CN110083895A - A kind of surface heat flux three-dismensional effect modification method neural network based - Google Patents

Abstract

The invention discloses a neural network-based three-dimensional effect correction method for surface heat flow identification. The correction method is to install a number of temperature sensors on the inner wall of the area around the heat flow at the stagnation point, first use the temperature data of each internal temperature measurement point, and obtain the heat flow on the corresponding heated surface point through the one-dimensional heat flow identification method, and then introduce the artificial neural network algorithm , normalize the identified heat flow corresponding to each measuring point in the previous step as the input sequence of the neural network, and obtain the output denormalized result through training in the neural network as the heat flow identification value of the area of interest. The correction method proposed by the invention avoids the time complexity of three-dimensional identification, and at the same time combines the good noise resistance of the sequential function method and the strong nonlinearity of the neural network, which can greatly simplify the traditional model, improve the identification accuracy of the heat flow at the stagnation point, and ensure The real-time performance of online identification is ensured.

Description

A Neural Network-Based Approach to Correct Three-Dimensional Effects of Surface Heat Flux Identification

technical field

The invention relates to a calculation method for surface heat flow identification and a neural network correction method, in particular to a three-dimensional effect correction method for surface heat flow identification based on a neural network.

Background technique

Hypersonic flight faces serious aerodynamic heating problems. Due to the strong friction and compression of the air, a large amount of kinetic energy is converted into heat energy, causing the air temperature around the aircraft to rise sharply. The high temperature affects the structural strength and rigidity of the aircraft, and even causes ablation damage to the outer surface. The design of thermal protection system is an important support for the rapid development of hypersonic flight technology, and its research design requires a large amount of test data from flight tests. The measurement of key parameters such as temperature and heat flow during aircraft service is a necessary means to evaluate the performance of thermal protection materials, verify the aerothermal model and algorithm, and guide the design of thermal protection. However, for areas with high heat flux density such as stagnation points, temperature sensors or heat flux sensors cannot usually be directly placed for measurement. On the one hand, due to structural openings, structural strength decreases and gap heating causes structural matching problems such as ablation asynchrony; On the one hand, some sensor body materials cannot withstand high thermal loads, and the embedding of the sensor brings discontinuity and circumferential interference in the wall temperature, resulting in heat flow measurement results that are not real aerodynamic heat. Therefore, the aerothermal identification method, which inverts the heat flow and temperature of the outer surface by measuring the temperature of the inner wall of the aircraft structure, has become an important solution to obtain the aerothermal environment.

Aerodynamic thermal identification belongs to a class of heat conduction inverse problems. The basic principle is to invert the time history of heat flow on the heating surface of the outer wall by measuring the temperature history of the temperature measurement points on the inner wall of the heat-conducting material. At present, a lot of research has been done on the inverse heat conduction problem at home and abroad. The usual method is to select an appropriate objective function and transform the identification problem into an optimization problem for solution. Qian Weiqi used the sequential function method and the conjugate gradient method to study the identification method of one-dimensional surface heat flow, and extended it to the identification of two-dimensional and three-dimensional regular shape surface heat flow. The physical process of heat conduction has damping and delay properties. The damping property shows that the change of boundary heat flow has a great influence on the temperature near the boundary, and as the distance from the boundary increases, the influence of heat flow change will decrease; the delay property is shown as The reaction of the internal temperature to the boundary heat flow is delayed in time. According to these characteristics, the identification of heat flow by the sequential function method is carried out gradually in time order, that is, the time step factor r is introduced, and the identification of heat flow at a certain moment depends on the temperature measurement value of r time steps after this moment. The conjugate gradient method is an iterative regularization method, which decomposes the optimization problem into three well-posed problems, namely heat conduction positive problem, sensitivity solution and accompanying variable solution, for solution.

