CN102419827B - Radial basis function (RBF) neural network-based boiling heat exchanging prediction method - Google Patents
Radial basis function (RBF) neural network-based boiling heat exchanging prediction method Download PDFInfo
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Abstract
The invention provides a radial basis function (RBF) neural network-based boiling heat exchanging prediction method, in particular a radial basis neural network-based boiling heat exchanging prediction method of mixed medium flowing inside a horizontal plain tube, and the method comprises the following steps that: collecting data, determining input and output vectors of a network, preprocessing data, training and testing an RBF neural network, utilizing the neural network after being trained for prediction to obtain the predicted flowing boiling heat exchanging coefficient, and realizing the prediction of boiling heat exchange of the mixed medium flowing inside the horizontal plain tube. Due to the adoption of the method, the complicated internal mechanism for analyzing a mixed medium flowing boiling heat exchanging process can be avoided, the experimental times can be reduced, the flowing boiling heat exchanging of the mixed medium can be correctly and rapidly predicted through the simulation test of a computer, the precision is remarkably improved compared to a traditional correlation way, and a good instruction significance on predicting the performance and optimizing the structure of a tube-type heat exchanger in a mixed medium refrigerating system can be realized.
Description
Technical field
The present invention relates to a kind of based on mixed working fluid flow boiling and heat transfer Forecasting Methodology in the horizontal plain tube of radial basis (Radial Basis Function, RBF) neural network, belong to refrigeration and Thermal Power Engineering Artificial technical field of intelligence.
Background technology
At present, global energy crisis and environmental problem are increasingly sharpened, and refrigerating and air conditioning industry is faced with and develops environmental-protection refrigeration working medium, improve system effectiveness and reduce the baptism of equipment cost.Mixed working fluid is more and more paid attention to because of the performance of its uniqueness, therefore grasps the Convective boiling heat transfer of mixed working fluid exactly, becomes the heat interchanger key point that design adopts Refrigeration Cycle Using Refrigerant Mixture.Chinese scholars had carried out large quantifier elimination for the Convective boiling heat transfer of mixed working fluid in the last few years, the situation of change of boiling heat transfer coefficient with each factor (as caliber, thermoflux, mass rate, mass dryness fraction and saturation temperature etc.) is have studied in experiment, obtaining the actual value of the coefficient of heat transfer, is development and to have checked general heat exchange models to establish reliable data basis.But because the mechanism of flow boiling heat transfer is very complicated, influence factor is numerous, has strong non-linear behavior, does not also form unified theoretic knowledge till now.
Existing each correlation be mostly researchers experimentally data propose experience or semiempirical correlation, sizable error is often brought when applying, the scope of application is very restricted, especially to mixed working fluid (as Liu-Winteron correlation, Guangor-Winteron correlation, Kandlikar correlation and Choi correlation etc.).RBF neural is a kind of typical partial approximation network, and its structure is simple, and training is succinct, without the need to specifically describing math equation and the physical significance of mapping relations in advance, can approach arbitrary nonlinear function.For this reason, select the RBF neural with good non-linear mapping capability, realistic model is set up to the flow boiling and heat transfer of mixed working fluid in horizontal plain tube, carrys out the flow boiling and heat transfer of forecast analysis mixed working fluid.
Summary of the invention
The present invention is directed to the deficiency of existing existence, propose a kind of based on mixed working fluid flow boiling and heat transfer Forecasting Methodology in the horizontal plain tube of artificial neural network, the method can avoid the internal mechanism analyzing mixed working fluid flow boiling and heat transfer process complexity, thus effectively solve the general larger problem of the traditional association formula error of calculation, improve the precision of prediction.
