Temperature field prediction method of hypersonic wind tunnel, electronic device and storage medium

Abstract

The temperature field prediction method of a hypersonic wind tunnel, an electronic device and a storage medium belong to the technical field of wind tunnel measurement and control. In order to solve the problem that the temperature field control effect of the hypersonic wind tunnel is poor, the working condition data of the hypersonic wind tunnel is collected, the input samples in the original data sample set are reconstructed in phase space, the input samples and the output samples used for model training are obtained, the sample training data set and the sample test data set are composed, the Bayesian regression method, the support vector regression method and the BP neural network method are used to establish the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel, the sample training data set is used to train the three outlet temperature prediction models of the temperature field of the hypersonic wind tunnel, the sample test data set is used to test the three outlet temperature prediction models of the temperature field of the hypersonic wind tunnel, and the optimal outlet temperature prediction model of the temperature field of the hypersonic wind tunnel is obtained. The present application is accurate in prediction.

Description

Technical Field

[0001] This invention belongs to the field of wind tunnel measurement and control technology, specifically relating to a method for predicting the temperature field of a hypersonic wind tunnel, electronic equipment, and storage medium. Background Technology

[0002] Hypersonic wind tunnels operate using a downdraft ejector system, employing free-jet testing. The operating Mach number is no less than 4, and the total operating pressure typically ranges from a few bar to tens of bar. To prevent airflow condensation during operation or to replicate the actual total temperature of flight, hypersonic wind tunnels generally have heaters installed before the stabilization section to heat the airflow and control the temperature field of the test section. Depending on the operating conditions, the maximum heating capacity of the heaters required for hypersonic wind tunnels ranges from several hundred Kelvin to thousands of Kelvin. Heater types include electric heaters and combustion heaters. Electric heaters consist of several heating modules using electric heating tubes as heating elements. Due to their high stability, safety, and the purity of the airflow, they are widely used in the design and construction of hypersonic wind tunnels. For hypersonic wind tunnels equipped with electric heaters, the heating temperature of the electric heating modules needs to be adjusted according to different inlet temperatures and pressures during temperature regulation to effectively control the outlet temperature, thereby controlling the temperature field of the test section. The factors affecting the temperature field control of the test section of a hypersonic wind tunnel mainly include: the delayed characteristics of the temperature effect, the coupling effect of wind tunnel pressure and temperature, the short duration of the wind tunnel test process, and the influence of ambient temperature. At present, the temperature field control of existing hypersonic wind tunnels mainly relies on human experience, and the temperature field control effect is not good, making it difficult to fully meet the test requirements. Summary of the Invention

[0003] This invention aims to solve the problem of poor temperature field control in hypersonic wind tunnels, and proposes a method for predicting the temperature field of hypersonic wind tunnels, electronic equipment, and storage medium.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A method for predicting the temperature field of a hypersonic wind tunnel includes the following steps:

[0006] S1. Collect operating data of the hypersonic wind tunnel, including the wind tunnel heater outlet temperature γ. i The temperature of h heating modules of the wind tunnel heater [T] i×1 ,T i×2 ,...,T i×h ], wind tunnel heater inlet airflow pressure P i q, the inlet airflow temperature of the wind tunnel heater i Then set the temperature of h heating modules of the wind tunnel heater [T].i×1 T i×2 ...,T i×h ] and the wind tunnel heater inlet airflow pressure P i , the wind tunnel heater inlet airflow temperature q i is an input sample x i , the wind tunnel heater outlet temperature y i is an output sample, and the original data sample set is obtained i = 1, 2,..., n, n is the number of original data samples, and i is any one of n;

[0007] S2, the input sample in the original data sample set obtained in step S1 is reconstructed in phase space to obtain an input sample and an output sample for model training, and a sample training data set and a sample test data set are formed;

[0008] S3, a Bayesian regression method, a support vector regression method, and a BP neural network method are used to establish an outlet temperature prediction model of the temperature field of the hypersonic wind tunnel, and the sample training data set obtained in step S2 is used to train the three outlet temperature prediction models of the temperature field of the hypersonic wind tunnel established in step S3;

[0009] S4, the sample test data set obtained in step S2 is used to test the three outlet temperature prediction models of the temperature field of the hypersonic wind tunnel established in step S3, and an optimal outlet temperature prediction model of the temperature field of the hypersonic wind tunnel is obtained.

