Ground engine plume infrared radiation end-to-end prediction method based on neural network

Abstract

The present application relates to the technical field of rocket engine, and particularly relates to a ground engine exhaust flame infrared radiation end-to-end prediction method based on a neural network, which comprises the following steps: step one: calculating a rocket engine exhaust flame infrared radiation dataset; step two: constructing an asymmetric convolutional encoder and a parallel deconvolutional decoding module; step three: taking a type spectrum parameter dataset as an input dataset; after processing exhaust flame infrared radiation intensity distribution cloud data, taking the exhaust flame infrared radiation intensity distribution cloud data together with exhaust flame infrared radiation integral intensity data as an output dataset; step four: dividing the input dataset and the output dataset into a training set and a test set; training and testing the neural network; step five: inputting the type spectrum parameters into the neural network to calculate exhaust flame infrared radiation data of a rocket engine to be tested. The present application solves the problems of a large number of calculation links, long calculation time and difficulty in meeting massive calculation requirements of the existing rocket engine exhaust flame infrared radiation calculation method, and is suitable for rocket engines.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of rocket engine, in particular to a ground engine exhaust flame infrared radiation end-to-end prediction method based on neural network. BACKGROUND

[0002] The diatomic and polyatomic molecules in the rocket engine exhaust flame gas emit infrared radiation of specific wave bands due to the vibration-rotation transition, which makes the exhaust flame present significant infrared radiation characteristics and become the radiation source focused by the space-based infrared system. By calculating the infrared radiation of the rocket engine exhaust flame, the combustion state and temperature distribution of the rocket engine can be understood, and thus performance optimization and fault diagnosis can be carried out. However, the existing rocket engine exhaust flame infrared radiation calculation method has the following problems due to its own principle: first, the existing calculation method has many calculation links and takes a long time to calculate. Second, the existing calculation method cannot quickly calculate the infrared radiation of the rocket engine exhaust flame under different spectral parameters, which is difficult to meet the massive calculation demand. Therefore, it is necessary to invent an end-to-end prediction method for ground engine exhaust flame infrared radiation based on neural network to solve the problems of the existing rocket engine exhaust flame infrared radiation calculation method, such as many calculation links, long calculation time and difficulty in meeting the massive calculation demand. SUMMARY

[0003] The present application provides an end-to-end prediction method for ground engine exhaust flame infrared radiation based on neural network to solve the problems of the existing rocket engine exhaust flame infrared radiation calculation method, such as many calculation links, long calculation time and difficulty in meeting the massive calculation demand.

[0004] The present application is implemented by adopting the following technical solutions:

[0005] The end-to-end prediction method for ground engine exhaust flame infrared radiation based on neural network includes the following steps:

[0006] Step one: constructing a rocket engine spectral parameter dataset; inputting the spectral parameter dataset into a full-link fine calculation model to calculate a rocket engine exhaust flame infrared radiation dataset; the exhaust flame infrared radiation data includes exhaust flame infrared radiation intensity distribution cloud data and exhaust flame infrared radiation integral intensity data;

[0007] Step two: constructing an asymmetric convolutional encoder and a parallel deconvolutional decoding module, which together form an end-to-end prediction neural network;

[0008] Step three: taking the spectral parameter dataset as the input dataset of the end-to-end prediction neural network; after normalization and interpolation processing of the exhaust flame infrared radiation intensity distribution cloud data, together with the exhaust flame infrared radiation integral intensity data, as the output dataset of the end-to-end prediction neural network;

[0009] Step four: dividing the input data set and the output data set into a training set and a test set; training and testing the end-to-end prediction neural network by using the training set and the test set;

[0010] Step five: collecting the type spectrum parameters of the rocket engine to be tested; inputting the type spectrum parameters into the trained end-to-end prediction neural network to calculate the plume infrared radiation data of the rocket engine to be tested.

[0011] Further, the type spectrum parameter data set is constructed by using a Latin hypercube sampling method; the type spectrum parameters include: combustion chamber temperature, combustion chamber pressure, nozzle expansion ratio, content of oxidizer in propellant, content of binder in propellant, nozzle diameter.

