CN116150995B - Rapid simulation method of switch arc model - Google Patents

Abstract

The invention discloses a fast simulation method of a switch arc model in the field of arc simulation technology, comprising: first establishing an arc model, giving a training task set and a task target set; constructing a corresponding deep neural network framework based on element initialization, constructing a loss function, constructing a element network based on element initialization, constructing a loss function, and selecting appropriate parameters of the neural network; Simulation results for the arc model. The present invention can perform model simulation more quickly in the case of the same switch arc model but with variable parameters; compared with the traditional method, the simulation method of the present invention does not rely on grid division, and can directly perform model simulation with higher precision.

Description

A Fast Simulation Method of Switching Arc Model

technical field

The invention belongs to the technical field of arc simulation, and in particular relates to a fast simulation method for a switch arc model.

Background technique

Arcing is a relatively common gas discharge phenomenon in power systems. As a high-temperature and high-conductivity discharge plasma, arc discharge can generate high temperatures of tens of thousands of degrees Celsius and above, and at the same time generate a large amount of heat radiation. It has the characteristics of high energy, high temperature and high conductivity, and small mass. Utilizing these characteristics of the arc can be properly applied to daily life and industrial production. However, since the arc is a gas with huge energy, it is very important to accurately understand the characteristics of the arc and its development process for the safety protection of the power system.

Numerical simulation is a common method to study arc characteristics, including finite difference, finite element, and finite volume method. However, this kind of traditional method has certain defects. The result depends on mesh division, which may cause inaccurate accuracy in solving high-dimensional problems. At the same time, it requires a large number of iterations in the solution of transient arc, and the calculation is slow. As a powerful nonlinear mapping tool, deep neural network has performed well in arc simulation as a new method.

However, although the neural network based on deep learning is effective in solving a single arc model, when faced with different solving conditions of the same model, the neural network often needs to retrain the network weights, which consumes a lot of calculations, and the meta-initialization method has great potential in solving such problems.

Contents of the invention

Aiming at the deficiencies of the prior art, the purpose of the present invention is to provide solutions to the problems raised in the background art above.

The purpose of the present invention can be achieved through the following technical solutions:

A fast simulation method for a switching arc model, comprising:

Step 1. First establish the arc model, and give the training task set and task target set;

Step 2, then constructing a corresponding deep neural network framework based on meta-initialization based on the arc model in step 1, constructing a loss function, constructing a meta-network based on meta-initialization according to the plasma equation, constructing a loss function based on the equation and corresponding boundary conditions and initial conditions, and selecting appropriate parameters of the neural network;

Step 3. Then train the arc model constructed in step 2 until the loss function value drops to a given threshold, and obtain the weight after the training is completed;

Step 4. Finally, set the weight of step 3 as the initial parameter of the network, and carry out the training of the target task until the value of the loss function drops to a given threshold, so as to realize the numerical calculation of the plasma equation based on element initialization, and obtain the output of the neural network, which is the simulation result of the corresponding arc model.

Preferably, in the step 1, the plasma equation model needs to be established first, and then the corresponding plasma equation model is rewritten into the following general formula:

u+N[u(x,t);λ]=0,X∈Ω

The boundary conditions are:

The initial conditions are:

u _i +N[u(x,t);λ]=β

In the formula, X(x,t) is the input quantity, x is the space quantity, t is the time quantity, u is the solution of the equation, the specific meaning depends on the type of the corresponding multiphysics field equation, λ is the variable parameter in the equation, N[·;λ] is the nonlinear operator parameterized by λ, is the corresponding boundary value, and β is the corresponding initial value;

Given the training task set λ _test =[λ ₁ ,λ ₂ ,...,λ _m ], each parameter of the task set constructs a corresponding plasma equation, and given the task target set λ _task =[λ ₁ ,λ ₂ ,...,λ _n ], each parameter of the task set corresponds to a plasma equation that needs to be calculated.

Preferably, the loss function L ^k includes three parts in the step 2:

Construct the first part of the loss function L _f of the i-th task according to the plasma equation:

In the formula, Is the number of sampling points in the calculation domain, Ψ is the activation function;

Construct the second part L _b of the function that loses the i-th task according to the boundary conditions:

In the formula, is the number of sampling points in the boundary domain;

Construct the third part L _i of the function that loses the i-th task according to the initial conditions:

In the formula, is the number of sampling points in the boundary domain, when no initial condition is given, Li=0;

Construct the loss function of the i-th task

Construct the total loss function through the loss function of each task

Beneficial effects of the present invention:

1. The method of the present invention can perform model simulation more quickly under the same switch arc model but with parameter changes;

2. Compared with the traditional method, the method of the present invention does not rely on grid division, and can directly perform model simulation with higher precision.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the accompanying drawings that need to be used in the description of the embodiments or prior art. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative work.

