CN114202111A - Electronic expansion valve flow characteristic prediction based on particle swarm optimization BP neural network - Google Patents

Electronic expansion valve flow characteristic prediction based on particle swarm optimization BP neural network Download PDF

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CN114202111A
CN114202111A CN202111410446.8A CN202111410446A CN114202111A CN 114202111 A CN114202111 A CN 114202111A CN 202111410446 A CN202111410446 A CN 202111410446A CN 114202111 A CN114202111 A CN 114202111A
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梁高帅
上官文斌
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South China University of Technology SCUT
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Abstract

The invention discloses a particle swarm optimization BP neural network-based electronic expansion valve flow characteristic prediction method, which comprises the following steps: acquiring an experimental data sample and preprocessing the experimental data sample; constructing a BP neural network topological structure; optimizing the initial weight and the threshold of the BP neural network by adopting a particle swarm algorithm; inputting the optimized initial weight and threshold value into a BP neural network for training and testing a sample; and predicting the flow characteristics of the trained neural network under different working conditions. The method has the advantages that the method adopts a BP neural network method to predict the flow characteristic of the electronic expansion valve, adopts a particle swarm optimization algorithm to optimize the initial weight and the threshold of the BP neural network, improves the defects that the BP neural network has low convergence speed, even does not converge or falls into a local minimum value, and is convenient, efficient and accurate in flow prediction.

Description

Electronic expansion valve flow characteristic prediction based on particle swarm optimization BP neural network
Technical Field
The invention relates to the field of new energy automobile thermal management systems, in particular to electronic expansion valve flow characteristic prediction based on particle swarm optimization BP neural network.
Background
The electronic expansion valve is used as a throttling device in a heat pump system and mainly plays a role in reducing pressure and regulating flow in the system. The flow characteristic is one of the key parameters of the electronic expansion valve, for a heat pump system working normally, different refrigerant flows are needed to achieve the purposes of refrigeration and heating under different working conditions, and for a designed electronic expansion valve, the research on the flow characteristic is of great significance.
In the conventional art, the flow characteristic of the expansion valve is studied from a theoretical level according to a flow characteristic formula of the fluid flowing through the orifice, but since the flow coefficient in the flow characteristic formula is unknown, only an empirical formula is used instead, and as a result, a large error exists between the flow characteristic of the expansion valve obtained by the flow characteristic formula of the orifice and the actual operation requirement. In the prior art, polynomial fitting is adopted or the relation between mass flow and influence factors is researched according to Ponkingham's law, and the fitted relation is particularly complex due to more considered influence factors. In the prior art, a flow characteristic is also researched by adopting an experimental method (Mass flow rate prediction of R1233zd through electronic expansion based on ANN and power-law compensation models), but the flow characteristic can only be researched under special working conditions in consideration of experimental equipment, cost and time, so that a new research method with strong practicability is needed to research the flow characteristic of the electronic expansion valve.
Disclosure of Invention
The invention provides a method for predicting the flow characteristic of an electronic expansion valve of a particle swarm optimization BP neural network algorithm, which is characterized in that the flow characteristic is researched by adopting a neural network method, a BP neural network model is established according to known representative flow data by utilizing the good nonlinear mapping capability and the self-adaptive learning capability of the BP neural network, and the flow characteristic under different working conditions is predicted, so that the method is convenient and efficient, and the prediction precision meets the requirements of the working conditions. However, because the initial weight and the threshold of the BP neural network are randomly given, the established model has the phenomena of low convergence speed, even no convergence or falling into a local minimum value. Aiming at the defects of the BP neural network, the particle swarm optimization is set to optimize the initial weight and the threshold of the BP neural network, and then the optimized initial weight and the optimized threshold are input into the established BP neural network model for flow characteristic prediction, so that the defects that the traditional BP neural network is low in convergence speed and easy to fall into a local minimum value can be avoided, and a satisfactory prediction result is obtained.
The invention is realized by at least one of the following technical schemes.