[0012] Further, the end-to-end prediction neural network is defined as follows:

[0013] ;

[0014] In the formula: represents the plume infrared radiation intensity distribution cloud image in the 2.7 μm band; represents the plume infrared radiation intensity distribution cloud image in the 4.3 μm band; represents the plume infrared radiation integral intensity in the 2.7 μm band; represents the plume infrared radiation integral intensity in the 4.3 μm band; represents the combustion chamber temperature; represents the combustion chamber pressure; represents the nozzle expansion ratio; represents the content of oxidizer in propellant; represents the content of binder in propellant; represents the nozzle diameter.

[0015] Further, the construction steps of the asymmetric convolutional encoder are as follows:

[0016] Firstly, three parallel convolutional blocks are constructed; the first convolutional block includes a convolutional layer with a convolution kernel size of 3×3, a ReLU function connected after the convolutional layer, and a batch normalization layer connected after the ReLU function; the second convolutional block includes a convolutional layer with a convolution kernel size of 1×3, a ReLU function connected after the convolutional layer, and a batch normalization layer connected after the ReLU function; the third convolutional block includes a convolutional layer with a convolution kernel size of 3×1, a ReLU function connected after the convolutional layer, and a batch normalization layer connected after the ReLU function; then, a ReLU function, a batch normalization layer, and a max pooling layer are jointly connected after the three convolutional blocks, thereby completing the construction of the asymmetric convolutional encoder.

[0017] In operation, the input data is first extracted by three convolutional blocks, and then the extracted features are activated by a ReLU function and batch normalization, and then the features after ReLU activation and batch normalization are further extracted by a maximum pooling layer to obtain more significant data features as the output of the asymmetric convolutional encoder.

[0018] The feature extraction process is represented as follows:

[0019] ;

[0020] In the formula: represents the extracted features; represents a convolutional layer with a kernel size of 3x3; represents a convolutional layer with a kernel size of 1x3; represents a convolutional layer with a kernel size of 3x1; represents a spectral parameter matrix; represents a summation operation at the corresponding position; represents a two-dimensional convolution operator;

[0021] The ReLU activation and batch normalization process is represented as follows:

[0022] ;

[0023] ;

[0024] In the formula: represents the extracted features; represents the features after ReLU activation and batch normalization; represents the output matrix of the ReLU function; represents the channel average value of batch normalization; represents the standard deviation of batch normalization; represents the scaling coefficient; represents the offset.

[0025] Further, the construction steps of the parallel deconvolution decoding module are as follows:

[0026] Firstly, two parallel deconvolution decoders are constructed; each of the deconvolution decoders comprises three deconvolution blocks connected in series: the first deconvolution block is used for reducing feature dimension, comprising a deconvolution layer with a deconvolution kernel size of 1x1, a ReLU function connected after the deconvolution layer, and a batch normalization layer connected after the ReLU function; the second deconvolution block is used for reducing the number of channels, comprising a deconvolution layer with a deconvolution kernel size of 3x1, a ReLU function connected after the deconvolution layer, and a batch normalization layer connected after the ReLU function; the third deconvolution block is used for restoring feature dimension, comprising a deconvolution layer with a deconvolution kernel size of 1x1, a ReLU function connected after the deconvolution layer, and a batch normalization layer connected after the ReLU function; then, a fully connected layer is connected after the two deconvolution decoders, thereby completing the construction of the parallel deconvolution decoding module.

[0027] In operation, the output of the asymmetric convolutional encoder is first up-sampled and feature-restored by using the two deconvolution decoders, and then the restored features are converted by using the fully connected layer and taken as the output of the end-to-end prediction neural network.

[0028] The conversion process is represented as follows:

[0029] ;

[0030] In the formula: represents the output of the end-to-end prediction neural network; represents the restored features; represents the weight; represents the bias.

[0031] Further, the normalization and interpolation processing steps of the plume infrared radiation intensity distribution cloud map data are as follows:

[0032] Firstly, the original size of the cloud map is divided by the nozzle radius, thereby obtaining the normalized cloud map size;

[0033] Then, according to the normalized cloud map size, the cloud map is interpolated by using the bilinear interpolation method, thereby obtaining the interpolated cloud map size;

[0034] Finally, the interpolated cloud map size is multiplied by the nozzle radius, thereby obtaining the restored cloud map size.