In addition, Xue Qiwen applied the Tikhonov method to study the multi-quantity identification of internal heat source strength, thermal conductivity and boundary conditions in the one-dimensional heat conduction inverse problem, and applied the Bregman distance weighting function as a regular term to the solution of the nonlinear heat conduction inverse problem, based on A time-domain fine algorithm and space discretization technology consider the nonlinearity of the heat source term, establish a mathematical model for the forward/inverse problem of transient heat conduction, and carry out a combined identification of multiple thermal parameters in one dimension. Cui Miao used the dimensionless objective equation to identify the parameters of the heat flow model, but it was limited to the known heat flow function form. Considering the material ablation retreat at hypersonic speed, Qian Weiqi used the simplified pyrolysis surface ablation model to study the heat flow identification on the one-dimensional ablation surface, and applied it to the blunt carbon phenolic material Narmco4028 specimen The analysis of test results in the ceramic heating wind tunnel proves the rationality of the ablation model and the validity of the method. Zhang Cong used the simplified one-dimensional and two-dimensional heat transfer models to identify the heat flow on the wall of the hypersonic combustion chamber, and achieved good results under the axisymmetric model.

The neural network algorithm has been widely used in various fields due to its powerful nonlinear fitting ability. S.DENG and Zhi Huiqiang et al studied the neural network and genetic algorithm to solve the inverse problem of heat conduction. In the case of simple heat flow loading, the artificial neural network was used to approximate the relationship between the internal temperature field and the unknown surface heat flow or material thermophysical parameters. At the same time, the inverse problem is transformed into an extremum optimization problem under the appropriate objective function, and the global optimization method of genetic algorithm is used to find the optimal solution of the inverse problem.

The present invention studies the three-dimensional effect correction method on the basis of one-dimensional heat flow identification, combines the one-dimensional heat flow identification algorithm of the sequential function method with the neural network algorithm, and proposes a set of correction methods for obtaining real-time and accurate identification results of stagnation point heat flow.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a three-dimensional effect correction method for surface heat flow identification based on neural network.

The method main technical scheme that the present invention proposes is as follows:

A neural network-based three-dimensional effect correction method for surface heat flow identification. A number of temperature sensors are installed on the inner wall of the area around the heat flow at the stagnation point. First, the temperature data of each internal temperature measurement point is used to obtain the corresponding heated surface through a one-dimensional heat flow identification method. Then, the artificial neural network algorithm is introduced to normalize the identified heat flow of each measuring point in the previous step as the input sequence of the neural network, and the denormalized result of the output is obtained through training in the neural network as Heat flow identification values for the region of interest. The specific method is as follows:

First, using the sequential function method, the temperature data of the temperature sensor on the inner wall of the structure is used to invert the heat flux density corresponding to the heated surface point through a one-dimensional heat flow identification algorithm.

For a one-dimensional unsteady heat conduction problem, the governing equation for temperature T(x,t), initial conditions and boundary conditions can be expressed as:

T(x,0)=T ₀ (x) (2)

In the formula, t represents the time, the initial temperature distribution of the material is T ₀ (x), the length is L, one end is loaded with heat flow q, and the other end is insulated, ρ is the density of the material, C _p is the specific heat capacity, and k(T) is the change with temperature of thermal conductivity.

The inverse problem corresponding to the forward problem is to deduce the heat flow at the current moment according to the temperature of the measurement point on the inner wall of the material, that is, to find the matching surface heat flow according to the temperature response of the internal point of the model. Unsteady heat conduction is of the diffusion type, so the heat flow can be estimated in time order based on the physical process of heat conduction. The so-called sequential function method is based on this idea, and the heat flow value at t _M is estimated by the temperature measured in r future time steps of t _M , t _M+1 ,…, t _M+r-1 .

The temperature measurement data of the temperature sensor at the measuring point x _m can be expressed as:

In the formula: x _m is the position of the measuring point, v(t) is the measurement noise.

The processing of the parameter identification problem in engineering can be transformed into a parameter optimization problem, and the appropriate parameters can be found according to the principle of minimum output error. According to this idea, the heat flow identification problem can be transformed into finding the solution that best matches the real heat flow based on the measured values of the temperature measuring points. Find the following objective function:

Among them, T(x _m ,t,q) is the calculated temperature of the measuring point, It is the corresponding measurement value. ||.|| represents a certain norm. The commonly used ones are 1-norm and 2-norm. Compared with 1-norm, 2-norm is more convenient for derivation optimization. Applying the 2-norm to formula (6) gives:

Considering the delay of the heat transfer problem, assuming that the heat flow at time t _M can only affect the temperature of the measuring point between t _M and t _M+r-1 , and considering the time dispersion in the numerical solution, then when the heat flow q at time t _M is identified (t _M ) (hereinafter abbreviated as q _M ), the function to be optimized can be expressed as:

For the above objective function, the optimization method can be used to optimize and solve it. The purpose of optimization is to make the formula (8) take the minimum value. Practice has proved that the Newton-Raphson algorithm is the most effective method for solving such optimization problems.