The method for predicting the flow characteristic of the electronic expansion valve based on the particle swarm optimization BP neural network comprises the following steps:
(1) acquiring and preprocessing an experimental data sample, wherein the experimental data sample comprises a training sample and a test sample;
(2) constructing a BP neural network topological structure;
(3) optimizing the initial weight and the threshold of the BP neural network by adopting a particle swarm algorithm;
(4) inputting the optimized initial weight and threshold value into a BP neural network for training and testing a sample;
(5) and predicting the flow characteristics under different working conditions by using the trained BP neural network.
Preferably, the step (1) of obtaining a sample and preprocessing: firstly, determining input variables and output variables, then carrying out experiments, obtaining a plurality of groups of experimental data, and normalizing the data to the range of [ -1,1] by using the following formula:
Figure BDA0003364785060000031
wherein X' is the normalized data, X represents the original experimental data, XminMinimum of the original experimental data, XmaxIs the maximum of the original experimental data.
Preferably, in the step (2), constructing the BP neural network topology includes, but is not limited to, the following steps:
(201) determining the number of layers of the BP neural network and the number of neurons of each layer;
(202) determining transfer functions of a hidden layer and an output layer of the BP neural network;
(203) BP neural network related parameters are determined, including but not limited to training functions, performance functions, and target errors.
Preferably, the optimization of the initial weight and the threshold of the BP neural network in the step (3) comprises the following steps:
(301) initializing a population, generating an initial position and an initial speed of particles and setting related parameters of the particle swarm;
(302) calculating the fitness of each particle in the initial population;
(303) determining an individual extreme value and an overall extreme value of an initial population;
(304) updating the position and the speed of each particle in the population;
(305) calculating the fitness of the new particles;
(306) determining new particle individual extreme values and overall extreme values;
(307) judging whether the global optimal fitness value is smaller than the set precision, if so, outputting the position of the optimal particle, otherwise, judging whether the current cycle time reaches the maximum iteration time, if not, returning to the step (304) to continue the cycle, and outputting the position of the optimal particle when the maximum iteration time is reached;
(308) and outputting the optimal weight and the threshold value, and assigning the optimal solution to the BP neural network for training and prediction.
Preferably, the population initialization includes setting a population particle number M, a maximum iteration number N, and a maximum inertia weight wmaxMinimum inertia weight wminMaximum velocity vmaxMinimum velocity vminMaximum displacement xmaxMinimum displacement xminLearning factor c1、c2And a particle dimension D, which is the sum of all connection weights and the threshold.
Preferably, the population is initialized to: randomly setting the initial position of the particle i
Figure BDA0003364785060000041
And initial velocity
Figure BDA0003364785060000042
D＝pn+nq+n+q
In the formula,
Figure BDA0003364785060000043
representing the initial position of the ith particle in the Dth dimension;
Figure BDA0003364785060000044
representing the initial velocity of the ith particle in the Dth dimension; p is the number of neurons in the input layer, namely the number of input variables; n is the number of neurons in the hidden layer and is also equal to the number of thresholds in the hidden layer; q is the number of neurons in the output layer, i.e. the number of output variables, which is also equal to the number of thresholds in the output layer.
Preferably, the fitness function is:
Figure BDA0003364785060000045
in the formula, fitness (i) is the current fitness value of the particle i, and n is the number of experimental samples; q is the number of neurons in the output layer; y iskThe mass flow is predicted value; t is tkIs the desired output value.
Preferably, the initial position of each particle i in the population is taken as the optimal position of the particle i at the initial moment and is recorded as pi,bestThe corresponding fitness value is denoted as pi,best_fThe minimum fitness value of all the particles in the initial population is recorded as the global optimal fitness value gbest_fThe initial position of the corresponding particle is the global optimum position and is marked as gbest。
Preferably, the current fitness value fitness (i) of the particle is compared with the self-history optimal individual extreme value pi,best_fMaking a comparison if fitness (i) < pi,best_fThen, the current fitness value fitness (i) of the particle is used as the self-history optimal individual extremum and the position of the current particle is used as the self-history optimal position; the current fitness value fitness (i) of the particle and the global optimum extreme value g of the particlebest_fMaking a comparison if fitness (i) < gbest_fThen the current fitness value fitness (i) of the particle is used as the global optimum extremum of the particle and the position of the current particle is used as the global optimum position.