[0035] Further, in the training process of the end-to-end prediction neural network, the root mean square error is taken as the training loss function, and the function expression is:

[0036] ;

[0037] In the formula: Root mean square error of the end-to-end prediction neural network; Infrared radiation data of the plume calculated by the end-to-end prediction neural network; Infrared radiation data of the plume calculated by the full-link fine calculation model; Number of grid points; Grid point;

[0038] In the training process of the end-to-end prediction neural network, the correction formula of the weight and the bias is as follows:

[0039] ;

[0040] ;

[0041] In the formula: Weight; Bias; Correction times; Learning rate; Root mean square error of the end-to-end prediction neural network.

[0042] Compared with the existing rocket engine plume infrared radiation calculation method, the end-to-end prediction method for the plume infrared radiation of the ground engine based on the neural network has the following advantages: first, the end-to-end prediction neural network from the type spectrum parameter to the plume infrared radiation data is constructed, so that the rapid calculation of the plume infrared radiation is realized, thereby effectively reducing the calculation link and effectively shortening the calculation time. Secondly, on the one hand, the flexible extraction of different dimensional and hierarchical features in the input data is realized by constructing an asymmetric convolutional encoder, and on the other hand, the feature recovery from the output of the asymmetric convolutional encoder from different channels is realized by constructing a parallel deconvolution decoding module, so that the nonlinear expression ability of the network can be enhanced while the prediction accuracy of the model is effectively improved. The constructed model can calculate the plume infrared radiation of the rocket engine under different type spectrum parameters in real time, so as to meet the massive calculation demand.

[0043] The present application effectively solves the problems of the existing rocket engine plume infrared radiation calculation method, such as multiple calculation links, long calculation time and difficulty in meeting the massive calculation demand, and is suitable for rocket engines. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 The present application effectively solves the problems of the existing rocket engine plume infrared radiation calculation method, such as multiple calculation links, long calculation time and difficulty in meeting the massive calculation demand, and is suitable for rocket engines.

[0045] Figure 2 The present application effectively solves the problems of the existing rocket engine plume infrared radiation calculation method, such as multiple calculation links, long calculation time and difficulty in meeting the massive calculation demand, and is suitable for rocket engines.

[0046] Figure 3is a schematic diagram of the calculation results of the present application compared with the calculation results of the prior art calculation method. DETAILED DESCRIPTION

[0047] The ground engine tail flame infrared radiation end-to-end prediction method based on a neural network comprises the following steps:

[0048] Step one: constructing a rocket engine type spectrum parameter dataset; inputting the type spectrum parameter dataset into a full-link fine calculation model, thereby calculating a rocket engine tail flame infrared radiation dataset; the tail flame infrared radiation data comprises tail flame infrared radiation intensity distribution cloud data and tail flame infrared radiation integral intensity data;

[0049] Step two: constructing an asymmetric convolutional encoder and a parallel deconvolutional decoding module, which together constitute an end-to-end prediction neural network;

[0050] Step three: taking the type spectrum parameter dataset as an input dataset of the end-to-end prediction neural network; after normalization and interpolation processing of the tail flame infrared radiation intensity distribution cloud data, taking the tail flame infrared radiation integral intensity data together as an output dataset of the end-to-end prediction neural network;

[0051] Step four: dividing the input dataset and the output dataset into a training set and a test set; training and testing the end-to-end prediction neural network by using the training set and the test set;

[0052] Step five: collecting type spectrum parameters of a rocket engine to be measured; inputting the type spectrum parameters into the trained end-to-end prediction neural network, thereby calculating tail flame infrared radiation data of the rocket engine to be measured.

[0053] The type spectrum parameter dataset is constructed by using a Latin hypercube sampling method; the type spectrum parameters comprise a combustion chamber temperature, a combustion chamber pressure, a nozzle expansion ratio, a content of an oxidizer in a propellant, a content of a binder in the propellant, and a nozzle diameter.

[0054] The end-to-end prediction neural network is defined as follows:

[0055] ;

[0056] In the formula, I2.7 represents a tail flame infrared radiation intensity distribution cloud at a 2.7 μm wavelength band; I2.7 represents a tail flame infrared radiation intensity distribution cloud at a 2.7 μm wavelength band; I4.3 represents a tail flame infrared radiation intensity distribution cloud at a 4.3 μm wavelength band; I2.7 represents a tail flame infrared radiation integral intensity at a 2.7 μm wavelength band; I4.3 represents a tail flame infrared radiation integral intensity at a 4.3 μm wavelength band; T represents a combustion chamber temperature; P represents a combustion chamber pressure; Indicates the nozzle expansion ratio; Indicates the content of oxidizer in the propellant; Indicates the content of binder in the propellant; Indicates the nozzle diameter.

