Transfer learning: A new aerodynamic force identification network based on adaptive EMD and soft thresholding in hypersonic wind tunnel

Yi SUN, Shicho LI,*, Hongli GAO, Xioqing ZHANG, Jinzhou LV,Weixiong LIU, Yingchun WU

a School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China

b China Aerodynamics Research and Development Center, Mianyang 621000, China

KEYWORDS Aerodynamic intelligent identification model;Transfer learning;Force measurement system;Residual attention block with soft threshold;Dense block with adaptive EMD

Abstract The aerodynamic test in the pulse combustion wind tunnel is very important for the design, evaluation and optimization of aerodynamic characteristics of the hypersonic aircraft.The test accuracy even affects the success or failure of hypersonic aircraft development.In the aerodynamic test of pulse combustion wind tunnel, the aerodynamic signal is disturbed by the inertial force signal, which seriously affects the test accuracy of aerodynamic force.Aiming at the above problems, this paper innovatively proposes an aerodynamic intelligent identification method, that is the transfer learning network based on adaptive Empirical Modal Decomposition (EMD) and Soft Thresholding (TLN-AE&ST).Compared with the existing aerodynamic intelligent identification model based on deep learning technology, this study introduces the transfer learning idea into the aerodynamic intelligent identification model for the first time.The TLN-AE&ST effectively alleviates the problem of scarcity of training samples for intelligent models due to the high cost of wind tunnel tests,and provides a new idea for further implementation of deep learning technology in the field of wind tunnel aerodynamic testing.And this study designed residual attention block with soft threshold and dense block with adaptive EMD in TLN-AE&ST model.Residual attention block with soft threshold module can more effectively suppress the influence of instrument noise signal on model training effect.Dense block with adaptive EMD makes the deep learning model no longer a black box to a certain extent,and has certain physical significance.Finally,a series of wind tunnel tests were carried out in the φ = 2.4 m pulse combustion wind tunnel of China Aerodynamic Research and Development Center to verify the effectiveness of TLN-AE&ST.

1.Introduction

Hypersonic wind tunnel aerodynamic test is very important for the design and optimization of aerodynamic shape of a Hypersonic Aircraft(HA),and even determines the success or failure of HA development.At present, the pulse combustion wind tunnel is a mainstream hypersonic wind tunnel used to generate high-temperature and high-speed airflow to simulate airflow under hypersonic flight conditions.The high-speed airflow (greater than 5 times the speed of sound) produces a transient impact on the aircraft test model, which causes the transient vibration of the aircraft test model.However, due to the short effective test time of the pulse combustion wind tunnel (only 500 ms), the vibration of the aircraft test model is difficult to attenuate rapidly in such a short time.Thus,the inertial force is introduced into the output of the wind tunnel Force Measurement System(FMS),which causes the aerodynamic force to be overwhelmed by inertial forces.1–3At the same time, instrument noise is introduced to the output signals.The above phenomenon resulting in unable to directly distinguish the real dynamic aerodynamic forces regularity,which seriously affects the accuracy of aerodynamic test.The structure of FMS in this paper and the noise source of the signal are shown in the top part of Fig.1.

Moreover, as the aircraft test model gradually develops to the full-scale (the full-size model is 7 m-8 m in length and several tons in weight, compared with the scaled-size model less than 2 m in length and 1ton in weight), its stiffness further decreases,which will further reduce the identification accuracy of the FMS output signals.

Many researchers in the field of hypersonic wind tunnel testing have carried out many valuable studies on the interference of inertial force on aerodynamic force,which can be summarized into two aspects, namely develop new FMS and develop effective aerodynamic load identification technology.For developing new FMS, such as the accelerometer balance,4–6the stress-wave balance,7–9the compensation balance10–13and the pulse strain balance14–16have been proposed in recent years.Although the above balance can effectively reduce the proportion of inertial force component in FMS output signals, it cannot fundamentally eliminate the influence of inertial force on aerodynamic force.For the aerodynamic load identification technology, researchers try to extract the hidden aerodynamic force from the oscillation signal output by FMS.Therefore, time–frequency transform methods such as filtering and Fast Fourier Transform (FFT)are introduced into FMS.These methods can effectively eliminate fixed frequency and noise interference, but also lead to some loss of the original signal component17near the fixed frequency component is inevitably eliminated.And the identification accuracy of FFT depends on the effective test time of wind tunnel.Because the effective test time of pulse combustion wind tunnel is only 200 ms, the highest frequency resolution of FFT is only 5 Hz, which will affect the identification accuracy of FFT.Therefore, FFT is often used in conventional wind tunnels with test time greater than 1 s.Wavelet transform can achieve 1 Hz frequency resolution, but its identification accuracy depends on the choice of a wavelet basis function.In addition, wavelet transform has Heisenberg uncertainty defect, that is, frequency-domain and time-domain cannot achieve high resolution at the same time.Compared with the above methods, EMD is adaptive, but it is prone to modal aliasing, which will reduce the identification accuracy of aerodynamic force, as shown in the bottom right part of Fig.1.18

