Real-time monitoring method for rotor-static rub-impact of high-speed turbine pump based on RSAF model

Abstract

The invention provides a real-time monitoring method for rotor-static rub-impact of a high-speed turbine pump based on an RSAF model, which comprises the following steps: firstly, determining characteristics participating in rub-impact monitoring, adding two characteristics of rotating speed and rotating speed variation to reflect a working condition state, introducing the influence of the total vibration level under the current assembly condition by using a displacement peak-to-peak value and a fundamental frequency value, and calculating the overall vibration level of the rotor-static rub-impact of the rotor-static rub-impact of the rotor-static rub-impact; therefore, data of different working conditions and states can be analyzed in a unified manner. An RSAF model is established based on the historical normal data of the turbine pump and is used as the representation of the normal state; and monitoring a displacement signal of the turbine pump in real time, extracting rub-impact fault characteristics of the displacement signal, calculating the similarity between the characteristics at each moment and the RSAF model, obtaining an estimated value at the moment, and judging whether the turbine pump deviates from a normal state or not according to the estimated value. According to the method, data of different rotating speed conditions of the turbine pump can be processed in a unified mode, and false alarms and missed alarms are effectively avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of turbine pump health monitoring, and in particular to a real-time monitoring method for rotor-static friction of a high-speed turbine pump based on a RSAF model. Background Art

[0002] The turbopump is one of the important and complex components in a rocket engine. It undertakes the critical task of transporting fuel and oxidizer to the combustion chamber. During the operation of the turbopump, the rotor may deviate from its ideal trajectory due to the influence of various factors such as unbalanced forces, thermal deformation, and fluid dynamic effects. In severe cases, this deviation movement will cause contact and rubbing between the rotor and the stationary parts of the turbopump (such as the pump casing, sealing rings, etc.). The occurrence of rubbing will not only reduce the efficiency of the turbopump, but also trigger a series of serious consequences, leading to mission failure and even casualties. Therefore, monitoring the rubbing fault of the turbopump and diagnosing its severity are crucial for subsequent health management.

[0003] At present, rocket engine health monitoring mainly uses a red-line shutdown health monitoring method based on key parameters, which mainly monitors rubbing faults by monitoring vibration signals. However, due to the complex working conditions and many actual fault characteristics involved in the actual operation of the turbopump, it is difficult to select the threshold value of the existing method, and the judgment logic is also relatively complex, resulting in limited fault coverage. In addition, due to improper threshold setting, in actual use, the existing method often has false alarms or missed alarms. For example, the vibration level of a certain rocket engine itself is relatively large, which makes it easier for the fault characteristics obtained by monitoring the vibration signal to exceed the threshold, but no rubbing fault occurs at this time, resulting in a false alarm. For rocket engines with small vibration levels, it is possible that although the fault characteristics have not exceeded the set threshold, rubbing has actually occurred. Summary of the Invention

[0004] To solve the problems existing in the prior art, the present invention proposes a real-time monitoring method for high-speed turbine pump rotor-static rub impact based on the RSAF model. Based on historical data and the rich harmonic component characteristics of turbine pump vibration and displacement data, a baseline that can unify the normal state of various working conditions is established. Based on the normal state, the rub impact is judged and its degree is quantified, thereby reducing the probability of false alarm or missed alarm.

[0005] The technical solution of the present invention is:

[0006] The method for real-time monitoring of high-speed turbine pump rotation-static friction based on the RSAF model comprises the following steps:

[0007] Step 1: Determine the eigenvector involved in rubbing monitoring as

[0008] [nt Δnt DF ch,1 …DF ch,k …DF ch,K P] 1×n

[0009] Among them, nt is the speed of the turbo pump, Δnt is the speed change, P is the vector composed of 1st, 2nd and 3rd order positive and negative precessions, DF ch,k is the feature vector of the kth detection channel, k = 1, 2, ..., K:

[0010] DF ch,k =[ppv k fb k fl 1,k … fl i,k … fl I,k f c,k f 2,k f 3,k f 4,k ]

