CN115979568A - Method for predicting temperature field of hypersonic wind tunnel, electronic device and storage medium - Google Patents
Method for predicting temperature field of hypersonic wind tunnel, electronic device and storage medium Download PDFInfo
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Abstract
A method for predicting a temperature field of a hypersonic wind tunnel, electronic equipment and a storage medium belong to the technical field of wind tunnel measurement and control. The method aims to solve the problem of poor control effect of the hypersonic wind tunnel temperature field. The method comprises the steps of collecting working condition data of the hypersonic wind tunnel, carrying out phase space reconstruction on input samples in an original data sample set to obtain input samples and output samples for model training, forming a sample training data set and a sample testing data set, respectively establishing outlet temperature prediction models of temperature fields of the hypersonic wind tunnel by using a Bayesian regression method, a support vector regression method and a BP neural network method, training the outlet temperature prediction models of the three established temperature fields of the hypersonic wind tunnel by using the sample training data set, carrying out model testing on the outlet temperature prediction models of the three established temperature fields of the hypersonic wind tunnel by using the sample testing data set, and obtaining an optimal outlet temperature prediction model of the temperature field of the hypersonic wind tunnel. The invention has accurate prediction.
Description
Technical Field
The invention belongs to the technical field of wind tunnel measurement and control, and particularly relates to a method for predicting a temperature field of a hypersonic wind tunnel, electronic equipment and a storage medium.
Background
The operating mode of the hypersonic wind tunnel is a down-blowing injection type, a free jet test is adopted, the operating Mach number of the hypersonic wind tunnel is not lower than 4, and the operating total pressure range is generally from several bars to dozens of bars. In order to achieve the purpose that the running air flow of the hypersonic wind tunnel does not condense or reproduces the actual total flying temperature, a heater is generally arranged in front of a stable section of the hypersonic wind tunnel to heat the air flow in the wind tunnel, so that the control of a temperature field of a wind tunnel test section is realized. The hypersonic wind tunnel has the advantages that the required maximum heating capacity of the heater ranges from hundreds K to thousands K according to different operation conditions, and the heater comprises an electric heater and a combustion heater. The electric heater is composed of a plurality of electric heating modules, and an electric heating pipe is used as a heating element, so that the electric heater is widely applied to design and construction of the hypersonic wind tunnel due to the advantages of good stability, high safety and pure airflow. For the hypersonic wind tunnel provided with the electric heater, in the temperature adjusting process, the heating temperature of the electric heating module needs to be adjusted according to different inlet temperatures and inlet pressures so as to achieve effective control of the outlet temperature, and further control of a hypersonic wind tunnel test section temperature field is achieved. The factors influencing the control of the temperature field of the hypersonic wind tunnel test section mainly comprise: the delay characteristic of the temperature effect, the coupling influence of the pressure and the temperature of the wind tunnel, the short-term performance of the wind tunnel test process and the influence of the environmental temperature, the existing temperature field control of the hypersonic wind tunnel mainly depends on manual experience, the temperature field control effect is poor, and the test requirements are difficult to completely meet.
Disclosure of Invention
The invention aims to solve the problem of poor control effect of a temperature field of a hypersonic wind tunnel, and further provides a method for predicting the temperature field of the hypersonic wind tunnel, electronic equipment and a storage medium.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a method for predicting a temperature field of a hypersonic wind tunnel comprises the following steps:
s1, collecting working condition data of the hypersonic wind tunnel, including outlet temperature y of a wind tunnel heater i Temperature [ T ] of h heating modules of wind tunnel heater i×1 ,T i×2 ,...,T i×h ]Inlet airflow pressure P of wind tunnel heater i And the inlet airflow temperature q of the wind tunnel heater i Then setting the temperature [ T ] of h heating modules of the wind tunnel heater i×1 ,T i×2 ,...,T i×h ]Wind tunnel heater inlet airflow pressure P i Inlet airflow temperature q of wind tunnel heater i For input sample x i Setting the outlet temperature y of the wind tunnel heater i For output samples, a set of raw data samples is obtained
N, n being the number of raw data samples, i being any one of n;
s2, performing phase space reconstruction on the input samples in the original data sample set obtained in the step S1 to obtain input samples and output samples for model training, and forming a sample training data set and a sample testing data set;
s3, respectively establishing outlet temperature prediction models of the temperature fields of the hypersonic wind tunnels by using a Bayes regression method, a support vector regression method and a BP neural network method, and training the outlet temperature prediction models of the temperature fields of the three hypersonic wind tunnels by using the sample training data set obtained in the step S2;
and S4, performing model testing on the outlet temperature prediction models of the three hypersonic wind tunnel temperature fields established in the step S3 by using the sample testing data set obtained in the step S2 to obtain an optimal outlet temperature prediction model of the hypersonic wind tunnel temperature field.