Preferably, in the step (4), the training process of the sample is performed according to a gradient descent method, and after the set precision is met, the test sample is input for prediction; the predicted result is determined by mean square error MSE and coefficient of determination R2Evaluation was performed, and the expression is as follows:
Figure BDA0003364785060000051
Figure BDA0003364785060000052
wherein,
Figure BDA0003364785060000053
is a predicted value of a sample, xiIs an experimental value for the sample that is,
Figure BDA0003364785060000054
is the average value of the samples, and n is the number of experimental samples.
Compared with the prior art, the invention has the beneficial effects that:
compared with the method of experiment, polynomial fitting or Ponkan law, the method for predicting the flow characteristic of the electronic expansion valve based on the particle swarm optimization BP neural network algorithm has strong applicability, convenience, rapidness and high efficiency. In addition, the particle swarm optimization is a search algorithm based on the whole and has stronger global search capability, after the initial weight and the threshold of the BP neural network are optimized by the particle swarm optimization method, the defects that the common BP neural network is low in convergence speed and easy to fall into local optimization can be avoided to a great extent, in addition, the optimized BP neural network is high in quality and flow prediction precision, and the requirements of actual working conditions can be met.
Drawings
FIG. 1 is a flow chart of a particle swarm algorithm for optimizing initial weights and thresholds of a BP neural network according to an embodiment of the present invention;
FIG. 2 is a topology structure diagram of a three-layer BP neural network according to an embodiment of the present invention;
FIG. 3 is a comparison graph of mass flow prediction values and test values of a particle swarm optimization BP (PSO-BP) neural network according to an embodiment of the present invention;
FIG. 4 is a diagram of a distribution of error bands of mass flow prediction values and experimental values of a particle swarm optimization BP (PSO-BP) neural network according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to the present preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout. The invention is further described below with reference to the accompanying drawings.
The method for predicting the flow characteristic of the electronic expansion valve based on the particle swarm optimization BP neural network comprises the following steps as shown in figure 1:
(1) obtaining an experimental sample and carrying out pretreatment
Four physical quantities of inlet pressure, inlet temperature, outlet pressure and valve opening are selected as input variables, and mass flow is selected as an output variable. And performing an experiment on the four input variables in a control variable mode to obtain a flow data L group, wherein 70% of data is used as a training set, and 30% of data is used as a test set. The experimental data were then normalized to the range of [ -1,1] using the following formula.
Figure BDA0003364785060000061
Wherein X' is the data after normalization, X represents the experimental data, XminAs the minimum of the experimental data, XmaxIs the maximum value of the experimental data.
(2) Constructing a BP neural network topology, including but not limited to the following steps:
(201) determining the number of layers of the BP neural network and the number of neurons of each layer;
(202) determining transfer functions of a hidden layer and an output layer of the BP neural network;
(203) determining related parameters of the BP neural network, including but not limited to a training function, a performance function and a target error;
as shown in fig. 2, the step (201) of determining the number of layers and the number of neurons in each layer of the BP neural network includes: selecting a neural network of three layers, input, single hidden and output, xiRepresents an input variable, yiRepresenting an output variable, wijRepresents the connection weight between the ith neuron and the jth neuron, wjkAnd representing the connection weight value between the jth neuron and the kth neuron. The number of input layer neurons is determined by the number of input variables, the number of output layer neurons is determined by the number of output variables, and the number of hidden layer neurons is determined by the following formula.
Figure BDA0003364785060000071
In the formula, n is the number of neurons in the hidden layer; p is the number of input variables; q is the number of output variables; m is a constant between 1 and 10.
The step (202) of determining the transfer functions of the hidden layer and the output layer of the BP neural network comprises the following steps of respectively selecting a tansig function and a purelin function by the transfer functions of the hidden layer and the output layer of the BP neural network, wherein the expression is as follows:
Figure BDA0003364785060000072
purelin(x)＝x(-1≤x≤1)
in the formula, x represents an input variable after normalization.
The step (203) of determining the training function, the performance function and the target error of the BP neural network comprises: the BP neural network training function selects train lm, the performance function selects mse, and the target error is 1 e-3.
