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

A kind of surface heat flux three-dismensional effect modification method neural network based Download PDF

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CN110083895A
CN110083895A CN201910294868.XA CN201910294868A CN110083895A CN 110083895 A CN110083895 A CN 110083895A CN 201910294868 A CN201910294868 A CN 201910294868A CN 110083895 A CN110083895 A CN 110083895A
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陈伟芳
赵文文
潘学浩
沈煊
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Abstract

本发明公开了一种基于神经网络的表面热流辨识三维效应修正方法。该修正方法是在驻点热流周围区域的内壁面安装若干温度传感器,先利用内部各个温度测点的温度数据,通过一维热流辨识方法得到相应受热表面点上的热流,然后引入人工神经网络算法,将上一步中各个测点相应的辨识热流归一化处理后作为神经网络的输入序列,在神经网络中通过训练得到输出的反归一化结果作为所关注区域的热流辨识值。本发明提出的修正方法避免了三维辨识的时间复杂性,同时结合了顺序函数法良好的抗噪性和神经网络的强非线性,能够大大简化传统模型,提高了驻点热流的辨识精度,保证了在线辨识的实时性。

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

一种基于神经网络的表面热流辨识三维效应修正方法A Neural Network-Based Approach to Correct Three-Dimensional Effects of Surface Heat Flux Identification

技术领域technical field

本发明涉及一种表面热流辨识的计算方法与神经网络修正方法,尤其涉及一种基于神经网络的表面热流辨识三维效应修正方法。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.

背景技术Background technique

高超声速飞行面临严重的气动加热问题。由于空气受到强烈的摩擦和压缩作用,大量动能转化为热能,致使飞行器周围空气温度急剧升高,高温影响飞行器的结构强度和刚度,甚至引起外表面的烧蚀破坏。热防护系统设计是高超声速飞行技术快速发展的重要支撑,其研究设计需要大量的飞行试验的测试数据。对飞行器服役过程中的温度、热流等关键参数的测量是评价热防护材料使用性能、验证气动热模型和算法、指导热防护设计的必要手段。但对于驻点等热流密度大的区域,通常不能直接安置温度传感器或热流传感器进行测量,一方面是由于结构开孔导致结构强度下降以及缝隙加热,引起烧蚀不同步等结构匹配问题;另一方面,有些传感器本体材料不能承受过高热载荷,而且传感器的嵌入带来壁温的不连续以及周向的干扰,导致热流测量结果并非真实的气动热。因此,通过测量飞行器结构内壁温度来反演外表面热流和温度的气动热辨识方法,成为了获取气动热环境的重要解决方案。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.

气动热辨识属于一类热传导反问题,基本原理是通过测量导热材料内壁的温度测点的温度历程,反演出外壁受热面的热流时间历程。目前,国内外对热传导反问题进行了大量的研究,通常做法是选取合适的目标函数,将辨识问题转化为优化问题求解。钱炜祺分别用顺序函数法和共轭梯度法研究了一维表面热流辨识方法,并拓展到二维和三维规则外形表面热流辨识。热传导物理过程具有阻尼性和延迟性,阻尼性表现为边界热流的变化对边界附近的温度产生大的影响,而随着离边界距离的增加,热流变化的影响将减小;延迟性则表现为内部温度对边界热流的反应在时间上具有延迟性。根据这些特点,顺序函数法对热流的辨识是按时间顺序逐渐推进进行,即引入时间步长因子r,对某时刻热流的辨识依靠的是该时刻之后r个时间步的温度测量值。共轭梯度法是迭代正则化方法,其将优化问题分解为热传导正问题、灵敏度求解和伴随变量求解这三个适定问题来进行求解。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.