[0011] PPV in the above characteristics k is the peak-to-peak amplitude of the kth detection channel, fb k is the amplitude corresponding to the fundamental frequency of the kth detection channel, fl 1,k …fl i,k …fl I,k is the amplitude corresponding to the I frequency point in the low-frequency spectrum of the kth detection channel; f c,k is the subharmonic amplitude corresponding to the kth detection channel, f 2,k 、f 3,k 、f 4,k is the amplitude corresponding to the 2nd, 3rd and 4th frequency in the kth detection channel;

[0012] Step 2: Obtain historical test data from the turbopump under normal working conditions, extract feature vectors from the test data under normal working conditions, divide the obtained feature vectors into a learning set and a test set, and train the RSAF model with the learning set as a representation of the normal state; input the test set into the trained RSAF model to obtain feature vector estimates, and calculate the deviation between the feature vector estimates and the true value of the feature vector in the test set. If all components of the deviation are less than a set threshold, the final RSAF model is obtained; otherwise, the RSAF model is trained again using the learning set;

[0013] Step 3: Monitor the detection signal of the turbo pump in real time. According to the definition of step 1, calculate the eigenvector of the measured detection signal. Input the obtained eigenvector into the RSAF model obtained in step 2 to obtain an estimated value of the eigenvector of the measured detection signal. Calculate the deviation between the estimated value of the eigenvector of the measured detection signal and the calculated value of the eigenvector of the measured detection signal. If the deviation exceeds the set threshold for three consecutive calculation cycles, it is considered that the working state of the turbo pump is abnormal.

[0014] Furthermore, in step 3, the threshold is set to 10% of the component corresponding to the estimated value of the characteristic vector of the measured detection signal.

[0015] Furthermore, in step 3, the mean of the component corresponding to the deviation between the estimated value of the test set eigenvector and the true value of the eigenvector in step 2 + 3σ is taken as the threshold, where σ is the variance of the deviation between the estimated value of the test set eigenvector and the true value of the eigenvector.

[0016] Furthermore, the method further includes step 4: classifying the fault according to the type of the component in the deviation that exceeds the threshold.

[0017] Furthermore, in step 4, if only the components corresponding to the fundamental frequency and the double frequency in the deviation exceed the threshold, it is considered that an imbalance or misalignment fault has occurred; if the components corresponding to other characteristics exceed the threshold, it is considered that a rubbing fault has occurred.

[0018] Furthermore, the method further includes step 5: if it is determined that a rubbing fault has occurred, the sum of the squares of the components in the deviation is used as an indicator to measure the severity of the rubbing.

[0019] Furthermore, in step 3, consider the case where a sensor abnormality occurs during the real-time monitoring of the turbo pump detection signal:

[0020] (1) If the speed sensor fails, the judgment is made based on the amplitude characteristics corresponding to one frequency point in the low-frequency spectrum. When calculating the estimated value, the contribution of the speed, speed change value, frequency multiplication characteristics, subharmonic characteristics, and precession characteristics of each channel is set to 0 to shield the influence of invalid characteristics. When calculating the deviation, the deviation of the speed, speed change value, frequency multiplication characteristics, subharmonic characteristics, and precession characteristics of each channel is set to 0.

[0021] (2) If a detection channel fails, the contribution of the corresponding feature of the detection channel is set to 0 when calculating the estimated value; and the deviation of the corresponding feature of the detection channel is set to 0 when calculating the deviation.

[0022] Furthermore, in step 2, the modeling process includes the following steps:

[0023] Step 2.1: Determine the steady-state segment based on the historical test data of the turbo pump under normal working conditions; in each steady-state segment, obtain the characteristic vectors at the maximum and minimum moments of each characteristic component as the coarse representative state set {SE};

[0024] Step 2.2: In the coarse typical state set {SE}, if the similarity of the feature vectors at two moments is higher than the set threshold, the feature vector at one moment is removed, and the subset {SE1} is retained;

[0025] Step 2.3: Based on the historical test data of the turbopump under normal working conditions, the variable operating condition section is determined; the feature vectors of all variable operating condition sections form a typical state set {TE}; in the typical state set {TE}, if the similarity of the feature vectors of two moments exceeds the set threshold, the feature vector of one moment is eliminated, and the subset {TE1} is retained;

[0026] Step 2.4: Combine {SE1} and {TE1} to form the RSAF model.