To solve the shortcomings, experts have tried to introduce Deep Learning (DL) techniques into the field of aerodynamic identification.19,20Deep learning, like dynamic calibration of FMS is to obtain the input-to-output model of FMS under dynamic force.Therefore, DL based aerodynamic intelligent identification techniques can eliminate the interference of inertial force on aerodynamic identification and has higher accuracy, as shown in the bottom left part of Fig.1.Compared to traditional aerodynamic identification techniques, aerodynamic intelligent identification techniques based on DL have the following advantages:

(1) This kind of method does not need manual participation in the aerodynamic identification process.Therefore,the influence of professional knowledge on identification effect is reduced.Moreover, the identification accuracy is not affected by the test time of wind tunnel and frequency resolution.

(2) The aerodynamic intelligent identification method based on deep learning consists of stacking multiple convolutional layers.Each channel of the convolution layer can be regarded as a trainable band-pass filter, which can suppress the specific noise signal in the FMS output signals adaptively.In contrast, traditional aerodynamic identification methods process the signal by manually selecting a filtering method.This mode has no universality for signals of different aircrafts and different FMSs,and needs to be adjusted according to the frequency of noise.However,the accuracy of the aerodynamic intelligent recognition model based on DL depends on the sample size used to train the model.The larger the sample size, the higher the identification accuracy.Moreover, the large-scale aircraft test model needs to be tested in the larger hypersonic wind tunnel.Highquality and sufficient data at the same Mach number are difficult to collect due to the excessively expensive single test cost.Therefore, when training the aerodynamic intelligent identification model, the scarcity of sample size is the key to restricting the identification accuracy of the aerodynamic intelligent identification model.This is also the direct reason for the low identification effect of intelligent methods based on Convolution Neural Network (CNN),20–23Recurrent Neural Network (RNN)24or Deep Belief Network (DBN).25

Fig.1 Noise sources and pre-processing of signal.The VMD’s calculation process and parameters in the lower right corner refer to the paper.18

Based on the above challenges, this paper proposes a new aerodynamic force identification method,transfer learning network with adaptive Empirical Mode Decomposition (EMD)and Soft Thresholding (TLN-AE&ST), from the engineering point of view.Firstly, the dynamic calibration test of FMS(i.e.applying the known excitation force and measuring the output of FMS) is carried out to obtain a large amount of training data, and then the pre-training of the model is completed.Subsequently, a small number of wind tunnel aerodynamic test samples were used to carry out the real aerodynamic test,and the feature distribution was transferred,so that the model can accurately identify the aerodynamic force.The contributions of this paper are summarized as follows:

(1) A new intelligent aerodynamic force identification model based on deep learning is proposed in this paper.The model is used to identify and filter out the inertial force signal and instrument noise signal from the FMS output signal in the wind tunnel test, so as to obtain‘‘pure”aerodynamic force.The model will greatly reduce the design difficulty of strain gauge balance with high precision, low cost and mature development, and improve the accuracy of pulse combustion wind tunnel aerodynamic force test.

(2) Compared with the existing aerodynamic intelligent identification model based on deep learning technology,this study introduces the transfer learning idea into the aerodynamic intelligent identification model for the first time.The TLN-AE&ST effectively alleviates the problem of scarcity of training samples for intelligent models due to the high cost of wind tunnel tests.

(3) To improve the identification accuracy of the aerodynamic force intelligent identification model, the residual attention block with soft threshold is introduced into the aerodynamic force intelligent identification model to filter the instrument noise signal, and a Dense block with adaptive EMD is innovatively proposed, which greatly filters the inertial force noise introduced by the aircraft test model.

