learning
Technical Field
The invention relates to the technical field of optical-mechanical-thermal multi-physical field coupling, in particular to an optical-mechanical-thermal coupling analysis model based on machine learning.
Background
Uneven distribution of heat and temperature across the optical element can cause structural distortion of the optical element or create wavefront aberrations, significantly limiting the performance of the optical system. In order to analyze, predict and correct thermally induced wavefront aberrations, heat flux or other factors causing temperature gradients can be linked to the temperature, distortion and Optical aberrations of the system by creating transient models, called "Structural-Thermal-mechanical-Performance-analysis" (STOP) models, which present many challenges to develop accurate STOP models due to the coupling of Thermal, structural mechanical and Optical equations, as well as different boundary conditions and physical parameters.
However, to accurately predict wavefront aberrations, a lower dimensional STOP model is required. The currently common method for reducing dimensionality is based on Model Order Reduction, book Model Order Reduction by Schilders: theory, research, attributes and Application proposes that the sparsity of a system matrix and a model reduction algorithm can be used for realizing the significant reduction of the dimension of a system model and simultaneously capturing the relevant dynamics of a high-order system. However, before the model can be applied, it is necessary to ensure that the STOP model is validated through extensive experimentation, and to adjust the parameters of the STOP model to ensure that the model predictions match the observed experimental data. Then, the parameters of the STOP model cannot be directly determined, and can only be continuously estimated according to experimental data, and in addition, a plurality of state variables need to be introduced into the STOP model in a complex optical system. Therefore, when the optical-mechanical thermal coupling analysis of the optical system is performed according to the existing STOP model, the mathematical calculation process is complex, the simulation time is long, and the method is not suitable for practical application.
In view of the above, there is a need to design an improved optical-mechanical-thermal coupling analysis model based on machine learning to solve the above problems.
Disclosure of Invention
The invention aims to provide an optical-mechanical-thermal coupling analysis model based on machine learning.
In order to achieve the above object, the present invention provides an optical-mechanical-thermal coupling analysis model based on machine learning, comprising the following steps:
s1, carrying out optical-mechanical-thermal coupling analysis on an optical system in an experiment or numerical simulation mode, and obtaining data sets under different time windows p, wherein the data sets comprise a training data set, a verification data set and a test data set which are mutually independent;
s2, converting the data set in the step S1 into an input-output matrix to construct a feedforward neural network model;
and S3, training, evaluating and testing the feedforward neural network model.
Preferably, in step S2, the input and output of the feedforward neural network model are the same as the input and output of the VARX model.
Preferably, the expression of the VARX model is as follows:
Figure 702892DEST_PATH_IMAGE001
wherein, subscript
Figure 682350DEST_PATH_IMAGE002
Which represents a discrete point in time of the time,
Figure 275136DEST_PATH_IMAGE003
in order to output the vector, the vector is,
Figure 575405DEST_PATH_IMAGE004
in order to input the vector, the vector is input,
Figure 733985DEST_PATH_IMAGE005
and
Figure 884344DEST_PATH_IMAGE006
the matrix product of the output vector and the input vector, respectively, p is the past time window point,
Figure 462962DEST_PATH_IMAGE007
is a zero mean white noise sequence.
Preferably, the output vector is a wavefront aberration observed by an image plane of the optical system, and the input vector is thermal power of a heater in the optical system and external thermal disturbance.
Preferably, the input and output data matrix formats learned by the VARX model are respectively as follows:
Figure 458600DEST_PATH_IMAGE008
and
Figure 409369DEST_PATH_IMAGE009
wherein, in the step (A),
Figure 933891DEST_PATH_IMAGE010
is a matrix of machine-learned input data,
Figure 16117DEST_PATH_IMAGE011
is a machine learning output data matrix, with each row of matrix U being used to predict a corresponding row of matrix Y.
Preferably, the input layer of the feedforward neural mesh model is composed of
Figure 267976DEST_PATH_IMAGE012
The output layer of the feedforward neural grid model consists of r nodes.