[0027] Furthermore, in step 2, the test set is input into the trained RSAF model, and the process of obtaining the feature vector estimation value is as follows:

[0028] For a certain feature vector in the test set, the similarity between the feature vector and all feature vectors in the RSAF model is calculated. The weight of each feature vector in the RSAF model is determined according to the similarity. Then, the weighted sum of each feature vector in the RSAF model is performed to obtain the estimated value of the feature vector.

[0029] Beneficial effects

[0030] The real-time monitoring method for high-speed turbine pump rotor-static rub impact based on the RSAF model proposed in the present invention can simultaneously consider multiple rub impact fault characteristics, generate comprehensive evaluation indicators, effectively identify rub impact faults, and avoid missed alarms.

[0031] When the model is established, by traversing historical operating conditions, different normal reference values ​​can be given to different operating conditions, rather than a single, absolute threshold. This can effectively accommodate different operating conditions and reduce missed alarms in low operating conditions due to excessively large thresholds or false alarms in high operating conditions due to excessively small thresholds.

[0032] The variable operating conditions are taken into consideration when the model is established, and the threshold of the variable operating conditions can be given, so that the steady state and the variable operating condition sections can be monitored simultaneously.

[0033] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which:

[0035] Figure 1 : Time domain waveform of the horizontal vibration displacement amplitude of the turbine pump under normal conditions;

[0036] Figure 2 : Turbine pump rotor axis trajectory diagram under normal conditions;

[0037] Figure 3 : Time domain waveform of the horizontal vibration displacement amplitude of the turbine pump under rotor-static friction fault;

[0038] Figure 4 : The trajectory of the turbine pump rotor axis under the rotation-static friction;

[0039] Figure 5 : Comparison chart of the estimated eigenvector value of a normal signal and the true value result;

[0040] Figure 6 : The total deviation between the estimated value and the true value of the eigenvector of the normal signal;

[0041] Figure 7 : Comparison chart of the estimated value and true value of the eigenvector of the fault signal;

[0042] Figure 8 : A graph showing the total deviation between the estimated value and the true value of the fault signal. DETAILED DESCRIPTION

[0043] The present invention uses historical detection data of the turbopump under normal working conditions as a sample data set, and constructs a RSAF model containing specific feature vectors based on the rich harmonic component characteristics of the turbopump detection data (speed, vibration, and displacement data), thereby obtaining a RSAF model that characterizes the normal state of the turbopump. During real-time monitoring, the real-time characteristics are estimated. If the estimated result is inconsistent with the actual result, it is considered that a state change or an abnormality has occurred.

[0044] The specific steps include:

[0045] Step 1: Feature Selection:

[0046] The amplitude signal is a direct representation of the turbine pump vibration, and the features in the amplitude signal are extracted as the basis for rubbing fault analysis. Based on the dynamic mechanism, the amplitude representation of rubbing fault mainly includes the corresponding amplitudes of the fundamental frequency, subharmonics (such as 0.5 times the frequency), and harmonics (2, 3, 4). However, vibration is closely related to working conditions, assembly and other conditions, and there are large differences between different units and different speed working conditions. Therefore, in this method, two features, speed and speed change, are added to reflect the working condition. The peak-to-peak amplitude and the corresponding amplitude of the fundamental frequency are used to introduce the influence of the overall vibration level under the current assembly conditions, so that the data of different working conditions and states can be unified for analysis.

[0047] Furthermore, our experiments revealed that severe rub-impact can easily generate large radial forces, causing random energy peaks in the low-frequency range. Therefore, we added amplitude features corresponding to the low-frequency spectrum to the features for rub-impact monitoring along with the other rub-impact features. Furthermore, the presence of reverse precession is also a prominent feature of rub-impact, so we added 1st, 2nd, and 3rd order forward and reverse precession as detection features.

[0048] The final features involved in rubbing monitoring include

[0049] [nt Δnt DF ch,1 …DF ch,k …DF ch,K P] 1×n

[0050] Among them, nt is the speed of the turbo pump, Δnt is the speed change, P is the vector composed of 1st, 2nd and 3rd order positive and negative precessions, DF ch,k is the feature vector of the kth detection channel, k = 1, 2, ..., K:

[0051] DF ch,k =[ppv k fb k fl 1，k … fl i,k … fl I,k f c,k f 2,k f 3,k f 4,k ]

[0052] PPV in the above characteristics k is the peak-to-peak amplitude of the kth detection channel, fb k is the amplitude corresponding to the fundamental frequency of the kth detection channel, fl 1，k …fl i,k …fl I,k is the amplitude corresponding to the I frequency point in the low-frequency spectrum of the kth detection channel; f c,k is the subharmonic amplitude corresponding to the kth detection channel, f2,k 、f 3,k 、f 4,k is the amplitude corresponding to 2 times the frequency, 3 times the frequency, and 4 times the frequency in the kth detection channel.