此外,薛齐文应用Tikhonov方法研究了一维热传导反问题中,内热源强度、导温系数及边界条件的多宗量辨识,将Bregman距离加权函数作为正则项应用到非线性热传导反问题的求解,基于一种时域精细算法和空间离散技术,考虑热源项的非线性,建立瞬态热传导正/反问题的数学模型,对一维的多个热学参数进行了组合识别。Cui Miao采用无量纲化目标方程,对热流模型进行参数辨识,但局限于已知的热流函数形式。钱炜祺考虑到高超声速的材料烧蚀后退,利用简化后的热解面烧蚀模型,对一维烧蚀表面热流辨识进行了研究,并将其用于钝头型碳酚醛材料Narmco4028试件在陶瓷加热风洞中的试验结果分析,证明了烧蚀模型的合理性和方法的有效性。张聪利用简化的一维和二维传热模型进行了高超声速燃烧室壁面热流的辨识,在轴对称模型下取得了较好的效果。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.

神经网络算法由于其强大的非线性拟合能力,在各个领域得到广泛的应用。S.DENG和智会强等人研究了神经网络和遗传算法求解热传导反问题,在考虑了简单的热流加载情况下,利用人工神经网络逼近内部温度场与未知的表面热流或材料热物性参数的函数关系,同时将反问题转化为适当目标函数下的极值优化问题,利用遗传算法的全局优化方法寻找反问题最优解。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.

本发明在一维热流辨识的基础上研究三维效应修正方法,将顺序函数法的一维热流辨识算法与神经网络算法结合起来,提出一套得到驻点热流实时准确的辨识结果的修正方法。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.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于提供一种基于神经网络的表面热流辨识三维效应修正方法。The object of the present invention is to provide a three-dimensional effect correction method for surface heat flow identification based on neural network.

本发明提出的方法主要技术方案如下:The method main technical scheme that the present invention proposes is as follows:

一种基于神经网络的表面热流辨识三维效应修正方法,是在驻点热流周围区域的内壁面安装若干温度传感器,先利用内部各个温度测点的温度数据,通过一维热流辨识方法得到相应受热表面点上的热流,然后引入人工神经网络算法,将上一步中各个测点相应的辨识热流归一化处理后作为神经网络的输入序列,在神经网络中通过训练得到输出的反归一化结果作为所关注区域的热流辨识值。具体方法如下: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:

首先利用顺序函数法,将结构内壁温度传感器的温度数据通过一维热流辨识算法反演出对应受热表面点的热流密度。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.

对于一维非稳态热传导问题,温度T(x,t)的控制方程,初始条件和边界条件可以表示为: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)=T0(x) (2)T(x,0)=T 0 (x) (2)

式中,t表示时间,材料初始温度分布为T0(x),长度为L,一端加载热流q,另一端绝热,ρ是材料的密度,Cp为比热容,k(T)是随温度变化的导热系数。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.

正问题对应的反问题就是根据材料内壁测点温度反推当前时刻的热流,也就是根据模型内点的温度响应找到吻合的表面热流。非稳态热传导是扩散型的,因此可以根据热传导的物理过程,按照时间顺序估计热流。所谓顺序函数法就是根据这个思想,通过tM,tM+1,…,tM+r-1共r个未来时间步所测得的温度来估计tM时刻的热流值。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 .

测点xm处温度传感器的温度测量数据可以表示为:The temperature measurement data of the temperature sensor at the measuring point x m can be expressed as:

式中:xm是测点所在位置,v(t)是测量噪声。In the formula: x m is the position of the measuring point, v(t) is the measurement noise.

工程上对参数辨识问题的处理可以转化为参数优化问题,按照输出误差最小原则,求出合适的参数。按照这种思路,热流辨识问题可以转化为根据温度测点的测量值,找到与真实热流最吻合的解,优化目标是求解正问题得到的测点温度与温度实测值的累积误差最小,因此可以找到如下的目标函数: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:

其中,T(xm,t,q)是测点温度计算值,则是相应的测量值,||.||代表某种范数,常用的有1-范数和2-范数,2-范数相较1-范数在求导优化上更加方便。将2-范数应用于式(6)可以得到: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:

考虑传热问题的延迟性,假设tM时刻热流仅能影响tM至tM+r-1之间的测点温度,并且考虑数值求解中时间的离散,那么当辨识tM时刻的热流q(tM)时(后文简写为qM),所要优化的函数可表示为: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:

针对如上的目标函数,可以利用优化方法对其进行优化求解,优化的目的是使式(8)取极小值。实践证明,Newton-Raphson算法是求解此类优化问题最有效的方法。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.