The necessary conditions for J(q) to take the minimum value are:

Omitting the second-order small quantity, Δq _k satisfies the following formula:

In the formula, M is called the information matrix. Record q(t _i )=q _i , because:

in It is the first derivative of the state quantity to the position parameter, which is called the sensitivity. Further derivation can be obtained:

It can be seen from the analysis that for the convergent solution, the first term in formula (12) will quickly approach zero and can be ignored directly, so it can be obtained:

As mentioned above, solving the temperature field T _M+r-1 not only depends on q _M , but also is affected by q _M ,…,q _M+r-1 , so it is also necessary to know t _M to t _M+ when identifying q _M The heat flow between _r-1 , that is, the relationship between q _M+i and q _M needs to be established. Assuming that the heat flow changes linearly during this period, when the sampling interval is fixed, there are:

The iterative correction formula of heat flow can be expressed as:

γ is the iterative correction step size of the Newton-Raphson method, also called the relaxation factor, and k is the number of iterations. When the relaxation factor is not introduced, the identification result may oscillate unreasonably in some cases, which is caused by the excessive correction amount in the iterative correction process, such as a positive excessive Large correction amount, in order to eliminate the influence of this correction amount, a larger negative correction amount will be generated in the next iteration step, in order to eliminate the influence of this negative correction amount, a larger negative correction amount will be generated in the next iteration step If there is a positive correction amount, there will be a situation where the result is oscillating. And the relaxation factor γ can control the correction amount in a small range, so as to improve the situation of the result oscillation.

The sensitivity of temperature to heat flow is written as Its solution can be obtained by deriving the heat flow from the heat transfer differential equation:

In summary, the calculation process of the sequential function method to identify surface heat flow can be summarized as follows: based on the initial heat flow q ₀ , firstly use the formula (14) to estimate the heat flow at the next moment, combine the initial temperature to solve the temperature value of the subsequent r moments, and then By solving the sensitivity of the temperature to the heat flow at this moment, and then using the Newton-Raphson method to iteratively correct the heat flow according to formula (15) until the accuracy requirements are met, the heat flow value calculated at this time is the identification value at the current moment, along the time direction Moving forward, the heat flow value at subsequent moments can be deduced using the same method.

The one-dimensional identification algorithm using the sequential function method inverts the heat flow value corresponding to the heated surface point, which is used as the input of the BP neural network, and the heat flow change at the stagnation point is output after training. The number of nodes in the input layer of the BP network is set to n, the number of nodes in the hidden layer is set to l, the number of nodes in the output layer is set to m, the input sequence is expressed as a vector X, and the output sequence is expressed as Y. According to the input X, the weight between each node of the input layer and the node of the hidden layer is defined as ω _i,j , and the threshold of the hidden layer is denoted as a. After the action of the summation unit and the activation function, the output H of the hidden layer can be expressed as :

where f is the activation function of the hidden layer. Note that the threshold of the output layer is b, and the result of the hidden layer is used as the input of the output layer. The weight between each node of the hidden layer and the node of the output layer is ω _j,k , and the actual output O of the output layer can also be calculated:

Then the error of this round of training is:

e _k =Y _k -O _k k=1,2,...,m (19)

The weights are iteratively updated using the gradient descent method. For the input layer and the hidden layer, the weight update formulas can be expressed as:

where η is the iterative step size in the optimization process, called the learning rate.

Similarly, the update formula of the network threshold in the gradient descent method is:

According to the above ideas, the BP neural network is built for learning and training, and the trained neural network has strong nonlinear mapping and generalization capabilities. Studies have shown that a multi-layer feed-forward network with a single hidden layer can approximate continuous functions of arbitrary complexity with arbitrary precision as long as there are enough neurons in the hidden layer. Therefore, the advantages of the neural network can be used to correct the three-dimensional effect of surface heat flow identification. First, the temperature data of each internal measurement point is used to obtain the heat flow on the corresponding heated surface point through the one-dimensional heat flow identification method, and then artificial The neural network algorithm takes the identified heat flux density corresponding to each measuring point in the previous step as the input sequence after normalization processing of the data, and the output denormalization result obtained through training in the neural network is used as the heat flux identification value of the area of interest .