The subsequent sections of this paper are structured as follows.Section 2,the principle of the related work is introduced.The details of the architecture proposed in this paper are described in Section 3.Section 4, the experimental set-up is described,and the performance of our architecture is analyzed.We close the paper with conclusions in Section 5.

2.Principle

2.1.Analysis of FMS output signals

Fig.2 Test stage of FMS and components of its output signals.

The upper left quarter of Fig.2 shows an aerodynamic test in the φ = 2.4 m impulse combustion wind tunnel with a Mach number of 6.5.The wind tunnel is a large hypersonic wind tunnel of the China Aerodynamics Research and Development Center (CARDC).The blue dotted line is the identified lift force;the red dotted line is the total pressure signal in the wind tunnel test section.Usually, a pulse-combustion wind tunnel aerodynamic test consists of three main stages: preparation stage, start-up stage, and effective experimental stage, and the signal components in the FMS output signal are different in different stages.Therefore, this section analyzes the signal components of the FMS output signals at different test stage,clarifies the characteristics of aerodynamic force signal and noise signal components, and provides theoretical support for gradually removing the noise signal component.Then,according to the characteristics of each noise signal component, the matching processing method is proposed.The components of the FMS output signals and their characteristics are as follows:

(1) Aerodynamic force.As shown in the upper left quarter of Fig.2.In the preparation stage, the wind tunnel has not yet started, and the aircraft test model will not be affected by aerodynamic force.Then the wind tunnel test enters the start-up stage, and the flow field around the aircraft test model is in the establishment process.The aircraft test model will be subjected to nonstationary aerodynamic forces at this stage.Finally, in the effective experimental stage of the wind tunnel, the flow field around the aircraft test model becomes stable,and the aircraft test model will be subjected to stable aerodynamic forces at this stage.

(2) Inertia force.In the wind tunnel start-up stage,the transient airflow is applied to the aircraft test model.The strong aerodynamic force causes the FMS to vibrate,and the effective test time of the pulse combustion wind tunnel is short,only 500 ms.The vibration of the aircraft test model is difficult to rapidly attenuate,which in turn introduces the inertial force signal into the output signals of FMS.Because of the high-amplitude periodic components of inertia force with different frequencies,the aerodynamic force signal is submerged by the inertial force signal, as shown in the right middle position of Fig.2.

(3) Quantization noise.The strain sensor outputs analog signals.ADC is needed to convert the aerodynamic force from the hypersonic wind tunnel test into a digital signal.The quantization bits of ADC are limited, so ADC can be regarded as a nonlinear mapping from continuous amplitude input to discrete amplitude output,which causes quantization noise.Quantization noise is a random error in output signals of FMS.Usually, the frequency of the quantization noise is high, but the amplitude of the quantization noise is small, as shown in the lower right quarter of Fig.2.

2.2.Mathematical description of FMS output signals

Based on the above analysis,it is not difficult to find that in the effective experimental stage of the pulse combustion wind tunnel aerodynamic test, the output signals of FMS mainly include the following three kinds: (A) the stationary aerodynamic force component with almost zero frequency; (B) periodic components of inertia force with different frequencies;(C)low amplitude and high frequency quantization noise component.The time-displacement of the balance signal could be modeled as follows:

3.Proposed method

The TLN-AE&ST method proposed in this study mainly includes the following two parts:

(1) To improve the identification accuracy of the aerodynamic force intelligent identification model, the residual attention block with soft threshold is introduced into the aerodynamic force intelligent identification model to filter the instrument noise signal, and a Dense block with adaptive EMD is innovatively proposed, which greatly filters the inertial force noise introduced by the largescale test model.

(2) In view of the scarcity of wind tunnel test samples, the idea of transfer learning is proposed to achieve the proliferation of wind tunnel test samples.Firstly, the FMS dynamic calibration test bench is used to simulate the loading of aerodynamic force on FMS in wind tunnel test,and a large number of training samples for aerodynamic intelligent recognition model are obtained.Subsequently, the feature similarity between the training samples generated by the test bench and the training samples generated by the wind tunnel test is evaluated,and the training samples generated by the test bench are updated to generate more training samples similar to the wind tunnel test.The above improvements can provide more abundant training sample sets for the aerodynamic intelligent identification model and improve the identification accuracy of the aerodynamic intelligent identification model.