J(q)取最小值的必要条件是:The necessary conditions for J(q) to take the minimum value are:

略去二阶小量得Δqk满足下式:Omitting the second-order small quantity, Δq k satisfies the following formula:

式中M称为信息矩阵。记q(ti)=qi,由于:In the formula, M is called the information matrix. Record q(t i )=q i , because:

其中是状态量对位置参数的一阶导数,称之为灵敏度。进一步求导可得:in It is the first derivative of the state quantity to the position parameter, which is called the sensitivity. Further derivation can be obtained:

分析可知,对于收敛的解,式(12)中的第一项会很快趋近于零,可以直接忽略,因此可得: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:

如前所述,求解温度场TM+r-1不仅取决于qM,还受qM,…,qM+r-1的影响,因此辨识qM时也需要知道tM至tM+r-1之间的热流,即需要建立qM+i与qM的关系。假设热流在此期间是线性变化的,当采样间隔固定时,有: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:

这样热流的迭代修正公式可以表示为:The iterative correction formula of heat flow can be expressed as:

γ是牛顿-拉夫逊方法的迭代修正步长,也叫松弛因子,k为迭代次数。在未引入松弛因子时,辨识结果在某些情况下会发生震荡的不合理情况,这是由于迭代修正过程中出现了修正量过大导致的,例如在某一次迭代过程中出现了正的过大的修正量,为了消除这个修正量的影响,下一个迭代步中会产生一个更大的负的修正量,为了消除这个负的修正量的影响,下一个迭代步中会产生一个更大的正的修正量,如此往复就出现了便是结果震荡的情况。而松弛因子γ能够将修正量控制在一个较小的范围内,进而很好的改善结果震荡的情况。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.

将温度对热流的灵敏度记作对它的求解可通过传热微分方程对热流求导得到: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:

综上所述,顺序函数法辨识表面热流的计算过程可以概括为:基于初始热流q0,首先利用公式(14)预估之后时刻的热流,结合初始温度求解后续r个时刻的温度值,再通过求解温度对该时刻热流的灵敏度,然后根据公式(15)利用牛顿-拉夫逊方法对热流进行迭代修正,直至满足精度要求,此时计算得到的热流值就是当前时刻的辨识值,沿时间方向往前推进,利用同样的方法即可推出后续时刻的热流值。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.

在利用顺序函数法的一维辨识算法反演出对应受热表面点的热流值,将其作为BP神经网络的输入,通过训练后输出驻点热流变化。将BP网络输入层的节点数设为n,隐层节点数设为l,输出层节点数为m,输入序列表示为向量X,输出序列则表示为Y。根据输入X,定义输入层每个节点与隐层节点之间的权值为ωi,j,隐层阈值记为a,在经过求和单元和激活函数作用后,隐层输出H可以表示为: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 :

其中f是隐层的激活函数。记输出层阈值为b,将隐层结果作为输出层的输入,隐层每个节点与输出层节点之间的权值为ωj,k,同样可以计算得到输出层的实际输出O: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:

则此轮训练的误差为:Then the error of this round of training is:

ek=Yk-Ok k=1,2,…,m (19)e k =Y k -O k k=1,2,...,m (19)

利用梯度下降法对权值进行迭代更新,对于输入层和隐层,其权值更新公式分别可以表示为: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:

其中η是优化过程中的迭代步长,称为学习速率。where η is the iterative step size in the optimization process, called the learning rate.