[0057] The construction steps of the asymmetric convolutional encoder are as follows:

[0058] First, three parallel convolutional blocks are constructed. The first convolutional block consists of a 3×3 convolutional layer, a ReLU function connected to the convolutional layer, and a batch normalization layer connected to the ReLU function. The second convolutional block consists of a 1×3 convolutional layer, a ReLU function connected to the convolutional layer, and a batch normalization layer connected to the ReLU function. The third convolutional block consists of a 3×1 convolutional layer, a ReLU function connected to the convolutional layer, and a batch normalization layer connected to the ReLU function. Then, a ReLU function, a batch normalization layer, and a max pooling layer are connected together after the three convolutional blocks, thus completing the construction of the asymmetric convolutional encoder.

[0059] During operation, three convolutional blocks are first used to extract features from the input data. Then, the ReLU function and batch normalization layer are used to activate and normalize the extracted features. Finally, the max pooling layer is used to extract the ReLU-activated and batch-normalized features to a deeper level, resulting in more significant data features, which are then used as the output of the asymmetric convolutional encoder.

[0060] The feature extraction process is represented as follows:

[0061] ;

[0062] In the formula: This represents the extracted features; This indicates a convolutional layer with a kernel size of 3×3; This indicates a convolutional layer with a kernel size of 1×3; This indicates a convolutional layer with a kernel size of 3×1; Represents the spectrum parameter matrix; This indicates a summation operation at the corresponding position; Represents a two-dimensional convolution operator;

[0063] The ReLU activation and batch normalization process is represented as follows:

[0064] ;

[0065] ;

[0066] wherein: represents the extracted feature; represents the feature after ReLU activation and batch normalization; represents the output matrix of the ReLU function; represents the channel mean value of the batch normalization; represents the standard deviation of the batch normalization; represents the scaling coefficient; represents the offset.

[0067] The construction steps of the parallel deconvolution decoding module are as follows:

[0068] Firstly, two parallel deconvolution decoders are constructed; each deconvolution decoder includes three deconvolution blocks connected in series: the first deconvolution block is used for reducing the feature dimension, including a deconvolution layer with a deconvolution kernel size of 1x1, a ReLU function connected after the deconvolution layer, and a batch normalization layer connected after the ReLU function; the second deconvolution block is used for reducing the number of channels, including a deconvolution layer with a deconvolution kernel size of 3x1, a ReLU function connected after the deconvolution layer, and a batch normalization layer connected after the ReLU function; the third deconvolution block is used for restoring the feature dimension, including a deconvolution layer with a deconvolution kernel size of 1x1, a ReLU function connected after the deconvolution layer, and a batch normalization layer connected after the ReLU function; then, a fully connected layer is connected after the two deconvolution decoders, thereby completing the construction of the parallel deconvolution decoding module;

[0069] In operation, the output of the asymmetric convolutional encoder is first up-sampled and the feature is restored by using the two deconvolution decoders, and then the restored feature is converted by using the fully connected layer and used as the output of the end-to-end prediction neural network;

[0070] The conversion process is represented as follows:

[0071] ;

[0072] wherein: represents the output of the end-to-end prediction neural network; represents the restored feature; represents the weight; represents the bias.

[0073] The normalization and interpolation processing steps of the plume infrared radiation intensity distribution cloud map data are as follows:

[0074] Firstly, the original size of the cloud map is divided by the nozzle radius, thereby obtaining the normalized cloud map size;

[0075] Then, based on the normalized cloud map size, bilinear interpolation is used to interpolate the cloud map, thereby obtaining the interpolated cloud map size;

[0076] Finally, multiply the interpolated cloud map size by the nozzle radius to obtain the restored cloud map size.