[0053] By setting the above features, when comparing the monitoring state with the typical normal state, the weights of typical situations at different speeds and different speed change rates can be distinguished, thereby taking both steady-state and variable operating conditions into consideration.

[0054] Step 2: Build the model:

[0055] The test data of the turbo pump under the historical normal working state is obtained, and the feature vectors of the test data under the historical normal working state are extracted. The obtained feature vectors are divided into a learning set and a test set, and the RSAF model is trained with the learning set as a representation of the normal state; the test set is input into the trained RSAF model to obtain a feature vector estimate, and the deviation between the feature vector estimate and the true value of the feature vector of the test set is calculated. If all components of the deviation are less than a set threshold, the final RSAF model is obtained; otherwise, the RSAF model is re-trained with the learning set.

[0056] The modeling process is:

[0057] Step 2.1: Determine the steady-state segment based on the historical test data of the turbo pump under normal working conditions; in each steady-state segment, obtain the characteristic vectors at the maximum and minimum moments of each characteristic component as the coarse representative state set {SE};

[0058] Step 2.2: In the coarse typical state set {SE}, if the similarity of the feature vectors at two moments is higher than the set threshold, the feature vector at one moment is removed, and the subset {SE1} is retained;

[0059] Step 2.3: Based on the historical test data of the turbopump under normal working conditions, the variable operating condition section is determined; the feature vectors of all variable operating condition sections form a typical state set {TE}; in the typical state set {TE}, if the similarity of the feature vectors of two moments exceeds the set threshold, the feature vector of one moment is eliminated, and the subset {TE1} is retained;

[0060] Step 2.4: Combine {SE1} and {TE1} to form the RSAF model.

[0061] For the obtained RSAF model, the test set is input into the trained RSAF model to obtain the feature vector estimation value as follows:

[0062] For a certain feature vector in the test set, the similarity between the feature vector and all feature vectors in the RSAF model is calculated. The weight of each feature vector in the RSAF model is determined according to the similarity. Then, the weighted sum of each feature vector in the RSAF model is performed to obtain the estimated value of the feature vector.

[0063] Step 3: Monitor the detection signal of the turbo pump in real time. According to the definition of step 1, calculate the eigenvector of the measured detection signal. Input the obtained eigenvector into the RSAF model obtained in step 2 to obtain an estimated value of the eigenvector of the measured detection signal. Calculate the deviation between the estimated value of the eigenvector of the measured detection signal and the calculated value of the eigenvector of the measured detection signal. If the deviation exceeds the set threshold for three consecutive calculation cycles, it is considered that the working state of the turbo pump is abnormal.

[0064] The threshold here can be based on experience, taking 10% of the corresponding component of the estimated value of the eigenvector of the measured detection signal as the threshold of the corresponding component; or taking the mean + 3σ of the corresponding component of the deviation between the estimated value of the eigenvector of the test set and the true value of the eigenvector in step 2 as the threshold, where σ is the variance of the deviation between the estimated value of the eigenvector of the test set and the true value of the eigenvector.

[0065] Step 4: After determining that the turbopump operating state is abnormal, the fault is further classified based on the type of components in the deviation that exceed the threshold. If only the components corresponding to the fundamental frequency and the double frequency in the deviation exceed the threshold, it is considered an imbalance or misalignment fault. If the corresponding components of other characteristics exceed the threshold, it is considered a rubbing fault. If a rubbing fault is determined to have occurred, the sum of the squares of the various components in the deviation is used as an indicator to measure the severity of the rubbing fault.

