Solid rocket based on Matlab and BP neural network? Prediction of engine specific impulse performance

(College of Science, Inner Mongolia University of Technology, Hohhot, Inner Mongolia 0 1005 1)?

In this paper, the artificial neural network technology based on back propagation of error (BP algorithm) is adopted, and the neural network model for predicting the specific impulse performance of solid rocket motor is established by using Mat lab neural network toolbox, which is verified by experimental data. The results show that this method can be used to predict the specific impulse performance of solid rocket motor. ?

Key words: specific impulse of solid rocket motor;

BP algorithm;

Mat lab neural network toolbox;

Artificial neural network?

China Library ClassificationNo.: V435∶TP 183 Document IdentificationNo.: A DocumentNo.:1007-6921(2007) 08-0073-02?

Predicting the performance parameters of solid rocket motor is one of the basic topics in engine design and research. Correctly predicting the performance parameters of solid rocket motor is the key and foundation to improve the performance index and accuracy of the engine and shorten the development cycle. At present, there are two methods to predict the specific impulse performance. One is to correct the theoretical specific impulse of the newly designed engine with the correction coefficient obtained from previous tests. The other is to estimate the specific impulse by calculating various losses. The disadvantages of these methods are large sample data and poor prediction accuracy. ?

Neural network theory has been widely used in many fields because of its inherent super adaptability and learning ability, and has solved many problems that are difficult to be solved by traditional methods. Because of the complex mathematical calculation and process of neural network learning algorithm, it is easy to make mistakes. Therefore, it is an inevitable choice to adopt neural network software package. In this paper, the prediction model of specific impulse performance of solid rocket motor is established by using MATLAB neural network toolbox which is widely used now, and artificial neural network based on BP algorithm, so as to improve the prediction accuracy of specific impulse. ?

1 BP neural network model?

BP network has become the most widely used neural network because of its simple structure and strong nonlinear mapping ability. The learning process of BP neural network is divided into two stages: the forward propagation process of information and the backward propagation process of error. The external input signal is processed layer by layer by the input layer and hidden layer neurons, and then propagated to the output layer, and the results are given. If the expected output is not obtained at the output layer, it will be transferred to the back propagation process, and the error between the actual value and the network output will return along the original connection path. By modifying the connection weight of each layer of neurons, the error is reduced, and then it is transferred to the forward propagation process and iterated until the error is less than the given value. ?

Application of MATLAB neural network toolbox?

Neural network toolbox is one of many toolboxes developed in Mat lab environment. Based on the theory of artificial neural network, the activation function of typical neural network is constructed by Mat lab language, and MATLAB is used in the network training process.

6.5 For Windows software, the neural network toolbox of Mat lab is used for network training. The MATLAB software package introduced by Math work Company in the United States is not only a very practical and effective software environment for scientific research programming, but also an interactive program for scientific and engineering calculation. MATLAB itself has a neural network toolbox, which can greatly facilitate weight training, reduce the workload of training programs and effectively improve work efficiency. ?

3. What are the factors that affect the specific impulse performance of solid rocket motor?

Specific impulse is an important technical index reflecting the energy level of propellant used in engine and the perfection of internal working process. There are many factors that affect the specific impulse performance, including the following: nozzle throat diameter, nozzle penetration ratio, average expansion ratio, working time, diffusion half angle, average working pressure, average burning rate and propellant density. Because the full-scale test of solid rocket engine needs a lot of manpower, material resources and financial resources. Therefore, the experimental data of specific impulse are relatively scarce. In this paper, six groups of data samples were collected, five of which were selected as training samples and 1 group as test samples. The first eight items of each data sample are input factors and the output factors are actual specific impulse. These six sets of data are used to train and test the network. ?

4 network model design?

The design of BP network mainly includes input layer, hidden layer, output layer and interlayer transfer function. ?

4. 1 network layer. BP network can contain different hidden layers. It is proved theoretically that the network with deviation and at least one S-shaped hidden layer plus one linear output layer can approximate any rational function. The empirical choice of hidden layers is: for linear problems, perceptron or adaptive network can be used to solve them, but nonlinear network can't be used, because single layer can't play the special role of nonlinear activation function;

For nonlinear problems, two or more hidden layers are generally used, but the improvement of error accuracy can actually be obtained by increasing the number of hidden layer neurons, and its training effect is easier to observe and adjust than increasing the number of layers, so in general, increasing the number of hidden layer neurons should be given priority.

