CN110516394A - Steady-state modeling method of aero-engine based on deep neural network - Google Patents

Abstract

The aero-engine steady-state model modeling method based on deep neural network that the invention discloses a kind of, aero-engine steady-state model is constructed using deep neural network, the deep neural network is successively to criticize normalized deep neural network, it increases by one batch of normalization layer between adjacent hidden layer, is standardized for the output to previous hidden layer.The present invention carries out the modeling of aero-engine steady-state model using deep neural network, and increases the neural network number of plies by introducing batch normalization layer in deep neural network, improves the capability of fitting of network, and then improve the precision of aero-engine steady-state model.

Description

Steady-state modeling method of aero-engine based on deep neural network

technical field

The invention relates to the technical field of aero-engine control, in particular to an aero-engine steady-state model modeling method.

Background technique

Aeroengine is a multivariable, strongly nonlinear and complex aerodynamic thermodynamic system. Its safe and stable operation puts forward high requirements on the engine control system. In order to control it well, a mathematical model must first be established. Using the mathematical model instead of the real engine as the controlled object for simulation research can save a lot of expensive experiment funds and avoid accidental out-of-control accidents that may occur when using a real engine to debug the control system. In addition, advanced aero-engine control technologies, such as model-based control, flight/propulsion system performance optimization control, direct thrust control, life extension control, emergency control, performance recovery, etc., are based on high-precision real-time models of airborne engines. Base.

There are many modeling methods for aero-engines. The most popular ones are component-level models, segmented linearization models, support vector machines, and traditional neural networks. Poor timeliness, it is difficult to be used as an airborne model; the piecewise linearization model has high realtimeness, but because the engine is a strongly nonlinear object, the modeling error caused by linearization is relatively large; the realtimeness of support vector machines and traditional neural networks And the modeling accuracy lies between the component-level model and the linearized model. The traditional neural network is easy to fall into the local optimum, which makes the model overfit. The support vector machine has strong generalization ability, but it is difficult to apply to large sample training data, while The engine is a multi-variable, complex operating environment, degenerate and strongly nonlinear object. Therefore, to establish an airborne model that can be applied to a large envelope, the training data will inevitably increase, which limits the application of support vector machines in aero-engine modeling. application.

Neural networks have attracted widespread attention due to their ability to fit arbitrary functions in theory. The traditional neural network generally uses three layers. As the number of network layers increases, its network fitting ability becomes stronger and stronger. However, after the number of network layers increases, the phenomenon of gradient disappearance and gradient explosion will appear. With the development of neural network technology in the past ten years, especially after Hinton GE proposed deep learning-deep confidence neural network, neural network has made breakthroughs in many key technologies and has been widely used in engineering, such as speech recognition, graphics Recognition, object detection, and text recognition. However, there are few applications of deep learning-deep neural network in the steady-state modeling of aeroengines.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a deep neural network-based modeling method for the steady-state model of the aero-engine, which can effectively improve the accuracy of the steady-state model of the aero-engine.

The present invention specifically adopts the following technical solutions to solve the above technical problems:

A method for modeling the steady-state model of an aero-engine based on a deep neural network, using a deep neural network to construct a steady-state model of an aero-engine, the deep neural network is a layer-by-layer batch normalized deep neural network, and its adjacent implicit A batch normalization layer is added between layers to normalize the output of the previous hidden layer.

Preferably, the standardization process is specifically as follows:

in, is the output after normalization processing, ε is a positive integer with a very small value, is the output of the neural network before entering the batch normalization layer, μ _B and are the mean and variance of the sample data set, respectively, and γ and β are two learning parameters.

Further preferably, the modeling method includes the following steps:

Step 1, obtaining the training data of the steady-state model of the aeroengine;

Step 2, determine the structure of the deep neural network of layer-by-layer batch normalization;

Step 3. Perform forward calculation on the layer-by-layer batch normalized deep neural network to obtain the loss function value;

Step 4. Use the backpropagation algorithm to calculate the layer-by-layer batch normalized depth neural network gradient, and update the weights;

Step 5. Determine whether the layer-by-layer batch normalized deep neural network is convergent, if yes, output the steady-state model, otherwise continue to iterate, and return to step 3.

Preferably, the training data of the steady-state model of the aeroengine is obtained through engine test experiments or/and engine nonlinear component-level models.