[0066] Of course, it is necessary to pay attention to the situation where sensor abnormalities occur during the monitoring of the detection signal. The present invention adapts to the situation of sensor abnormalities in the following two ways:

[0067] (1) If the speed sensor fails, the judgment is made only based on the amplitude characteristics corresponding to one frequency point in the low-frequency spectrum. When calculating the estimated value, the contribution of the speed, speed change value, frequency multiplication characteristics, subharmonic characteristics, and precession characteristics of each channel is set to 0 to shield the influence of invalid characteristics and avoid false alarms. When calculating the deviation, the deviation of the speed, speed change value, frequency multiplication characteristics, subharmonic characteristics, and precession characteristics of each channel is set to 0.

[0068] (2) If a detection channel fails, the contribution of the corresponding feature of the detection channel is set to 0 when calculating the estimated value, and the estimated value is calculated only by relying on other channels; when calculating the deviation, the deviation of the corresponding feature of the detection channel is set to 0 to avoid false alarms caused by invalid feature interference.

[0069] The following describes in detail embodiments of the present invention. The embodiments are exemplary and intended to explain the present invention, but are not to be construed as limiting the present invention.

[0070] In this embodiment, the rotor is divided into units such as disk, shaft segment, and bearing, and a four-point rotor model is established for fault simulation. By drawing on real fault data, fault forces are applied to the model, and rubbing faults are simulated. Fault signals and normal signals are obtained, such as Figures 1-4 shown.

[0071] Based on the normal signal, the RSAF model was established. The comparison between the estimated value of the model and the true value of the normal signal is shown in the figure below. Figure 5 and Figure 6 As shown, it can be seen that different speed conditions are well matched and the normal situation can be correctly estimated, indicating that the model is effective.

[0072] The comparison between the estimated value and the true value of the RSAF model for the rubbing fault data is as follows: Figure 7 and Figure 8 As shown, it can be seen that from the beginning, there is a large deviation between the estimated value and the true value. However, the corresponding amplitude of the fundamental frequency of the low working condition is close to the corresponding amplitude of the fundamental frequency of the high working condition. However, the anomaly can be detected at this time, which is difficult to achieve if the same threshold is used for all working conditions, thus avoiding missed alarms. Moreover, all working conditions can be processed uniformly, and multiple features can be considered at the same time, which is convenient for the definition of thresholds and the assessment of severity.

[0073] It can be seen that this method can effectively identify friction faults, can uniformly process data under different speed conditions, and effectively avoid false alarms and missed alarms.

[0074] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A real-time monitoring method for high-speed turbine pump rotor-static friction based on RSAF model, characterized by: The following steps are involved: Step 1: Determine the feature vector involved in rubbing monitoring as [nt Δnt DF ch,1 … DF ch,k … DF ch,K P] 1×n Where nt is the speed of the turbo pump, Δnt is the speed change, P is the vector composed of 1st, 2nd, and 3rd order positive and negative precessions, DF ch,k is the feature vector of the kth detection channel, k = 1, 2, ..., K: DF ch,k =[ppv k fb k fl 1,k … fl i,k … fl I,k f c,k f 2,k f 3,k f 4,k ] PPV in the above characteristics k is the peak-to-peak amplitude of the kth detection channel, fb k is the amplitude corresponding to the fundamental frequency of the kth detection channel, fl 1,k …fl i,k …fl I,k is the amplitude corresponding to the I frequency point in the low-frequency spectrum of the kth detection channel; f c,k is the subharmonic amplitude corresponding to the kth detection channel, f 2,k 、f 3,k 、f 4,k is the corresponding amplitude of 2 times, 3 times and 4 times of frequency in the kth detection channel; Step 2: Obtain the detection data of the turbine pump under the historical normal working state, and extract the feature vector of the detection data under the historical normal working state, divide the obtained feature vector into a learning set and a test set, and train the RSAF model with the learning set as the representation of the normal state; and input the test set into the trained RSAF model to obtain the feature vector estimation value, and calculate the deviation between the feature vector estimation value and the true value of the feature vector of the test set. If all components in the deviation are less than the set threshold, the final RSAF model is obtained, otherwise the RSAF model is retrained with the learning set; Step 3: Monitor the detection signal of the turbo pump in real time. According to the definition of step 1, calculate the characteristic vector of the measured detection signal. Input the obtained characteristic vector into the RSAF model obtained in step 2 to obtain the estimated value of the characteristic vector of the measured detection signal. Calculate the deviation between the estimated value of the characteristic vector of the measured detection signal and the calculated value of the characteristic vector of the measured detection signal. If the deviation exceeds the set threshold for three consecutive calculation cycles, it is considered that the working state of the turbo pump is abnormal.