Fig. 1 is a schematic flow sheet of the method of the present invention;

Fig. 2 is a schematic diagram of solving the 1-dimensional steady-state arc model in the present invention;

Fig. 3 is the contrast figure of the inventive method and common neural network training result;

Fig. 4 is the contrast figure of the inventive method and common neural network loss function value;

Fig. 5 is a comparison diagram of the L2 error between the method of the present invention and the common neural network.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

The present invention proposes a fast simulation method of a switching arc model, including 4 steps;

Step 1. First establish the arc model, given the training task set and task target set,

Step 2. Then, based on the arc model, construct a corresponding deep neural network framework based on element initialization, construct a loss function, and select appropriate network hyperparameters such as the number of layers of the neural network;

Step 3, then train the arc model until the loss function value drops to a given threshold, and get the weight after the training is completed;

Step 4. Finally, the weight is set as the initial parameter of the network, and the training of the target task is carried out until the value of the loss function drops to a given threshold, thereby realizing the numerical calculation of the plasma equation based on meta-initialization.

Step 1 is detailed as follows:

According to the specific problem, the corresponding plasma equation model is established, and then the corresponding plasma equation model is rewritten into the following general formula:

u+N[u(x,t);λ]=0,X∈Ω

The boundary conditions are:

The initial conditions are:

u _i +N[u(x,t);λ]=β

In the formula, X(x,t) is the input quantity, x is the space quantity, t is the time quantity, u is the solution of the equation, the specific meaning depends on the type of the corresponding multiphysics field equation, λ is the variable parameter in the equation, N[·;λ] is the nonlinear operator parameterized by λ, is the corresponding boundary value, and β is the corresponding initial value; given the training task set λ _test =[λ ₁ ,λ ₂ ,...,λ _m ], each parameter of the task set can construct a corresponding plasma equation, and given the task target set λ _task =[λ ₁ ,λ ₂ ,...,λ _n ], each parameter of the task set corresponds to a plasma equation that needs to be calculated.

Step 2 is detailed as follows;

Select the type of deep neural network; construct a meta-network based on meta-initialization according to the plasma equation, construct a loss function based on the equation and corresponding boundary conditions and initial conditions, and select appropriate parameters such as the number of layers of the neural network. The types of neural networks include but are not limited to feedforward neural networks, convolutional neural networks, and recurrent neural networks:

First construct the corresponding loss function L ^k according to the tasks of the training task set:

Construct the first part of the loss function L _f of the i-th task according to the plasma equation:

In the formula, Is the number of sampling points in the calculation domain, Ψ is the activation function;

Then construct the second part _Lb of the function that loses the i-th task according to the boundary conditions:

In the formula, is the number of sampling points in the boundary domain;

Then construct the third part L _i of the function that loses the i-th task according to the initial conditions:

In the formula, is the number of sampling points within the boundary domain. If no initial condition is given, L _i =0;

Finally, construct the loss function of the i-th task

Construct the total loss function according to the above-mentioned loss functions of each task Select appropriate neural network parameters, including but not limited to the number of layers, number of neurons, and learning rate.

Please refer to Figure 1. Taking the 1-dimensional steady-state arc as the research object, the simulation results of the 1-dimensional steady-state arc equation under different parameter conditions are calculated by the meta-initialization method, including the following steps:

Step 1. Establish a 1-dimensional steady-state arc model, the details are as follows:

Step 1.1, first establish a 1-dimensional arc equation model based on the mass conservation equation, energy conservation equation and Ohm's law equation:

Among them, the boundary conditions are:

T | _{r = R} = T _b

In the formula, r is arc radius, T is temperature, σ is electrical conductivity, g is arc conductance, k is thermal conductivity, E _rad is the energy loss caused by radiation, T _b is the given boundary temperature value when r=R;

Step 1.2, using the temperature parameter T as the variable parameter λ, given the training task set λ _test = [1600K, 1700K, 1800K, 1900K, 2000K], each parameter of the task set can construct a corresponding plasma equation;

Step 1.3. Given task target set λ _task =[1550K, 1650K, 1750K, 1850K, 1950K], each parameter of the task set corresponds to a plasma equation to be calculated.