同理,梯度下降法中网络阈值的更新公式为:Similarly, the update formula of the network threshold in the gradient descent method is:

根据以上的思路搭建BP神经网络进行学习训练,训练成熟的神经网络具有强大的非线性映射和泛化能力。研究表明,一个包含单隐层的多层前馈网络,只要隐层神经元足够多,那么就可以以任意精度逼近任意复杂度的连续函数。因此可以利用神经网络所具有的优势,将其用于表面热流辨识三维效应的修正,首先利用内部各个测点的温度数据,通过一维热流辨识方法得到相应受热表面点上的热流,然后引入人工神经网络算法,将上一步中各个测点相应的辨识热流密度通过数据的归一化处理后作为输入序列,在神经网络中通过训练得到输出的反归一化结果作为所关注区域的热流辨识值。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 .

本发明的有益效果是:The beneficial effects of the present invention are:

本发明提出的修正方法在已有顺序函数法对一维表面热流辨识的研究基础上,考虑到三维辨识实时性的困难,结合神经网络和顺序函数法结合,最终得到表面热流实时准确的辨识结果。本发明提出的修正方法避免了三维辨识的时间复杂性,同时结合了顺序函数法良好的抗噪性和神经网络的强非线性,能够大大简化传统模型,提高了驻点热流的辨识精度,保证了在线辨识的实时性。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.

附图说明Description of drawings

图1为本发明基于神经网络的表面热流辨识三维效应修正方法的流程图。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.

图2为三维传热模型几何示意图。Figure 2 is a schematic diagram of the geometry of the three-dimensional heat transfer model.

图3为内部温度测点布局。Figure 3 shows the layout of internal temperature measuring points.

图4为三维效应下的一维辨识结果比较。Figure 4 is a comparison of the one-dimensional identification results under the three-dimensional effect.

图5为驻点热流神经网络预测结果。Figure 5 shows the prediction results of the stagnation point heat flow neural network.

图6为驻点热流预测相对误差。Figure 6 shows the relative error of stagnation point heat flow prediction.

图7为不同时刻驻点热流预测结果。Figure 7 shows the prediction results of stagnation point heat flow at different times.

具体实施方式Detailed ways

下面结合附图详细描述本发明具体实施方式,本发明的目的和效果将变得更加明显。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.

本发明的一种基于神经网络的表面热流辨识三维效应修正方法,其核心内容是在驻点热流周围区域的内壁面安装若干温度传感器,用一维的顺序函数法将每个温度传感器的测量数据转化为相应的热流辨识序列,经过数据的归一化处理后作为BP网络的输入,网络输出的反归一化结果就是驻点热流的辨识结果。本发明的神经网络修正流程详见图1。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.

本实例通过一组三维效应修正模型验证算例来表明本方法的优越性。算例模型采用外径0.2m,厚度0.03m的空心半球壳,如图2所示,材料比热Cp=500J/(kg·K),密度ρ=8000kg/m3,导热系数k=80W/(m·K),初始温度300K,时间步长0.2s,总加热时间200s,时间步r取30,测温点数量为9个,呈放射状均布于内壁面,测温点布局在底面投影示意图如图3所示。测点1位于球壳端部,内侧2-5测点距离测点1球面距离约0.03m,外侧6-9测点距离测点1约0.06m。在球壳外表面施加随时间和空间变化的热流,热流函数形式为:为了评估三维效应的影响,仅使用温度测点1的温度数据来辨识驻点热流,图4是一维辨识的结果与驻点热流比较,对比结果显示不考虑三维效应的热流辨识结果出现了极大的偏差,甚至不能得到符合物理意义的正解,对于时空分布复杂的热流及曲率半径小的导热结构,三维效应是不可忽略的,必须予以修正。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.

采用本发明的方法,将9个测点的温度数据分别使用一维顺序函数法辨识出相应的热流序列,将其作为训练样本的输入,样本输出是已知的驻点热流序列。仿真得到1000组样本数据,随机选取其中900组用于网络训练,另外100组样本用于网络测试。这样神经网络有9个输入神经元,1个输出神经元。图5是训练成熟后的神经网络驻点热流预测结果与实际驻点热流结果比较,图6是驻点热流的预测误差。由于测试样本是随机选取的不同时刻结果,为方便观察,将测试样本按时间顺序排列,不同时刻的预测结果对比如图7所示。可见三维效应修正后的驻点热流预测误差小于1%,基于神经网络的三维效应修正模型是有效的。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.