2. According to the RSAF model-based real-time monitoring method for high-speed turbine pump rotor-static friction according to claim 1, it is characterized in that: In step 3, the threshold is set to 10% of the component corresponding to the estimated value of the feature vector of the measured detection signal.

3. According to claim 1, a real-time monitoring method for high-speed turbine pump rotor-static friction based on RSAF model, characterized in that: In step 3, the mean of the component corresponding to the deviation between the estimated value of the test set eigenvector and the true value of the eigenvector in step 2 + 3σ is taken as the threshold, where σ is the variance of the deviation between the estimated value of the test set eigenvector and the true value of the eigenvector.

4. According to claim 1, a real-time monitoring method for high-speed turbine pump rotor-static friction based on RSAF model, characterized in that: The method further includes step 4: classifying the fault according to the type of the component in the deviation that exceeds the threshold.

5. According to claim 4, a method for real-time monitoring of high-speed turbine pump rotor-static friction based on RSAF model, characterized in that: In step 4, if only the components corresponding to the fundamental frequency and the double frequency in the deviation exceed the threshold, it is considered that an unbalance or misalignment fault has occurred; if the components corresponding to other characteristics exceed the threshold, it is considered that a friction fault has occurred.

6. The method for real-time monitoring of high-speed turbine pump rotor-static friction based on RSAF model according to claim 5, characterized in that: The method further includes step 5: if it is determined that a rubbing fault has occurred, the sum of the squares of the components in the deviation is used as an indicator to measure the severity of the rubbing.

7. The method for real-time monitoring of high-speed turbine pump rotor-static friction based on RSAF model according to claim 1, characterized in that: In step 3, consider the case where a sensor anomaly occurs during real-time monitoring of the turbo pump detection signal: (1) If the speed sensor fails, the judgment is made only based on the amplitude characteristics corresponding to one frequency point in the low-frequency spectrum; When calculating the estimated value, the contribution of the rotation speed, the rotation speed change value, the frequency multiple characteristics, the subharmonic characteristics, and the precession characteristics of each channel are set to 0 to shield the influence of invalid characteristics; when calculating the deviation, the rotation speed, the rotation speed change value, the frequency multiple characteristics, the subharmonic characteristics, and the precession characteristics of each channel are set to 0; (2) If a detection channel fails, the contribution of the corresponding feature of the detection channel is set to 0 when calculating the estimated value; and the deviation of the corresponding feature of the detection channel is set to 0 when calculating the deviation.

8. The method for real-time monitoring of high-speed turbine pump rotor-static friction based on RSAF model according to claim 1, characterized in that: In step 2, the modeling process includes the following steps: Step 2.1: Determine the steady-state segment based on the detection data of the turbo pump under the normal working state in history; in each steady-state segment, obtain the characteristic vectors of the maximum value moment and the minimum value moment of each characteristic component as the rough typical state set {SE}; Step 2.2: In the coarse typical state set {SE}, if the similarity of the feature vectors at two moments is higher than the set threshold, the feature vector at one moment is removed, and finally the subset {SE1} is retained; Step 2.3: According to the detection data of the turbo pump under the normal working state in history, the variable operating condition section is determined; the characteristic vectors of all variable operating condition sections form a typical state set {TE}; in the typical state set {TE}, if the similarity of the characteristic vectors at two moments is higher than the set threshold, the characteristic vector at one moment is eliminated, and finally the subset {TE1} is retained; Step 2.4: Combine {SE1} and {TE1} to form the RSAF model.

9. A method for real-time monitoring of high-speed turbine pump rotor-static friction based on RSAF model according to claim 8, characterized in that: In step 2, the test set is input into the trained RSAF model, and the process of obtaining the feature vector estimate is as follows: For a certain feature vector in the test set, the similarity between the feature vector and all feature vectors in the RSAF model is calculated, the weight of each feature vector in the RSAF model is determined according to the similarity, and then the weighted sum of each feature vector in the RSAF model is performed to obtain the estimated value of the feature vector.

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