(3) Optimizing initial weight and threshold of the BP neural network by adopting a particle swarm algorithm, and comprising the following steps of:
(301) initializing a population;
(302) calculating the fitness of each particle in the initial population;
(303) determining an individual extreme value and an overall extreme value of an initial population;
(304) entering an iterative loop, and updating the position and the speed of each particle in the population;
(305) calculating the fitness of the new particles;
(306) determining new particle individual extreme values and overall extreme values;
(307) judging whether the global optimal fitness value is smaller than the set precision, if so, outputting the position of the optimal particle, otherwise, judging whether the current cycle time reaches the maximum iteration time, if not, returning to the step (304) to continue the cycle, and outputting the position of the optimal particle when the maximum iteration time is reached;
(308) and outputting the optimal weight and the threshold value, and assigning the optimal solution to the BP neural network for prediction.
Initializing the population in step (301) to set relevant parameters including population number M, maximum iteration number N and maximum inertia weight wmaxThe minimum inertia weight wminMaximum velocity vmaxMinimum velocity vminMaximum displacement xmaxMinimum displacement xminLearning factor c1、c2The particle dimension D is the sum of all the connection weights and the threshold value and is calculated by the following formula; randomly setting the initial position of the particle i
Figure BDA0003364785060000081
And initial velocity
Figure BDA0003364785060000082
D＝pn+nq+n+q
In the formula,
Figure BDA0003364785060000083
representing the initial position of the ith particle in the Dth dimension;
Figure BDA0003364785060000084
representing the initial velocity of the ith particle in the Dth dimension; p is the number of neurons in the input layer, namely the number of input variables; n is the number of neurons in the hidden layer and is also equal to the number of thresholds in the hidden layer; q is the number of neurons in the output layer, i.e. the number of output variables, which is also equal to the number of thresholds in the output layer.
Step (302) of calculating the fitness of each particle i of the initial population: defining the mean square value of the difference between the predicted value and the expected value of the mass flow of each experimental sample as a fitness function, and the fitness function is represented by the following formula:
Figure BDA0003364785060000091
in the formula, n is the number of experimental samples; q is the number of neurons in the output layer; y iskThe mass flow is predicted value; t is tkIs the desired output value.
Step (303) determining individual extrema and overall extrema of the initial population:
taking the initial position of each particle i in the population as the optimal position of the particle i at the initial moment, and marking the initial position as pi,bestThe corresponding fitness value is denoted as pi,best_fThe minimum fitness value of all the particles in the initial population is recorded as the global optimal fitness value gbest_fThe initial position of the corresponding particle is the global optimum position and is marked as gbest。
Step (304) entering an iterative loop, updating the speed and position of each particle in the population:
firstly, updating the inertia weight value by adopting a linear decreasing strategy every time iteration is performed, wherein the formula is as follows:
w＝wmax-(wmax-wmin)*(j/N)
in the formula, j represents the number of iterations; w is amaxIs the maximum weight; w is aminIs the minimum weight; w represents the updated inertia weight; and N is the maximum iteration number.
And respectively carrying out speed updating and position updating of each particle in each dimension by adopting the following two formulas:
Figure BDA0003364785060000092
Figure BDA0003364785060000093
in the formula,
Figure BDA0003364785060000094
the velocity of the ith particle in the kth dimension at the moment t;
Figure BDA0003364785060000095
the velocity of the ith particle in the kth dimension at the moment of t + 1; c. C1、c2Is a learning factor; rand () is a function of random values between 0-1;
Figure BDA0003364785060000096
the k-dimension historical optimal value of the ith particle at the time t;
Figure BDA0003364785060000097
the k-dimension value of the global optimal particle at the time t;
Figure BDA0003364785060000098
is the location of the ith particle in the kth dimension at time t;
Figure BDA0003364785060000099
the position of the kth dimension of the ith particle at the moment of t +1, wherein i is more than or equal to 1 and less than or equal to M, k is more than or equal to 1 and less than or equal to D, M is the number of population particles, and D is the dimension of the particle;
with respect to speed, if
Figure BDA00033647850600000910
Maximum velocity vmaxThen there is
Figure BDA00033647850600000911
If it is not
Figure BDA00033647850600000912
< minimum velocity vminThen there is
Figure BDA00033647850600000913
For the position, if
Figure BDA00033647850600000914
> maximum displacement xmaxThen there is
Figure BDA00033647850600000915
If it is not
Figure BDA00033647850600000916
< minimum displacement xminThen there is
Figure BDA0003364785060000101
Step (305) of calculating a new particle fitness:
the calculation of the fitness value is similar to the calculation of the fitness value in step (302).