Further, in step S1, a sample x is input i ＝[T i×1 ,T i×2 ,...,T i×h ,P i ,q i ]For input sample x i Data form rewriting is carried out, and finally:
wherein d is the dimension of the data in the input sample, d = h +2,x i d Is the d-dimension feature of the ith sample.
Further, the specific implementation method of step S2 includes the following steps:
s2.1, setting an input sample x i Is tau for the j-th delay time and the embedding dimension j And m j J =1,2.., d, the time series X (k) obtained by phase space reconstruction is:
X(k)＝[x 1 (k),x 1 (k-τ 1 ),...,x 1 (k-(m 1 -2)τ 1 ),x 1 (k-(m 1 -1)τ 1 ),
x 2 (k),x 2 (k-τ 2 ),...,x 2 (k-(m 2 -2)τ 2 ,x 2 (k-(m 2 -1)τ 2 ),
...
x d (k),x d (k-τ d ),...,x d (k-(m d -2)τ d ,x d (k-(m d -1)τ d )]
where k is the kth sample, x d (k) D-dimension characteristic of the kth sample;
s2.2, establishing a mapping relation of single-step prediction, setting F as mapping, and obtaining a time sequence by phase space reconstruction according to the following formula:
x d (k+1)＝F d (X(k))
wherein x is d (k + 1) is the d-dimensional feature of the k +1 th sample;
s2.3, utilizing the disclosure of step S2.2Generating a time sequence after phase space reconstruction by using the formula as an input sample of the prediction model, wherein the dimension of the input sample is D = m 1 +m 2 +...+m d ；
S2.4, determining the delay time tau by a mutual information method j And embedding dimension m j When the mutual information between the time sequence after phase space reconstruction and the sample output sequence is maximum, corresponding tau j And m j Obtaining an input and output sample data set of the temperature field prediction model training of the hypersonic wind tunnel as the delay time and the embedding dimension adopted by the temperature field prediction model of the hypersonic wind tunnel
And forming a sample training data set and a sample testing data set.
Further, the specific implementation method for establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel by the Bayesian regression method in the step S3 comprises the following steps:
s3.1, training data set for the sample in the step S2
The bayesian regression method assumes that the learning errors are independent and obey zero-mean gaussian distribution, and the calculation formula of the likelihood function p (Y | w, β) of the training data is:
n is the data quantity, w is a parameter of a undetermined Bayesian regression model, beta is a variance parameter of a likelihood function, and p (Y | w, beta) represents the occurrence probability of a variable Y after the parameter w is given;
s3.2, setting prior distribution p (w | alpha) of output weights of the Bayesian network as follows:
wherein, alpha is a variance parameter of the output weight;
s3.3, setting the posterior distribution of the undetermined Bayes regression model parameters as Gaussian distribution, and respectively representing the mean value and the variance matrix as m N And S N ：
m N ＝βS N XY
S N ＝(αI+βXX T ) -1
Wherein, I is a unit matrix;
s3.4, calculating the values of beta and alpha by an evidence approximation method, wherein the calculation formula is as follows:
wherein gamma is a characteristic value lambda i Sum of the ratios calculated from and, lambda i Is beta XX T Firstly initializing parameters beta and alpha, and then calculating a mean vector m by using the initialized beta and alpha N Sum variance vector S N Reuse the calculated m N And S N And (4) recalculating the values of beta and alpha, repeating the calculation until the algorithm converges, and finally obtaining the Bayes regression model of the outlet temperature of the temperature field of the hypersonic wind tunnel.
