CN102419827B - Radial basis function (RBF) neural network-based boiling heat exchanging prediction method - Google Patents

Abstract

The present invention provides a method for predicting boiling heat transfer based on RBF neural network, specifically a radial basis neural network based method for predicting boiling heat transfer of mixed working medium flow in a horizontal light pipe, including: data collection, network input and The determination of the output vector, the preprocessing of the data, the training and testing of the RBF neural network, and the prediction by using the fully trained neural network, that is, the predicted flow boiling heat transfer coefficient is obtained, and the prediction of the flow boiling heat transfer of the mixed working fluid in the horizontal light pipe is realized . The present invention avoids analyzing the complex internal mechanism of the mixed working medium flow boiling heat transfer process, reduces the number of experiments, and can accurately and quickly predict the flow boiling heat transfer of the mixed working medium through the computer simulation test, and the accuracy is higher than that of the traditional correlation formula. It has been significantly improved, and it has a good guiding significance for the performance prediction and structural optimization design of the tube heat exchanger in the mixed refrigerant refrigeration system.

Description

Prediction method of boiling heat transfer based on RBF neural network

technical field

The invention relates to a radial basis (Radial Basis Function, RBF) neural network-based method for predicting the flow and boiling heat transfer of a mixed working medium in a horizontal light tube, belonging to the technical field of computer artificial intelligence in refrigeration and thermal energy engineering.

Background technique

At present, the global energy crisis and environmental problems are intensifying, and the refrigeration and air-conditioning industry is facing the severe test of developing environmentally friendly refrigerants, improving system efficiency and reducing equipment costs. The mixed working fluid has been paid more and more attention due to its unique properties, so accurately grasping the flow boiling heat transfer performance of the mixed working fluid has become the key to the design of heat exchangers using mixed working fluid refrigeration systems. In recent years, scholars at home and abroad have conducted a lot of research on the flow boiling heat transfer performance of mixed working fluids. In the experiment, the boiling heat transfer coefficient has been studied with various factors (such as pipe diameter, heat flux, mass flow rate, dryness and saturation). temperature, etc.) to obtain the actual value of the heat transfer coefficient, laying a reliable data foundation for the development and testing of general heat transfer models. However, because the mechanism of flow boiling heat transfer is very complex, with many influencing factors and strong nonlinear behavior, a unified theoretical understanding has not been formed so far.

Most of the existing correlations are empirical or semi-empirical correlations proposed by researchers based on experimental data, which often bring considerable errors when popularized and applied, and the scope of application is very limited, especially for mixed working fluids (such as Liu- Winteron correlation, Guangor-Winteron correlation, Kandlikar correlation and Choi correlation, etc.). The RBF neural network is a typical local approximation network, which has a simple structure and concise training. It does not need to describe the mathematical equations and physical meanings of the mapping relationship in advance, and can approximate any nonlinear function. For this reason, the RBF neural network with good nonlinear mapping ability is selected to establish a simulation model for the flow boiling heat transfer of the mixed working fluid in the horizontal light pipe to predict and analyze the flow boiling heat transfer of the mixed working medium.

Contents of the invention

Aiming at the existing deficiencies, the present invention proposes an artificial neural network-based method for predicting the flow boiling heat transfer of the mixed working fluid in the horizontal light tube. This method can avoid analyzing the complicated internal mechanism of the mixed working fluid flow boiling heat transfer process, thereby effectively It solves the problem that the calculation error of traditional correlation is generally large, and improves the accuracy of prediction.