Preferably, in step S3, the feedforward neural lattice model is trained, evaluated and tested by using open source TensorFlow, and the specific process of training, evaluating and testing is as follows: firstly, training the feedforward neural network model by using the training data set and the verification data set obtained in the step S1, wherein the training data set is used for fitting parameters of the feedforward neural network model, the verification data set is used for carrying out hyper-parameter optimization on the fitted feedforward neural network model, and in the training process, a mean square error is used as a loss function, and an adopted training method is a gradient descent algorithm; in the training process, the training data set and the verification data set under each time window p can correspondingly obtain a trained feedforward neural network model; and finally, evaluating all the trained feedforward neural network models by using the test data set, and taking the feedforward neural network model corresponding to the condition that the relative error between the prediction result output by the evaluated feedforward neural network model and the output result in the test data set is minimum as the optimal feedforward neural network model.
Preferably, the gradient descent algorithm is a root mean square propagation optimization algorithm.
Preferably, the wavefront aberration of the optical system can be predicted by using the machine learning-based optical-mechanical-thermal coupling analysis model, wherein the wavefront aberration is expressed by Zernike coefficients, and the Zernike coefficients are mainly a translation term, a tilt term and a defocus term.
Preferably, in step S1, the optical system includes a newton telescope system.
The beneficial effects of the invention are:
the optical-mechanical-thermal coupling analysis model based on machine learning and the verification framework are constructed by combining the neural network in the machine learning with optics, the wave aberration of the optical system can be rapidly and accurately predicted by adopting the method, and the important reference value is achieved for performing feedback compensation on the aberration caused by heat in the optical system. In addition, the model provided by the invention can realize the prediction of the wave aberration of the optical system only by data driving, avoids the establishment of a mathematical equation of an optical-mechanical-thermal coupling analysis model of a complex optical system, reduces the difficulty of calculating the wave aberration of the optical system, can be applied to the fields of adaptive optics and the like, and has the characteristics of wide application range, low prediction time cost, high accuracy and the like.
Drawings
FIG. 1 is a flow chart of an optical-mechanical-thermal coupling analysis model based on machine learning of the present invention;
FIG. 2 is a schematic structural view of a Newtonian telescope system according to embodiment 1 of the present invention;
FIG. 3 is a graph of the relative error between the model prediction output and the true output of the system for a test data set trained at different time windows in example 1 of the present invention;
FIG. 4 is a comparison graph of defocus terms of a predicted and real system based on a feedforward neural network model in embodiment 1 of the present invention;
the reference numbers are as follows:
1. a primary mirror; 2. a mirror support structure; 3. an image plane; 4. a secondary mirror; 5. light transmission obstacles; 6. external thermal interference; 7. an array of wells; 8. a heater location.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
It should be noted that, in order to avoid obscuring the present invention with unnecessary details, only the structures and/or processing steps closely related to the aspects of the present invention are shown in the drawings, and other details not closely related to the present invention are omitted.
In addition, it is also to be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Referring to fig. 1, the optical-mechanical-thermal coupling analysis model based on machine learning according to the present invention includes the following steps:
s1, acquiring a data set;
performing optical-mechanical-thermal coupling analysis on the optical system in an experiment or numerical simulation mode, and acquiring data sets under different time windows p, wherein the data sets comprise a training data set, a verification data set and a test data set which are mutually independent;
s2, forming an input/output matrix and constructing a feedforward neural network model;
converting the data set in the step S1 into an input-output matrix to construct a feedforward neural network model; the inputs and outputs of the feedforward neural mesh model are the same as those of the VARX model, which is expressed as follows:
Figure 322519DEST_PATH_IMAGE013
wherein, in the process,
Figure 814680DEST_PATH_IMAGE014
which represents a discrete point in time of the time,
Figure 338197DEST_PATH_IMAGE015
the output vector, here the wavefront aberration observed at the image plane of the optical system,
Figure 675637DEST_PATH_IMAGE016
is an input vector, which is the thermal power of the heater in the optical system and the external thermal disturbance,
Figure 427430DEST_PATH_IMAGE017
and
Figure 824914DEST_PATH_IMAGE018
the matrix product of the output vector and the input vector, respectively, p is the past time window point,
Figure 101305DEST_PATH_IMAGE019
the VARX model is a Vector auto regression eXogenous model (Vector auto regression eXogenous), and is a white noise sequence with zero mean.