Further, the specific implementation method for establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel by the support vector regression method in the step S3 comprises the following steps:
s3.5, training data set for the sample in the step S2
Based on a non-linear mapping function->
Mapping each training sample X i The calculation formula of the function f (x) supporting the vector regression method is as follows:
wherein w T Is the weight vector of f (X), b is the intercept term;
S3.6、ξ i as a first variable of the relaxation, the first one,
for the second relaxation variable, the objective function is obtained as:
the support vector machine model for predicting the outlet temperature is obtained by the method, wherein | | | w | | is the L2 norm of w, C is a penalty coefficient, and epsilon is an insensitive loss function.
Further, the specific implementation method of establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel by the BP neural network method in the step S3 is to train the data set of the sample in the step S2
Establishing a neural network model, inputting data X through phase space reconstruction i D represents the characteristic quantity of the data, the number of the hidden layers is set to be M, the hidden layers are adjusted according to the data quantity, and the output data is the outlet temperature.
Further, the specific implementation method of step S4 includes the following steps: testing the sample data set obtained in the step S2
Performing model test on the outlet temperature prediction models of the three hypersonic wind tunnel temperature fields established in the step S3, outputting outlet temperature prediction values, and comparing root mean square errors, wherein the formula of the root mean square error RMSE is as follows:
the electronic equipment comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the method for predicting the temperature field of the hypersonic wind tunnel when executing the computer program.
A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements the method for predicting a temperature field of a hypersonic wind tunnel.
The invention has the beneficial effects that:
the invention relates to a method for predicting a temperature field of a hypersonic wind tunnel, which aims to solve the problem that the control of the temperature cannot be effectively and accurately realized in the control process of the traditional wind tunnel temperature field.
The prediction method of the temperature field of the hypersonic wind tunnel has smaller delay characteristic under the temperature effect, and can accurately obtain the predicted value of the outlet temperature.
The method for predicting the temperature field of the hypersonic wind tunnel predicts the temperature based on the support vector machine, the Bayes regression and the BP neural network, does not depend on the temperature regulation experience of people, and has high temperature regulation efficiency.
The method for predicting the temperature field of the hypersonic wind tunnel is based on a combination idea, and can be used for rapidly and accurately predicting the outlet temperature of the heater by combining the advantages of different algorithms so as to realize the control of the temperature field of the wind tunnel. According to the super wind tunnel temperature field prediction method based on the combination of multiple intelligent algorithms, aiming at the problems of poor prediction performance, poor generalization capability and the like of a single model, combination is carried out, namely, a support vector machine, bayesian regression and a Bp neural network are adopted to respectively establish prediction models with different outlet temperatures, the three established models are used for obtaining the outlet temperature through a test data set and calculating the root mean square error of the three models, the model with the minimum root mean square error is selected as a final model for predicting the outlet temperature to form a combined prediction model, and the combined prediction method can improve the control precision of the outlet temperature of a heater, becomes one of wind tunnel means in practical application, and has better application prospect.
Drawings
FIG. 1 is a flow chart of a method for predicting a temperature field of a hypersonic wind tunnel according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and the detailed description. It is to be understood that the embodiments described herein are illustrative of the present invention and are not to be construed as limiting thereof, i.e., the described embodiments are merely a subset of the embodiments of the invention and are not all embodiments. While the components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations, the present invention is capable of other embodiments.
Thus, the following detailed description of specific embodiments of the present invention presented in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the detailed description of the invention without inventive step, are within the scope of protection of the invention.
For a further understanding of the contents, features and effects of the present invention, the following embodiments are exemplified and explained in detail with reference to the accompanying drawings 1:
the first embodiment is as follows:
a method for predicting a temperature field of a hypersonic wind tunnel comprises the following steps:
s1, collecting working condition data of the hypersonic wind tunnel, including outlet temperature y of a wind tunnel heater i Temperature [ T ] of h heating modules of wind tunnel heater i×1 ,T i×2 ,...,T i×h ]Wind tunnel heater inlet airflow pressure P i Inlet airflow temperature q of wind tunnel heater i Then setting the temperature [ T ] of h heating modules of the wind tunnel heater i×1 ,T i×2 ,...,T i×h ]Inlet airflow pressure P of wind tunnel heater i And the inlet airflow temperature q of the wind tunnel heater i For input sample x i Setting the outlet temperature y of the wind tunnel heater i For output samples, a set of raw data samples is obtained
N, n being the number of raw data samples, i being any one of n;
further, in step S1, sample x is input i ＝[T i×1 ,T i×2 ,...,T i×h ,P i ,q i ]For input sample x i Data format rewriting is carried out, and finally:
x i ＝[x i 1 ,x i 2 ,...,x i d ] T ∈R d
wherein d is the dimension of the data in the input sample, d = h +2,x i d Is the d-dimension feature of the ith sample.