The present invention is realized by following technical proposal: a kind of boiling heat transfer Forecasting Methodology based on RBF neural, comprises following each step:
(1) collection of data: the measured data gathering mixed working fluid flow boiling and heat transfer process in tubular heat exchanger, comprises the influence factor of mixed working fluid Bottomhole pressure boiling heat transfer, namely mass rate (
g), thermoflux (
q), mass dryness fraction (
x), saturation temperature (
t sat), light pipe internal diameter (
d) and flow boiling and heat transfer coefficient (
h);
(2) determination of network input, output vector: set up RBF neural forecast model, the input layer of RBF neural is defined as 5, output layer neuron is defined as 1, by mass rate, thermoflux, mass dryness fraction, saturation temperature and these 5 physical descriptors of light pipe internal diameter are as the input of RBF neural, and flow boiling and heat transfer coefficient is as the output of RBF neural;
(3) pre-treatment of data: due to each component size great disparity of mode input, even there is difference several order of magnitude, large data will certainly fall into oblivion the effect of small data to RBF function, therefore the data to step (1) gathers are needed to be normalized [0,1] between, effectively can reduce the redundance of input data like this, and the convergence speed of network can be accelerated; Its formula is as follows:
(1)
(4) training and testing of RBF neural: the data after gained normalization in step (3) are input in RBF neural with training sample, network training is from the 0th neuron, by checking that output error makes network automatically increase neuron, the every cycle calculations of training sample once after, with the training sample made corresponding to network generation maximum error as weight vector wl, produce a new hidden layer neuron, then recalculate, and check the error of new network, repeat this process until reach training anticipation error or reach maximum hidden layer neuron number, obtain the RBF neural determined after training, wherein, network error adopts square error (mean square error, MSE) represent, its calculating formula is:
(2)
In formula,
e mSErepresent network error,
o (j)represent actual output,
nfor training data group number;
In addition, the output valve obtained is normalized value, then carries out renormalization process to it, is converted into true output valve, to contrast with former experimental data easily and intuitively; Its formula is as follows:
(3)
In formula
x maxfor the maximal value of measured data;
x minfor the minimum value of measured data;
xfor measured data;
x ^ for the data after normalization;
(5) again gather measured data, comprise mass rate (
g), thermoflux (
q), mass dryness fraction (
x), saturation temperature (
t sat), light pipe internal diameter (
d); By the method in step (3), data are normalized, in the RBF neural determined after the training of input step (4) gained again, obtain output valve, then carry out renormalization process by the method in step (4), namely obtain predict flow boiling and heat transfer coefficient (
h), realize the prediction of mixed working fluid flow boiling and heat transfer in horizontal plain tube.
Principle of the present invention: the method adopting Hybrid learning strategy, utilizes the radial basis function that K means clustering algorithm is hidden layer to determine suitable data center from input layer to hidden layer
c i, and according to the distance between each data center
σ idetermine the expansion constant spread of hidden layer node; From hidden layer to output layer, utilize gradient descent algorithm to train corresponding weight
w2 ik.
The computing of RBF neural of the present invention is specifically realized by following computation process: initialization RBF neural, determines the connected mode of network n-p-m, and namely input layer is n, and hidden layer neuron is p, and output layer neuron is m; To the weights random assignment of neural network; The input of RBF neural is expressed as
x r(r=l, 2 ..., n).If the
jbeing input as of group data RBF network
x 1 (j),
x 2 (j)...,
x n (j), the computing function of each layer of RBF neural is as follows:
Input layer is only responsible for the linear input signal that transmits to hidden layer, by signal source node
x r(r=l, 2 ..., n) form:
Input r (j)=
X r (j)，
Output r (j)=
Input r (j)，(r=l，2，…，n)； (4)
In formula
input r (j),
output r (j)represent the input and output of input layer respectively;
Hidden layer is made up of p neuron:
Input i (j)=‖
X(j)-C i ‖，
Output i (j)=Φ i (Input i (j))，(i=l，2，…，p)； (5)
In formula
input i (j),
output i (j)represent the input and output of hidden layer respectively,
x (j)=[
x 1 (j),
x 2 (j)...,
x n (j)]
trepresent the
jthe input value of group data, ‖
x (j)-C i ‖ represents
c iwith
x (j)between Euclidean distance,
Φ(*) represent Gaussian function, its form is
;
c irepresent hidden layer i-th neuronic central value,
σ irepresent hidden layer i-th neuronic center width.
Output layer only has a neuron, realize from
Φ(
x)-
ylinear mapping, that is:
，(k=1, 2 , … , m)； (6)
In formula, k represents output layer nodes,
y (j)represent the output of output layer,
w2 ikrepresent the weight of hidden layer to output layer.
Training data being inputted network, sets up study mechanism, when inputting the data of a certain group of operating point, namely providing mass rate, thermoflux, mass dryness fraction, saturation temperature, light pipe internal diameter and the such one group of data of flow boiling and heat transfer coefficient.Network carries out training study by as above learning algorithm, obtains an output valve, i.e. the predicted value of the flow boiling and heat transfer coefficient of this operating point, the error between comparing cell output valve and desired output (experiment measuring boiling heat transfer coefficient value).General training data are more, and the study of network is more abundant and empirical value is larger, and precision of prediction is also higher.After network training terminates, test data supervising network model is utilized whether to meet the requirements, comparison model predicts the outcome and error between measured result, when neural network each group of test data predicated error all lower than during prescribed level by test, can prediction work be started.