[0077] During the training process of the end-to-end prediction neural network, the root mean square error is used as the training loss function, and the function expression is:

[0078] ;

[0079] In the formula: This represents the root mean square error of the end-to-end prediction neural network. This represents the infrared radiation data of the exhaust plume calculated by the end-to-end predictive neural network; This represents the infrared radiation data of the exhaust plume calculated by the end-to-end fine-grained calculation model; Indicates the number of grid points; Represents grid points;

[0080] During the training process of the end-to-end prediction neural network, the correction formulas for the weights and biases are as follows:

[0081] ;

[0082] ;

[0083] In the formula: Indicates weight; Indicates bias; Indicates the number of corrections; Indicates the learning rate; This represents the root mean square error of the end-to-end prediction neural network.

[0084] Figure 2 This is a schematic diagram of the training loss function of the end-to-end prediction neural network in this invention. Figure 2 It can be seen that the end-to-end prediction neural network converges well.

[0085] Figure 3 This is a schematic diagram comparing the calculation results of the present invention (CNN-IR) with existing computational methods (NMC). Figure 3 It can be seen that the present invention exhibits better robustness and adaptability on the dataset of exhaust infrared radiation under different under-expansion states, and can calculate the exhaust infrared radiation of rocket engines under different spectral parameters more accurately.

[0086] Experiments show that the calculation time of the existing calculation method is about 6 hours, and the calculation time of the present application is only seconds, and the speedup ratio of the present application compared with the existing calculation method is 2.16*10 4 , which greatly improves the calculation efficiency of the rocket engine exhaust infrared radiation.

[0087] Although the specific embodiments of the present application are described above, those skilled in the art should understand that these are only illustrative, and the protection scope of the present application is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present application, and these changes and modifications all fall within the protection scope of the present application.

Claims

1. An end-to-end prediction method for infrared radiation from ground-based engine exhaust plumes based on neural networks, characterized in that: The method includes the following steps: Step 1: Construct a rocket engine type spectrum parameter dataset; input the type spectrum parameter dataset into the end-to-end fine calculation model to calculate the rocket engine exhaust plume infrared radiation dataset; The infrared radiation data of the tail flame includes: tail flame infrared radiation intensity distribution cloud map data and tail flame infrared radiation integral intensity data. Step 2: Construct an asymmetric convolutional encoder and a parallel deconvolutional decoding module. The asymmetric convolutional encoder and the parallel deconvolutional decoding module together form an end-to-end predictive neural network. Step 3: Use the spectrum parameter dataset as the input dataset for the end-to-end prediction neural network; normalize and interpolate the tail flame infrared radiation intensity distribution cloud map data, and use it together with the tail flame infrared radiation integral intensity data as the output dataset for the end-to-end prediction neural network. Step 4: Divide the input and output datasets into training and test sets; use the training and test sets to train and test the end-to-end prediction neural network. Step 5: Collect the spectrum parameters of the rocket engine under test; input the spectrum parameters into the trained end-to-end prediction neural network to calculate the infrared radiation data of the exhaust plume of the rocket engine under test. The construction steps of the asymmetric convolutional encoder are as follows: First, three parallel convolutional blocks are constructed. The first convolutional block consists of a 3×3 convolutional layer, a ReLU function connected to the convolutional layer, and a batch normalization layer connected to the ReLU function. The second convolutional block consists of a 1×3 convolutional layer, a ReLU function connected to the convolutional layer, and a batch normalization layer connected to the ReLU function. The third convolutional block consists of a 3×1 convolutional layer, a ReLU function connected to the convolutional layer, and a batch normalization layer connected to the ReLU function. Then, a ReLU function, a batch normalization layer, and a max pooling layer are connected together after the three convolutional blocks, thus completing the construction of the asymmetric convolutional encoder. The construction steps of the parallel deconvolution decoding module are as follows: First, two parallel deconvolutional decoders are constructed. Each deconvolutional decoder includes three cascaded deconvolutional blocks: the first deconvolutional block reduces the feature dimension and includes a 1×1 deconvolutional layer, a ReLU function connected to the deconvolutional layer, and a batch normalization layer connected to the ReLU function; the second deconvolutional block reduces the number of channels and includes a 3×1 deconvolutional layer, a ReLU function connected to the deconvolutional layer, and a batch normalization layer connected to the ReLU function; the third deconvolutional block restores the feature dimension and includes a 1×1 deconvolutional layer, a ReLU function connected to the deconvolutional layer, and a batch normalization layer connected to the ReLU function. Then, a fully connected layer is connected after both deconvolutional decoders, thus completing the construction of the parallel deconvolutional decoding module.