S2, performing phase space reconstruction on the input samples in the original data sample set obtained in the step S1 to obtain input samples and output samples for model training, and forming a sample training data set and a sample testing data set;
further, the specific implementation method of step S2 includes the following steps:
s2.1, setting an input sample x i Is tau for the j-th delay time and the embedding dimension j And m j J =1,2.., d, the time series X (k) obtained by phase space reconstruction is:
X(k)＝[x 1 (k),x 1 (k-τ 1 ),...,x 1 (k-(m 1 -2)τ 1 ),x 1 (k-(m 1 -1)τ 1 ),x 2 (k),x 2 (k-τ 2 ),...,x 2 (k-(m 2 -2)τ 2 ,x 2 (k-(m 2 -1)τ 2 ),...x d (k),x d (k-τ d ),...,x d (k-(m d -2)τ d ,x d (k-(m d -1)τ d )]
where k is the kth sample, x d (k) D-dimension characteristic of the kth sample;
s2.2, establishing a mapping relation of single-step prediction, setting F as mapping, and obtaining a time sequence by phase space reconstruction according to the following formula:
x d (k+1)＝F d (X(k))
wherein x is d (k + 1) is the d-dimensional feature of the k +1 th sample;
s2.3, generating a time sequence after the phase space reconstruction after mapping by using the formula in the step S2.2, and using the time sequence as an input sample of the prediction model, wherein the dimension of the input sample is D = m 1 +m 2 +...+m d ；
S2.4, determining the delay time tau by a mutual information method j And embedding dimension m j When the mutual information between the time sequence after the phase space reconstruction and the sample output sequence is maximum, corresponding tau j And m j Obtaining an input and output sample data set of the temperature field prediction model training of the hypersonic wind tunnel as the delay time and the embedding dimension adopted by the temperature field prediction model of the hypersonic wind tunnel
Forming a sample training data set and a sample testing data set;
s3, respectively establishing outlet temperature prediction models of the temperature fields of the hypersonic wind tunnels by using a Bayes regression method, a support vector regression method and a BP neural network method, and training the outlet temperature prediction models of the temperature fields of the three hypersonic wind tunnels by using the sample training data set obtained in the step S2;
further, the specific implementation method for establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel by the Bayesian regression method in the step S3 comprises the following steps:
s3.1, training a data set for the sample in the step S2
The bayesian regression method assumes that the learning errors are independent and obey zero-mean gaussian distribution, and the calculation formula of the likelihood function p (Y | w, β) of the training data is:
n is the data quantity, w is a parameter of a undetermined Bayesian regression model, beta is a variance parameter of a likelihood function, and p (Y | w, beta) represents the occurrence probability of a variable Y after the parameter w is given;
s3.2, setting prior distribution p (w | alpha) of output weights of the Bayesian network as follows:
wherein, alpha is a variance parameter of the output weight;
s3.3, setting the posterior distribution of the undetermined Bayes regression model parameters as Gaussian distribution, and respectively representing the mean value and the variance matrix as m N And S N ：
m N ＝βS N XY
S N ＝(αI+βXX T ) -1
Wherein I is an identity matrix;
s3.4, calculating the values of beta and alpha by an evidence approximation method, wherein the calculation formula is as follows:
wherein gamma is a characteristic value lambda i Sum of the ratios calculated from and, lambda i Is beta XX T Firstly initializing parameters beta and alpha, and then calculating a mean vector m by using the initialized beta and alpha N Sum variance vector S N Reuse the calculated m N And S N And (4) recalculating the values of beta and alpha, repeating the calculation until the algorithm converges, and finally obtaining the Bayes regression model of the outlet temperature of the temperature field of the hypersonic wind tunnel.