3.1.Residual attention block with soft threshold

The residual attention block with soft threshold in this paper is a variant of the residual block.The module is mainly used to filter out the instrument noise component in the FMS output signal,and avoid the effect of instrument noise on the learning and identification of inertial force characteristics by the intelligent model.

Fig.3(a)is the residual attention block,and Fig.3(b)is the residual attention block with soft threshold.Different from the residual block, the residual attention block with soft threshold has an attention mechanism module to calculate the soft threshold for each channel.In the attention mechanism module, the absolute value of feature map is pooled globally and reduced to 1-dimensional vector.In the attention mechanism module,the absolute value of the feature map is reduced to onedimensional vector by a Global Average Pooling (GAP) operation.Subsequently,one-dimensional vector is processed into scaling parameter through two fully connected layers.The two Fully Connected (FC) layers with batch normalization and leaky ReLU activation function accelerate network training by reducing internal covariate shifts.Finally,the output of the fully connected layer is scaled to the range of (0,1) using the sigmoid activation function, and the process can be expressed as:

Fig.3 Structure of residual attention block and residual attention block with a soft threshold.

where zcand αcare the feature and scaling parameter of the c th channel, respectively.The threshold γ of the soft threshold function is the average value of the scaling parameter αcmultiplied by the data of the c th channel.The purpose of this operation is to determine an adaptive dynamic threshold.Thus, the threshold γ of soft threshold function can be obtained as follows:

where i, j and c are the width index, height index and channel index of the feature graph x,respectively;γcis the threshold of the c th channel of the feature graph x.It can be seen from Eq.(3), the threshold γcmust be positive and cannot reach the maximum value of the data in the c th channel.At this time,the threshold γccan be maintained in a reasonable range to prevent the output features from being completely zero.

Multiple residual blocks with soft threshold are stacked so that the model can learn features through nonlinear changes.In this case, soft thresholding is used as a shrinkage function to eliminate noise-related features.The thresholds are adaptively updated in the model architecture and do not need to be set manually by researchers with specialized knowledge.

3.2.Dense block with adaptive EMD

EMD and mutual information entropy can effectively identify the trend characteristics of aerodynamics and suppress lowfrequency noise caused by inertial force, which can effectively improve the identification accuracy of the model.The structure of dense block with adaptive EMD is shown in Fig.4.In dense block with adaptive EMD, the dense connection between layers is processed by adaptive EMD.After adaptive EMD processing, the trend feature of aerodynamic force F（t) is obvious, but the resonance of inertia force Fi（t) is suppressed.Instead, the data in the dense block is directly connected.The dense block not only introduced the resonance caused by inertial force Fi（t) into the data processed by the convolutional neural network, it will also make the model difficult to train,because the data contains more high-frequency noise.

Fig.4 Structure of dense block with adaptive EMD.

The input–output relationship of convolutional neural network is shown in the following equation:

where l is the layer index of convolutional neural network;Hl（?)is a non-linear transformation of the l th layer in the network;tland tl-1are the output of the l th layer and the l-1 th layer,respectively.The dense block improves the flow of information between layers.Because, it introduces a direct connection from any layer to all subsequent layers.That is, the l th layer has the ability to integrate the feature maps of all preceding layers:

Fig.5 Process of TLN-AE&ST.

where ［t0,t1,...,tl-1] is the integrate of the feature maps generated from the 1st layer to the l-1 th layer.The dense block with adaptive EMD optimizes the connection mode of feature maps, and the structural are shown in Fig.5.The connection method is improved from direct connection to pre-processing the feature maps from 1st layer to the l-1 th layer by adaptive EMD, as follows:

where HEMD（?) is the adaptive EMD.It is not difficult to find that based on the above structure, the convolution layer can correct the output of adaptive EMD layer by layer.This improvement makes the model’s output close to the real aerodynamic force while retaining the rich high-frequency impact.

3.3.Procedure of TLN-AE&ST

Fig.5 shows the process of TLN-AE&ST.The main steps of TLN-AE&ST are as follows: high-frequency noise suppression,feature distribution alignment,aerodynamic force correction, and aerodynamic source identification.

Step 1.Suppression of high-frequency noise

The main purpose of Step 1 is to reduce the high-frequency noise resulting from measuring aerodynamic force.Therefore,the feature extraction part of the model is composed of stacked residual attention blocks with soft threshold.Also, this step uses examples from the source and target domains to train the model.