The beneficial effects of the present invention are:

The correction method proposed by the present invention is based on the research on the identification of one-dimensional surface heat flow by the existing sequential function method, considering the real-time difficulty of three-dimensional identification, combining the neural network and the sequential function method, and finally obtaining the real-time and accurate identification result of the surface heat flow . The correction method proposed by the invention avoids the time complexity of three-dimensional identification, and at the same time combines the good noise resistance of the sequential function method and the strong nonlinearity of the neural network, which can greatly simplify the traditional model, improve the identification accuracy of the heat flow at the stagnation point, and ensure The real-time performance of online identification is ensured.

Description of drawings

FIG. 1 is a flow chart of the neural network-based three-dimensional effect correction method for surface heat flow identification in the present invention.

Figure 2 is a schematic diagram of the geometry of the three-dimensional heat transfer model.

Figure 3 shows the layout of internal temperature measuring points.

Figure 4 is a comparison of the one-dimensional identification results under the three-dimensional effect.

Figure 5 shows the prediction results of the stagnation point heat flow neural network.

Figure 6 shows the relative error of stagnation point heat flow prediction.

Figure 7 shows the prediction results of stagnation point heat flow at different times.

Detailed ways

The specific embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, and the purpose and effect of the present invention will become more obvious.

A neural network-based three-dimensional effect correction method for surface heat flow identification of the present invention, its core content is to install a number of temperature sensors on the inner wall surface of the area around the stagnation point heat flow, and use the one-dimensional sequential function method to convert the measurement data of each temperature sensor It is transformed into the corresponding heat flow identification sequence, and after the data is normalized, it is used as the input of the BP network, and the denormalized result of the network output is the identification result of the stagnation point heat flow. The neural network correction process of the present invention is shown in Fig. 1 for details.

This example demonstrates the superiority of this method through a set of three-dimensional effect correction model verification examples. The example model adopts a hollow hemispherical shell with an outer diameter of 0.2m and a thickness of 0.03m, as shown in Figure 2, the specific heat of the material C _p =500J/(kg·K), the density ρ=8000kg/m ³ , and the thermal conductivity k=80W /(m K), the initial temperature is 300K, the time step is 0.2s, the total heating time is 200s, the time step r is set to 30, and the number of temperature measurement points is 9, which are radially evenly distributed on the inner wall surface, and the temperature measurement points are arranged on the bottom surface The schematic diagram of the projection is shown in Figure 3. Measuring point 1 is located at the end of the spherical shell, the inner measuring points 2-5 are about 0.03m away from the spherical surface of measuring point 1, and the outer measuring points 6-9 are about 0.06m away from measuring point 1. A heat flux that varies with time and space is applied on the outer surface of the spherical shell, and the heat flux function form is: In order to evaluate the influence of the three-dimensional effect, only the temperature data of the temperature measuring point 1 is used to identify the heat flow at the stagnation point. Figure 4 shows the comparison between the one-dimensional identification result and the heat flow at the stagnation point. If the deviation is large, a positive solution that conforms to the physical meaning cannot even be obtained. For heat flow with complex spatio-temporal distribution and heat conduction structures with a small radius of curvature, the three-dimensional effect cannot be ignored and must be corrected.

Using the method of the present invention, the temperature data of 9 measuring points are respectively identified by the one-dimensional sequential function method to identify the corresponding heat flow sequence, which is used as the input of the training sample, and the sample output is the known stagnation point heat flow sequence. The simulation obtained 1000 sets of sample data, among which 900 sets were randomly selected for network training, and the other 100 sets of samples were used for network testing. In this way, the neural network has 9 input neurons and 1 output neuron. Figure 5 is the comparison between the predicted results of the stagnation point heat flow of the neural network after training and the actual stagnation point heat flow results, and Figure 6 is the prediction error of the stagnation point heat flow. Since the test samples are randomly selected results at different times, for the convenience of observation, the test samples are arranged in chronological order, and the comparison of prediction results at different times is shown in Figure 7. It can be seen that the prediction error of stagnation point heat flow after three-dimensional effect correction is less than 1%, and the three-dimensional effect correction model based on neural network is effective.

