CN114626282A - Coil design method based on machine learning technology and coil - Google Patents
Coil design method based on machine learning technology and coil Download PDFInfo
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Abstract
The invention discloses a coil design method based on a machine learning technology, which comprises the following steps: starting from a Maxwell equation set, obtaining an expression of a magnetic field, and calculating the magnetic field unevenness of a specific area; setting the maximum iteration times by taking the position of the coaxial coil in the circuit board as a parameter, and selecting a machine learning algorithm according to the range of the parameter; combining a differential evolution algorithm with an artificial neural network, searching the neighborhood where the optimal solution is located, constructing a proxy model about the unevenness of the magnetic field, searching the minimum value by using an L-BFGS algorithm, and accelerating the convergence of the optimization algorithm; the optimal prediction parameters are given by the algorithm, and a coil system can be constructed according to the obtained coil position parameters. The invention also discloses a coil designed and obtained based on the design method. The invention provides a more universal and easy-to-use scheme for coil design under the limit of considering practical application, and can obtain a magnetic field with high uniformity so as to better improve the technical level in quantum precision measurement and quantum communication.
Description
Technical Field
The invention belongs to the field of coil design, and particularly relates to a coaxial coil design method.
Background
The quantum technology is to utilize the interaction of light and matter and utilize quantum coherence to implement high-precision detection and secret communication, and has been widely applied in items such as magnetoencephalography, gravitational wave detection and secret communication. However, coupling of quantum states to the environment can lead to decoherence effects, one of which is the gradient from the inhomogeneous magnetic field.
Conventional schemes for generating a uniform magnetic field are based on derivation of an expression of the magnetic field with respect to spatial distribution, or on generalized expansion of the expression, in which terms related to spatial position are eliminated as much as possible. Although the results of the schemes are good, some schemes need high-order derivation along with more parameters, are complex in calculation, and have various engineering problem limitations in practical application design, so that the schemes cannot be directly used.
Disclosure of Invention
In order to solve the defects in the prior art, the invention aims to provide a coil design method based on a machine learning technology.
The invention is inspired by the design of the gradient coil, and combines a computer algorithm with a theoretical model of coil design to provide a design method which is universally applicable and easy to operate. The coil designed by the design method can generate a magnetic field with high uniformity, provides a more universal and easy-to-use scheme for coil design under the limit of considering practical application, and can better improve the technical level in quantum precision measurement and quantum communication.
The invention provides a coil design method based on machine learning, which comprises the following steps:
starting from a Maxwell equation set, obtaining an expression of a magnetic field, using the expression as a theoretical model, and calculating the magnetic field unevenness of a specific area through a discretization area;
selecting the position of each pair of coaxial coils in the circuit board as a parameter, setting the maximum iteration number, limiting the range of the parameter according to the size of the circuit board, selecting a differential evolution algorithm as training data to provide an algorithm, and using a neural network as a machine learning algorithm for modeling;
combining a differential evolution algorithm with an artificial neural network, searching the neighborhood where the optimal solution is located by the aid of the differential evolution algorithm, constructing a proxy model by the neural network, searching the minimum value by the aid of an L-BFGS algorithm, and accelerating the convergence process of the optimization algorithm;
and step four, giving optimal prediction parameters by an algorithm, wherein the parameters correspond to the positions of each pair of coaxial coils on the flexible circuit board, and a coil system can be constructed according to the obtained parameters.
The objective function of the optimal prediction parameter is the magnetic field unevenness, the optimized parameter is the position parameter of each pair of coaxial coils on the circuit board and defines a good range, the machine learning algorithm searches the parameter in the parameter space by the differential evolution algorithm in the initial optimization stage, and inputs the parameter into a theoretical model for evaluation, and the obtained result is fed back to a neural network for training; if the maximum iteration number is not reached or the target optimization result is not expected, the optimization process is continued, the neural network makes a prediction every four iterations, the prediction result is given by a differential evolution algorithm, all feedback results are added into a training data set to further train the neural network, a better prediction result is obtained until the preset requirement is met or the preset maximum iteration number is reached, and the optimal prediction is output. The invention constructs a controller which takes a differential evolution algorithm as a data provider for training a neural network and takes charge of modeling for prediction, and the two algorithms jointly form a hybrid machine learning optimization algorithm to control the optimization process of coil design.
The algorithm part takes Python codes built by taking Numpy and m-loop as a framework as each computing module.
The Python code algorithm core part is mainly provided by the following calculation packet:
numpy is used for scientific calculation and is mainly responsible for building a calculation module of theoretical simulation;
and m-loop, namely an open source code library, provides a framework for combining a machine learning algorithm and a traditional optimization algorithm, and can be used for building a calculation module of the optimization algorithm.