Step (306) determines new particle individual extrema and global extrema:
the current fitness value fitness (i) of the particle and the self historical optimal individual extreme value pi,best_fMaking a comparison if fitness (i) < pi,best_fThen, the current fitness value fitness (i) of the particle is used as the self-history optimal individual extremum and the position of the current particle is used as the self-history optimal position. The current fitness value fitness (i) of the particle and the global optimum extreme value g of the particlebest_fMaking a comparison if fitness (i) < gbest_fThen the current fitness value fitness (i) of the particle is used as the global optimum extremum of the particle and the position of the current particle is used as the global optimum position.
Step (308) outputs optimal weight and threshold: and (4) assigning the optimal weight and the threshold value according to the weight and the threshold value of each layer output in the step (307), wherein p is the number of neurons of the input layer, n is the number of neurons of the hidden layer, and q is the number of neurons of the output layer. Taking 1-pn as the weight from the input layer to the hidden layer according to the left-to-right sequence of the global optimal particle position sequence; taking pn + 1-pn + n as a threshold value of an implicit layer neuron; the weights from pn + n +1 to pn + n + nq to the hidden layer and the output layer are taken as the weights; the threshold from the hidden layer to the output layer is pn + n + nq +1 to pn + n + nq + q.
(4) Inputting the optimized initial weight and threshold value into a BP neural network for training and testing samples
The training process of the sample is performed according to a gradient descent method, after the set precision is met, the test sample is input for prediction, and the pair of the predicted value and the test value is shown in fig. 3 and 4. The predicted result is determined by Mean Square Error (MSE) and coefficient of determination (R)2) Evaluation was performed, and the expression is as follows:
Figure BDA0003364785060000102
Figure BDA0003364785060000111
wherein,
Figure BDA0003364785060000112
is a predicted value of a sample, xiIs an experimental value for the sample that is,
Figure BDA0003364785060000113
is the average value of the samples, and n is the number of experimental samples.
(5) And predicting the flow characteristics under different working conditions by using the trained BP neural network. The different conditions include, but are not limited to, different inlet pressures, inlet subcooling and outlet pressures, valve opening, etc.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims (10)

1. The method for predicting the flow characteristic of the electronic expansion valve based on the particle swarm optimization BP neural network is characterized by comprising the following steps of:
(1) acquiring and preprocessing an experimental data sample, wherein the experimental data sample comprises a training sample and a test sample;
(2) constructing a BP neural network topological structure;
(3) optimizing the initial weight and the threshold of the BP neural network by adopting a particle swarm algorithm;
(4) inputting the optimized initial weight and threshold value into a BP neural network for training and testing a sample;
(5) and predicting the flow characteristics under different working conditions by using the trained BP neural network.
2. The particle swarm optimization BP neural network-based electronic expansion valve flow characteristic prediction according to claim 1, wherein the samples obtained in step (1) are preprocessed: firstly, determining input variables and output variables, then carrying out experiments, obtaining a plurality of groups of experimental data, and normalizing the data to the range of [ -1,1] by using the following formula:
Figure FDA0003364785050000011
wherein X' is the normalized data, X represents the original experimental data, XminMinimum of the original experimental data, XmaxIs the maximum of the original experimental data.
3. The particle swarm optimization-based electronic expansion valve flow characteristic prediction of the BP neural network according to claim 1, wherein in the step (2), constructing the BP neural network topology includes but is not limited to the following steps:
(201) determining the number of layers of the BP neural network and the number of neurons of each layer;
(202) determining transfer functions of a hidden layer and an output layer of the BP neural network;
(203) BP neural network related parameters are determined, including but not limited to training functions, performance functions, and target errors.