[0010] Further, the input sample x i in step S1 is i×1 = [T i×2 , T i×h ,..., T i , P i , q i ], the data form of the input sample x i is rewritten, and finally

[0011]

[0012] wherein d is the dimension of the data in the input sample, d = h + 2, x d is the dthdimensional feature of the ithsample.

[0013] Further, the specific implementation method of step S2 includes the following steps:

[0014] S2.1, the jthdelay time and embedding dimension of the input sample x i are set to τ j and m j, j = 1, 2,..., d, the time series X(k) obtained by phase space reconstruction is:

[0015] X(k) = [x1(k), x1(k-τ1),..., x1(k-(m1-2)τ1), x1(k-(m1-1)τ1),

[0016] x2(k), x2(k-τ2),..., x2(k-(m2-2)τ2, x2(k-(m2-1)τ2), ...

[0018] x d (k),x d (k-τ d ),...,x d (k-(m d -2)τ d ,x d (k-(m d -1)τ d ]

[0019] where k is the kth sample, x d (k) is the dth dimension feature of the kth sample;

[0020] S2.2, a mapping relationship of single-step prediction is established, and F is set as the mapping, then for the time series obtained by phase space reconstruction, the following formula is obtained:

[0021] x d (k+1) = F d (X(k))

[0022] where x d (k+1) is the dth dimension feature of the k+1th sample;

[0023] S2.3, the time series after phase space reconstruction is generated by using the formula of step S2.2, as the input sample of the prediction model, and the dimension of the input sample is D = m1+m2+...+m d ;

[0024] S2.4, the delay time τ j and the embedding dimension m j are determined by the mutual information method, when the mutual information between the time series after phase space reconstruction and the sample output sequence is maximum, the corresponding τ j and m j are taken as the delay time and embedding dimension used by the temperature field prediction model of the hypersonic wind tunnel, and the input and output sample data set of the temperature field prediction model of the hypersonic wind tunnel is obtained. The sample training data set and the sample test data set are composed.

[0025] Further, the specific implementation method of the Bayesian regression method for establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel in step S3 includes the following steps.

[0026] S3.1, training the sample data set in step S2 The Bayesian regression method assumes that the learning error is independent and subject to a zero-mean Gaussian distribution, and the calculation formula of the likelihood function p(Y|w, β) of the training data is:

[0027]

[0028] Where N is the number of data, w is the to-be-determined Bayesian regression model parameter, β is the variance parameter of the likelihood function, and p(Y|w, β) represents the occurrence probability of variable Y given the parameter w;

[0029] S3.2, set the prior distribution p(w|α) of the output weight of the Bayesian network as:

[0030]

[0031] Where α is the variance parameter of the output weight;

[0032] S3.3, set the posterior distribution of the to-be-determined Bayesian regression model parameter as a Gaussian distribution, and the mean and variance matrix thereof are respectively represented as m N and S N :

[0033] m N =βS N XY

[0034] S N =(αI+βXX T ) -1

[0035] Where I is an identity matrix;

[0036] S3.4, calculate the values of β and α by the evidence approximation method, and the calculation formula is:

[0037]

[0038]

[0039]

[0040] Where γ is the ratio of the eigenvalue λ i and α, λ i is the eigenvalue of βXX T , first initialize the parameters β and α, and then calculate the mean vector m Nand a variance vector S N , the calculated m N and S N Recalculate the value of β and α, and repeat the calculation until the algorithm converges, and finally obtain the Bayesian regression model of the outlet temperature of the hypersonic wind tunnel temperature field.