Step 2, constructing the corresponding meta-network framework based on the plasma equation model in step 1, as shown in Figure 2, details are as follows;

Step 2.1, select the type of deep neural network, such as feedforward neural network;

Step 2.2, constructing a meta-network based on meta-initialization according to the arc equation, the details are as follows;

Step 2.2.1. Construct corresponding loss functions L ^k according to the tasks of the training task set;

Step 2.2.1.1. Construct the first part L _f of the loss function of the i-th task according to the arc equation:

In the formula, Is the number of sampling points in the calculation domain, Ψ is the activation function;

Step 2.2.1.2. Construct the second part of the function that loses the i-th task according to the boundary conditions:

In the formula, Is the number of sampling points in the calculation domain, Ψ is the activation function;

Step 2.2.1.3. Construct the third part L _i of the loss function of the i-th task according to the initial conditions:

In the formula, is the number of sampling points within the boundary domain. If no initial condition is given, L _i =0;

Step 2.2.1.4, Construct the loss function of the i-th task

Step 2.2.2. Construct a total loss function according to the loss functions of each task in step 2.2.1:

Step 2.2.3. Set the hidden layer of the neural network to 6 layers, 50 neurons in each layer, initialize the weights randomly, set the learning rate to 10-5, and set the training times to 10,000 times.

Step 3. Train the arc model until the loss function value drops to a given threshold, and get the weight after the training is completed;

Step 3.1, randomly initializing the weight of the deep neural network selected in step 2.1;

Step 3.2, using the neural network to train the arc equation corresponding to each task of step 1.3;

Step 3.3, calculate the loss function value of the arc equation corresponding to each task, and calculate the total loss function value. The number of neural network training equations can be changed, and the specific number depends on the specific arc equation, and the network weight needs to be reset when the neural network changes the training task;

Step 3.4, according to the sum of the loss functions, use the gradient optimization algorithm to update the neural network weights;

Step 3.5, assigning the weight obtained in step 3.4 to the neural network;

Step 3.6, repeat steps 3.2-3.5, observe the total loss function value of the neural network until it drops to a given threshold;

Step 3.7, obtaining the weight parameters of the neural network.

Step 4, the weight of step 3 is set as the initial parameter of network, carries out the training of target task;

Step 4.1. Construct the target task network. The parameters of the network are consistent with the parameters of the above-mentioned meta-network, that is, the hidden layer of the neural network is 6 layers, each layer has 50 neurons, the weights are randomly initialized, and the learning rate is set to 10 ^-5 . ;

Step 4.2, setting the weight obtained in step 3.7 as the initial parameter of the target task network;

Step 4.3, the neural network trains the arc equation corresponding to each target task once to obtain an output value;

Step 4.4, calculating the loss function value;

Step 4.5, using the gradient optimization algorithm to update the neural network weights;

Step 4.6, repeat steps 4.3-4.5, observe the loss function value of the neural network until it drops to a given threshold;

In step 4.7, the output of the neural network is obtained, that is, the simulation result corresponding to the arc model.

At this time, the comparison diagrams of the neural network training results based on meta-initialization and ordinary neural network training results, loss function values, and L2 errors are shown in Figures 3, 4, and 5, respectively. It can be seen that, first, both the neural network based on meta-initialization and ordinary neural networks can obtain accurate simulation results. Second, compared with ordinary neural networks, the loss function value and L2 error decrease faster after using the neural network based on meta-initialization, and they can fall to a certain rated threshold (10 ^-2 ) in fewer times. Therefore, it is believed that after using the neural network based on meta-initialization, its convergence speed becomes faster, and the training efficiency of the arc model at different boundary temperatures is significantly improved.

By comparing this method with the traditional method and the common neural network method, it can be seen that the results obtained by the deep neural network method based on element initialization have a high degree of fitting with the results obtained by the original method, so that the results of this method are accurate. On the other hand, after using the method in this example, the simulation speed of the 1-dimensional steady-state arc model has been improved.

In the description of this specification, descriptions with reference to the terms "one embodiment", "example", "specific example" and the like mean that specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

The basic principles, main features and advantages of the present invention have been shown and described above. Those skilled in the art should understand that the present invention is not limited by the above-mentioned embodiments. What are described in the above-mentioned embodiments and the description only illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention also has various changes and improvements, and these changes and improvements all fall within the scope of the claimed invention.