Tensorflow: the deep learning library of Google is used for constructing a neural network;
scipy, used for scientific computation, provides an L-BFGS algorithm to find the minimum value of a proxy model constructed by a neural network, helps to give a prediction, and calls a Scipy.
Wherein, TensorFlow and Scipy are embedded in the m-loop.
The invention also provides a coil designed and obtained according to the design method, wherein the coil is a circular coil which is attached to the flexible circuit board and clings to the inner layer of the magnetic shield. The coils comprise 10 pairs of single-ring main coils, which are symmetrically arranged by taking the center of the magnetic shield as an original point, obtain an optimized result by taking the position as a parameter, and respectively compensate first-order and second-order gradients by adding two pairs of gradient coils to eliminate the influence of residual magnetism in the magnetic shield.
In particular, in the design of an actual coil, the present invention takes into account that the coil needs to be measured in a high permeability magnetic shield and primarily the axial magnetic field, and the present invention calculates the distribution of the magnetic field with a given coil system using a mirror image method. The mirror image model can be degenerated to the BiSafahr's law under certain conditions to calculate the axial magnetic field distribution in free space.
Under the theoretical framework, the invention utilizes Numpy numerical value to simulate the magnetic field generated by a coil system under given parameters, calculates the uniformity of the magnetic field within a certain range, and uses the magnetic field as a calculation module of a theoretical model.
In a calculation module of an optimization algorithm, the method is mainly constructed by using m-loop.
In order to improve the optimization efficiency, the differential evolution algorithm is combined with the artificial neural network, the position of the coil is selected as a parameter to be optimized, and the differential evolution algorithm is used for searching in a parameter space initially. And randomly generating parameters by a differential evolution algorithm, then simulating by a theoretical model, evaluating the corresponding uniformity, and feeding back to an optimization algorithm module.
The randomly generated parameters and corresponding feedback form a training data set which is provided for a neural network constructed by TensorFlow to train. After the neural network training is completed, the best parameter before is selected as an initial point of an L-BFGS algorithm, and a minimum value point is searched in the proxy model as a prediction result and is given to a theoretical model for simulation evaluation. The new assessment results are added to the training data set for better prediction results.
The method leads the evolutionary algorithm to search data in advance, evaluates the data by the model and then carries out prediction by the network, and the steps are repeated until the prediction given by the algorithm meets the preset requirement or reaches the preset maximum iteration number, the optimization is finished and the optimal prediction result is given.
The invention also proposes a device comprising: a memory and a processor; the memory has stored thereon a computer program which, when executed by the processor, carries out the method described above.
The invention also proposes a computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the above-mentioned method.
The beneficial effects of the invention include: the coil design method provided by the invention provides a more universal and easy-to-use scheme for coil design under the limitation of considering practical application, and can obtain a magnetic field with high uniformity, so that the technical level is better improved in quantum precision measurement and quantum communication. In addition, the hybrid machine learning algorithm provided by the invention has a mechanism similar to active learning, and through the algorithm, a machine learner autonomously explores an area where an optimal solution is located, continuously explores within given iteration times, and on the problem of coil optimization, compared with the traditional algorithm, the hybrid machine learning algorithm not only greatly improves the operation efficiency, but also can better approach the optimal solution in high-dimensional optimization. The neural network used in the invention is proved to be capable of better fitting the magnetic field unevenness function generated by the multi-turn coil system. By using the optimization algorithm, the method can be well combined with a theoretical model and finite element simulation, and the usability of the coil design method can be greatly improved.
Drawings
FIG. 1 is a flow chart of the machine learning algorithm of the present invention.
FIG. 2 is a structure of the machine learning neural network of the present invention.
Fig. 3 and 4 are schematic diagrams of a coil system designed by the design method of the invention.
Detailed Description
The invention is further described in detail with reference to the following specific examples and the accompanying drawings. The procedures, conditions, experimental methods and the like for carrying out the present invention are general knowledge and common general knowledge in the art except for the contents specifically mentioned below, and the present invention is not particularly limited.
The invention discloses a coil design method based on a machine learning technology, which comprises the following steps: starting from a Maxwell equation set, obtaining an expression of a magnetic field, and calculating the magnetic field unevenness of a specific area; setting the maximum iteration times by taking the position of the coaxial coil in the circuit board as a parameter, and selecting a machine learning algorithm according to the range of the parameter; combining a differential evolution algorithm with an artificial neural network, searching the neighborhood where the optimal solution is located, constructing a proxy model about the unevenness of the magnetic field, searching the minimum value by using an L-BFGS algorithm, and accelerating the convergence of the optimization algorithm; the optimal prediction parameters are given by the algorithm, and a coil system can be constructed according to the obtained coil position parameters. The invention also discloses a coil designed and obtained based on the design method. The invention provides a more universal and easy-to-use scheme for coil design under the limit of considering practical application, and can obtain a magnetic field with high uniformity so as to better improve the technical level in quantum precision measurement and quantum communication.