[0041] Further, the specific implementation method of the support vector regression method for establishing the outlet temperature prediction model of the hypersonic wind tunnel temperature field in step S3 includes the following steps:

[0042] S3.5, the sample training data set in step S2 Through the nonlinear mapping function Map each training sample X i The calculation formula of the function f(x) of the support vector regression method is:

[0043]

[0044] Where, w T is the weight vector of f(X), and b is the intercept term;

[0045] S3.6, ξ i is the first relaxation variable, is the second relaxation variable, and the objective function is:

[0046]

[0047]

[0048] Where, ||w|| is the L2 norm of w, C is the penalty coefficient, and ε is the insensitive loss function. The support vector machine model for outlet temperature prediction is obtained by the above method.

[0049] Further, the specific implementation method of the BP neural network method for establishing the outlet temperature prediction model of the hypersonic wind tunnel temperature field in step S3 is to train the sample training data set in step S2 Establish a neural network model, and the input data is the data X i reconstructed by the phase space, D represents the number of data features, the number of hidden layers is set to M, and the output data is the outlet temperature.

[0050] Further, the specific implementation method of step S4 includes the following steps: taking the sample test data set obtained in step S2 Test the three outlet temperature prediction models of the hypersonic wind tunnel temperature field established in step S3, output the outlet temperature prediction value, and compare the root mean square error. The formula of the root mean square error RMSE is:

[0051]

[0052] The electronic device comprises a memory and a processor, the memory stores a computer program, and the processor realizes the steps of the temperature field prediction method of the hypersonic wind tunnel when executing the computer program.

[0053] The computer readable storage medium stores a computer program, and the computer program is executed by a processor to realize the temperature field prediction method of the hypersonic wind tunnel.

[0054] The present application has the following beneficial effects:

[0055] The temperature field prediction method of the hypersonic wind tunnel aims to solve the problem that the temperature cannot be effectively and accurately controlled in the traditional wind tunnel temperature field control process.

[0056] The temperature field prediction method of the hypersonic wind tunnel has less delay characteristics of temperature effect and can accurately obtain the predicted value of the outlet temperature.

[0057] The temperature field prediction method of the hypersonic wind tunnel is based on support vector machine, Bayesian regression and BP neural network to predict temperature, and does not depend on human temperature adjustment experience, so the temperature adjustment efficiency is high.

[0058] The temperature field prediction method of the hypersonic wind tunnel is based on the combination idea, and the method can quickly and accurately predict the outlet temperature of the heater by combining the advantages of different algorithms, and then realize the wind tunnel temperature field control. According to the temperature field prediction method of the hypersonic wind tunnel based on the combination of multiple intelligent algorithms, the single model prediction performance is not good, and the generalization ability is not strong, and the combination is carried out, that is, the support vector machine, the Bayesian regression and the BP neural network are used to establish the prediction model of different outlet temperatures. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 This is a flowchart of the temperature field prediction method for hypersonic wind tunnels described in this invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0061] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0062] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 Detailed explanation is as follows: Specific implementation method one:

[0064] A method for predicting the temperature field of a hypersonic wind tunnel includes the following steps:

[0065] S1. Collect operating data of the hypersonic wind tunnel, including the wind tunnel heater outlet temperature γ. i The temperature of h heating modules of the wind tunnel heater [T] i×1 ,T i×2 ,...,T i×h ], wind tunnel heater inlet airflow pressure P i q, the inlet airflow temperature of the wind tunnel heater i Then set the temperature of h heating modules of the wind tunnel heater [T]. i×1 ,T i×2 ,...,T i×h ], wind tunnel heater inlet airflow pressure P i q, the inlet airflow temperature of the wind tunnel heater i For input sample x i Set the wind tunnel heater outlet temperature y i To produce the output samples, we obtain the original data sample set. i = 1, 2...n, where n is the number of original data samples and i is any one of n;

[0066] Further, the input sample x in step S1 is i = [T i×1 ,T i×2 ,...,T i×h ,P i ,q i ] is data form rewriting to the input sample x i , and finally obtains:

[0067] x i = [x i 1 ,x i 2 ,...,x i d ] T ∈R d

[0068] Wherein, d is the dimension of data in the input sample, d = h + 2, x i d is the d-dimensional feature of the i-th sample.