It can be seen from the test results of numerical simulation examples that the method proposed by the present invention has high accuracy for the identification of peak heat flow, and the model training can be carried out offline, avoiding the time-consuming and low-precision three-dimensional identification, which cannot realize real-time online identification At the same time, it has good noise resistance and stability, and has broad application prospects in the online real-time identification of peak heat flux on the surface of spacecraft.

Claims (3)

1. a kind of surface heat flux three-dismensional effect modification method neural network based, which is characterized in that

If this method is that the inner wall in stationary point hot-fluid peripheral region installs dry temperature sensor, surveyed first with internal each temperature The temperature data of point, obtains the hot-fluid on corresponding generating surface point by one-dimensional heat flux method, then introduces artificial neuron Measuring point each in previous step is recognized the list entries after hot-fluid normalized as neural network by network algorithm accordingly, Heat flux value of the renormalization result exported in neural network by training as interest region.

2. surface heat flux three-dismensional effect modification method neural network based according to claim 1, feature exist In,

One-dimensional heat flux is carried out using sequential function method using the temperature data of inside configuration temperature point and obtains corresponding be heated The heat flow density of surface point, process are as follows:

For one-dimensional and unsteady state heat conduction problem, the governing equation of temperature T (x, t), primary condition and boundary condition can be indicated Are as follows:

T (x, 0)=T₀(x)

In formula, t indicates the time, and material initial temperature is distributed as T₀(x), length L, one end load hot-fluid q, other end insulation, ρ It is the density of material, C_pFor specific heat capacity, k (T) is the thermal coefficient varied with temperature；

According to the physical process of heat transfer, hot-fluid is estimated sequentially in time, that is, passes through t_M,t_M+1,…,t_M+r-1When total r future Temperature measured by spacer step estimates t_MThe heat flow value at moment；

Measuring point x_mThe temperature measuring data of place's temperature sensor can indicate are as follows:

In formula: x_mIt is measuring point position, v (t) is measurement noise；

With the minimum objective function of accumulated error of measuring point temperature calculations and temperature measured value, and assume t_MMoment hot-fluid is only capable of Influence t_MTo t_M+r-1Between measuring point temperature, and the discrete of time in numerical solution is considered, then as identification t_MThe hot-fluid q at moment (t_M) when, the objective function to be optimized are as follows:

It is solved using Newton-Raphson algorithm；

Establish t_M+iMoment hot-fluid q_M+iWith t_MMoment hot-fluid q_MRelationship, it is assumed that hot-fluid is linear change during this period, works as sampling When interval is fixed, have:

q_M+1=q_M+(q_M-q_M-1)

q_M+n=q_M+n(q_M-q_M-1)

Then the iterated revision formula of hot-fluid may be expressed as:

γ is the iterated revision step-length of Newton-Raphson method, i.e. relaxation factor；K is the number of iterations, is wanted until meeting precision It asks, the heat flow value being calculated at this time is exactly t_MThe identifier at moment.

3. surface heat flux three-dismensional effect modification method neural network based according to claim 1, feature exist In will make after heat flow data normalized after the heat flow value for being finally inversed by corresponding generating surface point by one-dimensional discrimination method For the input of neural network, if the number of nodes of neural network input layer is n, the number of hidden nodes is set as l, and output layer number of nodes is m, List entries is expressed as vector X, and output sequence is then expressed as Y；According to input X, each node of input layer and hidden node are defined Between weight be ω_i,j, hidden layer threshold value is denoted as a, and after summation unit and activation primitive effect, hidden layer exports H can be with table It is shown as:

Wherein f is the activation primitive of hidden layer, and note output layer threshold value is b, and using hidden layer result as the input of output layer, hidden layer is each Weight between node and output node layer is ω_j,k, the reality output O of output layer can equally be calculated:

The then error of this wheel training are as follows:

e_k=Y_k-O_kK=1,2 ..., m

Update is iterated to weight using gradient descent method, for input layer and hidden layer, right value update formula respectively can be with It indicates are as follows:

ω_j,k=ω_j,k+ηH_je_kK=1,2 ..., m；J=1,2 ..., l

Wherein η is the iteration step length in optimization process, i.e. learning rate；

Similarly, in gradient descent method network threshold more new formula are as follows:

b_k=b_k+e_kK=1,2 ..., m.