Further, the specific implementation method for establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel by the support vector regression method comprises the following steps:
s3.5, training data set for the sample in the step S2
Method for determining the number of functional blocks in a non-linear mapping function>
Mapping each training sample X i The calculation formula of the function f (x) supporting the vector regression method is as follows:
wherein, w T Is the weight vector of f (X), b is the intercept term;
S3.6、ξ i as a first variable of the relaxation, the first one,
for the second relaxation variable, the objective function is obtained as: />
The support vector machine model for predicting the outlet temperature is obtained by the method, wherein | | | w | | is the L2 norm of w, C is a penalty coefficient, and epsilon is an insensitive loss function.
Further, the specific implementation method of establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel by the BP neural network method in the step S3 is to train the data set of the sample in the step S2
Establishing a neural network model, inputting data X through phase space reconstruction i D represents the characteristic quantity of the data, the number of hidden layers is set to be M, the hidden layers are adjusted according to the size of the data quantity, and the output data is the outlet temperature;
s4, performing model testing on the outlet temperature prediction models of the temperature fields of the three hypersonic wind tunnels established in the step S3 by using the sample test data set obtained in the step S2 to obtain an optimal outlet temperature prediction model of the temperature field of the hypersonic wind tunnel;
further, the specific implementation method of step S4 includes the following steps: testing the sample data set obtained in the step S2
The temperature of the three hypersonic wind tunnels established in the step S3Carrying out model test on an outlet temperature prediction model of the field, outputting an outlet temperature prediction value, and comparing a Root Mean Square Error (RMSE), wherein the RMSE has a formula as follows:
according to the method for predicting the temperature field of the hypersonic wind tunnel, due to the fact that the temperature is a typical nonlinear time sequence, prediction and control of the temperature belong to the problem of processing of the nonlinear time sequence, the corresponding relation of the inlet temperature, the inlet pressure and the outlet temperature is obtained by means of a mathematical method, and the method is required to have certain nonlinear data processing capacity. Before the model is established, phase space reconstruction processing needs to be carried out on data, a sample training set and a sample testing set are divided, then modeling is carried out on the data of the sample training set by using a BP neural network, a support vector machine and Bayesian regression, the data of the sample testing set are solved through the established model respectively, a predicted outlet temperature value is obtained, root mean square errors of the outlet temperature predicted by each algorithm on the sample testing set and the actual outlet temperature of the sample testing set are compared, and therefore a final prediction model is determined.
The second embodiment is as follows:
the electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method for predicting the temperature field of the hypersonic wind tunnel according to a specific embodiment when executing the computer program.
The computer device of the present invention may be a device including a processor, a memory, and the like, for example, a single chip microcomputer including a central processing unit and the like. And the processor is used for implementing the steps of the recommendation method for modifying the relationship-driven recommendation data based on the CREO software when executing the computer program stored in the memory.
The Processor may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic, discrete hardware components, etc. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required by at least one function (such as a sound playing function, an image playing function, etc.), and the like; the storage data area may store data (such as audio data, a phonebook, etc.) created according to the use of the cellular phone, and the like. In addition, the memory may include high speed random access memory, and may also include 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 memory Card (Flash Card), at least one magnetic disk storage device, a Flash memory device, or other volatile solid state storage device.
The third concrete implementation mode:
a computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements a method for predicting a temperature field of a hypersonic wind tunnel according to one of the embodiments.
The computer readable storage medium of the present invention may be any form of storage medium read by a processor of a computer device, including but not limited to non-volatile memory, ferroelectric memory, etc., on which a computer program is stored, which when read and executed by the processor of the computer device, may implement the steps of the above-described CREO software-based modeling method that can modify relationship-driven modeling data. The computer program comprises computer program code which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, usb disk, removable hard disk, magnetic disk, optical disk, computer Memory, read-Only Memory (ROM), random Access Memory (RAM), electrical carrier wave signals, telecommunications signals, software distribution medium, and the like. It should be noted that the computer readable medium may contain content that is subject to appropriate increase or decrease as required by legislation and patent practice in jurisdictions, for example, in some jurisdictions, computer readable media does not include electrical carrier signals and telecommunications signals as is required by legislation and patent practice.