Preferably, the aero-engine steady-state model takes flight altitude, Mach number, fuel flow, nozzle throat area, fan guide vane angle and compressor guide vane angle as model inputs, and takes engine fuel consumption rate, installed Thrust, fan rotor speed, compressor rotor speed, fan surge margin, compressor surge margin and high pressure turbine inlet temperature are model outputs.

Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

The present invention utilizes the deep neural network to model the steady-state model of the aero-engine, and increases the number of layers of the neural network by introducing a batch normalization layer into the deep neural network, improves the fitting ability of the network, and then improves the steady-state model of the aero-engine accuracy.

Description of drawings

Fig. 1 is a schematic diagram of a five-layer neural network structure;

Fig. 2 is the structural representation of the deep neural network of layer-by-layer batch normalization;

Fig. 3 is a data distribution diagram;

Fig. 4 is a Sigmod curve;

Figure 5 is a schematic diagram of the principle of backpropagation;

Fig. 6 is the relative training error of deep neural network training;

Fig. 7 is the relative training error of three-layer BP neural network training;

Figure 8 is the relative test error of deep neural network training;

Figure 9 shows the relative test error of three-layer BP neural network training.

Detailed ways

The present invention mainly aims at the situation that the precision of the traditional aero-engine steady-state process modeling method is difficult to improve, and proposes a kind of aero-engine steady-state model modeling method based on a deep neural network, which uses the deep neural network of the layer-by-layer batch normalization method , which adds a batch normalization layer between adjacent hidden layers to normalize the output of the previous hidden layer, so that the proposed modeling method has a high number of network layers and a good fitting ability Strong, and then improve the modeling accuracy of the aeroengine steady-state model.

The present invention proposes a method for modeling the steady-state model of an aero-engine based on a deep neural network, which mainly includes the following steps: Step 1, obtaining the training data of the steady-state model of the aero-engine;

Step 2, determine the structure of the deep neural network of layer-by-layer batch normalization;

Step 3. Perform forward calculation on the layer-by-layer batch normalized deep neural network to obtain the loss function value;

Step 4. Use the backpropagation algorithm to calculate the layer-by-layer batch normalized depth neural network gradient, and update the weights;

Step 5. Determine whether the layer-by-layer batch normalized deep neural network is convergent, if yes, output the steady-state model, otherwise continue to iterate, and return to step 3.

The engine steady-state data is the engine parameters when the engine is running stably, and its data can be obtained through engine test experiments or/and engine nonlinear component-level models. Due to the high cost of test run experiments, engine steady-state data are generally obtained through engine nonlinear component-level models data.

Taking the five-layer neural network as an example, its basic structure is shown in Figure 1. In the figure, w _i and b _i i=1, 2, 3, 4 are the weight and bias respectively, and J is the loss function. Taking partial derivatives with respect to w ₁ and b ₁ gives:

Because the derivative of σ′(h _i ) is less than 0.25, when w _i ≤1, w ₂ σ′(h ₂ )≤0.25, which means that the more layers there are, the gradient index decreases. This problem is called gradient disappear; moreover, assuming w _i ≥100, σ′(h ₂ )=0.1, then w ₂ σ′(h ₂ )≥10, this will appear again, as the number of layers increases, the gradient degree increases exponentially, the problem called gradient overflow.

In order to overcome the problem of gradient disappearance, the present invention adopts layer-by-layer batch normalization (BNBatchNormalization), which adds a BN layer between two hidden layers, which can effectively avoid the problem of gradient disappearance and gradient overflow, and its network structure is shown in the figure 2 shown.

When the weights of the neural network are initialized, the weights are often made to conform to a Gaussian distribution with a mean value of zero and a variance of 1. At the same time, the input data is standardized, and the output data is normalized or standardized. After mapping and training, the data distribution of each layer has changed, and the difference is very large, which leads to a large difference in the distribution of the weight of each layer of neural network, and the learning rate of each layer of neural network is often the same during training. It greatly reduces the convergence speed of the network. If the data is whitened, the principle is shown in the figure below. Figure 3a is the training data distribution diagram. It can be seen in the figure that the data distribution deviates from the Gaussian distribution, and the mean value is subtracted. After decorrelation and other operations, the obtained The data shown in 3b makes the data conform to the Gaussian distribution, thus speeding up the learning rate of the neural network.