4. The particle swarm optimization based electronic expansion valve flow characteristic prediction of the BP neural network as claimed in claim 1, wherein the optimization of the initial weight and the threshold of the BP neural network in the step (3) comprises the following steps:
(301) initializing a population, generating an initial position and an initial speed of particles and setting related parameters of the particle swarm;
(302) calculating the fitness of each particle in the initial population;
(303) determining an individual extreme value and an overall extreme value of an initial population;
(304) updating the position and the speed of each particle in the population;
(305) calculating the fitness of the new particles;
(306) determining new particle individual extreme values and overall extreme values;
(307) judging whether the global optimal fitness value is smaller than the set precision, if so, outputting the position of the optimal particle, otherwise, judging whether the current cycle time reaches the maximum iteration time, if not, returning to the step (304) to continue the cycle, and outputting the position of the optimal particle when the maximum iteration time is reached;
(308) and outputting the optimal weight and the threshold value, and assigning the optimal solution to the BP neural network for training and prediction.
5. The particle swarm optimization BP neural network-based electronic expansion valve flow characteristic prediction according to claim 4, wherein the population initialization comprises setting a population particle number M, a maximum iteration number N, and a maximum inertia weight wmaxMinimum inertia weight wminMaximum velocity vmaxMinimum, isVelocity vminMaximum displacement xmaxMinimum displacement xminLearning factor c1、c2And a particle dimension D, which is the sum of all connection weights and the threshold.
6. The particle swarm optimization BP neural network-based electronic expansion valve flow characteristic prediction according to claim 4, characterized by the population initialization: randomly setting the initial position of the particle i
Figure FDA0003364785050000021
And initial velocity
Figure FDA0003364785050000022
D＝pn+nq+n+q
In the formula,
Figure FDA0003364785050000031
representing the initial position of the ith particle in the Dth dimension;
Figure FDA0003364785050000032
representing the initial velocity of the ith particle in the Dth dimension; p is the number of neurons in the input layer, namely the number of input variables; n is the number of neurons in the hidden layer and is also equal to the number of thresholds in the hidden layer; q is the number of neurons in the output layer, i.e. the number of output variables, which is also equal to the number of thresholds in the output layer.
7. The particle swarm optimization BP neural network-based electronic expansion valve flow characteristic prediction according to claim 4, characterized by a fitness function of:
Figure FDA0003364785050000033
in the formula, fitness (i) is the current fitness value of the particle i, and n is the number of experimental samples; q is the number of neurons in the output layer; y iskAs a mass flowA quantity predicted value; t is tkIs the desired output value.
8. The particle swarm optimization BP neural network-based electronic expansion valve flow characteristic prediction of claim 6, wherein an initial position of each particle i in a swarm is taken as an optimal position of the particle i at an initial moment and is recorded as pi,bestThe corresponding fitness value is denoted as pi,best_fThe minimum fitness value of all the particles in the initial population is recorded as the global optimal fitness value gbest_fThe initial position of the corresponding particle is the global optimum position and is marked as gbest。
9. The particle swarm optimization BP neural network-based electronic expansion valve flow characteristic prediction according to claim 8, wherein the current fitness value fitness (i) of the particle and the self-history optimal individual extremum p are combinedi,best_fMaking a comparison if fitness (i) < pi,best_fThen, the current fitness value fitness (i) of the particle is used as the self-history optimal individual extremum and the position of the current particle is used as the self-history optimal position; the current fitness value fitness (i) of the particle and the global optimum extreme value g of the particlebest_fMaking a comparison if fitness (i) < gbest_fThen the current fitness value fitness (i) of the particle is used as the global optimum extremum of the particle and the position of the current particle is used as the global optimum position.
10. The prediction of the flow characteristic of the electronic expansion valve based on the particle swarm optimization BP neural network according to any one of claims 1 to 9, wherein in the step (4), a training process of a sample is performed according to a gradient descent method, and after a set precision is met, a test sample is input for prediction; the predicted result is determined by mean square error MSE and coefficient of determination R2Evaluation was performed, and the expression is as follows:
Figure FDA0003364785050000041
Figure FDA0003364785050000042
wherein,
Figure FDA0003364785050000043
is a predicted value of a sample, xiIs an experimental value for the sample that is,
Figure FDA0003364785050000044
is the average value of the samples, and n is the number of experimental samples.
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