4.2 Number of nodes in input layer and number of nodes in output layer. The input layer acts as a buffer memory, which receives external input data, so its number of nodes depends on the dimension of the input vector. Because the input sample for predicting the specific impulse performance of solid rocket motor is an 8-dimensional input vector, there are 8 neurons in the input layer I * * *. ?

The number of nodes in the output layer depends on two aspects, the output data type and the data size required to represent the type. Because the output sample of specific impulse performance prediction of solid rocket motor is 1 dimension output vector, there are 1 neurons in the output layer. ?

4.3 Number of nodes of neurons in hidden layer. The number of nodes of hidden neurons is determined by training and comparing different neuron numbers, and then adding a little margin appropriately. According to the previous experience, the design can refer to the following formula:

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Where: n is the number of hidden nodes;

N i is the number of input nodes;

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N 0 is the number of output nodes;

A is a constant between 1 and 10. ?

According to this principle, the number of hidden nodes in this BP network is [KF (] 8+1[KF)]+A (a =1~10), which is taken as 13. ?

4.4 Transfer function. Generally speaking, the structure of BP network adopts S-shaped activation function in the hidden layer and linear activation function in the output layer. ?

4.5 Selection of training methods. The additional momentum method is used for back propagation, which reduces the possibility of the network falling into a trough on the error surface and helps to reduce the training time. Too large a learning rate leads to unstable learning, and too small a value leads to extremely long training time. The adaptive learning rate can reach a reasonable high speed under the condition of ensuring the stability of training, which can reduce the training time. ?

4.6 Experience selection of learning rate. In general, we tend to choose a smaller learning rate to ensure the stability of the system, and the learning rate ranges from 0.0 1 ~ 0.8. The learning rate of this network is 0.05. ?

4.7 Selection of expected error. Generally speaking, as a comparison, two networks with different expected error values can be trained at the same time, and finally one of them can be determined by comprehensive consideration. ?

To sum up, the topology of BP network is 8× 13× 1. The transfer function of middle layer neurons is S-shaped tangent function tansig. Since the output has been normalized to the interval [0, 1], the transfer function of neurons in the output layer can be set as S-type logarithmic function logsig. The training function of the network adopts momentum BP algorithm with variable learning rate to modify the weights and threshold functions of the neural network. ?

5 network training and testing?

When learning and training neural network and predicting specific impulse, the input and output data must be preprocessed, that is, normalized or standardized, and the input and output data of the network should be limited to the range of [0, 1]. The main reasons for normalization are as follows: ① The input data of the network often have different physical meanings and dimensions, and normalization can give each input component the same important position;

② The values of some input variables may be far from those of other input variables, and normalization can prevent the variables with large values from covering up the variables with small values;

③ Neuron saturation can be avoided. ?

See table 1 for the normalized data of six groups of measured data samples.

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The simulation function sim is used to calculate the output of the network, and its prediction error curve is shown in figure 1.

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As can be seen from the figure, the errors between the network predicted value and the real value are very small, both less than 3%. Completely meet the application requirements. ?

6 conclusion?

As a highly nonlinear mapping of input/output, neural network can predict the specific impulse performance parameters of solid rocket motor through multiple compounding of action functions. And get the following conclusions:

6. 1 There is no need to establish a mathematical model of the system, and it can be predicted as long as there are enough training samples (obtained from experimental data or simulation data). ?

6.2 BP network finds out the relationship between input and output according to sample data through learning and training, so as to find the solution to the problem, rather than judging the problem according to experience, so it has the adaptive function and overcomes the shortcomings of statistical regression method in analyzing small sample data. ?

6.3 The results show that the trained BP network model can accurately predict the specific impulse performance of solid rocket motor. ?

6.4 The prediction rules of the model are influenced by the nature of the sample. Due to the lack of specific impulse experimental data of solid rocket motor, the model needs further experimental data verification. ?

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