There are many kinds of whitening operations, the commonly used one is PCA whitening, which makes the data satisfy 0 mean, unit variance and weak correlation. However, whitening is not advisable, mainly because the whitening operation needs to calculate the covariance matrix, inverse and other operations, the amount of calculation Large, and, when backpropagating, the whitening operation is not necessarily derivable, so batch normalization is used to standardize each hidden layer node. After the weight product and before the activation function, it is assumed that the neural network is forward propagating is the output of the i-th node in layer l as Where j∈χ _k , k represents the kth group of training data sets, then

in is the output after normalization, ε is a positive integer with a very small value, is the neural network output before entering the BN layer, μ _B and are the mean and variance, respectively, and are calculated as follows

h ^l ＝σ(W ^l-1 h ^l-1 +b ^l-1 ) (4)

However, if only batch normalization is performed, it will reduce the expressive power of the network. As shown in Figure 4, if the activation function is sigmoid, the data is limited to zero mean unit variance, then it is only equivalent to using the linear part of the activation function, and the nonlinear part on both sides is rarely involved, which will obviously reduce the network. expression ability.

For this reason, the present invention adds these two learning parameters of γ and β again, to keep the expressive ability of the network, its expression is as follows:

The μ _B and It is obtained under the minimum batch (Min-batch), and theoretically it should be the mean and variance of the entire data set.

The training method of the deep neural network also adopts the backpropagation algorithm. The network parameters that need to be updated are W, b, γ, and β. The gradient descent method is used, and the update is as follows:

The backpropagation algorithm is used to obtain the gradient, the principle is shown in Figure 5, assuming for

Suppose δ ^l is

where l=n _net , n _net -2,...,2

For l=n _net -1,n _net -2,...,2 Have

Therefore, the gradient of the network parameters obtained is:

Except for the BN layer, the derivation formulas of other layers are the same as those of MGDNN.

In order to verify the effectiveness and advancement of the aero-engine steady-state modeling method proposed in the present invention, the aero-engine model for performance optimization based on the method proposed in the present invention is established by taking the component-level model of the aero-engine with small bypass ratio as the simulation object. Load the model and compare it with MGD-NN. MGD-NN uses the minimum batch gradient descent method (MGD, mini-batch gradient descent) to train the network, which overcomes the fact that the traditional neural network cannot be applied to large sample data. In order to make the deep neural network Network use and large sample training are also trained using the MGD method. Hereinafter, the deep neural network steady-state model proposed in this paper is called BN-MGD-DNN. After cross-validation brush selection, the network structure of BN-MGD-DNN is [6,10,15,15,10,7], the network structure of MGD-NN is [6,40,7], the minimum training in MGD algorithm The sample set is 3000, and the regularization constant is 10 ^-6 .

When the aircraft is cruising, the flight altitude H and the Mach number Ma are changing slowly. In addition to the fuel oil W _fb and the nozzle throat area A ₈ , the engine control quantity, the guide vane angle of the fan and the compressor also have a great influence on the fuel consumption rate. Therefore, this paper takes H, Ma, W _fb , A ₈ , fan guide vane angle α _f and compressor guide vane angle α _c as model inputs, engine fuel consumption rate S _fc , installed thrust F _in , fan rotor The rotational speed N _f , compressor rotor rotational speed N _c , fan surge margin S _mf , compressor surge margin S _mc and high pressure turbine inlet temperature T ₄ are the output of the model, and the engine parameter prediction model is constructed as follows:

y=f _BN-MGD-DNN (x) (22)

in

Since the neural network is similar to a nonlinear interpolator, it has high precision during interpolation and low precision during extrapolation, so the selected training samples contain the maximum and minimum values of the input parameters as much as possible, and in order to avoid overfitting, training The number of samples should be as large as possible. For subsonic and supersonic cruising, the value range of H is 9-13km, Ma is selected from 0.7-1.5, the range of W _fb changes with PLA and Ma, and the range of A ₈ changes from the tail of the design point. Nozzle throat area A _8,ds to 1.3A _8,ds , α _f and α _c vary from -3° to 3°. The training sample set is selected to be 3726498, and the test sample set is selected to be 7536

Figure 6-9 shows the relative training errors of BN-MGD-DNN and MGD-NN respectively. It can be seen from the figure that the error of BN-MGD-DNN is basically below 3%, which meets the accuracy requirements, and its training accuracy is obvious Higher than MGD-NN, especially S _fc , N _f , S _mf and S _mc , its training accuracy is about double that of MGD-NN. Figures 6 and 7 show the relative training errors of BN-MGD-DNN and MGD-NN. It can be seen from the figure that the test error of BN-MGD-DNN is within 2% except for S _mf and S _mc . The accuracy is within 1%, which meets the accuracy requirements, and it can be seen from Figures 8 and 9 that the accuracy of the deep neural network has been greatly improved compared with the traditional BP neural network, especially the fan and compressor rotor speed and surge margin. It shows that BN-MGD-DNN has stronger generalization ability.