[0069] S2, the input sample in the original data sample set obtained in step S1 is reconstructed in phase space, and the input sample and the output sample used for model training are obtained, and the sample training data set and the sample test data set are composed;

[0070] Further, the specific implementation method of step S2 includes the following steps:

[0071] S2.1, the delay time and embedding dimension of the j-th dimension of the input sample x i are respectively τ j and m j , j = 1, 2,..., d, and the time series X(k) obtained by phase space reconstruction is:

[0072] X(k) = [x1(k), x1(k-τ1),...,x1(k-(m1-2)τ1),x1(k-(m1-1)τ1),x2(k),x2(k-τ2),...,x2(k-(m2-2)τ2,x2(k-(m2-1)τ2),...x d (k),x d (k-τ d ),...,x d (k-(m d -2)τ d ,x d (k-(m d -1)τ d )]

[0073] Wherein, k is the k-th sample, xd (k) is the dth dimensional feature of the kth sample;

[0074] S2.2, a mapping relationship of single-step prediction is established, and F is set as the mapping, so that for the time series obtained by phase space reconstruction, the following formula is obtained:

[0075] x d (k+1) = F d (x(k))

[0076] wherein, x d (k+1) is the dth dimensional feature of the k+1th sample;

[0077] S2.3, the time series after phase space reconstruction after mapping is generated by using the formula of step S2.2, as the input sample of the prediction model, and the dimension of the input sample is D = m1+m2+...+m d ;

[0078] S2.4, the delay time τ j and the embedding dimension m j are determined by the mutual information method, when the mutual information between the time series after phase space reconstruction and the sample output sequence is maximum, the corresponding τ j and m j are taken as the delay time and embedding dimension used by the temperature field prediction model of the hypersonic wind tunnel, and the input and output sample data set of the temperature field prediction model of the hypersonic wind tunnel is obtained as The sample training data set and the sample test data set are composed;

[0079] S3, the Bayesian regression method, the support vector regression method and the BP neural network method are used to establish the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel respectively, and the sample training data set obtained in step S2 is used to train the three outlet temperature prediction models of the temperature field of the hypersonic wind tunnel.

[0080] Further, the specific implementation method of the Bayesian regression method for establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel in step S3 includes the following steps:

[0081] S3.1, the sample training data set in step S2 is used to train the Bayesian regression model. The Bayesian regression method assumes that the learning error is independent and subject to zero-mean Gaussian distribution, so the calculation formula of the likelihood function p(Y|w,β) of the training data is:

[0082]

[0083] wherein, N is the number of data, w is the to-be-determined Bayesian regression model parameter, β is the variance parameter of the likelihood function, and p(Y|w,β) represents the occurrence probability of variable Y after the parameter w is given.

[0084] S3.2, set the prior distribution p(w|a) of the output weight value of the Bayesian network as:

[0085]

[0086] wherein a is a variance parameter of the output weight value;

[0087] S3.3, set the posterior distribution of the pending Bayesian regression model parameter as a Gaussian distribution, and the mean and variance matrix thereof are respectively represented as m N and S N :

[0088] m N = βS N XY

[0089] S N = (aI + βXX T ) -1

[0090] wherein I is a unit matrix;

[0091] S3.4, calculate the values of β and a by using the evidence approximation method, and the calculation formula is:

[0092]

[0093]

[0094]

[0095] wherein γ is the ratio of the eigenvalue λ i and a, λ i is the eigenvalue of βXX T , first, initialize the parameters β and a, then calculate the mean vector m N and the variance vector S N using the initialized β and a, and then recalculate the values of β and a using the calculated m N and S N , and repeat the calculation until the algorithm converges, and finally obtain the Bayesian regression model of the outlet temperature of the temperature field of the hypersonic wind tunnel.