Methods such as autoregressive moving average inverse model, Kalman filter, recursive least square, L2 norm have been used by researchers to suppress high-frequency noise in the signal by the aerodynamic force measurement.26It is not difficult to find that the essence of these methods is to parse the signal into real aerodynamic force through a transfer matrix H, as follows:

However, the matrix H is usually an ill-conditioned matrix due to the increase in the dimension of solving the inverse problem, that is, the matrix H is a non-singular matrix with a large condition number.Therefore,the matrix H is extremely sensitive to the noise in the output F（t) of the FMS, and it is difficult to output real aerodynamic force.

To solve the above problem, this paper uses a residual attention block with a soft threshold for characterization learning of the data.This block is a deep learning structure with multiple convolutional layers, which can adaptively filter instrument noise.Further, the method of stacking residual blocks can form a more abstract high-level representation of low-level features to completely describe the aerodynamic features.

Step 2.Transfer of features

The main purpose of Step 2 is to make network learning source domain and target domain signal common features.The feature similarity between the training samples generated by the test bench and the training samples generated by the wind tunnel test is evaluated, and the training samples generated by the test bench are updated to generate more training samples similar to the wind tunnel test.The output signal of hypersonic FMS is called target domain signal.The signal of FMS test bench is called source domain signal,which also conforms to the above feature.The similarity of trends between the two signals makes the introduction of transfer learning possible.Using these signals for training can make the network quickly understand the trend features of aerodynamic force.

The output of an input signal in the neural network should be consistent with its target value,and the consistency evaluation function is called the objective function.In this paper,the cross-entropy loss function is used to evaluate the consistency between the source domain signal and the target domain signal.To make the cross-entropy loss function focus on the difference of signal trend,rather than the difference of amplitude,the softmax activation function is used in the output of Step 1 to convert the aerodynamic trend into a probability distribution with sum of 1.The process is as follows:

where m is the size of the mini-batch.

Step 3.Correction of aerodynamic force

The main purpose of Step 3 is to suppress the inertial force Fi（t)in the signal.After processing Step 1 and Step 2,the highfrequency noise caused by sensor noise of the aerodynamic force measurement have been suppressed,but the inertial force Fi（t) still causes interference to the real aerodynamic force.Therefore, Dense block with adaptive EMD is adopted to reduce the influence of inertial force Fi（t) on the identification accuracy of aerodynamic loads.

Through EMD reconstruction, the network can quickly identify the trend of aerodynamic components in the signal.However, EMD has no training parameters, for a fixed input,the reconstructed signal is the same.Therefore, the impact component of the aerodynamic force is suppressed as highfrequency noise by the EMD.To address the above situation,this paper uses convolutional neural networks to dynamically compensate the immersion impact component.The Step 3 can improve the accuracy of pneumatic identification, and the process is as follows:

Step 4.Learning of source domain features

The main purpose of Step 4 is to make the network learn the trend features of aerodynamic force.MMD, a nonparametric method, is adopted in this paper to measure the difference between the network output signals and the real aerodynamic signals in the source domain.The principle of MMD: (A) the aerodynamic trend features in the source and target domains are mapped to the Regenerated Kernel Hilbert Space (RKHS) through a high-dimensional mapping function f:X →S.(B) MMD is the supremum of the expected difference between two domain features in RHKS, as follows:

Step 5.Optimization object

In the above part,the function of each module of the TLNAE&ST and its corresponding loss function are introduced respectively.The optimization objective of the model is established by comprehensively considering each loss function, and the TLN-AE&ST is trained by random gradient descent method.Lcrsand LMMDare the difference of domain feature and the difference of source domain trend feature extraction,respectively.The optimization objective of TLN-AE&ST can be expressed as:

4.Experiment

4.1.Experimental setup

Fig.6 Three-dimensional model of suspension force measuring system.

In the field of hypersonic wind tunnel aerodynamic test, the aircraft test model is developing towards large-scale and heavy-duty (the large-size aircraft test model is 7 m-8 m in length and several tons in weight, compared with the scaledsize aircraft test model less than 2 min length and 1 ton in weight).When the aerodynamic test of hypersonic wind tunnel is carried out on the large-scale and heavy-duty aircraft test model,it is required that the FMS has high stiffness,small disturbance to the flow field, and can carry out the airframe/propulsion integration test at the same time.The traditional force measurement technology is difficult to meet the above requirements at the same time.In view of the above problems,our research group proposed a new FMS, namely the suspension FMS,as shown in Fig.6.The device has been successfully applied in φ = 2.4 m pulse combustion wind tunnel of China Aerodynamics Research and Development Center(CARDC).27Therefore,the suspension FMS is selected to verify the effectiveness of TLN-AE&ST.The working principle of the suspension force measuring system is shown in Fig.7.During the hypersonic wind tunnel test,the aerodynamic force acting on the aircraft model is transmitted to the force measurement sensors through the force measurement pull rods, and the voltage signal is output to realize the aerodynamic force test.