Claims (7)

1. A fast simulation method of a switch arc model is characterized by comprising the following steps:

step 1, firstly, establishing an arc model, and giving a training task set and a task target set;

step 2, constructing a corresponding deep neural network frame based on element initialization based on the arc model in the step 1, constructing a loss function, constructing a element network based on element initialization according to a plasma equation, constructing the loss function based on the equation and corresponding boundary conditions and initial conditions, and selecting proper parameters of the neural network;

step 3, training the arc model constructed in the step 2 until the loss function value is reduced to a given threshold value, and obtaining weight after training is completed;

and step 4, finally, setting the weight in the step 3 as an initial parameter of the network, and training a target task until the loss function value is reduced to a given threshold value, so as to realize the numerical calculation of the plasma equation based on element initialization, and obtain the output of the neural network, namely the simulation result corresponding to the arc model.

2. The method for fast simulation of a switching arc model according to claim 1, wherein in step 1, a plasma equation model is required to be established first, and then the corresponding plasma equation model is rewritten into the following general formula:

u+N[u(x,t)；λ]＝0,X∈Ω

the boundary conditions are:

the initial conditions are:

u _i +N[u(x,t)；λ]＝β

wherein X (X, t) is the input quantity, X is the spatial quantity, t is the temporal quantity, u is the solution of the equation, the specific meaning depends on the type of the corresponding multi-physical field equation, λ is the variable parameter in the equation, N [. Cndot.; lambda (lambda)]Is a nonlinear operator parameterized by lambda,is the corresponding boundary value, and beta is the corresponding initial value;

given training task set lambda _test ＝[λ ₁ ,λ ₂ ,...,λ _m ]Each parameter of the task set constructs a corresponding plasma equation, giving a task target set lambda _task ＝[λ ₁ ,λ ₂ ,...,λ _n ]Each parameter of the task set corresponds to a plasma equation that needs to be calculated.

3. The method according to claim 1, wherein the neural network types in the step 2 include a feed-forward neural network, a convolutional neural network and a cyclic neural network.

4. The method according to claim 1, wherein the loss function L in the step 2 ^k Comprises three parts:

constructing a first part L of a loss function of an ith task according to a plasma equation _f ：

In the method, in the process of the invention,is the number of sampling points in the computational domain, ψ is the activation function;

constructing a second part L of the function losing the ith task according to boundary conditions _b ：

In the method, in the process of the invention,is the number of sampling points in the boundary domain;

constructing a third part L of the function losing the ith task according to the initial conditions _i ：

In the method, in the process of the invention,is the number of samples in the boundary domain, li=0 when no initial conditions are given;

constructing a loss function for an ith task

Constructing a total loss function from task loss functions

5. The method according to claim 1, wherein the parameters of the neural network in step 2 include the number of layers, the number of neurons and the learning rate.

6. The method for rapid simulation of a switching arc model according to claim 1, wherein the step 3 specifically comprises the steps of:

step 3.1, randomly initializing the weight of the deep neural network selected in the step 2;

step 3.2, training an arc equation corresponding to each task of the step 1 by using a neural network;

step 3.3, calculating a loss function value of an arc equation corresponding to each task, and calculating a total loss function value, wherein the number of times of the neural network training equation is changeable, the specific number of times is determined according to the specific arc equation, and the neural network needs to reset the network weight when the training task is replaced;

step 3.4, updating the weight of the neural network by using a gradient optimization algorithm according to the sum of the loss functions;

step 3.5, giving the weight obtained in the step 3.4 to the neural network;

step 3.6, repeating the steps 3.2-3.5, and observing the total loss function value of the neural network until the total loss function value is reduced to a given threshold value;

and 3.7, obtaining the weight parameters of the neural network.

7. The method for rapid simulation of a switching arc model according to claim 6, wherein the step 4 specifically comprises the steps of:

step 4.1, constructing a target task network, wherein each parameter of the network is consistent with the parameters of the meta-network;

step 4.2, setting the weight obtained in the step 3.7 as an initial parameter of a target task network;

step 4.3, training the arc equation corresponding to each target task once by the neural network to obtain an output value;

step 4.4, calculating a loss function value;

step 4.5, updating the weight of the neural network by using a gradient optimization algorithm;

step 4.6, repeating the steps 4.3-4.5, and observing the loss function value of the neural network until the loss function value is reduced to a given threshold value;

and 4.7, obtaining the output of the neural network, namely the simulation result of the corresponding arc model.