[0096] Further, the specific implementation method of the support vector regression method for establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel comprises the following steps:

[0097] S3.5, map each training sample X to the training data set in step S2 through a nonlinear mapping function i ​, the calculation formula of the function f(x) of the support vector regression method is:

[0098]

[0099] wherein, w T is the weight vector of f(X), and b is the intercept term;

[0100] S3.6, ξ i is the first relaxation variable, is the second relaxation variable, and the objective function is obtained as:

[0101]

[0102]

[0103] wherein, ||w|| is the L2 norm of w, C is the penalty coefficient, and ε is the insensitive loss function, and the support vector machine model for predicting the outlet temperature is obtained through the above method.

[0104] Further, the specific implementation method of the BP neural network method for establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel in step S3 is to establish a neural network model for the sample training data set in step S2 , and the input data is the data X reconstructed in the phase space i , D represents the number of data characteristics, the number of hidden layers is set to M, the output data is the outlet temperature, and the size is adjusted according to the data amount.

[0105] S4, the sample test data set obtained in step S2 is used to test the three outlet temperature prediction models of the temperature field of the hypersonic wind tunnel established in step S3, and the optimal outlet temperature prediction model of the temperature field of the hypersonic wind tunnel is obtained.

[0106] Further, the specific implementation method of step S4 includes the following steps: the sample test data set obtained in step S2 is used to test the three outlet temperature prediction models of the temperature field of the hypersonic wind tunnel established in step S3, the outlet temperature prediction value is output, and the root mean square error is compared, and the formula of the root mean square error RMSE is:

[0107]

[0108] The temperature field prediction method of the hypersonic wind tunnel has certain nonlinear data processing capability, because temperature is a typical nonlinear time series, and the prediction and control of temperature belong to the processing problem of nonlinear time series, and it is necessary to obtain the corresponding relationship of the inlet temperature, the inlet pressure and the outlet temperature by means of a mathematical method. Before the model is established, the data needs to be reconstructed in phase space and divided into a sample training set and a sample test set, and then the BP neural network, the support vector machine and the Bayesian regression are used to model the sample training set data, the sample test set data is solved by the established model respectively, the predicted outlet temperature value is obtained, the root mean square errors of the outlet temperature predicted by each algorithm for the sample test set and the actual outlet temperature of the sample test set are compared, and finally the prediction model is determined. Specific embodiment two:

[0110] The electronic device comprises a memory and a processor, the memory stores a computer program, and the processor realizes the steps of the temperature field prediction method of the hypersonic wind tunnel in the specific embodiment one when executing the computer program.

[0111] The computer device of the application can be a device comprising a processor and a memory, such as a single-chip microcomputer comprising a central processing unit. The processor is used to realize the steps of the recommendation method of the recommendation data driven by the relationship based on the CREO software when executing the computer program stored in the memory.

[0112] The processor can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor.

[0113] The memory can mainly include a program storage area and a data storage area. The program storage area can store an operating system, application programs required by at least one function (such as a sound playing function, an image playing function, etc.), and the like. The data storage area can store data (such as audio data, a phone book, etc.) created according to the use of the mobile phone, and the like. In addition, the memory can include a high-speed random access memory, and can also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, at least one disk storage device, a flash memory device, or other volatile solid-state memory devices. Specific embodiment three

[0115] A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the temperature field prediction method of the hypersonic wind tunnel according to specific embodiment one.

[0116] The computer readable storage medium of the present application can be any form of storage medium readable by the processor of the computer device, including but not limited to non-volatile memory, volatile memory, ferroelectric memory, etc., and the computer readable storage medium has stored thereon a computer program. When the processor of the computer device reads and executes the computer program stored in the memory, the steps of the modeling method for modifying modeling data driven by relationships based on the CREO software can be realized. The computer program includes computer program code, which can be in the form of source code, object code, executable file or some intermediate form, etc. The computer readable medium can include any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the content included in the computer readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction, for example, in some jurisdictions, according to legislation and patent practice, the computer readable medium does not include electrical carrier signals and telecommunication signals.