For predicting system output
Figure 242437DEST_PATH_IMAGE020
Using the already acquired system input data set
Figure 317578DEST_PATH_IMAGE021
And system output data set
Figure 964591DEST_PATH_IMAGE022
The input and output matrix formats of the feedforward neural network model learning can be expressed as:
Figure 977546DEST_PATH_IMAGE023
and
Figure 171636DEST_PATH_IMAGE024
wherein, in the step (A),
Figure 789699DEST_PATH_IMAGE010
is the input data matrix of the feedforward neural network model,
Figure 76455DEST_PATH_IMAGE025
is the output data matrix of the feedforward neural network model, and each row of the matrix U is used to predict a corresponding row of the matrix Y. That is, the rows of the matrix U should be used as feed-forward neural network inputs, while Y is used as the output of the feed-forward neural network. Therefore, the input layer of the feedforward neural net model for training should be composed of
Figure 45548DEST_PATH_IMAGE026
The system comprises a plurality of nodes, an output layer consists of r nodes, and the number of internal layers is a determined tuning variable.
S3, training, evaluating and testing a feedforward neural network model:
training, evaluating and testing the neural network model by using an open-source TensorFlow platform, wherein the training, evaluating and testing process comprises the following steps: firstly, training a feedforward neural network model by using a training data set and a verification data set obtained in the step S1, wherein the training data set is used for fitting parameters of the feedforward neural network model, the verification data set is used for carrying out hyper-parameter optimization on the fitted model, in the training process, a mean square error is used as a loss function, and an adopted training method is a root mean square propagation optimization algorithm in a gradient descent algorithm; in the model training process, a trained feedforward neural network model can be obtained correspondingly by a training data set and a verification data set under each time window p; and finally, evaluating the prediction effects of all the trained feedforward neural network models by using the test data set, and taking the feedforward neural network model corresponding to the time when the relative error between the prediction result output by the feedforward neural network model and the output result in the test data set is minimum as the optimal feedforward neural network model.
It should be noted that the reason why the feedforward neural network model and the VARX model are selected as the model structures in the present invention is as follows: once the parameters of the neural network are learned, a VARX model can be easily constructed from the learned parameters, and the constructed VARX model can also be used for designing advanced estimation and feedback control algorithms; second, the feedforward neural network structure is easier to learn than the recurrent neural network structure.
The optical-mechanical-thermal coupling analysis model based on machine learning of the present invention is further described below with reference to specific examples:
example 1
The embodiment provides an optical-mechanical-thermal coupling analysis model based on machine learning, which comprises the following steps:
s1, obtaining a data set:
performing optical-mechanical-thermal coupling analysis on the optical system in an experimental or numerical simulation mode, and acquiring a data set under each time window of which the time window p =0 to 24, wherein the data set comprises a training data set, a verification data set and a test data set which are independent of each other:
referring to fig. 2, the optical system adopted in this embodiment is a newton telescope system, and includes a primary mirror 1, and an image plane 3 and a secondary mirror 4 disposed on the front side of the primary mirror 1, the primary mirror 1 is supported and fixed by a mirror surface support structure 2, a light propagation barrier 5 is disposed on the side of the secondary mirror 4 away from the primary mirror 1, a hole array 7 is disposed on the side of the primary mirror 1 away from the secondary mirror 4, the hole array 7 is used for placing a heater or a cooler, and a thermocouple for measuring a temperature field, in this embodiment, 9 heaters 8 are disposed in the hole array 7, and the heaters 8 are disposed to develop a feedback temperature control system, so as to achieve spatial and temporal thermal stability, thereby ensuring that wavefront aberration and system structural deformation caused by external thermal interference are kept below a maximum allowable value. With the heater 8 and the external thermal disturbance 6 as inputs to the optical system and the Zernike coefficients of the wavefront aberrations observed at the image plane 3 as outputs from the optical system, only the main three terms of the Zernike coefficients, the translation, tilt and defocus terms, respectively, are selected here. Three statistically independent sets of input data were simulated by COMSOL software to generate statistically independent training, validation and testing data sets, yielding 301 data samples in total. In other embodiments, the number of the heaters 8 may be adjusted according to actual needs, and is not limited herein.