The specific process of verifying the effectiveness of the aerodynamic intelligent identification model (TLN-AE&ST)is as follows:

(1) The sample data used for TLN-AE&ST model training is very important, which will directly affect the training process and results.To obtain high-quality training sample data, this study designed a force loading device that can apply a step force to an aircraft test model to simulate the aerodynamic forces experienced by the aircraft test model in hypersonic wind tunnel tests, as shown in the left upper part of Fig.8.The step load is achieved by suddenly releasing weights of known mass.The loading point is fixed on the surface of the aircraft test model.The step force transfer path from the loading point to the weight is shown in the middle left part of Fig.8.The principle of generating step force is as follows: first place a known weight on the weight plate,then send a control command to make the electromagnetic sucker power off and lose suction, thus generating step force.In the test,the force sensor measures the step force signal, and the suspension FMS outputs the response signal.The multi-component dynamic response signals were collected by LMS SCADAS Mobile SCM 202 acquisition instrument.In this study, 126 sets of training samples were generated based on the dynamic calibration test bench, i.e.source domain samples.

(2) The suspension FMS was tested in the φ= 2.4 m pulse combustion wind tunnel of CARDC,and its output signals were used as the target domain sample,as shown in Fig.9.This study obtained a total of 12 sets of training sample sets(real wind tunnel test signals),namely target domain samples.The φ=2.4 m pulse combustion wind tunnel is mainly used to carry out the performance test research of large-scale scramjet and the performance test research of integrated hypersonic vehicle with power.The test contents and parameters of wind tunnel test are shown in Table 1.The test conditions are Ma=5.5,6.5,7.0.The aircraft test model angle of attack and sideslip are both 0°.The suspension FMS used in the wind tunnel test in this paper is shown in the right middle part in Fig.8.In the figure,Fx,Fy,Fz,Mx,Myand Mzrepresent the output signals of six degrees of freedom (normal,axial, yaw, pitch, roll and nod) of the force measuring system.

Fig.7 Principle diagram of suspension force measuring system.

(3) 126 source domain samples and 12 target domain samples were used to train and verify the accuracy and effectiveness of the TLN-AE&ST model.

In this section, various traditional aerodynamic identification methods are compared with TLN-AE&ST.The methods involved in this section are shown in Table 219,22,28–30.

Frequency domain model: Considering the complexity of wind tunnel FMS signal, the time–frequency aerodynamic force identification model is used to reduce noise signal and process the wind tunnel FMS signal of the pulse wave of the aircraft test model, and output reliable aerodynamic force results.In this paper, three mainstream aerodynamic force identification models are used as comparison,which are Wavelet Transform (WT),19EMD28and Extremum field Mean Mode Decomposition (EMMD).29

Intelligence model:Since 2017,the dynamic self-calibration model based on deep learning technology has been applied to the FMS of wind tunnel (especially hypersonic high-enthalpy wind tunnel).The intelligent model obtains the ideal aerodynamic force by dynamically correcting the force measurement results of inertial vibration interference.In this paper, CNN and RNN are selected as the comparison models.22,30

4.2.Evaluation indicators and results

The model is evaluated by Mean Absolute Error (MAE),Mean Square Error (MSE) and Root Mean Square Error(RMSE).MAE reflects the average absolute error between real and predicted values.MSE reflects the error between real and predicted values expectation,that is,the stability of the model.RMSE reflects the square root of the mean of the squared differences between true and predicted values, and is more sensitive to outliers than MSE.The formulas for the different evaluation indicators are as follows:

where y and ^y are the true and predicted value, respectively.n is the number of data points.t is the number of channels output by the FMS.The real aerodynamic force in the target domain is obtained by filtering mean method.The TLNAE&ST is compared with models in Table 2 by the above evaluation indexes.The results are shown in Fig.10, and the detailed data are shown in Table 3.The following conclusions can be drawn from the analysis:

Fig.8 Structure and output signals of rod-type suspension force measuring device and its scaled-down force measurement device.