[0117] It has to be noted that the terms "first", "second", and the like in connection with an entity or action refer to this entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises", "comprising", or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises... a" does not, without further constraints, exclude the presence of additional elements of the process, method, article, or apparatus.

[0118] While the application has been described with reference to specific implementations thereof, it should be understood that various modifications and substitutions can be made by those skilled in the art without departing from the scope of the present application. In particular, any one of the features of the present application disclosed above can be utilized independently of any other and the scope of the application should not be limited by the specific embodiments disclosed herein. Further, the description herein is intended to cover all alternatives, modifications, and equivalents of the specific embodiments disclosed herein. Thus, the application includes all alternatives, modifications and equivalents that can be made in light of the above description. Many changes and modifications can be made to the embodiments described above, by those having ordinary skill in the art. Such changes and modifications can be made without departing from the scope of the application and the above description should not be construed as limiting the application.

Claims

1. A method for predicting the temperature field of a hypersonic wind tunnel, characterized in that, Includes the following steps: S1. Collect operating data of the hypersonic wind tunnel, including the wind tunnel heater outlet temperature γ. i The temperature of h heating modules of the wind tunnel heater [T] i×1 ,T i×2 ,...,T i×h ], wind tunnel heater inlet airflow pressure P i q, the inlet airflow temperature of the wind tunnel heater i Then set the temperature of h heating modules of the wind tunnel heater [T]. i×1 ,T i×2 ,...,T i×h ], wind tunnel heater inlet airflow pressure P i q, the inlet airflow temperature of the wind tunnel heater i For input sample x i Set the wind tunnel heater outlet temperature y i To produce the output samples, we obtain the original data sample set. i = 1, 2...n, where n is the number of original data samples and i is any one of n; S2. Reconstruct the phase space of the input samples in the original data sample set obtained in step S1 to obtain the input samples and output samples for model training, forming the sample training dataset and the sample test dataset. S3. Establish exit temperature prediction models for the temperature field of hypersonic wind tunnels using Bayesian regression, support vector regression, and BP neural network methods respectively. Train the three exit temperature prediction models for the temperature field of hypersonic wind tunnels using the sample training dataset obtained in step S2. S4. Use the sample test dataset obtained in step S2 to test the exit temperature prediction models of the three hypersonic wind tunnels established in step S3, and obtain the optimal exit temperature prediction model of the hypersonic wind tunnel.

2. The method for predicting the temperature field of a hypersonic wind tunnel according to claim 1, characterized in that, In step S1, input sample x i =[T i×1 ,T i×2 ,...,T i×h ,P i ,q i ], for input sample x i After rewriting the data, we finally get: x i =[x i 1 ,x i 2 ,...,x i d ] T ∈R d Where d is the dimension of the data in the input sample, d = h + 2, x i d Let d be the d-th feature of the i-th sample.

3. The method for predicting the temperature field of a hypersonic wind tunnel according to claim 2, characterized in that, The specific implementation method of step S2 includes the following steps: S2.1, Set the input sample x i The j-th dimension delay time and the embedding dimension are τ, respectively. j and m j For j = 1, 2, ..., d, the time series X(k) obtained by phase space reconstruction is: X(k)=[x1(k),x1(k-τ1),...,x1(k-(m1-2)τ1),x1(k-(m1-1)τ1), x2(k),x2(k-τ2),...,x2(k-(m2-2)τ2,x2(k-(m2-1)τ2), ... x d (k),x d (k-t d ),...,x d (k-(m d -2)t d ,x d (k-(m d -1)t d )] Where k is the kth sample, x d (k) represents the d-th dimension feature of the k-th sample; S2.2 Establish the mapping relationship for single-step prediction. Let F be the mapping. Then, for the time series obtained by phase space reconstruction, we have the following formula: x d (k+1)=F d (X(k)) Where, x d (k+1) represents the d-th feature of the (k+1)-th sample; S2.