It is noted that relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another 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 may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising a … …" does not exclude the presence of another identical element in a process, method, article, or apparatus that comprises the element.
While the application has been described above with reference to specific embodiments, various modifications may be made and equivalents may be substituted for elements thereof without departing from the scope of the application. In particular, the various features of the embodiments disclosed herein may be used in any combination that is not inconsistent with the structure, and the failure to exhaustively describe such combinations in this specification is merely for brevity and resource conservation. Therefore, it is intended that the application not be limited to the particular embodiments disclosed, but that the application will include all embodiments falling within the scope of the appended claims.
Claims (9)
1. A method for predicting a temperature field of a hypersonic wind tunnel is characterized by comprising the following steps:
s1, collecting working condition data of the hypersonic wind tunnel, including outlet temperature y of a wind tunnel heater i Temperature [ T ] of h heating modules of wind tunnel heater i×1 ,T i×2 ,...,T i×h ]Wind tunnel heater inlet airflow pressure P i And the inlet airflow temperature q of the wind tunnel heater i Then setting the temperature [ T ] of h heating modules of the wind tunnel heater i×1 ,T i×2 ,...,T i×h ]Wind tunnel heater inlet airflow pressure P i Inlet airflow temperature q of wind tunnel heater i For input samples x i Setting the outlet temperature y of the wind tunnel heater i For output samples, a set of raw data samples is obtained
N, n being the number of raw data samples, i being any one of n;
s2, performing phase space reconstruction on the input samples in the original data sample set obtained in the step S1 to obtain input samples and output samples for model training, and forming a sample training data set and a sample testing data set;
s3, respectively establishing outlet temperature prediction models of the temperature fields of the hypersonic wind tunnels by using a Bayes regression method, a support vector regression method and a BP neural network method, and training the outlet temperature prediction models of the temperature fields of the three hypersonic wind tunnels established by using the sample training data set obtained in the step S2;
and S4, performing model testing on the outlet temperature prediction models of the three hypersonic wind tunnel temperature fields established in the step S3 by using the sample testing data set obtained in the step S2 to obtain an optimal outlet temperature prediction model of the hypersonic wind tunnel temperature field.
2. The method for predicting the temperature field of the hypersonic wind tunnel according to claim 1, wherein a sample x is input in the step S1 i ＝[T i×1 ,T i×2 ,...,T i×h ,P i ,q i ]For input sample x i Data format rewriting is carried out, and finally:
x i ＝[x i 1 ,x i 2 ,...,x i d ] T ∈R d
wherein d is the dimension of the data in the input sample, d = h +2,x i d Is the d-dimension feature of the i-th sample.
3. The method for predicting the temperature field of the hypersonic wind tunnel according to claim 2, wherein the concrete implementation method of the step S2 comprises the following steps:
s2.1, setting an input sample x i Is τ and the embedding dimension j And m j J =1,2.., d, the time series X (k) obtained by phase space reconstruction is:
X(k)＝[x 1 (k),x 1 (k-τ 1 ),...,x 1 (k-(m 1 -2)τ 1 ),x 1 (k-(m 1 -1)τ 1 ),
x 2 (k),x 2 (k-τ 2 ),...,x 2 (k-(m 2 -2)τ 2 ,x 2 (k-(m 2 -1)τ 2 ),
...