2. The end-to-end prediction method for infrared radiation from ground-based engine exhaust plumes based on neural networks according to claim 1, characterized in that: The spectrum parameter dataset was constructed using the Latin hypercube sampling method; the spectrum parameters include: combustion chamber temperature, combustion chamber pressure, nozzle expansion ratio, oxidizer content in the propellant, binder content in the propellant, and nozzle diameter.

3. The end-to-end prediction method for infrared radiation from ground-based engine exhaust plumes based on neural networks according to claim 2, characterized in that: The end-to-end prediction neural network is defined as follows: ； In the formula: A cloud map showing the distribution of infrared radiation intensity of the exhaust plume within the 2.7μm band; A cloud map showing the distribution of infrared radiation intensity of the exhaust plume within the 4.3μm band; This represents the integrated intensity of the infrared radiation from the exhaust plume within the 2.7 μm band; This represents the integrated intensity of the infrared radiation from the exhaust plume within the 4.3 μm band; Indicates the combustion chamber temperature; Indicates combustion chamber pressure; Indicates the nozzle expansion ratio; Indicates the content of oxidizer in the propellant; Indicates the content of binder in the propellant; Indicates the nozzle diameter.

4. The end-to-end prediction method for infrared radiation from ground-based engine exhaust plumes based on neural networks according to claim 3, characterized in that: When the asymmetric convolutional encoder is working, it first uses three convolutional blocks to extract features from the input data. Then, it uses the ReLU function and batch normalization layer to activate and normalize the extracted features. Finally, it uses the max pooling layer to extract the ReLU-activated and batch-normalized features more deeply to obtain more significant data features, which are used as the output of the asymmetric convolutional encoder. The feature extraction process is represented as follows: ； In the formula: This represents the extracted features; This indicates a convolutional layer with a kernel size of 3×3; This indicates a convolutional layer with a kernel size of 1×3; This indicates a convolutional layer with a kernel size of 3×1; Represents the spectrum parameter matrix; This indicates a summation operation at the corresponding position; Represents a two-dimensional convolution operator; The ReLU activation and batch normalization process is represented as follows: ； ； In the formula: This represents the extracted features; This represents the features after ReLU activation and batch normalization; This represents the output matrix of the ReLU function; This represents the average value of the channels in the batch standardization. This represents the standard deviation of the batch standardization. Indicates the scaling factor; This indicates the offset.

5. The end-to-end prediction method for infrared radiation from ground-based engine exhaust plumes based on neural networks according to claim 4, characterized in that: When the parallel deconvolution decoding module is working, it first uses two deconvolution decoders to upsample and restore the output of the asymmetric convolution encoder, and then uses a fully connected layer to transform the restored features as the output of the end-to-end prediction neural network. The conversion process is shown below: ； In the formula: This represents the output of an end-to-end prediction neural network; Indicates the characteristics after restoration; Indicates weight; Indicates bias.

6. The end-to-end prediction method for infrared radiation from ground-based engine exhaust plumes based on neural networks according to claim 5, characterized in that: The normalization and interpolation processing steps for the infrared radiation intensity distribution cloud map data of the exhaust plume are as follows: First, divide the original size of the cloud map by the nozzle radius to obtain the normalized cloud map size; Then, based on the normalized cloud map size, bilinear interpolation is used to interpolate the cloud map, thereby obtaining the interpolated cloud map size; Finally, multiply the interpolated cloud map size by the nozzle radius to obtain the restored cloud map size.

7. The end-to-end prediction method for infrared radiation from ground-based engine exhaust plumes based on neural networks according to claim 6, characterized in that: During the training process of the end-to-end prediction neural network, the root mean square error is used as the training loss function, and the function expression is: ； In the formula: This represents the root mean square error of the end-to-end prediction neural network. This represents the infrared radiation data of the exhaust plume calculated by the end-to-end predictive neural network; This represents the infrared radiation data of the exhaust plume calculated by the end-to-end fine-grained calculation model; Indicates the number of grid points; Represents grid points; During the training process of the end-to-end prediction neural network, the correction formulas for the weights and biases are as follows: ； ； In the formula: Indicates weight; Indicates bias; Indicates the number of corrections; Indicates the learning rate; This represents the root mean square error of the end-to-end prediction neural network.

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