(1) Compared with the mainstream frequency domain models and intelligent models in the field of FMS, TLNAE&ST achieves the best results.

(2) Among the frequency domain models, the MEA results of the three models are close, but the MSE results of EMD and EEMD are significantly smaller than WT.This is because the WT can not effectively suppress the pulse signal caused by inertial force in large scale balance.On the contrary, EMD and EEMD models have stronger anti-interference ability.

(3) Interestingly, in the scenario of aerodynamic feature transfer, the identification accuracy of the intelligent models is lower than that of the traditional frequency domain models.The parameters of CNN and RNN are fixed after training.Therefore, they only have good identification effect for a specific FMS (that is, both the training and the test set come from the source domain), and lack sufficient robustness.TLN-AE&ST can learn the common features of source and target domain based on Eq.(14), and still maintain good aerodynamic identification effect in the target area.

Table 1 Test contents and parameters of φ = 2.4 m pulse combustion wind tunnel.

Fig.11 Performance of each model under different sample sizes.

Table 2 Task settings for each model.

Fig.10 Performance of each model.

Table 3 Detailed performance of each model.

4.3.Model performance analysis

4.3.1.Sample size analysis

The results of intelligent models are dependent on the number of samples due to their excessive trainable parameters.In fields such as face recognition, natural language processing, and fault diagnosis,intelligent models are established based on sufficient data.However, in the FMS of hypersonic wind tunnel,due to the expensive experimental cost, there are not enough samples to train the model.Therefore, it is necessary to studythe performance of intelligent models in the scarcity of samples.In this section, four datasets with different specifications are selected as the source domain data, namely 10,25,50 and 100.The MSE was selected to evaluate the performance of models.and the results are shown in Fig.11, and the detailed data are shown in Table 4.

Table 4 Detailed performance of each model under different sample sizes.

The frequency domain methods are not affected by the number of samples,all of which can maintain good discrimination accuracy.When the number of samples in the source domain is less than 25, the TLN-AE&ST is underfitted and its effect is slightly worse than EEMD.When the source domain samples are more than 50, the TLN-AE&ST is fully trained,and its identification effect is the best among all models.On the contrary, the identification accuracy of intelligent models such as CNN and RNN decreases significantly when the source domain samples are scarce (less than 50).When the source domain samples are 100, these models can only maintain the similar identification accuracy of WT.It can be seen that such intelligent models have a certain distance in the large-scale application of FMS.

Fig.12 Performance of TLN-AE&ST under different sample sizes.

For each dataset, the circle on the left is the MSE for each experiment, and the violin plot on the right is the logarithmic normal fitting to the data from 50 replicate experiments.

To further analyze the stability of TLN-AE&ST, 50 replicate experiments were performed with different sample sizes,and the results are shown in Fig.12.It is not difficult to find that when the sample size is 10, the stability of the model is poor, and the average and the standard deviation of the 50 experiments are 0.108 and 0.017, respectively.When the number of samples is 50 and 100,the identification accuracy of the model is slightly improved, but its stability is significantly improved, and its average is increased from 0.085 to 0.082.

4.3.2.Model complexity analysis

Real-time aerodynamic force identification is a challenge for most intelligent models at present.This is because, the FMS is a typical industrial environment with sensitive and private output signals that cannot be processed using online highperformance servers.Real-time identification of aerodynamic force on the limited computing resources of mobile devices is also one of the problems solved in this study.In order to evaluate the usability of intelligent models in FMS, it is necessary to validate the model complexity in addition to the aerodynamic identification accuracy.The evaluation indexes of model complexity include model parameters and the multiplyaccumulate operations(MADDs)time.Fig.13 shows the comparison between TLN-AE&ST and the current mainstream intelligent models.The radius of the circle represents the number of model parameters.

The experimental platform is Jetson TX2.To prevent the interference of other tasks on the platform,20 repeated experiments were carried out and the minimum value was taken.As shown in the figure, the RNN model has achieved the fastest operation time of 265 ms, which fully meets the real-time requirements of aerodynamic identification on the mobile platform.The parameter number of TLN-AE&ST is 1.3 M,which has a significant reduction compared with CNN and RNN.The number of model parameters also explains that TLNAE&ST can be fully trained when there are only 50 samples in the source domain, while CNN and RNN are underfitting.