S2, forming an input-output matrix, and constructing a feedforward neural network model:
converting any data set in the step S1 into an input-output matrix to construct a feedforward neural network model; the inputs and outputs of the feed forward neural mesh model are the same as the inputs and outputs of the VARX model, which is expressed as follows:
Figure 777750DEST_PATH_IMAGE027
wherein, subscript
Figure 578216DEST_PATH_IMAGE014
Which represents a discrete point in time of the time,
Figure 504714DEST_PATH_IMAGE015
the output vectors, in particular the three main Zernike coefficients of the wavefront aberration observed at the image plane 3, i.e. the translation, tilt and defocus terms,
Figure 492262DEST_PATH_IMAGE028
as input vectors, specifically heater 8 and external thermal disturbance 6,
Figure 762575DEST_PATH_IMAGE017
and
Figure 151968DEST_PATH_IMAGE029
the matrix product of the output vector and the input vector, respectively, p is the past time window point,
Figure 701898DEST_PATH_IMAGE007
is a white noise sequence with zero mean value, and the simulation of the embodiment
Figure 193054DEST_PATH_IMAGE030
Is 0.
To predict the system output
Figure 126112DEST_PATH_IMAGE020
Input of a data set using a system in which a simulation has been developed is required
Figure 651903DEST_PATH_IMAGE021
And the simulated system output data set
Figure 294105DEST_PATH_IMAGE031
The input and output matrix formats of the feedforward neural network model learning can be expressed as:
Figure 256245DEST_PATH_IMAGE032
and
Figure 930678DEST_PATH_IMAGE033
，
Figure 294663DEST_PATH_IMAGE010
is the input data matrix of the feedforward neural network model,
Figure 937128DEST_PATH_IMAGE025
is the output data matrix of the feedforward neural network model, and each row of the matrix U is used for a corresponding row of the prediction matrix Y. That is, the rows of the matrix U are used as inputs to the feedforward neural network model, and Y is used as an output of the feedforward neural network model. The training results of this example show that only the nodes of the input layer of the trained feedforward neural net model are
Figure 386564DEST_PATH_IMAGE026
When the nodes of the output layer are r, the feedforward neural networkThe lattice model can accurately predict the performance of the system, and the feedforward neural network model constructed in the embodiment only comprises an input layer and an output layer.
S3, training, evaluating and testing the feedforward neural network model:
the feedforward neural network model is trained, evaluated and tested by an open source TensorFlow platform, and the training, evaluating and testing processes are as follows: firstly, carrying out training of a feedforward neural network model by using a training data set and a verification data set obtained in the step S1, wherein the training data set is used for fitting parameters of the feedforward neural network model, and the verification data set is used for carrying out hyper-parameter optimization on the fitted model; in the training process, the mean square error is used as a loss function, and the adopted training method is a root mean square propagation optimization algorithm in a gradient descent algorithm; in the training process, a trained feedforward neural network model can be obtained correspondingly by the training data set and the verification data set under each time window p, and the number of the training models is 24 in the embodiment; finally, the prediction effects of the 24 training models are evaluated by using the test data set, the relative error between the prediction results output by the training models in different time windows and the output data of the test data is used as an evaluation index, the relative error between the prediction results and the output data of the test data is shown in fig. 3, and it can be seen from fig. 3 that the relative error is the smallest when the time window p =10, so that the training model corresponding to p is selected as the optimal feedforward neural network model.
Further, a set of data is arbitrarily extracted from the test data set to verify the prediction result, the distribution of the predicted defocus terms of the Zernike coefficients and the real output result is shown in fig. 4, and it can be seen from fig. 4 that the defocus terms of the Zernike coefficients and the real output result are substantially consistent, and the above results show that the wavefront aberration of the optical system can be accurately predicted by using the analysis model of the embodiment.