Table 1 presents the average relative test error and average relative training error of BN-MGD-DNN and MGD-NN, compared with MGD-NN, BN-MGD-DNN has higher training accuracy and test accuracy. Among them, the average training relative errors of S _fc , N _f , N _c , F _in , T ₄ , S _mf and S _mc of the BN-MGD-DNN modeling method proposed in this paper are 1.4, 2.17, A factor of 2.0, 1.3, 1.13, 2.4 and 2.8, and a factor of 1.75, 2.0, 2.3, 1.3, 1.3, 2.3 and 3.3, respectively, for the average relative test error, which is particularly relevant to model generalization performance.

Table 2 shows the data storage, computational complexity, and average test time of MGD-NN and BN-MGD-DNN. It can be seen from the table that the algorithm complexity of the two is low, the data storage is small, and the average test time is short. Meet airborne requirements.

Among them, the data storage capacity of MGD-NN is 567 (weight 520 (6×40+40×7)+47 bias (40+7)); the data storage capacity of BN-MGD-DNN is 940

The computational complexity of MGD-NN is 614 (multiplication 520(6×40+40×7)+addition 47(40+7)+activation function 47(40+7));

The data storage capacity of BN-MGD-DNN is 940 (multiplication operation 712 (6×10+10×15+15×15+15×10+10×7+10+15+15+10+7)+division operation 57 (10+15+15+10+7)+addition 57(10+15+15+10+7+10+15+15+10+7)+subtraction 57(10+15+15+10+7 )+activation function 57(10+15+15+10+7))

The running environments of both programs are: the operating system Windows 7 Ultimate with Service Pack 1 (x64); the processor (CPU) is Intel(R) Core(TM) i5-4590h, its main frequency is 3.30GHz, and the memory (RAM) It is 8G, and the running software is MATLAB2016a. The simulation environment of the performance optimization mode is the same as this, which will not be elaborated below. It can be seen from the table that the test times of MGD-NN and BN-MGD-DNN are 0.067 milliseconds and 0.223 milliseconds respectively.

Table 1 Average relative test and training error table

Table 2 Comparison of MGD-NN and BN-MGD-DNN algorithms

Claims (5)

1. an aeroengine steady-state model modeling method based on deep neural network, utilize deep neural network to construct aeroengine steady-state model, it is characterized in that, described deep neural network is the deep neural network of layer-by-layer batch normalization, It adds a batch normalization layer between adjacent hidden layers to standardize the output of the previous hidden layer. 2. aero-engine steady-state model modeling method as claimed in claim 1, is characterized in that, described standardization process is specifically as follows: in, is the output after normalization processing, ε is a positive integer with a very small value, is the output of the neural network before entering the batch normalization layer, μ _B and are the mean and variance of the sample data set, respectively, and γ and β are two learning parameters. 3. aero-engine steady-state model modeling method as claimed in claim 2, is characterized in that, described modeling method comprises the following steps: Step 1, obtaining the training data of the steady-state model of the aeroengine; Step 2, determine the structure of the deep neural network of layer-by-layer batch normalization; Step 3. Perform forward calculation on the layer-by-layer batch normalized deep neural network to obtain the loss function value; Step 4. Use the backpropagation algorithm to calculate the layer-by-layer batch normalized depth neural network gradient, and update the weights; Step 5. Determine whether the layer-by-layer batch normalized deep neural network is convergent, if yes, output the steady-state model, otherwise continue to iterate, and return to step 3. 4. aero-engine steady-state model modeling method as claimed in claim 3, is characterized in that, obtain the training data of described aero-engine steady-state model through engine test run experiment or/and engine nonlinear component level model. 5. as any one of claim 1～4 described aero-engine steady-state model modeling method, it is characterized in that, described aero-engine steady-state model is based on flight height, Mach number, fuel flow, tail nozzle throat area, The fan guide vane angle and the compressor guide vane angle are used as model inputs, and the engine fuel consumption rate, installation thrust, fan rotor speed, compressor rotor speed, fan surge margin, compressor surge margin and high-pressure turbine inlet Temperature is the model output.