3. Using the formula in step S2.2, generate the reconstructed phase space time series as the input sample for the prediction model. The dimension of the input sample is D = m1 + m2 + ... + m d ; S2.4 Determine the delay time τ using the mutual information method. j and embedding dimension m j When the mutual information between the reconstructed phase space time series and the sample output series is maximized, the corresponding τ j and m j The delay time and embedding dimension used as the parameters for the temperature field prediction model of the hypersonic wind tunnel are used to obtain the input and output sample dataset for training the temperature field prediction model of the hypersonic wind tunnel. It consists of a sample training dataset and a sample test dataset.

4. The method for predicting the temperature field of a hypersonic wind tunnel according to claim 3, characterized in that, The specific implementation method of establishing the exit temperature prediction model of the temperature field of the hypersonic wind tunnel using the Bayesian regression method in step S3 includes the following steps: S3.1, Training the dataset from step S2 Bayesian regression assumes that the learning errors are independent and follow a zero-mean Gaussian distribution. Therefore, the likelihood function p(Y|w,β) of the training data is calculated as follows: Where N is the number of data points, w is the parameter of the undetermined Bayesian regression model, β is the variance parameter of the likelihood function, and p(Y|w,β) represents the probability of occurrence of variable Y given parameter w. S3.

2. Set the prior distribution p(w|α) of the Bayesian network output weights as follows: Where α is the variance parameter of the output weights; S3.

3. Set the posterior distribution of the parameters of the undetermined Bayesian regression model to a Gaussian distribution, with its mean and variance matrices represented as m. N and S N : m N =βS N XY S N =(αI+βXX T ) -1 Where I is the identity matrix; S3.4 Calculate the values ​​of β and α using the evidence approximation method. The calculation formula is as follows: Where γ is the eigenvalue λ i The sum of the ratios calculated with α, and λ i For βXX T The eigenvalues ​​are determined by first initializing the parameters β and α, and then using the initialized β and α to calculate the mean vector m. N S and variance vector S N Then use the calculated m N and S N The values ​​of β and α are recalculated, and this process is repeated until the algorithm converges, ultimately yielding a Bayesian regression model of the outlet temperature of the hypersonic wind tunnel's temperature field.

5. The method for predicting the temperature field of a hypersonic wind tunnel according to claim 3, characterized in that, The specific implementation method of establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel using the support vector regression method in step S3 includes the following steps: S3.5, Training the dataset from step S2 Through nonlinear mapping function Map each training sample X i The formula for calculating the function f(x) in the support vector regression method is: Among them, w T Let f(X) be the weight vector, and b be the intercept term; S3.6、ξ i As the first slack variable, Let be the second slack variable. Therefore, the objective function is: Where ||w|| is the L2 norm of w, C is the penalty coefficient, and ε is the insensitive loss function, the support vector machine model for predicting the outlet temperature is obtained through the above method.

6. The method for predicting the temperature field of a hypersonic wind tunnel according to claim 3, characterized in that, In step S3, the BP neural network method is used to establish an exit temperature prediction model for the temperature field of the hypersonic wind tunnel. The specific implementation method is to use the sample training dataset from step S2. Establish a neural network model, with input data being data X reconstructed from phase space. i D represents the number of data features, the number of hidden layers is set to M and adjusted according to the data volume, and the output data is the outlet temperature.

7. A method for predicting the temperature field of a hypersonic wind tunnel according to claim 4, 5, or 6, characterized in that, The specific implementation method of step S4 includes the following steps: The sample test dataset obtained in step S2... The exit temperature prediction models for the three hypersonic wind tunnels established in step S3 are tested, and the predicted exit temperature values ​​are output. The root mean square error (RMSE) is then compared. The formula for the RMSE is:

8. An electronic device, characterized in that, It includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the method for predicting the temperature field of a hypersonic wind tunnel as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for predicting the temperature field of a hypersonic wind tunnel as described in any one of claims 1-7.

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