x d (k),x d (k-τ d ),...,x d (k-(m d -2)τ d ,x d (k-(m d -1)τ d )]
where k is the kth sample, x d (k) D-dimension characteristic of the kth sample;
s2.2, establishing a mapping relation of single-step prediction, setting F as mapping, and obtaining a time sequence by phase space reconstruction according to the following formula:
x d (k+1)＝F d (X(k))
wherein x is d (k + 1) is the d-dimensional feature of the k +1 th sample;
s2.3, generating phase space reconstruction by using the formula in the step S2.2As input samples of the prediction model, the dimension of the input samples is D = m 1 +m 2 +...+m d ；
S2.4, determining the delay time tau by a mutual information method j And embedding dimension m j When the mutual information between the time sequence after phase space reconstruction and the sample output sequence is maximum, corresponding tau j And m j Obtaining an input and output sample data set of the temperature field prediction model training of the hypersonic wind tunnel as the delay time and the embedding dimension adopted by the temperature field prediction model of the hypersonic wind tunnel
And forming a sample training data set and a sample testing data set. />
4. The method for predicting the temperature field of the hypersonic wind tunnel according to claim 3, wherein the specific implementation method for establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel by the Bayesian regression method in the step S3 comprises the following steps:
s3.1, training a data set for the sample in the step S2
The bayesian regression method assumes that the learning errors are independent and obey zero-mean gaussian distribution, and the calculation formula of the likelihood function p (Y | w, β) of the training data is:
n is the data quantity, w is a parameter of the undetermined Bayesian regression model, beta is a variance parameter of a likelihood function, and p (Y | w, beta) represents the occurrence probability of a variable Y after the parameter w is given;
s3.2, setting prior distribution p (w | alpha) of output weights of the Bayesian network as follows:
wherein, alpha is a variance parameter of the output weight;
s3.3, setting the posterior distribution of the undetermined Bayes regression model parameters as Gaussian distribution, and respectively representing the mean value and the variance matrix as m N And S N ：
m N ＝βS N XY
S N ＝(αI+βXX T ) -1
Wherein I is an identity matrix;
s3.4, calculating the values of beta and alpha by an evidence approximation method, wherein the calculation formula is as follows:
wherein gamma is a characteristic value lambda i Sum of the ratios calculated from and, lambda i Is beta XX T Firstly initializing parameters beta and alpha, and then calculating a mean vector m by using the initialized beta and alpha N Sum variance vector S N And then using the calculated m N And S N And (4) recalculating the values of beta and alpha, repeating the calculation until the algorithm converges, and finally obtaining the Bayes regression model of the outlet temperature of the temperature field of the hypersonic wind tunnel.
5. The method for predicting the temperature field of the hypersonic wind tunnel according to claim 3, wherein the method for specifically realizing the model for predicting the outlet temperature of the temperature field of the hypersonic wind tunnel by the support vector regression method in the step S3 comprises the following steps:
s3.5, training data set for the sample in the step S2
Based on a non-linear mapping function->
Mapping each training sample X i The calculation formula of the function f (x) supporting the vector regression method is as follows:
wherein w T Is the weight vector of f (X), b is the intercept term;
S3.6、ξ i as a first variable of the relaxation, the first one,
is the second slack variable, thus, the objective function is obtained as:
the support vector machine model of the outlet temperature prediction is obtained by the method, wherein | | | w | | is the L2 norm of w, C is a penalty coefficient, and epsilon is an insensitive loss function.
6. The method for predicting the temperature field of the hypersonic wind tunnel according to claim 3, wherein the method for establishing the outlet temperature prediction model of the temperature field of the hypersonic wind tunnel by the BP neural network method in the step S3 is specifically realized by training a data set of a sample in the step S2
Establishing a neural network model, and inputting data X through phase space reconstruction i D represents the characteristic quantity of the data, the number of the hidden layers is set to be M, the hidden layers are adjusted according to the data quantity, and the output data is the outlet temperature.
7. The method for predicting the temperature field of the hypersonic wind tunnel according to the claim 4, the claim 5 or the claim 6, wherein the step S4 is realized by the following steps: testing the sample data set obtained in the step S2
Performing model test on the outlet temperature prediction models of the three hypersonic wind tunnel temperature fields established in the step S3, outputting outlet temperature prediction values, and comparing root mean square errors, wherein the formula of the root mean square error RMSE is as follows:
8. electronic device, characterized in that it comprises a memory and a processor, the memory storing a computer program, the processor implementing the steps of a method for predicting a temperature field of a hypersonic wind tunnel according to any of claims 1 to 7 when executing said computer program.
9. Computer readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out a method for predicting a temperature field of a hypersonic wind tunnel according to any one of claims 1 to 7.
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| CN116305588B (en) * | 2023-05-17 | 2023-08-11 | 中国航空工业集团公司沈阳空气动力研究所 | Wind tunnel test data anomaly detection method, electronic equipment and storage medium |
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