In summary, according to the optical-mechanical-thermal coupling analysis model based on machine learning provided by the invention, the relevant data set is firstly obtained, then the feedforward neural network model is constructed and optimized, and then the optimized feedforward neural network model is used for predicting the wavefront aberration of the optical system. The optical-mechanical-thermal coupling analysis model based on machine learning has the characteristics of wide application range, low prediction time cost, high accuracy and the like, and has an important reference value for performing feedback compensation on aberration caused by heat in an optical system.
Although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the present invention.

Claims (4)

1. An optical-mechanical-thermal coupling analysis model based on machine learning, comprising the steps of:
s1, carrying out optical-mechanical thermal coupling analysis on an optical system in an experiment or numerical simulation mode, and obtaining data sets under different time windows p, wherein the data sets comprise a training data set, a verification data set and a test data set which are mutually independent;
s2, converting the data set in the step S1 into an input-output matrix to construct a feedforward neural network model, wherein the input and the output of the feedforward neural network model are the same as those of the VARX model, and the input layer of the feedforward neural network model is required to be composed of
Figure DEST_PATH_IMAGE001
The output layer of the feedforward neural grid model consists of
Figure 300549DEST_PATH_IMAGE002
Each node is formed;
the expression of the VARX model is as follows:
Figure DEST_PATH_IMAGE003
wherein the subscript
Figure 561897DEST_PATH_IMAGE004
Which represents a discrete point in time of the time,
Figure DEST_PATH_IMAGE005
is the output vector of the output vector,
Figure 810476DEST_PATH_IMAGE006
is a function of the input vector or vectors,
Figure DEST_PATH_IMAGE007
and
Figure 159680DEST_PATH_IMAGE008
respectively the product of the input and output matrices,
Figure DEST_PATH_IMAGE009
is the point in the time window in the past,
Figure 911735DEST_PATH_IMAGE010
is a zero mean white noise sequence, said
Figure DEST_PATH_IMAGE011
Wavefront aberrations observed for the image plane of an optical system, said
Figure 422613DEST_PATH_IMAGE012
Thermal power of a heater in the optical system and external thermal disturbance;
the input and output data matrix formats learned by the VARX model are respectively as follows:
Figure DEST_PATH_IMAGE013
and
Figure 807154DEST_PATH_IMAGE014
wherein, in the step (A),
Figure DEST_PATH_IMAGE015
is a matrix of machine-learned input data,
Figure 366574DEST_PATH_IMAGE016
is a machine learning output data matrix, matrix
Figure DEST_PATH_IMAGE017
Is used for the prediction matrix
Figure 786185DEST_PATH_IMAGE018
The corresponding row of (2);
and S3, training, evaluating and testing the feedforward neural network model, and predicting the wavefront aberration of the optical system by using the optical-mechanical-thermal coupling analysis model based on machine learning, wherein the wavefront aberration is expressed as Zernike coefficients which are mainly a translation term, a tilt term and a defocus term.
2. The machine-learning-based opto-mechanical-thermal coupling analysis model according to claim 1, wherein in step S3, the feedforward neural net model is trained, evaluated and tested by using open-source TensorFlow, and the specific process of training, evaluating and testing is as follows: firstly, training the feedforward neural network model by using the training data set and the verification data set obtained in the step S1, wherein the training data set is used for fitting parameters of the feedforward neural network model, the verification data set is used for carrying out hyper-parameter optimization on the fitted feedforward neural network model, and in the training process, a mean square error is used as a loss function, and an adopted training method is a gradient descent algorithm; in the training process, the training data set and the verification data set under each time window can correspondingly obtain a trained feedforward neural network model; and finally, evaluating all the trained feedforward neural network models by using the test data set, and taking the feedforward neural network model corresponding to the minimum relative error between the prediction result output by the evaluated feedforward neural network model and the output result in the test data set as the optimal feedforward neural network model.
3. The machine-learning based opto-mechanical-thermal coupling analysis model of claim 2, wherein the gradient descent algorithm is a root mean square propagation optimization algorithm.
4. The machine-learning based opto-mechanical-thermal coupling analytical model of claim 1, wherein in step S1 the optical system comprises a newtonian telescope system.
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