The invention provides a coil design method based on the system, which comprises the following steps:
starting from a Maxwell equation set, obtaining an expression of a magnetic field, using the expression as a theoretical model, and calculating the magnetic field unevenness of a specific area through a discretization area;
selecting the position of each pair of coaxial coils in the circuit board as a parameter, setting the maximum iteration number, limiting the range of the parameter according to the size of the circuit board, selecting a differential evolution algorithm as training data to provide an algorithm, and using a neural network as a machine learning algorithm for modeling;
combining a differential evolution algorithm with an artificial neural network, searching the neighborhood where the optimal solution is located by the aid of the evolution algorithm, constructing a proxy model by the neural network, searching the minimum value by the aid of an L-BFGS algorithm, and accelerating the convergence process of the optimization algorithm;
and step four, giving optimal prediction parameters by an algorithm, wherein the parameters correspond to the positions of each pair of coaxial coils on the flexible circuit board, and a coil system can be constructed according to the obtained parameters.
The invention constructs a controller which takes a differential evolution algorithm as a data provider for training a neural network, the neural network is responsible for modeling and predicting, and the two algorithms jointly form a hybrid machine learning optimization algorithm for controlling the optimization process of coil design.
The algorithm part takes Python codes built by taking Numpy and m-loop as a framework as each computing module.
The Python code algorithm core part is mainly provided by the following calculation packet:
numpy is used for scientific calculation and is mainly responsible for building a calculation module of theoretical simulation;
and m-loop, namely an open source code library, provides a framework for combining a machine learning algorithm and a traditional optimization algorithm, and can be used for building a calculation module of the optimization algorithm.
Tensorflow: the deep learning library of Google is used for constructing a neural network;
scipy, used for scientific computation, provides an L-BFGS algorithm to find the minimum value of a proxy model constructed by a neural network, helps to give a prediction, and calls a Scipy.
Wherein, TensorFlow and Scipy are embedded in the m-loop.
In particular, in the design of an actual coil, the present invention takes into account that the coil needs to be measured in a high permeability magnetic shield and primarily the axial magnetic field, and the present invention calculates the distribution of the magnetic field with a given coil system using a mirror image method. The mirror image model can be degenerated to the BiSafahr's law under certain conditions to calculate the axial magnetic field distribution in free space.
Under the theoretical framework, the invention utilizes Numpy numerical value to simulate the magnetic field generated by a coil system under given parameters, calculates the uniformity of the magnetic field within a certain range, and uses the magnetic field as a calculation module of a theoretical model.
In a calculation module of an optimization algorithm, the method is mainly constructed by using m-loop.
In order to improve the optimization efficiency, the differential evolution algorithm is combined with the artificial neural network, the position of the coil is selected as a parameter to be optimized, and the differential evolution algorithm is used for searching in a parameter space initially. Randomly generating parameters by a differential evolution algorithm, and generating 20 groups of parameters when the dimension N of the parameters is less than or equal to 10; when the parameter dimension N is greater than 10, generating 2N groups of parameters; and then, the model is simulated by a theoretical model, the corresponding uniformity is evaluated, and the uniformity is fed back to an optimization algorithm module.
The randomly generated parameters and corresponding feedback form a training data set which is provided for a neural network constructed by TensorFlow to train. After the neural network training is completed, the best parameter before is selected as an initial point of an L-BFGS algorithm, and a minimum value point is searched in the proxy model as a prediction result and is given to a theoretical model for simulation evaluation. The new assessment results are added to the training data set for better prediction results.
The method leads the evolutionary algorithm to search data in advance, evaluates the data by the model and then carries out prediction by the network, and the steps are repeated until the prediction given by the algorithm meets the preset requirement or reaches the preset maximum iteration number, the optimization is finished and the optimal prediction result is given.
The invention also proposes a device comprising: a memory and a processor; the memory has stored thereon a computer program which, when executed by the processor, carries out the method described above.
The invention also proposes a computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the above-mentioned method.
The invention also provides a coil designed and obtained according to the design method, wherein the coil is a circular coil which is attached to the flexible circuit board and clings to the inner layer of the magnetic shield. The coils comprise 10 pairs of single-ring main coils, which are symmetrically arranged by taking the center of the magnetic shield as an original point, obtain an optimized result by taking the position as a parameter, and respectively compensate first-order and second-order gradients by adding two pairs of gradient coils to eliminate the influence of residual magnetism in the magnetic shield.