The present invention is realized through the following technical solutions: a method for predicting boiling heat transfer based on RBF neural network, comprising the following steps:

(1) Data collection: Collect the measured data of the flow boiling heat transfer process of the mixed working fluid in the tube heat exchanger, including the influencing factors of the flow boiling heat transfer in the mixed working medium tube, namely mass flow rate ( G ), heat flux ( q ), dryness ( x ), saturation temperature ( T _sat ), inner diameter of bare tube ( D ) and flow boiling heat transfer coefficient ( h );

(2) Determination of network input and output vectors: establish the RBF neural network prediction model, determine the input layer neurons of the RBF neural network as 5, and determine the output layer neurons as 1, that is, mass flow, heat flux, and dryness , the saturation temperature and the inner diameter of the light pipe are the five physical variables as the input of the RBF neural network, and the flow boiling heat transfer coefficient is the output of the RBF neural network;

(3) Pre-processing of data: Since the size of each component of the model input varies greatly, even by several orders of magnitude, big data will inevitably obliterate the effect of small data on the RBF function, so it is necessary to normalize the data collected in step (1) It can be processed between [0, 1], which can effectively reduce the redundancy of input data and speed up the convergence speed of network training; the formula is as follows:

(1)

(4) Training and testing of the RBF neural network: Input the normalized data obtained in step (3) into the RBF neural network as training samples, the network training starts from the 0th neuron, and the network is made Automatically increase neurons, after the training samples are calculated once per cycle, use the training samples corresponding to the maximum error of the network as the weight vector wl to generate a new hidden layer neuron, then recalculate, and check the error of the new network , repeat this process until the expected training error is reached or the maximum number of neurons in the hidden layer is reached, and the RBF neural network determined after training is obtained, where the network error is represented by mean square error (MSE), and its calculation formula for:

(2)

In the formula, E _MSE represents the network error, O(j) represents the actual output, and N is the number of training data sets;

In addition, the obtained output value is a normalized value, and then it is denormalized and converted into a real output value, so as to compare it with the original experimental data conveniently and intuitively; the formula is as follows:

(3)

In the formula, X _max is the maximum value of the measured data; X _min is the minimum value of the measured data; X is the measured data; X ^{^} is the normalized data;

(5) Collect measured data again, including mass flow rate ( G ), heat flux ( q ), dryness ( x ), saturation temperature ( T _sat ), and inner diameter of bare tube ( D ); follow the method in step (3) Normalize the data, and then input it into the RBF neural network determined after training in step (4) to obtain the output value, and then denormalize it according to the method in step (4), that is, the predicted The flow boiling heat transfer coefficient ( h ) is used to realize the prediction of the flow boiling heat transfer of the mixed working fluid in the horizontal light tube.

The principle of the present invention: adopt the method of hybrid learning strategy, use K-means clustering algorithm from the input layer to the hidden layer to determine the appropriate data center C _i for the radial basis function of the hidden layer, and according to the The distance σ _i determines the spread constant of the hidden layer nodes; from the hidden layer to the output layer, the gradient descent algorithm is used to train the corresponding weight w2 _ik .

The operation of the RBF neural network of the present invention is specifically realized by the following calculation process: initialize the RBF neural network, determine the connection mode of the network npm, that is, there are n neurons in the input layer, p neurons in the hidden layer, and p neurons in the output layer The number of neurons is m; the weights of the neural network are randomly assigned; the input of the RBF neural network is expressed as X _r (r=l, 2, ..., n). Suppose the input of the RBF network of the jth data set is X ₁ (j) , X ₂ (j) , ..., X _n (j) , the calculation functions of each layer of the RBF neural network are as follows:

The input layer is only responsible for linearly transmitting the input signal to the hidden layer, which consists of signal source nodes X _r (r=l, 2,...,n):

Input _r (j) = X _r (j) , Output _r (j) = Input _r (j) , (r=l,2,...,n); (4)

In the formula, Input _r (j) and Output _r (j) respectively represent the input and output of the input layer;

The hidden layer consists of p neurons:

Input _i (j) =‖ X(j)-C _i ‖， Output _i (j)=Φ _i (Input _i (j)) ，(i=l，2，…，p); (5)

where Input _i (j) and Output _i (j) represent the input and output of the hidden layer respectively, X(j)= [ X ₁ (j) , X ₂ (j) ,…, X _n (j) ] ^T Indicates the input value of the jth group of data, ‖ X(j)-C _i ‖ indicates the Euclidean distance between C _i and X(j) , Φ (*) indicates the Gaussian function, and its form is ; C _i represents the center value of the i-th neuron in the hidden layer, and σ _i represents the center width of the i-th neuron in the hidden layer.