The effect that the present invention possesses and advantage: the neural network model that the present invention sets up all has good interrelating effect to training sample and test sample book.Instant invention overcomes the deficiency that traditional association formula exists, when influence factor is numerous, can be accurate, the flow boiling and heat transfer of mixed working fluid in prediction level light pipe rapidly, avoid the study mechanism of the flow boiling and heat transfer to working medium, to the performance prediction and Optimal Structure Designing adopting tubular heat exchanger in Refrigeration Cycle Using Refrigerant Mixture, there is certain directive significance.
Accompanying drawing explanation
Fig. 1 is RBF neural structure;
Fig. 2 is that the present invention utilizes RBF neural to predict the process flow diagram of mixed working fluid flow boiling and heat transfer coefficient;
Fig. 3 is network error training change;
Fig. 4 be RBF network model predict the outcome with experimental result compare schematic diagram;
Fig. 5 is the change schematic diagram of the coefficient of heat transfer with mass dryness fraction;
When Fig. 6 is different quality flow, the coefficient of heat transfer is with the variation diagram of mass dryness fraction;
When Fig. 7 is different thermoflux, the coefficient of heat transfer is with the variation diagram of mass dryness fraction.
Embodiment
Below in conjunction with embodiment and accompanying drawing, the present invention will be further described, but protection scope of the present invention is not limited to this, is equally applicable to the flow boiling and heat transfer of other mixed working fluids in horizontal plain tube.
Choose tertiary non-azeotropic mixed working medium R407C as research object, based on the flow boiling and heat transfer Forecasting Methodology of mixed working fluid in the horizontal plain tube of RBF neural, wherein the training of RBF network and test process all carry out under MATLAB R2008 environment, mainly comprise the steps (as Fig. 2):
(1) collection of data: the measured data totally 489 groups gathering the flow boiling and heat transfer process of the mixture refrigerant R407C in different operating mode pipe type heat interchanger, comprises the influence factor of mixed working fluid Bottomhole pressure boiling heat transfer, namely mass rate (
g), thermoflux (
q), mass dryness fraction (
x), saturation temperature (
t sat), light pipe internal diameter (
d) and flow boiling and heat transfer coefficient (
h); Rand function in Calling MATLAB R2008 Neural Network Toolbox, in the total sample of random selecting 80% data, namely 391 groups of data are as training sample, residue 20% data then as forecast sample;
(2) determination of network input, output vector: set up RBF neural forecast model, the input layer of RBF neural is defined as 5, output layer neuron is defined as 1, by mass rate, thermoflux, mass dryness fraction, saturation temperature and these 5 physical descriptors of light pipe internal diameter are as the input of RBF neural, and flow boiling and heat transfer coefficient is as the output of RBF neural;
(3) pre-treatment of data: due to each component size great disparity of mode input, even there is difference several order of magnitude, large data will certainly fall into oblivion the effect of small data to RBF function, therefore the data to step (1) gathers are needed to be normalized [0,1] between, effectively can reduce the redundance of input data like this, and the convergence speed of network can be accelerated; Its formula is as follows:
(1)
(4) training and testing of RBF neural: the data after gained normalization in step (3) are input in RBF neural with training sample, determine the connected mode (as Fig. 1) of RBF neural 5-p-1, namely network be input as mass rate (
g), thermoflux (
q), mass dryness fraction (
x), saturation temperature (
t sat) and light pipe internal diameter (
d) these 5 physical descriptors, export into flow boiling and heat transfer coefficient (
h); To the initial weight random assignment of neural network; Network training is from the 0th neuron, by checking that output error makes network automatically increase neuron, the every cycle calculations of training sample once after, with the training sample made corresponding to network generation maximum error as weight vector wl, produce a new hidden layer neuron, then recalculate, and check the error of new network, repeat this process until reach training anticipation error 0.001, obtain the RBF neural determined after training, wherein, network error adopts square error to represent, its calculating formula is:
(2)
In formula,
e mSErepresent network error,
o (j)represent actual output,
nfor training data group number;
In addition, the output valve obtained is normalized value, then carries out renormalization process to it, is converted into true output valve, to contrast with former experimental data easily and intuitively; Its formula is as follows:
(3)
In formula
x maxfor the maximal value of measured data;
x minfor the minimum value of measured data;
xfor measured data;
x ^ for the data after normalization;
Adopt the method for Hybrid learning strategy, from input layer to hidden layer, utilize the radial basis function that self-organizing clustering method is hidden layer to determine suitable data center
c i, and according to the distance between each data center
σ idetermine the expansion constant spread of hidden layer node; From hidden layer to output layer, utilize gradient descent algorithm to train corresponding weight