4.3.3.Ablation experiment

(1) TLN-AE&ST w/ or w/o cross entropy function

Fig.13 Complexity of each model.

Fig.14 Effect comparison of models in source domain and target domain.

To clearly determine the role of the cross-entropy function in STEP-2, TLN-AE&ST and TLN-AE&ST without crossentropy function are plotted in Fig.14 for both source and target domain effects.In the source domain, both methods achieve ideal results with MES of 0.06.However,in the target domain, TLN-AE&ST without cross-entropy function cannot effectively identify aerodynamic signal, and its performance declines sharply.Because TLN-AE&ST without crossentropy function is unable to learn the aerodynamic signal features during the training process.TLN-AE&ST, due to its cross-entropy function, can learn the common features of the aerodynamic force in the source and the target domain, so it maintains a good identification effect.

(2) TLN-AE&ST w/ or w/o Residual attention block

To verify the importance of the attention mechanism module on the accuracy of aerodynamic force identification, this study uses the experimental data of the φ=2.4 m pulse combustion wind tunnel to analyze the influence of TLN-AE&ST and TLN-AE&ST without residual attention block on the accuracy of aerodynamic identification.The test conditions are Ma=6.5.The aircraft test model angle of attack and sideslip are both 0°.The identification results are shown in Fig.15.The blue line in Fig.15 is the output signals of TLN-AE&ST without Residual attention block.It is not difficult to find that the output signals contain a large amount of burr noise,which shows that the network cannot deal with medium–high frequency noise well.The output signals of TLN-AE&ST are smoother,and the MAE and MSE are much higher than those of TLN-AE&ST without residual attention block.In conclusion,residual attention block with soft threshold is an effective method to suppress medium–high frequency noise.And TLNAE&ST can combine the advantages of convolutional neural network and soft threshold to adaptively reduce the medium–high frequency noise component in the signal.

Fig.15 Output signals of TLN-AE&ST w/ or w/o residual attention block.

Fig.16 Output signals of TLN-AE&ST w/ or w/o dense block.

(3) TLN-AE&ST w/ or w/o without dense block

From a certain point of view, the implementation process of dense block can be regarded as the intelligent filtering process of inertial force, which can be more clearly understood from the following spectrum comparison.From Fig.16,FFT is performed on the output signal of FMS in φ=2.4 m pulse combustion wind tunnel,the signal processed by the TLN-AE&ST model and TLN-AE&ST without dense block.It can be clearly seen that the main frequencies of the inertial force in the wind tunnel test are completely filtered out.The upper right corner of Fig.16 is the spectrogram of the output signals of TLN-AE&ST without dense block.As shown by the yellow line, the spectrogram has the selfoscillation frequency near 100 Hz, which can be inferred that the signals are disturbed by the inertial force caused by the intrinsic frequency of the FMS.The lower right corner of Fig.16 is the spectrogram of the output signals of TLNAE&ST.As shown by the red dotted line, the spectrogram has the self-oscillation frequency near 20 Hz.It can be seen that TLN-AE&ST can effectively eliminate the inertial force interference caused by the intrinsic frequency.

5.Conclusions and future work

At present, the research on the intelligence of FMS based on deep learning is relatively new, and the related methods and technologies are still in the development stage.In this paper,the transfer learning is introduced into the hypersonic FMS for the first time, which greatly reduces the requirements of sample quantity and quality for intelligent model.Moreover,the residual attention block with soft threshold and dense block with adaptive EMD are proposed, which can not only accurately identify the aerodynamic signal, but also effectively suppress other interference signals.TLN-AE&ST has application prospect,which provides key technology and data support for accurate evaluation of hypersonic vehicle aerodynamic characteristics with high enthalpy.

Although aerodynamic identification results of cross-model size are promising, some limitations of this work should be pointed out.First, in this study, the FMS involved in the test is single.The aerodynamic identification network with good robustness is not considered (by using the dataset of the existing full-scale FMS)and used to guide the design of new FMS.Second,time–frequency transform method is widely studied in the field of FMS.By incorporating the latest research results,enhancing the identification capabilities of TLN-AE&ST is a task that should be pursued in the future.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was co-supported by the National Natural Science Foundation of China (52105562), the Fundamental Research Funds for the Central Universities, China (XJ2021KJZK037),the Fundamental Research Funds for the Central Universities,China (2682022CX058).