The output layer has only one neuron, which realizes the linear mapping from Φ ( X )- Y , namely:

, (k=1, 2 , … , m); (6)

In the formula, k represents the number of nodes in the output layer, Y(j) represents the output of the output layer, and w2 _ik represents the weight from the hidden layer to the output layer.

Input the training data into the network and establish a learning mechanism. When the data of a certain set of operating points is input, a set of mass flow rate, heat flux, dryness, saturation temperature, smooth tube inner diameter and flow boiling heat transfer coefficient is given. data. The network is trained and learned according to the above learning algorithm, and an output value is obtained, that is, the predicted value of the flow boiling heat transfer coefficient at this working point, and the network output value is compared with the expected output value (experimentally measured boiling heat transfer coefficient value). error. Generally, the more training data, the more fully the learning of the network and the greater the experience value, the higher the prediction accuracy. After the network training is over, use the test data to check whether the network model meets the requirements, and compare the error between the model prediction results and the actual measurement results. When the prediction errors of the neural network in each group of test data are lower than the specified level, the test is passed. Start forecasting.

Effects and advantages of the present invention: the neural network model established by the present invention has a good correlation effect on both training samples and test samples. The invention overcomes the shortcomings of the traditional correlation, and can accurately and quickly predict the flow boiling heat transfer of the mixed working fluid in the horizontal light tube under the condition of many influencing factors, avoiding the mechanism research on the flow boiling heat transfer of the working medium , which has a certain guiding significance for the performance prediction and structural optimization design of the tubular heat exchanger in the mixed refrigerant refrigeration system.

Description of drawings

Fig. 1 is RBF neural network structure;

Fig. 2 is the flow chart of the present invention utilizing RBF neural network to predict mixed working fluid flow boiling heat transfer coefficient;

Figure 3 is the network error training changes;

Figure 4 is a schematic diagram of the comparison between the prediction results of the RBF network model and the experimental results;

Figure 5 is a schematic diagram of the variation of heat transfer coefficient with dryness;

Figure 6 is a graph showing the variation of heat transfer coefficient with dryness at different mass flow rates;

Figure 7 is a graph showing the variation of heat transfer coefficient with dryness at different heat fluxes.

Detailed ways

The present invention will be further described below with reference to the examples and accompanying drawings, but the scope of protection of the present invention is not limited thereto, and is also applicable to flow boiling heat exchange of other mixed working fluids in horizontal light pipes.

The ternary non-azeotropic mixed refrigerant R407C was selected as the research object, and the prediction method of flow boiling heat transfer of the mixed refrigerant in the horizontal light tube based on RBF neural network was adopted. The training and testing process of the RBF network were carried out under the environment of MATLAB R2008. Including the following steps (as shown in Figure 2):

(1) Data collection: A total of 489 sets of measured data of the flow boiling heat transfer process of the mixed working fluid R407C in the tube heat exchanger were collected under different working conditions, including the influencing factors of the flow boiling heat transfer in the mixed working medium tube, namely Mass flow ( G ), heat flux ( q ), dryness ( x ), saturation temperature ( T _sat ), inner diameter of light pipe ( D ) and flow boiling heat transfer coefficient ( h ); call MATLAB R2008 neural network toolbox The Rand function randomly selects 80% of the data in the total sample, that is, 391 sets of data as training samples, and the remaining 20% of the data as prediction samples;

(2) Determination of network input and output vectors: establish the RBF neural network prediction model, determine the input layer neurons of the RBF neural network as 5, and determine the output layer neurons as 1, that is, mass flow, heat flux, and dryness , the saturation temperature and the inner diameter of the light pipe are the five physical variables as the input of the RBF neural network, and the flow boiling heat transfer coefficient is the output of the RBF neural network;

(3) Pre-processing of data: Since the size of each component of the model input varies greatly, even by several orders of magnitude, big data will inevitably obliterate the effect of small data on the RBF function, so it is necessary to normalize the data collected in step (1) It can be processed between [0, 1], which can effectively reduce the redundancy of input data and speed up the convergence speed of network training; the formula is as follows:

(1)

(4) Training and testing of the RBF neural network: Input the normalized data obtained in step (3) into the RBF neural network as training samples, and determine the connection mode of the RBF neural network 5-p-1 (as shown in Figure 1 ), that is, the input of the network is the five physical variables of mass flow ( G ), heat flux ( q ), dryness ( x ), saturation temperature ( T _sat ) and inner diameter of the bare tube ( D ), and the output is flow boiling heat transfer Coefficient ( h ); randomly assign the initial weight of the neural network; network training starts from the 0th neuron, and the network automatically increases neurons by checking the output error. After the training samples are calculated once per cycle, the network produces the maximum error The corresponding training sample is used as the weight vector wl to generate a new hidden layer neuron, then recalculate, and check the error of the new network, repeat this process until the expected training error of 0.001 is reached, and the RBF neuron determined after training is obtained Network, where the network error is represented by the mean square error, and its calculation formula is:

(2)

In the formula, E _MSE represents the network error, O(j) represents the actual output, and N is the number of training data sets;

In addition, the obtained output value is a normalized value, and then it is denormalized and converted into a real output value, so as to compare it with the original experimental data conveniently and intuitively; the formula is as follows:

(3)

In the formula, X _max is the maximum value of the measured data; X _min is the minimum value of the measured data; X is the measured data; X ^{^} is the normalized data;

Using a hybrid learning strategy, from the input layer to the hidden layer, the self-organizing clustering method is used to determine the appropriate data center C _i for the radial basis function of the hidden layer, and the hidden layer is determined according to the distance σ _i between the data centers. Contains the expansion constant spread of layer nodes; from the hidden layer to the output layer, use the gradient descent algorithm to train the corresponding weight w2 _ik . After the network training is over, a network output value is obtained, that is, the predicted value of the flow boiling heat transfer coefficient corresponding to the operating point, and the error between the network output value and the expected output value (experimentally measured boiling heat transfer coefficient value) is compared. The more training sample data, the more sufficient the learning of the network and the greater the experience value, the higher the prediction accuracy; for this reason, the network is trained repeatedly, and when the error reaches the target error of 0.001 or reaches the maximum number of neurons, the network stops training; When the training of the RBF network is completed after 144 steps, the mean square error between the output value and the expected value is 0.0009824 (as shown in Figure 3), and the network training meets the requirements;

In order to further investigate the generalization performance of the network, the test data is input into the trained network; at this time, the average error of the prediction results of the network model is -0.9%, the absolute error is 5.5%, the root mean square error is 10.9%, and About 92% of the data point errors are within ±10%, and the fitting degree between the predicted value and the measured value is good (as shown in Figure 4); as shown in Figure 5, it has been significantly improved compared with the traditional correlation, The fitting effect is better, which can meet the accuracy requirements of engineering applications;

(5) The remaining 20% of the measured data collected in step (1), including mass flow rate ( G ), heat flux ( q ), dryness ( x ), saturation temperature ( T _sat ), inner diameter of bare tube ( D ); according to the method in step (3), the data is normalized, and then input into the RBF neural network determined after training obtained in step (4), and the output value is obtained, and then it is carried out according to the method in step (4). Inverse normalization processing, that is, to obtain the predicted flow boiling heat transfer coefficient ( h ), to realize the prediction of the flow boiling heat transfer of the mixed working medium in the horizontal light tube.

The above results show that the established neural network model has a good correlation effect on both training samples and test samples. This embodiment shows that this method overcomes the shortcomings of the traditional correlation, can accurately and quickly predict the flow boiling heat transfer of the mixed working medium in the horizontal light tube, and predict the performance of the tubular heat exchanger in the mixed working medium refrigeration system And structure optimization design has a certain guiding significance. If the ternary non-azeotropic working medium R407C is used under different working conditions, the predicted value and the measured value not only have a good fitting degree, but also can well conform to the variation law of the experimental results, as shown in Figure 6 and Figure 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).