w2 ik.After network training terminates, obtain a network output valve, i.e. the flow boiling and heat transfer coefficient predictors of corresponding operating point, the error between comparing cell output valve and desired output (experiment measuring boiling heat transfer coefficient value).Training sample data are more, and the study of network is more abundant and empirical value is larger, and precision of prediction is also higher; For this is to network repetition training, when error reaches target error 0.001 or when reaching maximum neuron number, network deconditioning; The now training of RBF network completes through 144 steps, and the square error of output valve and expectation value is that 0.0009824(is as Fig. 3), network training reaches requirement;
For investigating the Generalization Capability of network further, test data is input in the network trained; The average error that now network model predicts the outcome is-0.9%, and absolute error is 5.5%, and root-mean-square error is 10.9%, and about has the data point error of 92% within ± 10%, and its predicted value and measured value fitting degree be (shown in Fig. 4) better; As shown in Figure 5, had and improve significantly compared with traditional association formula, fitting effect is better, can meet the accuracy requirement of engineer applied;
(5) measured data of the residue 20% step (1) gathered, comprise mass rate (
g), thermoflux (
q), mass dryness fraction (
x), saturation temperature (
t sat), light pipe internal diameter (
d); By the method in step (3), data are normalized, in the RBF neural determined after the training of input step (4) gained again, obtain output valve, then carry out renormalization process by the method in step (4), namely obtain predict flow boiling and heat transfer coefficient (
h), realize the prediction of mixed working fluid flow boiling and heat transfer in horizontal plain tube.
These results suggest that, the neural network model set up all has good interrelating effect to training sample and test sample book.The present embodiment shows, this method overcomes the deficiency that traditional association formula exists, can be accurate, the flow boiling and heat transfer of mixed working fluid in prediction level light pipe rapidly, has certain directive significance to the performance prediction and Optimal Structure Designing adopting tubular heat exchanger in Refrigeration Cycle Using Refrigerant Mixture.According to tertiary non-azeotropic mixed working medium R407C under different operating mode, its predicted value and measured value not only fitting degree are better, and can meet experimental result Changing Pattern well, see Fig. 6 and Fig. 7.
Claims (1)
1., based on a boiling heat transfer Forecasting Methodology for RBF neural, it is characterized in that comprising following each step:
(1) collection of data: the measured data gathering mixed working fluid flow boiling and heat transfer process in tubular heat exchanger, comprises the influence factor of mixed working fluid Bottomhole pressure boiling heat transfer, namely mass rate (
g), thermoflux (
q), mass dryness fraction (
x), saturation temperature (
t sat), light pipe internal diameter (
d) and flow boiling and heat transfer coefficient (
h);
(2) determination of network input, output vector: set up RBF neural forecast model, the input layer of RBF neural is defined as 5, output layer neuron is defined as 1, by mass rate, thermoflux, mass dryness fraction, saturation temperature and these 5 physical descriptors of light pipe internal diameter are as the input of RBF neural, and flow boiling and heat transfer coefficient is as the output of RBF neural;
(3) pre-treatment of data: the data gathered step (1) are normalized between [0,1], and its formula is as follows:
(1)
(4) training and testing of RBF neural: the data after gained normalization in step (3) are input in RBF neural with training sample, network training is from the 0th neuron, by checking that output error makes network automatically increase neuron, the every cycle calculations of training sample once after, with the training sample made corresponding to network generation maximum error as weight vector wl, produce a new hidden layer neuron, then recalculate, and check the error of new network, repeat this process until reach training anticipation error or reach maximum hidden layer neuron number, obtain the RBF neural determined after training, wherein, network error adopts square error (mean square error, MSE) represent, its calculating formula is:
(2)
In formula,
e mSErepresent network error,
o (j)represent actual output,
nfor training data group number,
y (j)represent the output of output layer;
In addition, it is normalized value that the data after gained normalization in step (3) are input to training sample the output valve obtained in RBF neural, then carries out renormalization process to it, and its formula is as follows:
(3)
In formula
x maxfor the maximal value of measured data;
x minfor the minimum value of measured data;
xfor measured data;
x ^ for the data after normalization;
(5) again gather measured data, comprise mass rate (
g), thermoflux (
q), mass dryness fraction (
x), saturation temperature (
t sat), light pipe internal diameter (
d); By the method in step (3), data are normalized, in the RBF neural determined after the training of input step (4) gained again, obtain output valve, then carry out renormalization process by the method in step (4), namely obtain predict flow boiling and heat transfer coefficient (
h).
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