通过数值仿真的算例测试结果可以看出,本发明提出的方法对于峰值热流的辨识结果准确度高,模型训练可在线下进行,避免了三维辨识耗时大、精度低、无法实现实时在线辨识的缺点,同时具有良好的抗噪性和稳定性,在航天器表面峰值热流在线实时辨识中有广阔的应用前景。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, CpFor 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 tM,tM+1,…,tM+r-1When total r future Temperature measured by spacer step estimates tMThe heat flow value at moment;
Measuring point xmThe temperature measuring data of place's temperature sensor can indicate are as follows:
In formula: xmIt 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 tMMoment hot-fluid is only capable of Influence tMTo tM+r-1Between measuring point temperature, and the discrete of time in numerical solution is considered, then as identification tMThe hot-fluid q at moment (tM) when, the objective function to be optimized are as follows:
It is solved using Newton-Raphson algorithm;
Establish tM+iMoment hot-fluid qM+iWith tMMoment hot-fluid qMRelationship, it is assumed that hot-fluid is linear change during this period, works as sampling When interval is fixed, have:
qM+1=qM+(qM-qM-1)
qM+n=qM+n(qM-qM-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 tMThe 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 ωi,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 ωj,k, the reality output O of output layer can equally be calculated:
The then error of this wheel training are as follows:
ek=Yk-OkK=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:
ωj,kj,k+ηHjekK=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:
bk=bk+ekK=1,2 ..., m.
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Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111307481A (en) * 2020-02-24 2020-06-19 中国空气动力研究与发展中心超高速空气动力研究所 Dynamic hot wall heat flow inverse estimation method based on nonlinear artificial neural network
CN112990442A (en) * 2021-04-21 2021-06-18 北京瑞莱智慧科技有限公司 Data determination method and device based on spatial position and electronic equipment
CN113065275A (en) * 2021-03-05 2021-07-02 浙江大学 An online prediction method for stagnant heat flow during aircraft flight
CN113255181A (en) * 2021-04-27 2021-08-13 北京航空航天大学 Recognition method and device for heat transfer inverse problem based on deep learning
CN113553779A (en) * 2021-09-22 2021-10-26 中国航天空气动力技术研究院 Method, device, electronic device and medium for predicting heat flow at the stagnation point of Mars enterer
CN116935985A (en) * 2023-07-17 2023-10-24 中国地质调查局油气资源调查中心 Sensitivity analysis method for experimental parameter change in coal gasification process
CN117910348A (en) * 2024-01-11 2024-04-19 哈尔滨工业大学 A heat flow identification method based on multi-source information fusion dynamic Bayesian network

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103559537A (en) * 2013-10-30 2014-02-05 南京邮电大学 Template matching method based on error back propagation in out-of-order data streams

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103559537A (en) * 2013-10-30 2014-02-05 南京邮电大学 Template matching method based on error back propagation in out-of-order data streams

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
彭玉酌: "高超声速飞行环境参数辨识方法研究", 《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑》 *

Cited By (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111307481A (en) * 2020-02-24 2020-06-19 中国空气动力研究与发展中心超高速空气动力研究所 Dynamic hot wall heat flow inverse estimation method based on nonlinear artificial neural network
CN111307481B (en) * 2020-02-24 2021-09-07 中国空气动力研究与发展中心超高速空气动力研究所 Dynamic hot wall heat flow inverse estimation method based on nonlinear artificial neural network
CN113065275A (en) * 2021-03-05 2021-07-02 浙江大学 An online prediction method for stagnant heat flow during aircraft flight
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CN112990442B (en) * 2021-04-21 2021-08-06 北京瑞莱智慧科技有限公司 Data determination method and device based on spatial position and electronic equipment
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Application publication date: 20190802