And setting the position of the coil as a parameter to be optimized, and setting the range of the parameter to be optimized, the number of times of optimization or target cost. The following is a simple example of one main routine of the present invention:
the method comprises the steps of creating a controller, giving a self-defined data interface of the method to the controller, selecting a differential evolution algorithm module of an m-loop as a training _ type to provide training data, calling a default neural network constructed by tenserflow in the m-loop as a controller _ type, and taking charge of data regression and prediction. And setting the maximum iteration number to 15000, not setting the target cost, and giving a parameter range.
The coil design program constructed by the m-loop and the numpy is simple and easy to use, combines with the flexible circuit board, and has better performance compared with the traditional coil system which is designed and optimized by an evolutionary algorithm or a simulated annealing algorithm.
The protection of the present invention is not limited to the above embodiments. Variations and advantages that may occur to those skilled in the art may be incorporated into the invention without departing from the spirit and scope of the inventive concept, and the scope of the appended claims is intended to be protected.
Claims (7)
1. A coil design method based on machine learning technology is characterized by comprising the following steps:
starting from a Maxwell equation set, obtaining an expression of a magnetic field, using the expression as a theoretical model, and calculating the magnetic field unevenness of a specific area through a discretization area;
selecting the position of each pair of coaxial coils in the circuit board as a parameter, setting the maximum iteration number, limiting the range of the parameter according to the size of the circuit board, selecting a differential evolution algorithm as training data to provide an algorithm, and using a neural network as a machine learning algorithm for modeling;
combining a differential evolution algorithm with an artificial neural network, searching the neighborhood where the optimal solution is located by the aid of the differential evolution algorithm, constructing a proxy model by the neural network, searching the minimum value by the aid of an L-BFGS algorithm, and accelerating the convergence process of the optimization algorithm;
and step four, giving optimal prediction parameters by an algorithm, wherein the parameters correspond to the positions of each pair of coaxial coils on the flexible circuit board, and constructing a coil system according to the obtained parameters.
2. The design method of claim 1, wherein the objective function of the optimal prediction parameter is magnetic field non-uniformity, the optimized parameter is a position parameter of each pair of coaxial coils on the circuit board and defines a good range, and the machine learning algorithm searches the parameter in a parameter space by a differential evolution algorithm at the initial stage of optimization, inputs the parameter into a theoretical model for evaluation, and feeds the obtained result back to a neural network for training; if the maximum iteration number is not reached or the target optimization result is not expected, the optimization process is continued, the neural network makes a prediction every four iterations, the prediction result is given by a differential evolution algorithm, all feedback results are added into a training data set to further train the neural network, a better prediction result is obtained until the preset requirement is met or the preset maximum iteration number is reached, and the optimal prediction is output.
3. The design method of claim 1, wherein the machine learning algorithm is a hybrid machine algorithm, and the differential evolution algorithm is used as a data provider for training a neural network, and the neural network is responsible for modeling a controller for prediction, and controlling a coil design optimization process for coil design to generate a high-uniformity magnetic field.
4. The design method according to claim 3, wherein the algorithm uses Python codes constructed based on Numpy and m-loop as a framework as each calculation module;
the calculation package of the Python code algorithm core part comprises the following steps: numpy, m-loop; wherein the TensorFlow and Scipy are embedded in the m-loop;
numpy is used for scientific calculation and is mainly responsible for building a calculation module of theoretical simulation;
an open source code library, which provides a framework for combining a machine learning algorithm and a traditional optimization algorithm and can be used for building a computing module of the optimization algorithm;
tensorflow: the deep learning library of Google is used for constructing a neural network;
scipy is used for scientific calculation, and an L-BFGS algorithm is provided for finding the minimum value of a proxy model constructed by a neural network to help to give a prediction.
5. A coil designed according to the design method of any one of claims 1 to 4, wherein the coil is composed of 10 pairs of main coils, one pair of first order gradient coils, and one pair of second order gradient coils; the parameters of the coil obtained by the method are constructed on the flexible circuit board.
6. An apparatus, comprising: a memory and a processor;
the memory has stored thereon a computer program which, when executed by the processor, implements the method of any of claims 1-4.
7. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the method according to any one of claims 1-4.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114818392A (en) * | 2022-06-28 | 2022-07-29 | 山东奥新医疗科技有限公司 | Shielding coil design method and related assembly |
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| CN114818392A (en) * | 2022-06-28 | 2022-07-29 | 山东奥新医疗科技有限公司 | Shielding coil design method and related assembly |
| CN114818392B (en) * | 2022-06-28 | 2022-09-06 | 山东奥新医疗科技有限公司 | Shielding coil design method and related assembly |
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